z3py Namespace Reference

Data Structures
class	Context
class	Z3PPObject
	ASTs base class. More...
class	AstRef
class	SortRef
class	FuncDeclRef
	Function Declarations. More...
class	ExprRef
	Expressions. More...
class	BoolSortRef
	Booleans. More...
class	BoolRef
class	PatternRef
	Patterns. More...
class	QuantifierRef
	Quantifiers. More...
class	ArithSortRef
	Arithmetic. More...
class	ArithRef
class	IntNumRef
class	RatNumRef
class	AlgebraicNumRef
class	BitVecSortRef
	Bit-Vectors. More...
class	BitVecRef
class	BitVecNumRef
class	ArraySortRef
	Arrays. More...
class	ArrayRef
class	Datatype
class	ScopedConstructor
class	ScopedConstructorList
class	DatatypeSortRef
class	DatatypeRef
class	ParamsRef
	Parameter Sets. More...
class	ParamDescrsRef
class	Goal
class	AstVector
class	AstMap
class	FuncEntry
class	FuncInterp
class	ModelRef
class	Statistics
	Statistics. More...
class	CheckSatResult
class	Solver
class	Fixedpoint
	Fixedpoint. More...
class	FiniteDomainSortRef
class	FiniteDomainRef
class	FiniteDomainNumRef
class	OptimizeObjective
	Optimize. More...
class	Optimize
class	ApplyResult
class	Tactic
class	Probe
class	ParserContext
class	FPSortRef
class	FPRMSortRef
class	FPRef
class	FPRMRef
class	FPNumRef
class	SeqSortRef
	Strings, Sequences and Regular expressions. More...
class	CharSortRef
class	SeqRef
class	CharRef
class	ReSortRef
class	ReRef
class	OnClause
class	PropClosures
class	UserPropagateBase

Functions
def	z3_debug ()
def	enable_trace (msg)
def	disable_trace (msg)
def	get_version_string ()
def	get_version ()
def	get_full_version ()
def	open_log (fname)
def	append_log (s)
def	to_symbol (s, ctx=None)
def	z3_error_handler (c, e)
def	main_ctx ()
def	get_ctx (ctx)
def	set_param (*args, **kws)
def	reset_params ()
def	set_option (*args, **kws)
def	get_param (name)
def	is_ast (a)
def	eq (a, b)
def	is_sort (s)
def	DeclareSort (name, ctx=None)
def	is_func_decl (a)
def	Function (name, *sig)
def	FreshFunction (*sig)
def	RecFunction (name, *sig)
def	RecAddDefinition (f, args, body)
def	deserialize (st)
def	is_expr (a)
def	is_app (a)
def	is_const (a)
def	is_var (a)
def	get_var_index (a)
def	is_app_of (a, k)
def	If (a, b, c, ctx=None)
def	Distinct (*args)
def	Const (name, sort)
def	Consts (names, sort)
def	FreshConst (sort, prefix="c")
def	Var (idx, s)
def	RealVar (idx, ctx=None)
def	RealVarVector (n, ctx=None)
def	is_bool (a)
def	is_true (a)
def	is_false (a)
def	is_and (a)
def	is_or (a)
def	is_implies (a)
def	is_not (a)
def	is_eq (a)
def	is_distinct (a)
def	BoolSort (ctx=None)
def	BoolVal (val, ctx=None)
def	Bool (name, ctx=None)
def	Bools (names, ctx=None)
def	BoolVector (prefix, sz, ctx=None)
def	FreshBool (prefix="b", ctx=None)
def	Implies (a, b, ctx=None)
def	Xor (a, b, ctx=None)
def	Not (a, ctx=None)
def	mk_not (a)
def	And (*args)
def	Or (*args)
def	is_pattern (a)
def	MultiPattern (*args)
def	is_quantifier (a)
def	ForAll (vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
def	Exists (vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[])
def	Lambda (vs, body)
def	is_arith_sort (s)
def	is_arith (a)
def	is_int (a)
def	is_real (a)
def	is_int_value (a)
def	is_rational_value (a)
def	is_algebraic_value (a)
def	is_add (a)
def	is_mul (a)
def	is_sub (a)
def	is_div (a)
def	is_idiv (a)
def	is_mod (a)
def	is_le (a)
def	is_lt (a)
def	is_ge (a)
def	is_gt (a)
def	is_is_int (a)
def	is_to_real (a)
def	is_to_int (a)
def	IntSort (ctx=None)
def	RealSort (ctx=None)
def	IntVal (val, ctx=None)
def	RealVal (val, ctx=None)
def	RatVal (a, b, ctx=None)
def	Q (a, b, ctx=None)
def	Int (name, ctx=None)
def	Ints (names, ctx=None)
def	IntVector (prefix, sz, ctx=None)
def	FreshInt (prefix="x", ctx=None)
def	Real (name, ctx=None)
def	Reals (names, ctx=None)
def	RealVector (prefix, sz, ctx=None)
def	FreshReal (prefix="b", ctx=None)
def	ToReal (a)
def	ToInt (a)
def	IsInt (a)
def	Sqrt (a, ctx=None)
def	Cbrt (a, ctx=None)
def	is_bv_sort (s)
def	is_bv (a)
def	is_bv_value (a)
def	BV2Int (a, is_signed=False)
def	Int2BV (a, num_bits)
def	BitVecSort (sz, ctx=None)
def	BitVecVal (val, bv, ctx=None)
def	BitVec (name, bv, ctx=None)
def	BitVecs (names, bv, ctx=None)
def	Concat (*args)
def	Extract (high, low, a)
def	ULE (a, b)
def	ULT (a, b)
def	UGE (a, b)
def	UGT (a, b)
def	UDiv (a, b)
def	URem (a, b)
def	SRem (a, b)
def	LShR (a, b)
def	RotateLeft (a, b)
def	RotateRight (a, b)
def	SignExt (n, a)
def	ZeroExt (n, a)
def	RepeatBitVec (n, a)
def	BVRedAnd (a)
def	BVRedOr (a)
def	BVAddNoOverflow (a, b, signed)
def	BVAddNoUnderflow (a, b)
def	BVSubNoOverflow (a, b)
def	BVSubNoUnderflow (a, b, signed)
def	BVSDivNoOverflow (a, b)
def	BVSNegNoOverflow (a)
def	BVMulNoOverflow (a, b, signed)
def	BVMulNoUnderflow (a, b)
def	is_array_sort (a)
def	is_array (a)
def	is_const_array (a)
def	is_K (a)
def	is_map (a)
def	is_default (a)
def	get_map_func (a)
def	ArraySort (*sig)
def	Array (name, *sorts)
def	Update (a, *args)
def	Default (a)
def	Store (a, *args)
def	Select (a, *args)
def	Map (f, *args)
def	K (dom, v)
def	Ext (a, b)
def	SetHasSize (a, k)
def	is_select (a)
def	is_store (a)
def	SetSort (s)
	Sets. More...
def	EmptySet (s)
def	FullSet (s)
def	SetUnion (*args)
def	SetIntersect (*args)
def	SetAdd (s, e)
def	SetDel (s, e)
def	SetComplement (s)
def	SetDifference (a, b)
def	IsMember (e, s)
def	IsSubset (a, b)
def	CreateDatatypes (*ds)
def	DatatypeSort (name, ctx=None)
def	TupleSort (name, sorts, ctx=None)
def	DisjointSum (name, sorts, ctx=None)
def	EnumSort (name, values, ctx=None)
def	args2params (arguments, keywords, ctx=None)
def	Model (ctx=None)
def	is_as_array (n)
def	get_as_array_func (n)
def	SolverFor (logic, ctx=None, logFile=None)
def	SimpleSolver (ctx=None, logFile=None)
def	FiniteDomainSort (name, sz, ctx=None)
def	is_finite_domain_sort (s)
def	is_finite_domain (a)
def	FiniteDomainVal (val, sort, ctx=None)
def	is_finite_domain_value (a)
def	AndThen (*ts, **ks)
def	Then (*ts, **ks)
def	OrElse (*ts, **ks)
def	ParOr (*ts, **ks)
def	ParThen (t1, t2, ctx=None)
def	ParAndThen (t1, t2, ctx=None)
def	With (t, *args, **keys)
def	WithParams (t, p)
def	Repeat (t, max=4294967295, ctx=None)
def	TryFor (t, ms, ctx=None)
def	tactics (ctx=None)
def	tactic_description (name, ctx=None)
def	describe_tactics ()
def	is_probe (p)
def	probes (ctx=None)
def	probe_description (name, ctx=None)
def	describe_probes ()
def	FailIf (p, ctx=None)
def	When (p, t, ctx=None)
def	Cond (p, t1, t2, ctx=None)
def	simplify (a, *arguments, **keywords)
	Utils. More...
def	help_simplify ()
def	simplify_param_descrs ()
def	substitute (t, *m)
def	substitute_vars (t, *m)
def	substitute_funs (t, *m)
def	Sum (*args)
def	Product (*args)
def	Abs (arg)
def	AtMost (*args)
def	AtLeast (*args)
def	PbLe (args, k)
def	PbGe (args, k)
def	PbEq (args, k, ctx=None)
def	solve (*args, **keywords)
def	solve_using (s, *args, **keywords)
def	prove (claim, show=False, **keywords)
def	parse_smt2_string (s, sorts={}, decls={}, ctx=None)
def	parse_smt2_file (f, sorts={}, decls={}, ctx=None)
def	get_default_rounding_mode (ctx=None)
def	set_default_rounding_mode (rm, ctx=None)
def	get_default_fp_sort (ctx=None)
def	set_default_fp_sort (ebits, sbits, ctx=None)
def	Float16 (ctx=None)
def	FloatHalf (ctx=None)
def	Float32 (ctx=None)
def	FloatSingle (ctx=None)
def	Float64 (ctx=None)
def	FloatDouble (ctx=None)
def	Float128 (ctx=None)
def	FloatQuadruple (ctx=None)
def	is_fp_sort (s)
def	is_fprm_sort (s)
def	RoundNearestTiesToEven (ctx=None)
def	RNE (ctx=None)
def	RoundNearestTiesToAway (ctx=None)
def	RNA (ctx=None)
def	RoundTowardPositive (ctx=None)
def	RTP (ctx=None)
def	RoundTowardNegative (ctx=None)
def	RTN (ctx=None)
def	RoundTowardZero (ctx=None)
def	RTZ (ctx=None)
def	is_fprm (a)
def	is_fprm_value (a)
def	is_fp (a)
def	is_fp_value (a)
def	FPSort (ebits, sbits, ctx=None)
def	fpNaN (s)
def	fpPlusInfinity (s)
def	fpMinusInfinity (s)
def	fpInfinity (s, negative)
def	fpPlusZero (s)
def	fpMinusZero (s)
def	fpZero (s, negative)
def	FPVal (sig, exp=None, fps=None, ctx=None)
def	FP (name, fpsort, ctx=None)
def	FPs (names, fpsort, ctx=None)
def	fpAbs (a, ctx=None)
def	fpNeg (a, ctx=None)
def	fpAdd (rm, a, b, ctx=None)
def	fpSub (rm, a, b, ctx=None)
def	fpMul (rm, a, b, ctx=None)
def	fpDiv (rm, a, b, ctx=None)
def	fpRem (a, b, ctx=None)
def	fpMin (a, b, ctx=None)
def	fpMax (a, b, ctx=None)
def	fpFMA (rm, a, b, c, ctx=None)
def	fpSqrt (rm, a, ctx=None)
def	fpRoundToIntegral (rm, a, ctx=None)
def	fpIsNaN (a, ctx=None)
def	fpIsInf (a, ctx=None)
def	fpIsZero (a, ctx=None)
def	fpIsNormal (a, ctx=None)
def	fpIsSubnormal (a, ctx=None)
def	fpIsNegative (a, ctx=None)
def	fpIsPositive (a, ctx=None)
def	fpLT (a, b, ctx=None)
def	fpLEQ (a, b, ctx=None)
def	fpGT (a, b, ctx=None)
def	fpGEQ (a, b, ctx=None)
def	fpEQ (a, b, ctx=None)
def	fpNEQ (a, b, ctx=None)
def	fpFP (sgn, exp, sig, ctx=None)
def	fpToFP (a1, a2=None, a3=None, ctx=None)
def	fpBVToFP (v, sort, ctx=None)
def	fpFPToFP (rm, v, sort, ctx=None)
def	fpRealToFP (rm, v, sort, ctx=None)
def	fpSignedToFP (rm, v, sort, ctx=None)
def	fpUnsignedToFP (rm, v, sort, ctx=None)
def	fpToFPUnsigned (rm, x, s, ctx=None)
def	fpToSBV (rm, x, s, ctx=None)
def	fpToUBV (rm, x, s, ctx=None)
def	fpToReal (x, ctx=None)
def	fpToIEEEBV (x, ctx=None)
def	StringSort (ctx=None)
def	CharSort (ctx=None)
def	SeqSort (s)
def	CharVal (ch, ctx=None)
def	CharFromBv (ch, ctx=None)
def	CharToBv (ch, ctx=None)
def	CharToInt (ch, ctx=None)
def	CharIsDigit (ch, ctx=None)
def	is_seq (a)
def	is_string (a)
def	is_string_value (a)
def	StringVal (s, ctx=None)
def	String (name, ctx=None)
def	Strings (names, ctx=None)
def	SubString (s, offset, length)
def	SubSeq (s, offset, length)
def	Empty (s)
def	Full (s)
def	Unit (a)
def	PrefixOf (a, b)
def	SuffixOf (a, b)
def	Contains (a, b)
def	Replace (s, src, dst)
def	IndexOf (s, substr, offset=None)
def	LastIndexOf (s, substr)
def	Length (s)
def	StrToInt (s)
def	IntToStr (s)
def	StrToCode (s)
def	StrFromCode (c)
def	Re (s, ctx=None)
def	ReSort (s)
def	is_re (s)
def	InRe (s, re)
def	Union (*args)
def	Intersect (*args)
def	Plus (re)
def	Option (re)
def	Complement (re)
def	Star (re)
def	Loop (re, lo, hi=0)
def	Range (lo, hi, ctx=None)
def	Diff (a, b, ctx=None)
def	AllChar (regex_sort, ctx=None)
def	PartialOrder (a, index)
def	LinearOrder (a, index)
def	TreeOrder (a, index)
def	PiecewiseLinearOrder (a, index)
def	TransitiveClosure (f)
def	to_Ast (ptr)
def	to_ContextObj (ptr)
def	to_AstVectorObj (ptr)
def	on_clause_eh (ctx, p, clause)
def	ensure_prop_closures ()
def	user_prop_push (ctx, cb)
def	user_prop_pop (ctx, cb, num_scopes)
def	user_prop_fresh (ctx, _new_ctx)
def	user_prop_fixed (ctx, cb, id, value)
def	user_prop_created (ctx, cb, id)
def	user_prop_final (ctx, cb)
def	user_prop_eq (ctx, cb, x, y)
def	user_prop_diseq (ctx, cb, x, y)
def	user_prop_decide (ctx, cb, t_ref, idx_ref, phase_ref)
def	PropagateFunction (name, *sig)

Variables
	Z3_DEBUG = __debug__
	sat = CheckSatResult(Z3_L_TRUE)
	unsat = CheckSatResult(Z3_L_FALSE)
	unknown = CheckSatResult(Z3_L_UNDEF)

Function Documentation

Abs()

def z3py.Abs

(

arg

)

Create the absolute value of an arithmetic expression

Definition at line 8932 of file z3py.py.

def Abs(arg):
    """Create the absolute value of an arithmetic expression"""
    return If(arg > 0, arg, -arg)
    
 

AllChar()

def z3py.AllChar	(		regex_sort,
			ctx = None
	)

Create a regular expression that accepts all single character strings

Definition at line 11298 of file z3py.py.

def AllChar(regex_sort, ctx=None):
    """Create a regular expression that accepts all single character strings
    """
    return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
 
# Special Relations
 
 

And()

def z3py.And

(

*

args

)

Create a Z3 and-expression or and-probe.

>>> p, q, r = Bools('p q r')
>>> And(p, q, r)
And(p, q, r)
>>> P = BoolVector('p', 5)
>>> And(P)
And(p__0, p__1, p__2, p__3, p__4)

Definition at line 1849 of file z3py.py.

def And(*args):
    """Create a Z3 and-expression or and-probe.
 
    >>> p, q, r = Bools('p q r')
    >>> And(p, q, r)
    And(p, q, r)
    >>> P = BoolVector('p', 5)
    >>> And(P)
    And(p__0, p__1, p__2, p__3, p__4)
    """
    last_arg = None
    if len(args) > 0:
        last_arg = args[len(args) - 1]
    if isinstance(last_arg, Context):
        ctx = args[len(args) - 1]
        args = args[:len(args) - 1]
    elif len(args) == 1 and isinstance(args[0], AstVector):
        ctx = args[0].ctx
        args = [a for a in args[0]]
    else:
        ctx = None
    args = _get_args(args)
    ctx = _get_ctx(_ctx_from_ast_arg_list(args, ctx))
    if z3_debug():
        _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression or probe")
    if _has_probe(args):
        return _probe_and(args, ctx)
    else:
        args = _coerce_expr_list(args, ctx)
        _args, sz = _to_ast_array(args)
        return BoolRef(Z3_mk_and(ctx.ref(), sz, _args), ctx)
 
 

Referenced by Fixedpoint.add_rule(), Goal.as_expr(), Fixedpoint.query(), Fixedpoint.query_from_lvl(), and Fixedpoint.update_rule().

AndThen()

def z3py.AndThen	(	*	ts,
		**	ks
	)

Return a tactic that applies the tactics in `*ts` in sequence.

>>> x, y = Ints('x y')
>>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
>>> t(And(x == 0, y > x + 1))
[[Not(y <= 1)]]
>>> t(And(x == 0, y > x + 1)).as_expr()
Not(y <= 1)

Definition at line 8297 of file z3py.py.

def AndThen(*ts, **ks):
    """Return a tactic that applies the tactics in `*ts` in sequence.
 
    >>> x, y = Ints('x y')
    >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
    >>> t(And(x == 0, y > x + 1))
    [[Not(y <= 1)]]
    >>> t(And(x == 0, y > x + 1)).as_expr()
    Not(y <= 1)
    """
    if z3_debug():
        _z3_assert(len(ts) >= 2, "At least two arguments expected")
    ctx = ks.get("ctx", None)
    num = len(ts)
    r = ts[0]
    for i in range(num - 1):
        r = _and_then(r, ts[i + 1], ctx)
    return r
 
 

Referenced by Then().

append_log()

def z3py.append_log

(

s

)

Append user-defined string to interaction log. 

Definition at line 119 of file z3py.py.

def append_log(s):
    """Append user-defined string to interaction log. """
    Z3_append_log(s)
 
 

args2params()

def z3py.args2params	(		arguments,
			keywords,
			ctx = None
	)

Convert python arguments into a Z3_params object.
A ':' is added to the keywords, and '_' is replaced with '-'

>>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
(params model true relevancy 2 elim_and true)

Definition at line 5466 of file z3py.py.

def args2params(arguments, keywords, ctx=None):
    """Convert python arguments into a Z3_params object.
    A ':' is added to the keywords, and '_' is replaced with '-'
 
    >>> args2params(['model', True, 'relevancy', 2], {'elim_and' : True})
    (params model true relevancy 2 elim_and true)
    """
    if z3_debug():
        _z3_assert(len(arguments) % 2 == 0, "Argument list must have an even number of elements.")
    prev = None
    r = ParamsRef(ctx)
    for a in arguments:
        if prev is None:
            prev = a
        else:
            r.set(prev, a)
            prev = None
    for k in keywords:
        v = keywords[k]
        r.set(k, v)
    return r
 
 

Referenced by Tactic.apply(), Solver.set(), Fixedpoint.set(), Optimize.set(), simplify(), and With().

Array()

def z3py.Array	(		name,
		*	sorts
	)

Return an array constant named `name` with the given domain and range sorts.

>>> a = Array('a', IntSort(), IntSort())
>>> a.sort()
Array(Int, Int)
>>> a[0]
a[0]

Definition at line 4733 of file z3py.py.

def Array(name, *sorts):
    """Return an array constant named `name` with the given domain and range sorts.
 
    >>> a = Array('a', IntSort(), IntSort())
    >>> a.sort()
    Array(Int, Int)
    >>> a[0]
    a[0]
    """
    s = ArraySort(sorts)
    ctx = s.ctx
    return ArrayRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), s.ast), ctx)
 
 

ArraySort()

def z3py.ArraySort

(

*

sig

)

Return the Z3 array sort with the given domain and range sorts.

>>> A = ArraySort(IntSort(), BoolSort())
>>> A
Array(Int, Bool)
>>> A.domain()
Int
>>> A.range()
Bool
>>> AA = ArraySort(IntSort(), A)
>>> AA
Array(Int, Array(Int, Bool))

Definition at line 4700 of file z3py.py.

def ArraySort(*sig):
    """Return the Z3 array sort with the given domain and range sorts.
 
    >>> A = ArraySort(IntSort(), BoolSort())
    >>> A
    Array(Int, Bool)
    >>> A.domain()
    Int
    >>> A.range()
    Bool
    >>> AA = ArraySort(IntSort(), A)
    >>> AA
    Array(Int, Array(Int, Bool))
    """
    sig = _get_args(sig)
    if z3_debug():
        _z3_assert(len(sig) > 1, "At least two arguments expected")
    arity = len(sig) - 1
    r = sig[arity]
    d = sig[0]
    if z3_debug():
        for s in sig:
            _z3_assert(is_sort(s), "Z3 sort expected")
            _z3_assert(s.ctx == r.ctx, "Context mismatch")
    ctx = d.ctx
    if len(sig) == 2:
        return ArraySortRef(Z3_mk_array_sort(ctx.ref(), d.ast, r.ast), ctx)
    dom = (Sort * arity)()
    for i in range(arity):
        dom[i] = sig[i].ast
    return ArraySortRef(Z3_mk_array_sort_n(ctx.ref(), arity, dom, r.ast), ctx)
 
 

Referenced by Array(), Context.MkArraySort(), and SetSort().

AtLeast()

def z3py.AtLeast

(

*

args

)

Create an at-most Pseudo-Boolean k constraint.

>>> a, b, c = Bools('a b c')
>>> f = AtLeast(a, b, c, 2)

Definition at line 8955 of file z3py.py.

def AtLeast(*args):
    """Create an at-most Pseudo-Boolean k constraint.
 
    >>> a, b, c = Bools('a b c')
    >>> f = AtLeast(a, b, c, 2)
    """
    args = _get_args(args)
    if z3_debug():
        _z3_assert(len(args) > 1, "Non empty list of arguments expected")
    ctx = _ctx_from_ast_arg_list(args)
    if z3_debug():
        _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
    args1 = _coerce_expr_list(args[:-1], ctx)
    k = args[-1]
    _args, sz = _to_ast_array(args1)
    return BoolRef(Z3_mk_atleast(ctx.ref(), sz, _args, k), ctx)
 
 

AtMost()

def z3py.AtMost

(

*

args

)

Create an at-most Pseudo-Boolean k constraint.

>>> a, b, c = Bools('a b c')
>>> f = AtMost(a, b, c, 2)

Definition at line 8937 of file z3py.py.

def AtMost(*args):
    """Create an at-most Pseudo-Boolean k constraint.
 
    >>> a, b, c = Bools('a b c')
    >>> f = AtMost(a, b, c, 2)
    """
    args = _get_args(args)
    if z3_debug():
        _z3_assert(len(args) > 1, "Non empty list of arguments expected")
    ctx = _ctx_from_ast_arg_list(args)
    if z3_debug():
        _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
    args1 = _coerce_expr_list(args[:-1], ctx)
    k = args[-1]
    _args, sz = _to_ast_array(args1)
    return BoolRef(Z3_mk_atmost(ctx.ref(), sz, _args, k), ctx)
 
 

BitVec()

def z3py.BitVec	(		name,
			bv,
			ctx = None
	)

Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
If `ctx=None`, then the global context is used.

>>> x  = BitVec('x', 16)
>>> is_bv(x)
True
>>> x.size()
16
>>> x.sort()
BitVec(16)
>>> word = BitVecSort(16)
>>> x2 = BitVec('x', word)
>>> eq(x, x2)
True

Definition at line 4037 of file z3py.py.

def BitVec(name, bv, ctx=None):
    """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
    If `ctx=None`, then the global context is used.
 
    >>> x  = BitVec('x', 16)
    >>> is_bv(x)
    True
    >>> x.size()
    16
    >>> x.sort()
    BitVec(16)
    >>> word = BitVecSort(16)
    >>> x2 = BitVec('x', word)
    >>> eq(x, x2)
    True
    """
    if isinstance(bv, BitVecSortRef):
        ctx = bv.ctx
    else:
        ctx = _get_ctx(ctx)
        bv = BitVecSort(bv, ctx)
    return BitVecRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), bv.ast), ctx)
 
 

Referenced by BitVecs().

BitVecs()

def z3py.BitVecs	(		names,
			bv,
			ctx = None
	)

Return a tuple of bit-vector constants of size bv.

>>> x, y, z = BitVecs('x y z', 16)
>>> x.size()
16
>>> x.sort()
BitVec(16)
>>> Sum(x, y, z)
0 + x + y + z
>>> Product(x, y, z)
1*x*y*z
>>> simplify(Product(x, y, z))
x*y*z

Definition at line 4061 of file z3py.py.

def BitVecs(names, bv, ctx=None):
    """Return a tuple of bit-vector constants of size bv.
 
    >>> x, y, z = BitVecs('x y z', 16)
    >>> x.size()
    16
    >>> x.sort()
    BitVec(16)
    >>> Sum(x, y, z)
    0 + x + y + z
    >>> Product(x, y, z)
    1*x*y*z
    >>> simplify(Product(x, y, z))
    x*y*z
    """
    ctx = _get_ctx(ctx)
    if isinstance(names, str):
        names = names.split(" ")
    return [BitVec(name, bv, ctx) for name in names]
 
 

BitVecSort()

def z3py.BitVecSort	(		sz,
			ctx = None
	)

Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.

>>> Byte = BitVecSort(8)
>>> Word = BitVecSort(16)
>>> Byte
BitVec(8)
>>> x = Const('x', Byte)
>>> eq(x, BitVec('x', 8))
True

Definition at line 4005 of file z3py.py.

def BitVecSort(sz, ctx=None):
    """Return a Z3 bit-vector sort of the given size. If `ctx=None`, then the global context is used.
 
    >>> Byte = BitVecSort(8)
    >>> Word = BitVecSort(16)
    >>> Byte
    BitVec(8)
    >>> x = Const('x', Byte)
    >>> eq(x, BitVec('x', 8))
    True
    """
    ctx = _get_ctx(ctx)
    return BitVecSortRef(Z3_mk_bv_sort(ctx.ref(), sz), ctx)
 
 

Referenced by BitVec(), BitVecVal(), Context.mkBitVecSort(), and Context.MkBitVecSort().

BitVecVal()

def z3py.BitVecVal	(		val,
			bv,
			ctx = None
	)

Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.

>>> v = BitVecVal(10, 32)
>>> v
10
>>> print("0x%.8x" % v.as_long())
0x0000000a

Definition at line 4020 of file z3py.py.

def BitVecVal(val, bv, ctx=None):
    """Return a bit-vector value with the given number of bits. If `ctx=None`, then the global context is used.
 
    >>> v = BitVecVal(10, 32)
    >>> v
    10
    >>> print("0x%.8x" % v.as_long())
    0x0000000a
    """
    if is_bv_sort(bv):
        ctx = bv.ctx
        return BitVecNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), bv.ast), ctx)
    else:
        ctx = _get_ctx(ctx)
        return BitVecNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), BitVecSort(bv, ctx).ast), ctx)
 
 

Bool()

def z3py.Bool	(		name,
			ctx = None
	)

Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.

>>> p = Bool('p')
>>> q = Bool('q')
>>> And(p, q)
And(p, q)

Definition at line 1728 of file z3py.py.

def Bool(name, ctx=None):
    """Return a Boolean constant named `name`. If `ctx=None`, then the global context is used.
 
    >>> p = Bool('p')
    >>> q = Bool('q')
    >>> And(p, q)
    And(p, q)
    """
    ctx = _get_ctx(ctx)
    return BoolRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), BoolSort(ctx).ast), ctx)
 
 

Referenced by Solver.assert_and_track(), Optimize.assert_and_track(), Bools(), and BoolVector().

Bools()

def z3py.Bools	(		names,
			ctx = None
	)

Return a tuple of Boolean constants.

`names` is a single string containing all names separated by blank spaces.
If `ctx=None`, then the global context is used.

>>> p, q, r = Bools('p q r')
>>> And(p, Or(q, r))
And(p, Or(q, r))

Definition at line 1740 of file z3py.py.

def Bools(names, ctx=None):
    """Return a tuple of Boolean constants.
 
    `names` is a single string containing all names separated by blank spaces.
    If `ctx=None`, then the global context is used.
 
    >>> p, q, r = Bools('p q r')
    >>> And(p, Or(q, r))
    And(p, Or(q, r))
    """
    ctx = _get_ctx(ctx)
    if isinstance(names, str):
        names = names.split(" ")
    return [Bool(name, ctx) for name in names]
 
 

BoolSort()

def z3py.BoolSort

(

ctx = None

)

Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.

>>> BoolSort()
Bool
>>> p = Const('p', BoolSort())
>>> is_bool(p)
True
>>> r = Function('r', IntSort(), IntSort(), BoolSort())
>>> r(0, 1)
r(0, 1)
>>> is_bool(r(0, 1))
True

Definition at line 1691 of file z3py.py.

def BoolSort(ctx=None):
    """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
 
    >>> BoolSort()
    Bool
    >>> p = Const('p', BoolSort())
    >>> is_bool(p)
    True
    >>> r = Function('r', IntSort(), IntSort(), BoolSort())
    >>> r(0, 1)
    r(0, 1)
    >>> is_bool(r(0, 1))
    True
    """
    ctx = _get_ctx(ctx)
    return BoolSortRef(Z3_mk_bool_sort(ctx.ref()), ctx)
 
 

Referenced by Goal.assert_exprs(), Solver.assert_exprs(), Fixedpoint.assert_exprs(), Optimize.assert_exprs(), Bool(), Solver.check(), FreshBool(), Context.getBoolSort(), If(), Implies(), Context.mkBoolSort(), Not(), SetSort(), QuantifierRef.sort(), and Xor().

BoolVal()

def z3py.BoolVal	(		val,
			ctx = None
	)

Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.

>>> BoolVal(True)
True
>>> is_true(BoolVal(True))
True
>>> is_true(True)
False
>>> is_false(BoolVal(False))
True

Definition at line 1709 of file z3py.py.

def BoolVal(val, ctx=None):
    """Return the Boolean value `True` or `False`. If `ctx=None`, then the global context is used.
 
    >>> BoolVal(True)
    True
    >>> is_true(BoolVal(True))
    True
    >>> is_true(True)
    False
    >>> is_false(BoolVal(False))
    True
    """
    ctx = _get_ctx(ctx)
    if val:
        return BoolRef(Z3_mk_true(ctx.ref()), ctx)
    else:
        return BoolRef(Z3_mk_false(ctx.ref()), ctx)
 
 

Referenced by Goal.as_expr(), ApplyResult.as_expr(), BoolSortRef.cast(), UserPropagateBase.conflict(), AlgebraicNumRef.index(), is_quantifier(), and Solver.to_smt2().

BoolVector()

def z3py.BoolVector	(		prefix,
			sz,
			ctx = None
	)

Return a list of Boolean constants of size `sz`.

The constants are named using the given prefix.
If `ctx=None`, then the global context is used.

>>> P = BoolVector('p', 3)
>>> P
[p__0, p__1, p__2]
>>> And(P)
And(p__0, p__1, p__2)

Definition at line 1756 of file z3py.py.

def BoolVector(prefix, sz, ctx=None):
    """Return a list of Boolean constants of size `sz`.
 
    The constants are named using the given prefix.
    If `ctx=None`, then the global context is used.
 
    >>> P = BoolVector('p', 3)
    >>> P
    [p__0, p__1, p__2]
    >>> And(P)
    And(p__0, p__1, p__2)
    """
    return [Bool("%s__%s" % (prefix, i)) for i in range(sz)]
 
 

BV2Int()

def z3py.BV2Int	(		a,
			is_signed = False
	)

Return the Z3 expression BV2Int(a).

>>> b = BitVec('b', 3)
>>> BV2Int(b).sort()
Int
>>> x = Int('x')
>>> x > BV2Int(b)
x > BV2Int(b)
>>> x > BV2Int(b, is_signed=False)
x > BV2Int(b)
>>> x > BV2Int(b, is_signed=True)
x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
>>> solve(x > BV2Int(b), b == 1, x < 3)
[x = 2, b = 1]

Definition at line 3973 of file z3py.py.

def BV2Int(a, is_signed=False):
    """Return the Z3 expression BV2Int(a).
 
    >>> b = BitVec('b', 3)
    >>> BV2Int(b).sort()
    Int
    >>> x = Int('x')
    >>> x > BV2Int(b)
    x > BV2Int(b)
    >>> x > BV2Int(b, is_signed=False)
    x > BV2Int(b)
    >>> x > BV2Int(b, is_signed=True)
    x > If(b < 0, BV2Int(b) - 8, BV2Int(b))
    >>> solve(x > BV2Int(b), b == 1, x < 3)
    [x = 2, b = 1]
    """
    if z3_debug():
        _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
    ctx = a.ctx
    # investigate problem with bv2int
    return ArithRef(Z3_mk_bv2int(ctx.ref(), a.as_ast(), is_signed), ctx)
 
 

BVAddNoOverflow()

def z3py.BVAddNoOverflow	(		a,
			b,
			signed
	)

A predicate the determines that bit-vector addition does not overflow

Definition at line 4459 of file z3py.py.

def BVAddNoOverflow(a, b, signed):
    """A predicate the determines that bit-vector addition does not overflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvadd_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
 
 

BVAddNoUnderflow()

def z3py.BVAddNoUnderflow	(		a,
			b
	)

A predicate the determines that signed bit-vector addition does not underflow

Definition at line 4466 of file z3py.py.

def BVAddNoUnderflow(a, b):
    """A predicate the determines that signed bit-vector addition does not underflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvadd_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

BVMulNoOverflow()

def z3py.BVMulNoOverflow	(		a,
			b,
			signed
	)

A predicate the determines that bit-vector multiplication does not overflow

Definition at line 4501 of file z3py.py.

def BVMulNoOverflow(a, b, signed):
    """A predicate the determines that bit-vector multiplication does not overflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvmul_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
 
 

BVMulNoUnderflow()

def z3py.BVMulNoUnderflow	(		a,
			b
	)

A predicate the determines that bit-vector signed multiplication does not underflow

Definition at line 4508 of file z3py.py.

def BVMulNoUnderflow(a, b):
    """A predicate the determines that bit-vector signed multiplication does not underflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvmul_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

BVRedAnd()

def z3py.BVRedAnd

(

a

)

Return the reduction-and expression of `a`.

Definition at line 4445 of file z3py.py.

def BVRedAnd(a):
    """Return the reduction-and expression of `a`."""
    if z3_debug():
        _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
    return BitVecRef(Z3_mk_bvredand(a.ctx_ref(), a.as_ast()), a.ctx)
 
 

BVRedOr()

def z3py.BVRedOr

(

a

)

Return the reduction-or expression of `a`.

Definition at line 4452 of file z3py.py.

def BVRedOr(a):
    """Return the reduction-or expression of `a`."""
    if z3_debug():
        _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
    return BitVecRef(Z3_mk_bvredor(a.ctx_ref(), a.as_ast()), a.ctx)
 
 

BVSDivNoOverflow()

def z3py.BVSDivNoOverflow	(		a,
			b
	)

A predicate the determines that bit-vector signed division does not overflow

Definition at line 4487 of file z3py.py.

def BVSDivNoOverflow(a, b):
    """A predicate the determines that bit-vector signed division does not overflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvsdiv_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

BVSNegNoOverflow()

def z3py.BVSNegNoOverflow

(

a

)

A predicate the determines that bit-vector unary negation does not overflow

Definition at line 4494 of file z3py.py.

def BVSNegNoOverflow(a):
    """A predicate the determines that bit-vector unary negation does not overflow"""
    if z3_debug():
        _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
    return BoolRef(Z3_mk_bvneg_no_overflow(a.ctx_ref(), a.as_ast()), a.ctx)
 
 

BVSubNoOverflow()

def z3py.BVSubNoOverflow	(		a,
			b
	)

A predicate the determines that bit-vector subtraction does not overflow

Definition at line 4473 of file z3py.py.

def BVSubNoOverflow(a, b):
    """A predicate the determines that bit-vector subtraction does not overflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvsub_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

BVSubNoUnderflow()

def z3py.BVSubNoUnderflow	(		a,
			b,
			signed
	)

A predicate the determines that bit-vector subtraction does not underflow

Definition at line 4480 of file z3py.py.

def BVSubNoUnderflow(a, b, signed):
    """A predicate the determines that bit-vector subtraction does not underflow"""
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvsub_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
 
 

Cbrt()

def z3py.Cbrt	(		a,
			ctx = None
	)

 Return a Z3 expression which represents the cubic root of a.

>>> x = Real('x')
>>> Cbrt(x)
x**(1/3)

Definition at line 3424 of file z3py.py.

def Cbrt(a, ctx=None):
    """ Return a Z3 expression which represents the cubic root of a.
 
    >>> x = Real('x')
    >>> Cbrt(x)
    x**(1/3)
    """
    if not is_expr(a):
        ctx = _get_ctx(ctx)
        a = RealVal(a, ctx)
    return a ** "1/3"
 

CharFromBv()

def z3py.CharFromBv	(		ch,
			ctx = None
	)

Definition at line 10856 of file z3py.py.

def CharFromBv(ch, ctx=None):
    if not is_expr(ch):
        raise Z3Expression("Bit-vector expression needed")
    return _to_expr_ref(Z3_mk_char_from_bv(ch.ctx_ref(), ch.as_ast()), ch.ctx)
 

CharIsDigit()

def z3py.CharIsDigit	(		ch,
			ctx = None
	)

Definition at line 10869 of file z3py.py.

def CharIsDigit(ch, ctx=None):
    ch = _coerce_char(ch, ctx)
    return ch.is_digit()
 

CharSort()

def z3py.CharSort

(

ctx = None

)

Create a character sort
>>> ch = CharSort()
>>> print(ch)
Char

Definition at line 10755 of file z3py.py.

def CharSort(ctx=None):
    """Create a character sort
    >>> ch = CharSort()
    >>> print(ch)
    Char
    """
    ctx = _get_ctx(ctx)
    return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
 
 

Referenced by Context.mkCharSort().

CharToBv()

def z3py.CharToBv	(		ch,
			ctx = None
	)

Definition at line 10861 of file z3py.py.

def CharToBv(ch, ctx=None):
    ch = _coerce_char(ch, ctx)
    return ch.to_bv()
 

CharToInt()

def z3py.CharToInt	(		ch,
			ctx = None
	)

Definition at line 10865 of file z3py.py.

def CharToInt(ch, ctx=None):
    ch = _coerce_char(ch, ctx)
    return ch.to_int()
 

CharVal()

def z3py.CharVal	(		ch,
			ctx = None
	)

Definition at line 10848 of file z3py.py.

def CharVal(ch, ctx=None):
    ctx = _get_ctx(ctx)
    if isinstance(ch, str):
        ch = ord(ch)
    if not isinstance(ch, int):
        raise Z3Exception("character value should be an ordinal")
    return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
    

Referenced by SeqRef.__gt__().

Complement()

def z3py.Complement

(

re

)

Create the complement regular expression.

Definition at line 11250 of file z3py.py.

def Complement(re):
    """Create the complement regular expression."""
    return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
 
 

Concat()

def z3py.Concat

(

*

args

)

Create a Z3 bit-vector concatenation expression.

>>> v = BitVecVal(1, 4)
>>> Concat(v, v+1, v)
Concat(Concat(1, 1 + 1), 1)
>>> simplify(Concat(v, v+1, v))
289
>>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
121

Definition at line 4082 of file z3py.py.

def Concat(*args):
    """Create a Z3 bit-vector concatenation expression.
 
    >>> v = BitVecVal(1, 4)
    >>> Concat(v, v+1, v)
    Concat(Concat(1, 1 + 1), 1)
    >>> simplify(Concat(v, v+1, v))
    289
    >>> print("%.3x" % simplify(Concat(v, v+1, v)).as_long())
    121
    """
    args = _get_args(args)
    sz = len(args)
    if z3_debug():
        _z3_assert(sz >= 2, "At least two arguments expected.")
 
    ctx = None
    for a in args:
        if is_expr(a):
            ctx = a.ctx
            break
    if is_seq(args[0]) or isinstance(args[0], str):
        args = [_coerce_seq(s, ctx) for s in args]
        if z3_debug():
            _z3_assert(all([is_seq(a) for a in args]), "All arguments must be sequence expressions.")
        v = (Ast * sz)()
        for i in range(sz):
            v[i] = args[i].as_ast()
        return SeqRef(Z3_mk_seq_concat(ctx.ref(), sz, v), ctx)
 
    if is_re(args[0]):
        if z3_debug():
            _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
        v = (Ast * sz)()
        for i in range(sz):
            v[i] = args[i].as_ast()
        return ReRef(Z3_mk_re_concat(ctx.ref(), sz, v), ctx)
 
    if z3_debug():
        _z3_assert(all([is_bv(a) for a in args]), "All arguments must be Z3 bit-vector expressions.")
    r = args[0]
    for i in range(sz - 1):
        r = BitVecRef(Z3_mk_concat(ctx.ref(), r.as_ast(), args[i + 1].as_ast()), ctx)
    return r
 
 

Referenced by SeqRef.__add__(), and SeqRef.__radd__().

Cond()

def z3py.Cond	(		p,
			t1,
			t2,
			ctx = None
	)

Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.

>>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))

Definition at line 8754 of file z3py.py.

def Cond(p, t1, t2, ctx=None):
    """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
 
    >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
    """
    p = _to_probe(p, ctx)
    t1 = _to_tactic(t1, ctx)
    t2 = _to_tactic(t2, ctx)
    return Tactic(Z3_tactic_cond(t1.ctx.ref(), p.probe, t1.tactic, t2.tactic), t1.ctx)
 

Referenced by If().

Const()

def z3py.Const	(		name,
			sort
	)

Create a constant of the given sort.

>>> Const('x', IntSort())
x

Definition at line 1437 of file z3py.py.

def Const(name, sort):
    """Create a constant of the given sort.
 
    >>> Const('x', IntSort())
    x
    """
    if z3_debug():
        _z3_assert(isinstance(sort, SortRef), "Z3 sort expected")
    ctx = sort.ctx
    return _to_expr_ref(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), sort.ast), ctx)
 
 

Referenced by Consts().

Consts()

def z3py.Consts	(		names,
			sort
	)

Create several constants of the given sort.

`names` is a string containing the names of all constants to be created.
Blank spaces separate the names of different constants.

>>> x, y, z = Consts('x y z', IntSort())
>>> x + y + z
x + y + z

Definition at line 1449 of file z3py.py.

def Consts(names, sort):
    """Create several constants of the given sort.
 
    `names` is a string containing the names of all constants to be created.
    Blank spaces separate the names of different constants.
 
    >>> x, y, z = Consts('x y z', IntSort())
    >>> x + y + z
    x + y + z
    """
    if isinstance(names, str):
        names = names.split(" ")
    return [Const(name, sort) for name in names]
 
 

Contains()

def z3py.Contains	(		a,
			b
	)

Check if 'a' contains 'b'
>>> s1 = Contains("abc", "ab")
>>> simplify(s1)
True
>>> s2 = Contains("abc", "bc")
>>> simplify(s2)
True
>>> x, y, z = Strings('x y z')
>>> s3 = Contains(Concat(x,y,z), y)
>>> simplify(s3)
True

Definition at line 11025 of file z3py.py.

def Contains(a, b):
    """Check if 'a' contains 'b'
    >>> s1 = Contains("abc", "ab")
    >>> simplify(s1)
    True
    >>> s2 = Contains("abc", "bc")
    >>> simplify(s2)
    True
    >>> x, y, z = Strings('x y z')
    >>> s3 = Contains(Concat(x,y,z), y)
    >>> simplify(s3)
    True
    """
    ctx = _get_ctx2(a, b)
    a = _coerce_seq(a, ctx)
    b = _coerce_seq(b, ctx)
    return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

CreateDatatypes()

def z3py.CreateDatatypes

(

*

ds

)

Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.

In the following example we define a Tree-List using two mutually recursive datatypes.

>>> TreeList = Datatype('TreeList')
>>> Tree     = Datatype('Tree')
>>> # Tree has two constructors: leaf and node
>>> Tree.declare('leaf', ('val', IntSort()))
>>> # a node contains a list of trees
>>> Tree.declare('node', ('children', TreeList))
>>> TreeList.declare('nil')
>>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
>>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
>>> Tree.val(Tree.leaf(10))
val(leaf(10))
>>> simplify(Tree.val(Tree.leaf(10)))
10
>>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
>>> n1
node(cons(leaf(10), cons(leaf(20), nil)))
>>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
>>> simplify(n2 == n1)
False
>>> simplify(TreeList.car(Tree.children(n2)) == n1)
True

Definition at line 5158 of file z3py.py.

def CreateDatatypes(*ds):
    """Create mutually recursive Z3 datatypes using 1 or more Datatype helper objects.
 
    In the following example we define a Tree-List using two mutually recursive datatypes.
 
    >>> TreeList = Datatype('TreeList')
    >>> Tree     = Datatype('Tree')
    >>> # Tree has two constructors: leaf and node
    >>> Tree.declare('leaf', ('val', IntSort()))
    >>> # a node contains a list of trees
    >>> Tree.declare('node', ('children', TreeList))
    >>> TreeList.declare('nil')
    >>> TreeList.declare('cons', ('car', Tree), ('cdr', TreeList))
    >>> Tree, TreeList = CreateDatatypes(Tree, TreeList)
    >>> Tree.val(Tree.leaf(10))
    val(leaf(10))
    >>> simplify(Tree.val(Tree.leaf(10)))
    10
    >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
    >>> n1
    node(cons(leaf(10), cons(leaf(20), nil)))
    >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
    >>> simplify(n2 == n1)
    False
    >>> simplify(TreeList.car(Tree.children(n2)) == n1)
    True
    """
    ds = _get_args(ds)
    if z3_debug():
        _z3_assert(len(ds) > 0, "At least one Datatype must be specified")
        _z3_assert(all([isinstance(d, Datatype) for d in ds]), "Arguments must be Datatypes")
        _z3_assert(all([d.ctx == ds[0].ctx for d in ds]), "Context mismatch")
        _z3_assert(all([d.constructors != [] for d in ds]), "Non-empty Datatypes expected")
    ctx = ds[0].ctx
    num = len(ds)
    names = (Symbol * num)()
    out = (Sort * num)()
    clists = (ConstructorList * num)()
    to_delete = []
    for i in range(num):
        d = ds[i]
        names[i] = to_symbol(d.name, ctx)
        num_cs = len(d.constructors)
        cs = (Constructor * num_cs)()
        for j in range(num_cs):
            c = d.constructors[j]
            cname = to_symbol(c[0], ctx)
            rname = to_symbol(c[1], ctx)
            fs = c[2]
            num_fs = len(fs)
            fnames = (Symbol * num_fs)()
            sorts = (Sort * num_fs)()
            refs = (ctypes.c_uint * num_fs)()
            for k in range(num_fs):
                fname = fs[k][0]
                ftype = fs[k][1]
                fnames[k] = to_symbol(fname, ctx)
                if isinstance(ftype, Datatype):
                    if z3_debug():
                        _z3_assert(
                            ds.count(ftype) == 1,
                            "One and only one occurrence of each datatype is expected",
                        )
                    sorts[k] = None
                    refs[k] = ds.index(ftype)
                else:
                    if z3_debug():
                        _z3_assert(is_sort(ftype), "Z3 sort expected")
                    sorts[k] = ftype.ast
                    refs[k] = 0
            cs[j] = Z3_mk_constructor(ctx.ref(), cname, rname, num_fs, fnames, sorts, refs)
            to_delete.append(ScopedConstructor(cs[j], ctx))
        clists[i] = Z3_mk_constructor_list(ctx.ref(), num_cs, cs)
        to_delete.append(ScopedConstructorList(clists[i], ctx))
    Z3_mk_datatypes(ctx.ref(), num, names, out, clists)
    result = []
    # Create a field for every constructor, recognizer and accessor
    for i in range(num):
        dref = DatatypeSortRef(out[i], ctx)
        num_cs = dref.num_constructors()
        for j in range(num_cs):
            cref = dref.constructor(j)
            cref_name = cref.name()
            cref_arity = cref.arity()
            if cref.arity() == 0:
                cref = cref()
            setattr(dref, cref_name, cref)
            rref = dref.recognizer(j)
            setattr(dref, "is_" + cref_name, rref)
            for k in range(cref_arity):
                aref = dref.accessor(j, k)
                setattr(dref, aref.name(), aref)
        result.append(dref)
    return tuple(result)
 
 

Referenced by Datatype.create().

DatatypeSort()

def z3py.DatatypeSort	(		name,
			ctx = None
	)

Create a reference to a sort that was declared, or will be declared, as a recursive datatype

Definition at line 5358 of file z3py.py.

def DatatypeSort(name, ctx = None):
    """Create a reference to a sort that was declared, or will be declared, as a recursive datatype"""
    ctx = _get_ctx(ctx)
    return DatatypeSortRef(Z3_mk_datatype_sort(ctx.ref(), to_symbol(name, ctx)), ctx)
 

Referenced by Context.MkDatatypeSort(), and Context.MkDatatypeSorts().

DeclareSort()

def z3py.DeclareSort	(		name,
			ctx = None
	)

Create a new uninterpreted sort named `name`.

If `ctx=None`, then the new sort is declared in the global Z3Py context.

>>> A = DeclareSort('A')
>>> a = Const('a', A)
>>> b = Const('b', A)
>>> a.sort() == A
True
>>> b.sort() == A
True
>>> a == b
a == b

Definition at line 693 of file z3py.py.

def DeclareSort(name, ctx=None):
    """Create a new uninterpreted sort named `name`.
 
    If `ctx=None`, then the new sort is declared in the global Z3Py context.
 
    >>> A = DeclareSort('A')
    >>> a = Const('a', A)
    >>> b = Const('b', A)
    >>> a.sort() == A
    True
    >>> b.sort() == A
    True
    >>> a == b
    a == b
    """
    ctx = _get_ctx(ctx)
    return SortRef(Z3_mk_uninterpreted_sort(ctx.ref(), to_symbol(name, ctx)), ctx)
 

Default()

def z3py.Default

(

a

)

 Return a default value for array expression.
>>> b = K(IntSort(), 1)
>>> prove(Default(b) == 1)
proved

Definition at line 4779 of file z3py.py.

def Default(a):
    """ Return a default value for array expression.
    >>> b = K(IntSort(), 1)
    >>> prove(Default(b) == 1)
    proved
    """
    if z3_debug():
        _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
    return a.default()
 
 

describe_probes()

def z3py.describe_probes

(

)

Display a (tabular) description of all available probes in Z3.

Definition at line 8675 of file z3py.py.

def describe_probes():
    """Display a (tabular) description of all available probes in Z3."""
    if in_html_mode():
        even = True
        print('<table border="1" cellpadding="2" cellspacing="0">')
        for p in probes():
            if even:
                print('<tr style="background-color:#CFCFCF">')
                even = False
            else:
                print("<tr>")
                even = True
            print("<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(probe_description(p), 40)))
        print("</table>")
    else:
        for p in probes():
            print("%s : %s" % (p, probe_description(p)))
 
 

describe_tactics()

def z3py.describe_tactics

(

)

Display a (tabular) description of all available tactics in Z3.

Definition at line 8469 of file z3py.py.

def describe_tactics():
    """Display a (tabular) description of all available tactics in Z3."""
    if in_html_mode():
        even = True
        print('<table border="1" cellpadding="2" cellspacing="0">')
        for t in tactics():
            if even:
                print('<tr style="background-color:#CFCFCF">')
                even = False
            else:
                print("<tr>")
                even = True
            print("<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(tactic_description(t), 40)))
        print("</table>")
    else:
        for t in tactics():
            print("%s : %s" % (t, tactic_description(t)))
 
 

deserialize()

def z3py.deserialize

(

st

)

inverse function to the serialize method on ExprRef.
It is made available to make it easier for users to serialize expressions back and forth between
strings. Solvers can be serialized using the 'sexpr()' method.

Definition at line 1119 of file z3py.py.

def deserialize(st):
    """inverse function to the serialize method on ExprRef.
    It is made available to make it easier for users to serialize expressions back and forth between
    strings. Solvers can be serialized using the 'sexpr()' method.
    """
    s = Solver()
    s.from_string(st)
    if len(s.assertions()) != 1:
        raise Z3Exception("single assertion expected")
    fml = s.assertions()[0]
    if fml.num_args() != 1:
        raise Z3Exception("dummy function 'F' expected")
    return fml.arg(0)
 

Diff()

def z3py.Diff	(		a,
			b,
			ctx = None
	)

Create the difference regular epression

Definition at line 11293 of file z3py.py.

def Diff(a, b, ctx=None):
    """Create the difference regular epression
    """
    return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
 

disable_trace()

def z3py.disable_trace

(

msg

)

Definition at line 79 of file z3py.py.

def disable_trace(msg):
    Z3_disable_trace(msg)
 
 

DisjointSum()

def z3py.DisjointSum	(		name,
			sorts,
			ctx = None
	)

Create a named tagged union sort base on a set of underlying sorts
Example:
    >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])

Definition at line 5375 of file z3py.py.

def DisjointSum(name, sorts, ctx=None):
    """Create a named tagged union sort base on a set of underlying sorts
    Example:
        >>> sum, ((inject0, extract0), (inject1, extract1)) = DisjointSum("+", [IntSort(), StringSort()])
    """
    sum = Datatype(name, ctx)
    for i in range(len(sorts)):
        sum.declare("inject%d" % i, ("project%d" % i, sorts[i]))
    sum = sum.create()
    return sum, [(sum.constructor(i), sum.accessor(i, 0)) for i in range(len(sorts))]
 
 

Distinct()

def z3py.Distinct

(

*

args

)

Create a Z3 distinct expression.

>>> x = Int('x')
>>> y = Int('y')
>>> Distinct(x, y)
x != y
>>> z = Int('z')
>>> Distinct(x, y, z)
Distinct(x, y, z)
>>> simplify(Distinct(x, y, z))
Distinct(x, y, z)
>>> simplify(Distinct(x, y, z), blast_distinct=True)
And(Not(x == y), Not(x == z), Not(y == z))

Definition at line 1404 of file z3py.py.

def Distinct(*args):
    """Create a Z3 distinct expression.
 
    >>> x = Int('x')
    >>> y = Int('y')
    >>> Distinct(x, y)
    x != y
    >>> z = Int('z')
    >>> Distinct(x, y, z)
    Distinct(x, y, z)
    >>> simplify(Distinct(x, y, z))
    Distinct(x, y, z)
    >>> simplify(Distinct(x, y, z), blast_distinct=True)
    And(Not(x == y), Not(x == z), Not(y == z))
    """
    args = _get_args(args)
    ctx = _ctx_from_ast_arg_list(args)
    if z3_debug():
        _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression")
    args = _coerce_expr_list(args, ctx)
    _args, sz = _to_ast_array(args)
    return BoolRef(Z3_mk_distinct(ctx.ref(), sz, _args), ctx)
 
 

Empty()

def z3py.Empty

(

s

)

Create the empty sequence of the given sort
>>> e = Empty(StringSort())
>>> e2 = StringVal("")
>>> print(e.eq(e2))
True
>>> e3 = Empty(SeqSort(IntSort()))
>>> print(e3)
Empty(Seq(Int))
>>> e4 = Empty(ReSort(SeqSort(IntSort())))
>>> print(e4)
Empty(ReSort(Seq(Int)))

Definition at line 10955 of file z3py.py.

def Empty(s):
    """Create the empty sequence of the given sort
    >>> e = Empty(StringSort())
    >>> e2 = StringVal("")
    >>> print(e.eq(e2))
    True
    >>> e3 = Empty(SeqSort(IntSort()))
    >>> print(e3)
    Empty(Seq(Int))
    >>> e4 = Empty(ReSort(SeqSort(IntSort())))
    >>> print(e4)
    Empty(ReSort(Seq(Int)))
    """
    if isinstance(s, SeqSortRef):
        return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
    if isinstance(s, ReSortRef):
        return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
    raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
 
 

EmptySet()

def z3py.EmptySet

(

s

)

Create the empty set
>>> EmptySet(IntSort())
K(Int, False)

Definition at line 4922 of file z3py.py.

def EmptySet(s):
    """Create the empty set
    >>> EmptySet(IntSort())
    K(Int, False)
    """
    ctx = s.ctx
    return ArrayRef(Z3_mk_empty_set(ctx.ref(), s.ast), ctx)
 
 

enable_trace()

def z3py.enable_trace

(

msg

)

Definition at line 75 of file z3py.py.

def enable_trace(msg):
    Z3_enable_trace(msg)
 
 

ensure_prop_closures()

def z3py.ensure_prop_closures

(

)

Definition at line 11408 of file z3py.py.

def ensure_prop_closures():
    global _prop_closures
    if _prop_closures is None:
        _prop_closures = PropClosures()
 
 

Referenced by UserPropagateBase.__init__().

EnumSort()

def z3py.EnumSort	(		name,
			values,
			ctx = None
	)

Return a new enumeration sort named `name` containing the given values.

The result is a pair (sort, list of constants).
Example:
    >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])

Definition at line 5387 of file z3py.py.

def EnumSort(name, values, ctx=None):
    """Return a new enumeration sort named `name` containing the given values.
 
    The result is a pair (sort, list of constants).
    Example:
        >>> Color, (red, green, blue) = EnumSort('Color', ['red', 'green', 'blue'])
    """
    if z3_debug():
        _z3_assert(isinstance(name, str), "Name must be a string")
        _z3_assert(all([isinstance(v, str) for v in values]), "Eumeration sort values must be strings")
        _z3_assert(len(values) > 0, "At least one value expected")
    ctx = _get_ctx(ctx)
    num = len(values)
    _val_names = (Symbol * num)()
    for i in range(num):
        _val_names[i] = to_symbol(values[i])
    _values = (FuncDecl * num)()
    _testers = (FuncDecl * num)()
    name = to_symbol(name)
    S = DatatypeSortRef(Z3_mk_enumeration_sort(ctx.ref(), name, num, _val_names, _values, _testers), ctx)
    V = []
    for i in range(num):
        V.append(FuncDeclRef(_values[i], ctx))
    V = [a() for a in V]
    return S, V
 

Referenced by Context.MkEnumSort().

eq()

def z3py.eq	(		a,
			b
	)

Return `True` if `a` and `b` are structurally identical AST nodes.

>>> x = Int('x')
>>> y = Int('y')
>>> eq(x, y)
False
>>> eq(x + 1, x + 1)
True
>>> eq(x + 1, 1 + x)
False
>>> eq(simplify(x + 1), simplify(1 + x))
True

Definition at line 472 of file z3py.py.

def eq(a, b):
    """Return `True` if `a` and `b` are structurally identical AST nodes.
 
    >>> x = Int('x')
    >>> y = Int('y')
    >>> eq(x, y)
    False
    >>> eq(x + 1, x + 1)
    True
    >>> eq(x + 1, 1 + x)
    False
    >>> eq(simplify(x + 1), simplify(1 + x))
    True
    """
    if z3_debug():
        _z3_assert(is_ast(a) and is_ast(b), "Z3 ASTs expected")
    return a.eq(b)
 
 

Referenced by substitute().

Exists()

def z3py.Exists	(		vs,
			body,
			weight = 1,
			qid = "",
			skid = "",
			patterns = [],
			no_patterns = []
	)

Create a Z3 exists formula.

The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.


>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> q = Exists([x, y], f(x, y) >= x, skid="foo")
>>> q
Exists([x, y], f(x, y) >= x)
>>> is_quantifier(q)
True
>>> r = Tactic('nnf')(q).as_expr()
>>> is_quantifier(r)
False

Definition at line 2240 of file z3py.py.

def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
    """Create a Z3 exists formula.
 
    The parameters `weight`, `qif`, `skid`, `patterns` and `no_patterns` are optional annotations.
 
 
    >>> f = Function('f', IntSort(), IntSort(), IntSort())
    >>> x = Int('x')
    >>> y = Int('y')
    >>> q = Exists([x, y], f(x, y) >= x, skid="foo")
    >>> q
    Exists([x, y], f(x, y) >= x)
    >>> is_quantifier(q)
    True
    >>> r = Tactic('nnf')(q).as_expr()
    >>> is_quantifier(r)
    False
    """
    return _mk_quantifier(False, vs, body, weight, qid, skid, patterns, no_patterns)
 
 

Referenced by Fixedpoint.abstract().

Ext()

def z3py.Ext	(		a,
			b
	)

Return extensionality index for one-dimensional arrays.
>> a, b = Consts('a b', SetSort(IntSort()))
>> Ext(a, b)
Ext(a, b)

Definition at line 4868 of file z3py.py.

def Ext(a, b):
    """Return extensionality index for one-dimensional arrays.
    >> a, b = Consts('a b', SetSort(IntSort()))
    >> Ext(a, b)
    Ext(a, b)
    """
    ctx = a.ctx
    if z3_debug():
        _z3_assert(is_array_sort(a) and (is_array(b) or b.is_lambda()), "arguments must be arrays")
    return _to_expr_ref(Z3_mk_array_ext(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
 
 

Extract()

def z3py.Extract	(		high,
			low,
			a
	)

Create a Z3 bit-vector extraction expression.
Extract is overloaded to also work on sequence extraction.
The functions SubString and SubSeq are redirected to Extract.
For this case, the arguments are reinterpreted as:
    high - is a sequence (string)
    low  - is an offset
    a    - is the length to be extracted

>>> x = BitVec('x', 8)
>>> Extract(6, 2, x)
Extract(6, 2, x)
>>> Extract(6, 2, x).sort()
BitVec(5)
>>> simplify(Extract(StringVal("abcd"),2,1))
"c"

Definition at line 4128 of file z3py.py.

def Extract(high, low, a):
    """Create a Z3 bit-vector extraction expression.
    Extract is overloaded to also work on sequence extraction.
    The functions SubString and SubSeq are redirected to Extract.
    For this case, the arguments are reinterpreted as:
        high - is a sequence (string)
        low  - is an offset
        a    - is the length to be extracted
 
    >>> x = BitVec('x', 8)
    >>> Extract(6, 2, x)
    Extract(6, 2, x)
    >>> Extract(6, 2, x).sort()
    BitVec(5)
    >>> simplify(Extract(StringVal("abcd"),2,1))
    "c"
    """
    if isinstance(high, str):
        high = StringVal(high)
    if is_seq(high):
        s = high
        offset, length = _coerce_exprs(low, a, s.ctx)
        return SeqRef(Z3_mk_seq_extract(s.ctx_ref(), s.as_ast(), offset.as_ast(), length.as_ast()), s.ctx)
    if z3_debug():
        _z3_assert(low <= high, "First argument must be greater than or equal to second argument")
        _z3_assert(_is_int(high) and high >= 0 and _is_int(low) and low >= 0,
                   "First and second arguments must be non negative integers")
        _z3_assert(is_bv(a), "Third argument must be a Z3 bit-vector expression")
    return BitVecRef(Z3_mk_extract(a.ctx_ref(), high, low, a.as_ast()), a.ctx)
 
 

Referenced by SubSeq(), and SubString().

FailIf()

def z3py.FailIf	(		p,
			ctx = None
	)

Return a tactic that fails if the probe `p` evaluates to true.
Otherwise, it returns the input goal unmodified.

In the following example, the tactic applies 'simplify' if and only if there are
more than 2 constraints in the goal.

>>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
>>> x, y = Ints('x y')
>>> g = Goal()
>>> g.add(x > 0)
>>> g.add(y > 0)
>>> t(g)
[[x > 0, y > 0]]
>>> g.add(x == y + 1)
>>> t(g)
[[Not(x <= 0), Not(y <= 0), x == 1 + y]]

Definition at line 8712 of file z3py.py.

def FailIf(p, ctx=None):
    """Return a tactic that fails if the probe `p` evaluates to true.
    Otherwise, it returns the input goal unmodified.
 
    In the following example, the tactic applies 'simplify' if and only if there are
    more than 2 constraints in the goal.
 
    >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
    >>> x, y = Ints('x y')
    >>> g = Goal()
    >>> g.add(x > 0)
    >>> g.add(y > 0)
    >>> t(g)
    [[x > 0, y > 0]]
    >>> g.add(x == y + 1)
    >>> t(g)
    [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
    """
    p = _to_probe(p, ctx)
    return Tactic(Z3_tactic_fail_if(p.ctx.ref(), p.probe), p.ctx)
 
 

FiniteDomainSort()

def z3py.FiniteDomainSort	(		name,
			sz,
			ctx = None
	)

Create a named finite domain sort of a given size sz

Definition at line 7716 of file z3py.py.

def FiniteDomainSort(name, sz, ctx=None):
    """Create a named finite domain sort of a given size sz"""
    if not isinstance(name, Symbol):
        name = to_symbol(name)
    ctx = _get_ctx(ctx)
    return FiniteDomainSortRef(Z3_mk_finite_domain_sort(ctx.ref(), name, sz), ctx)
 
 

Referenced by Context.MkFiniteDomainSort().

FiniteDomainVal()

def z3py.FiniteDomainVal	(		val,
			sort,
			ctx = None
	)

Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.

>>> s = FiniteDomainSort('S', 256)
>>> FiniteDomainVal(255, s)
255
>>> FiniteDomainVal('100', s)
100

Definition at line 7786 of file z3py.py.

def FiniteDomainVal(val, sort, ctx=None):
    """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
 
    >>> s = FiniteDomainSort('S', 256)
    >>> FiniteDomainVal(255, s)
    255
    >>> FiniteDomainVal('100', s)
    100
    """
    if z3_debug():
        _z3_assert(is_finite_domain_sort(sort), "Expected finite-domain sort")
    ctx = sort.ctx
    return FiniteDomainNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), sort.ast), ctx)
 
 

Float128()

def z3py.Float128

(

ctx = None

)

Floating-point 128-bit (quadruple) sort.

Definition at line 9440 of file z3py.py.

def Float128(ctx=None):
    """Floating-point 128-bit (quadruple) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
 
 

Float16()

def z3py.Float16

(

ctx = None

)

Floating-point 16-bit (half) sort.

Definition at line 9404 of file z3py.py.

def Float16(ctx=None):
    """Floating-point 16-bit (half) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
 
 

Float32()

def z3py.Float32

(

ctx = None

)

Floating-point 32-bit (single) sort.

Definition at line 9416 of file z3py.py.

def Float32(ctx=None):
    """Floating-point 32-bit (single) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
 
 

Float64()

def z3py.Float64

(

ctx = None

)

Floating-point 64-bit (double) sort.

Definition at line 9428 of file z3py.py.

def Float64(ctx=None):
    """Floating-point 64-bit (double) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
 
 

FloatDouble()

def z3py.FloatDouble

(

ctx = None

)

Floating-point 64-bit (double) sort.

Definition at line 9434 of file z3py.py.

def FloatDouble(ctx=None):
    """Floating-point 64-bit (double) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
 
 

FloatHalf()

def z3py.FloatHalf

(

ctx = None

)

Floating-point 16-bit (half) sort.

Definition at line 9410 of file z3py.py.

def FloatHalf(ctx=None):
    """Floating-point 16-bit (half) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
 
 

FloatQuadruple()

def z3py.FloatQuadruple

(

ctx = None

)

Floating-point 128-bit (quadruple) sort.

Definition at line 9446 of file z3py.py.

def FloatQuadruple(ctx=None):
    """Floating-point 128-bit (quadruple) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
 
 

FloatSingle()

def z3py.FloatSingle

(

ctx = None

)

Floating-point 32-bit (single) sort.

Definition at line 9422 of file z3py.py.

def FloatSingle(ctx=None):
    """Floating-point 32-bit (single) sort."""
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
 
 

ForAll()

def z3py.ForAll	(		vs,
			body,
			weight = 1,
			qid = "",
			skid = "",
			patterns = [],
			no_patterns = []
	)

Create a Z3 forall formula.

The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> x = Int('x')
>>> y = Int('y')
>>> ForAll([x, y], f(x, y) >= x)
ForAll([x, y], f(x, y) >= x)
>>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
ForAll([x, y], f(x, y) >= x)
>>> ForAll([x, y], f(x, y) >= x, weight=10)
ForAll([x, y], f(x, y) >= x)

Definition at line 2222 of file z3py.py.

def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
    """Create a Z3 forall formula.
 
    The parameters `weight`, `qid`, `skid`, `patterns` and `no_patterns` are optional annotations.
 
    >>> f = Function('f', IntSort(), IntSort(), IntSort())
    >>> x = Int('x')
    >>> y = Int('y')
    >>> ForAll([x, y], f(x, y) >= x)
    ForAll([x, y], f(x, y) >= x)
    >>> ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
    ForAll([x, y], f(x, y) >= x)
    >>> ForAll([x, y], f(x, y) >= x, weight=10)
    ForAll([x, y], f(x, y) >= x)
    """
    return _mk_quantifier(True, vs, body, weight, qid, skid, patterns, no_patterns)
 
 

Referenced by Fixedpoint.abstract().

FP()

def z3py.FP	(		name,
			fpsort,
			ctx = None
	)

Return a floating-point constant named `name`.
`fpsort` is the floating-point sort.
If `ctx=None`, then the global context is used.

>>> x  = FP('x', FPSort(8, 24))
>>> is_fp(x)
True
>>> x.ebits()
8
>>> x.sort()
FPSort(8, 24)
>>> word = FPSort(8, 24)
>>> x2 = FP('x', word)
>>> eq(x, x2)
True

Definition at line 10072 of file z3py.py.

def FP(name, fpsort, ctx=None):
    """Return a floating-point constant named `name`.
    `fpsort` is the floating-point sort.
    If `ctx=None`, then the global context is used.
 
    >>> x  = FP('x', FPSort(8, 24))
    >>> is_fp(x)
    True
    >>> x.ebits()
    8
    >>> x.sort()
    FPSort(8, 24)
    >>> word = FPSort(8, 24)
    >>> x2 = FP('x', word)
    >>> eq(x, x2)
    True
    """
    if isinstance(fpsort, FPSortRef) and ctx is None:
        ctx = fpsort.ctx
    else:
        ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
 
 

Referenced by FPs().

fpAbs()

def z3py.fpAbs	(		a,
			ctx = None
	)

Create a Z3 floating-point absolute value expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FPVal(1.0, s)
>>> fpAbs(x)
fpAbs(1)
>>> y = FPVal(-20.0, s)
>>> y
-1.25*(2**4)
>>> fpAbs(y)
fpAbs(-1.25*(2**4))
>>> fpAbs(-1.25*(2**4))
fpAbs(-1.25*(2**4))
>>> fpAbs(x).sort()
FPSort(8, 24)

Definition at line 10115 of file z3py.py.

def fpAbs(a, ctx=None):
    """Create a Z3 floating-point absolute value expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FPVal(1.0, s)
    >>> fpAbs(x)
    fpAbs(1)
    >>> y = FPVal(-20.0, s)
    >>> y
    -1.25*(2**4)
    >>> fpAbs(y)
    fpAbs(-1.25*(2**4))
    >>> fpAbs(-1.25*(2**4))
    fpAbs(-1.25*(2**4))
    >>> fpAbs(x).sort()
    FPSort(8, 24)
    """
    ctx = _get_ctx(ctx)
    [a] = _coerce_fp_expr_list([a], ctx)
    return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
 
 

fpAdd()

def z3py.fpAdd	(		rm,
			a,
			b,
			ctx = None
	)

Create a Z3 floating-point addition expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpAdd(rm, x, y)
x + y
>>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
fpAdd(RTZ(), x, y)
>>> fpAdd(rm, x, y).sort()
FPSort(8, 24)

Definition at line 10206 of file z3py.py.

def fpAdd(rm, a, b, ctx=None):
    """Create a Z3 floating-point addition expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpAdd(rm, x, y)
    x + y
    >>> fpAdd(RTZ(), x, y) # default rounding mode is RTZ
    fpAdd(RTZ(), x, y)
    >>> fpAdd(rm, x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
 
 

Referenced by FPRef.__add__(), and FPRef.__radd__().

fpBVToFP()

def z3py.fpBVToFP	(		v,
			sort,
			ctx = None
	)

Create a Z3 floating-point conversion expression that represents the
conversion from a bit-vector term to a floating-point term.

>>> x_bv = BitVecVal(0x3F800000, 32)
>>> x_fp = fpBVToFP(x_bv, Float32())
>>> x_fp
fpToFP(1065353216)
>>> simplify(x_fp)
1

Definition at line 10528 of file z3py.py.

def fpBVToFP(v, sort, ctx=None):
    """Create a Z3 floating-point conversion expression that represents the
    conversion from a bit-vector term to a floating-point term.
 
    >>> x_bv = BitVecVal(0x3F800000, 32)
    >>> x_fp = fpBVToFP(x_bv, Float32())
    >>> x_fp
    fpToFP(1065353216)
    >>> simplify(x_fp)
    1
    """
    _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
    _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
    ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
 
 

fpDiv()

def z3py.fpDiv	(		rm,
			a,
			b,
			ctx = None
	)

Create a Z3 floating-point division expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpDiv(rm, x, y)
x / y
>>> fpDiv(rm, x, y).sort()
FPSort(8, 24)

Definition at line 10253 of file z3py.py.

def fpDiv(rm, a, b, ctx=None):
    """Create a Z3 floating-point division expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpDiv(rm, x, y)
    x / y
    >>> fpDiv(rm, x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
 
 

Referenced by FPRef.__div__(), and FPRef.__rdiv__().

fpEQ()

def z3py.fpEQ	(		a,
			b,
			ctx = None
	)

Create the Z3 floating-point expression `fpEQ(other, self)`.

>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpEQ(x, y)
fpEQ(x, y)
>>> fpEQ(x, y).sexpr()
'(fp.eq x y)'

Definition at line 10436 of file z3py.py.

def fpEQ(a, b, ctx=None):
    """Create the Z3 floating-point expression `fpEQ(other, self)`.
 
    >>> x, y = FPs('x y', FPSort(8, 24))
    >>> fpEQ(x, y)
    fpEQ(x, y)
    >>> fpEQ(x, y).sexpr()
    '(fp.eq x y)'
    """
    return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
 
 

Referenced by fpNEQ().

fpFMA()

def z3py.fpFMA	(		rm,
			a,
			b,
			c,
			ctx = None
	)

Create a Z3 floating-point fused multiply-add expression.

Definition at line 10312 of file z3py.py.

def fpFMA(rm, a, b, c, ctx=None):
    """Create a Z3 floating-point fused multiply-add expression.
    """
    return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
 
 

fpFP()

def z3py.fpFP	(		sgn,
			exp,
			sig,
			ctx = None
	)

Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.

>>> s = FPSort(8, 24)
>>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
>>> print(x)
fpFP(1, 127, 4194304)
>>> xv = FPVal(-1.5, s)
>>> print(xv)
-1.5
>>> slvr = Solver()
>>> slvr.add(fpEQ(x, xv))
>>> slvr.check()
sat
>>> xv = FPVal(+1.5, s)
>>> print(xv)
1.5
>>> slvr = Solver()
>>> slvr.add(fpEQ(x, xv))
>>> slvr.check()
unsat

Definition at line 10460 of file z3py.py.

def fpFP(sgn, exp, sig, ctx=None):
    """Create the Z3 floating-point value `fpFP(sgn, sig, exp)` from the three bit-vectors sgn, sig, and exp.
 
    >>> s = FPSort(8, 24)
    >>> x = fpFP(BitVecVal(1, 1), BitVecVal(2**7-1, 8), BitVecVal(2**22, 23))
    >>> print(x)
    fpFP(1, 127, 4194304)
    >>> xv = FPVal(-1.5, s)
    >>> print(xv)
    -1.5
    >>> slvr = Solver()
    >>> slvr.add(fpEQ(x, xv))
    >>> slvr.check()
    sat
    >>> xv = FPVal(+1.5, s)
    >>> print(xv)
    1.5
    >>> slvr = Solver()
    >>> slvr.add(fpEQ(x, xv))
    >>> slvr.check()
    unsat
    """
    _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
    _z3_assert(sgn.sort().size() == 1, "sort mismatch")
    ctx = _get_ctx(ctx)
    _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
    return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
 
 

fpFPToFP()

def z3py.fpFPToFP	(		rm,
			v,
			sort,
			ctx = None
	)

Create a Z3 floating-point conversion expression that represents the
conversion from a floating-point term to a floating-point term of different precision.

>>> x_sgl = FPVal(1.0, Float32())
>>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
>>> x_dbl
fpToFP(RNE(), 1)
>>> simplify(x_dbl)
1
>>> x_dbl.sort()
FPSort(11, 53)

Definition at line 10545 of file z3py.py.

def fpFPToFP(rm, v, sort, ctx=None):
    """Create a Z3 floating-point conversion expression that represents the
    conversion from a floating-point term to a floating-point term of different precision.
 
    >>> x_sgl = FPVal(1.0, Float32())
    >>> x_dbl = fpFPToFP(RNE(), x_sgl, Float64())
    >>> x_dbl
    fpToFP(RNE(), 1)
    >>> simplify(x_dbl)
    1
    >>> x_dbl.sort()
    FPSort(11, 53)
    """
    _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
    _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
    _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
    ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
 
 

fpGEQ()

def z3py.fpGEQ	(		a,
			b,
			ctx = None
	)

Create the Z3 floating-point expression `other >= self`.

>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpGEQ(x, y)
x >= y
>>> (x >= y).sexpr()
'(fp.geq x y)'

Definition at line 10424 of file z3py.py.

def fpGEQ(a, b, ctx=None):
    """Create the Z3 floating-point expression `other >= self`.
 
    >>> x, y = FPs('x y', FPSort(8, 24))
    >>> fpGEQ(x, y)
    x >= y
    >>> (x >= y).sexpr()
    '(fp.geq x y)'
    """
    return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
 
 

Referenced by FPRef.__ge__().

fpGT()

def z3py.fpGT	(		a,
			b,
			ctx = None
	)

Create the Z3 floating-point expression `other > self`.

>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpGT(x, y)
x > y
>>> (x > y).sexpr()
'(fp.gt x y)'

Definition at line 10412 of file z3py.py.

def fpGT(a, b, ctx=None):
    """Create the Z3 floating-point expression `other > self`.
 
    >>> x, y = FPs('x y', FPSort(8, 24))
    >>> fpGT(x, y)
    x > y
    >>> (x > y).sexpr()
    '(fp.gt x y)'
    """
    return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
 
 

Referenced by FPRef.__gt__().

fpInfinity()

def z3py.fpInfinity	(		s,
			negative
	)

Create a Z3 floating-point +oo or -oo term.

Definition at line 10000 of file z3py.py.

def fpInfinity(s, negative):
    """Create a Z3 floating-point +oo or -oo term."""
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    _z3_assert(isinstance(negative, bool), "expected Boolean flag")
    return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
 
 

fpIsInf()

def z3py.fpIsInf	(		a,
			ctx = None
	)

Create a Z3 floating-point isInfinite expression.

>>> s = FPSort(8, 24)
>>> x = FP('x', s)
>>> fpIsInf(x)
fpIsInf(x)

Definition at line 10342 of file z3py.py.

def fpIsInf(a, ctx=None):
    """Create a Z3 floating-point isInfinite expression.
 
    >>> s = FPSort(8, 24)
    >>> x = FP('x', s)
    >>> fpIsInf(x)
    fpIsInf(x)
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
 
 

fpIsNaN()

def z3py.fpIsNaN	(		a,
			ctx = None
	)

Create a Z3 floating-point isNaN expression.

>>> s = FPSort(8, 24)
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpIsNaN(x)
fpIsNaN(x)

Definition at line 10330 of file z3py.py.

def fpIsNaN(a, ctx=None):
    """Create a Z3 floating-point isNaN expression.
 
    >>> s = FPSort(8, 24)
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpIsNaN(x)
    fpIsNaN(x)
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
 
 

fpIsNegative()

def z3py.fpIsNegative	(		a,
			ctx = None
	)

Create a Z3 floating-point isNegative expression.

Definition at line 10371 of file z3py.py.

def fpIsNegative(a, ctx=None):
    """Create a Z3 floating-point isNegative expression.
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
 
 

fpIsNormal()

def z3py.fpIsNormal	(		a,
			ctx = None
	)

Create a Z3 floating-point isNormal expression.

Definition at line 10359 of file z3py.py.

def fpIsNormal(a, ctx=None):
    """Create a Z3 floating-point isNormal expression.
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
 
 

fpIsPositive()

def z3py.fpIsPositive	(		a,
			ctx = None
	)

Create a Z3 floating-point isPositive expression.

Definition at line 10377 of file z3py.py.

def fpIsPositive(a, ctx=None):
    """Create a Z3 floating-point isPositive expression.
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
 
 

fpIsSubnormal()

def z3py.fpIsSubnormal	(		a,
			ctx = None
	)

Create a Z3 floating-point isSubnormal expression.

Definition at line 10365 of file z3py.py.

def fpIsSubnormal(a, ctx=None):
    """Create a Z3 floating-point isSubnormal expression.
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
 
 

fpIsZero()

def z3py.fpIsZero	(		a,
			ctx = None
	)

Create a Z3 floating-point isZero expression.

Definition at line 10353 of file z3py.py.

def fpIsZero(a, ctx=None):
    """Create a Z3 floating-point isZero expression.
    """
    return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
 
 

fpLEQ()

def z3py.fpLEQ	(		a,
			b,
			ctx = None
	)

Create the Z3 floating-point expression `other <= self`.

>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpLEQ(x, y)
x <= y
>>> (x <= y).sexpr()
'(fp.leq x y)'

Definition at line 10400 of file z3py.py.

def fpLEQ(a, b, ctx=None):
    """Create the Z3 floating-point expression `other <= self`.
 
    >>> x, y = FPs('x y', FPSort(8, 24))
    >>> fpLEQ(x, y)
    x <= y
    >>> (x <= y).sexpr()
    '(fp.leq x y)'
    """
    return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
 
 

Referenced by FPRef.__le__().

fpLT()

def z3py.fpLT	(		a,
			b,
			ctx = None
	)

Create the Z3 floating-point expression `other < self`.

>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpLT(x, y)
x < y
>>> (x < y).sexpr()
'(fp.lt x y)'

Definition at line 10388 of file z3py.py.

def fpLT(a, b, ctx=None):
    """Create the Z3 floating-point expression `other < self`.
 
    >>> x, y = FPs('x y', FPSort(8, 24))
    >>> fpLT(x, y)
    x < y
    >>> (x < y).sexpr()
    '(fp.lt x y)'
    """
    return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
 
 

Referenced by FPRef.__lt__().

fpMax()

def z3py.fpMax	(		a,
			b,
			ctx = None
	)

Create a Z3 floating-point maximum expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpMax(x, y)
fpMax(x, y)
>>> fpMax(x, y).sort()
FPSort(8, 24)

Definition at line 10297 of file z3py.py.

def fpMax(a, b, ctx=None):
    """Create a Z3 floating-point maximum expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpMax(x, y)
    fpMax(x, y)
    >>> fpMax(x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
 
 

fpMin()

def z3py.fpMin	(		a,
			b,
			ctx = None
	)

Create a Z3 floating-point minimum expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpMin(x, y)
fpMin(x, y)
>>> fpMin(x, y).sort()
FPSort(8, 24)

Definition at line 10282 of file z3py.py.

def fpMin(a, b, ctx=None):
    """Create a Z3 floating-point minimum expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpMin(x, y)
    fpMin(x, y)
    >>> fpMin(x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
 
 

fpMinusInfinity()

def z3py.fpMinusInfinity

(

s

)

Create a Z3 floating-point -oo term.

Definition at line 9994 of file z3py.py.

def fpMinusInfinity(s):
    """Create a Z3 floating-point -oo term."""
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
 
 

Referenced by FPVal().

fpMinusZero()

def z3py.fpMinusZero

(

s

)

Create a Z3 floating-point -0.0 term.

Definition at line 10013 of file z3py.py.

def fpMinusZero(s):
    """Create a Z3 floating-point -0.0 term."""
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
 
 

Referenced by FPVal().

fpMul()

def z3py.fpMul	(		rm,
			a,
			b,
			ctx = None
	)

Create a Z3 floating-point multiplication expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpMul(rm, x, y)
x * y
>>> fpMul(rm, x, y).sort()
FPSort(8, 24)

Definition at line 10238 of file z3py.py.

def fpMul(rm, a, b, ctx=None):
    """Create a Z3 floating-point multiplication expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpMul(rm, x, y)
    x * y
    >>> fpMul(rm, x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
 
 

Referenced by FPRef.__mul__(), and FPRef.__rmul__().

fpNaN()

def z3py.fpNaN

(

s

)

Create a Z3 floating-point NaN term.

>>> s = FPSort(8, 24)
>>> set_fpa_pretty(True)
>>> fpNaN(s)
NaN
>>> pb = get_fpa_pretty()
>>> set_fpa_pretty(False)
>>> fpNaN(s)
fpNaN(FPSort(8, 24))
>>> set_fpa_pretty(pb)

Definition at line 9960 of file z3py.py.

def fpNaN(s):
    """Create a Z3 floating-point NaN term.
 
    >>> s = FPSort(8, 24)
    >>> set_fpa_pretty(True)
    >>> fpNaN(s)
    NaN
    >>> pb = get_fpa_pretty()
    >>> set_fpa_pretty(False)
    >>> fpNaN(s)
    fpNaN(FPSort(8, 24))
    >>> set_fpa_pretty(pb)
    """
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
 
 

Referenced by FPVal().

fpNeg()

def z3py.fpNeg	(		a,
			ctx = None
	)

Create a Z3 floating-point addition expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> fpNeg(x)
-x
>>> fpNeg(x).sort()
FPSort(8, 24)

Definition at line 10138 of file z3py.py.

def fpNeg(a, ctx=None):
    """Create a Z3 floating-point addition expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> fpNeg(x)
    -x
    >>> fpNeg(x).sort()
    FPSort(8, 24)
    """
    ctx = _get_ctx(ctx)
    [a] = _coerce_fp_expr_list([a], ctx)
    return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
 
 

Referenced by FPRef.__neg__().

fpNEQ()

def z3py.fpNEQ	(		a,
			b,
			ctx = None
	)

Create the Z3 floating-point expression `Not(fpEQ(other, self))`.

>>> x, y = FPs('x y', FPSort(8, 24))
>>> fpNEQ(x, y)
Not(fpEQ(x, y))
>>> (x != y).sexpr()
'(distinct x y)'

Definition at line 10448 of file z3py.py.

def fpNEQ(a, b, ctx=None):
    """Create the Z3 floating-point expression `Not(fpEQ(other, self))`.
 
    >>> x, y = FPs('x y', FPSort(8, 24))
    >>> fpNEQ(x, y)
    Not(fpEQ(x, y))
    >>> (x != y).sexpr()
    '(distinct x y)'
    """
    return Not(fpEQ(a, b, ctx))
 
 

fpPlusInfinity()

def z3py.fpPlusInfinity

(

s

)

Create a Z3 floating-point +oo term.

>>> s = FPSort(8, 24)
>>> pb = get_fpa_pretty()
>>> set_fpa_pretty(True)
>>> fpPlusInfinity(s)
+oo
>>> set_fpa_pretty(False)
>>> fpPlusInfinity(s)
fpPlusInfinity(FPSort(8, 24))
>>> set_fpa_pretty(pb)

Definition at line 9977 of file z3py.py.

def fpPlusInfinity(s):
    """Create a Z3 floating-point +oo term.
 
    >>> s = FPSort(8, 24)
    >>> pb = get_fpa_pretty()
    >>> set_fpa_pretty(True)
    >>> fpPlusInfinity(s)
    +oo
    >>> set_fpa_pretty(False)
    >>> fpPlusInfinity(s)
    fpPlusInfinity(FPSort(8, 24))
    >>> set_fpa_pretty(pb)
    """
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
 
 

Referenced by FPVal().

fpPlusZero()

def z3py.fpPlusZero

(

s

)

Create a Z3 floating-point +0.0 term.

Definition at line 10007 of file z3py.py.

def fpPlusZero(s):
    """Create a Z3 floating-point +0.0 term."""
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
 
 

Referenced by FPVal().

fpRealToFP()

def z3py.fpRealToFP	(		rm,
			v,
			sort,
			ctx = None
	)

Create a Z3 floating-point conversion expression that represents the
conversion from a real term to a floating-point term.

>>> x_r = RealVal(1.5)
>>> x_fp = fpRealToFP(RNE(), x_r, Float32())
>>> x_fp
fpToFP(RNE(), 3/2)
>>> simplify(x_fp)
1.5

Definition at line 10565 of file z3py.py.

def fpRealToFP(rm, v, sort, ctx=None):
    """Create a Z3 floating-point conversion expression that represents the
    conversion from a real term to a floating-point term.
 
    >>> x_r = RealVal(1.5)
    >>> x_fp = fpRealToFP(RNE(), x_r, Float32())
    >>> x_fp
    fpToFP(RNE(), 3/2)
    >>> simplify(x_fp)
    1.5
    """
    _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
    _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
    _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
    ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
 
 

fpRem()

def z3py.fpRem	(		a,
			b,
			ctx = None
	)

Create a Z3 floating-point remainder expression.

>>> s = FPSort(8, 24)
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpRem(x, y)
fpRem(x, y)
>>> fpRem(x, y).sort()
FPSort(8, 24)

Definition at line 10268 of file z3py.py.

def fpRem(a, b, ctx=None):
    """Create a Z3 floating-point remainder expression.
 
    >>> s = FPSort(8, 24)
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpRem(x, y)
    fpRem(x, y)
    >>> fpRem(x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
 
 

Referenced by FPRef.__mod__(), and FPRef.__rmod__().

fpRoundToIntegral()

def z3py.fpRoundToIntegral	(		rm,
			a,
			ctx = None
	)

Create a Z3 floating-point roundToIntegral expression.

Definition at line 10324 of file z3py.py.

def fpRoundToIntegral(rm, a, ctx=None):
    """Create a Z3 floating-point roundToIntegral expression.
    """
    return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
 
 

FPs()

def z3py.FPs	(		names,
			fpsort,
			ctx = None
	)

Return an array of floating-point constants.

>>> x, y, z = FPs('x y z', FPSort(8, 24))
>>> x.sort()
FPSort(8, 24)
>>> x.sbits()
24
>>> x.ebits()
8
>>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
x + y * z

Definition at line 10096 of file z3py.py.

def FPs(names, fpsort, ctx=None):
    """Return an array of floating-point constants.
 
    >>> x, y, z = FPs('x y z', FPSort(8, 24))
    >>> x.sort()
    FPSort(8, 24)
    >>> x.sbits()
    24
    >>> x.ebits()
    8
    >>> fpMul(RNE(), fpAdd(RNE(), x, y), z)
    x + y * z
    """
    ctx = _get_ctx(ctx)
    if isinstance(names, str):
        names = names.split(" ")
    return [FP(name, fpsort, ctx) for name in names]
 
 

fpSignedToFP()

def z3py.fpSignedToFP	(		rm,
			v,
			sort,
			ctx = None
	)

Create a Z3 floating-point conversion expression that represents the
conversion from a signed bit-vector term (encoding an integer) to a floating-point term.

>>> x_signed = BitVecVal(-5, BitVecSort(32))
>>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
>>> x_fp
fpToFP(RNE(), 4294967291)
>>> simplify(x_fp)
-1.25*(2**2)

Definition at line 10583 of file z3py.py.

def fpSignedToFP(rm, v, sort, ctx=None):
    """Create a Z3 floating-point conversion expression that represents the
    conversion from a signed bit-vector term (encoding an integer) to a floating-point term.
 
    >>> x_signed = BitVecVal(-5, BitVecSort(32))
    >>> x_fp = fpSignedToFP(RNE(), x_signed, Float32())
    >>> x_fp
    fpToFP(RNE(), 4294967291)
    >>> simplify(x_fp)
    -1.25*(2**2)
    """
    _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
    _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
    _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
    ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
 
 

FPSort()

def z3py.FPSort	(		ebits,
			sbits,
			ctx = None
	)

Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.

>>> Single = FPSort(8, 24)
>>> Double = FPSort(11, 53)
>>> Single
FPSort(8, 24)
>>> x = Const('x', Single)
>>> eq(x, FP('x', FPSort(8, 24)))
True

Definition at line 9901 of file z3py.py.

def FPSort(ebits, sbits, ctx=None):
    """Return a Z3 floating-point sort of the given sizes. If `ctx=None`, then the global context is used.
 
    >>> Single = FPSort(8, 24)
    >>> Double = FPSort(11, 53)
    >>> Single
    FPSort(8, 24)
    >>> x = Const('x', Single)
    >>> eq(x, FP('x', FPSort(8, 24)))
    True
    """
    ctx = _get_ctx(ctx)
    return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
 
 

Referenced by get_default_fp_sort(), Context.mkFPSort(), Context.MkFPSort(), Context.MkFPSort128(), Context.mkFPSort128(), Context.MkFPSort16(), Context.mkFPSort16(), Context.MkFPSort32(), Context.mkFPSort32(), Context.MkFPSort64(), Context.mkFPSort64(), Context.MkFPSortDouble(), Context.mkFPSortDouble(), Context.MkFPSortHalf(), Context.mkFPSortHalf(), Context.MkFPSortQuadruple(), Context.mkFPSortQuadruple(), Context.MkFPSortSingle(), and Context.mkFPSortSingle().

fpSqrt()

def z3py.fpSqrt	(		rm,
			a,
			ctx = None
	)

Create a Z3 floating-point square root expression.

Definition at line 10318 of file z3py.py.

def fpSqrt(rm, a, ctx=None):
    """Create a Z3 floating-point square root expression.
    """
    return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
 
 

fpSub()

def z3py.fpSub	(		rm,
			a,
			b,
			ctx = None
	)

Create a Z3 floating-point subtraction expression.

>>> s = FPSort(8, 24)
>>> rm = RNE()
>>> x = FP('x', s)
>>> y = FP('y', s)
>>> fpSub(rm, x, y)
x - y
>>> fpSub(rm, x, y).sort()
FPSort(8, 24)

Definition at line 10223 of file z3py.py.

def fpSub(rm, a, b, ctx=None):
    """Create a Z3 floating-point subtraction expression.
 
    >>> s = FPSort(8, 24)
    >>> rm = RNE()
    >>> x = FP('x', s)
    >>> y = FP('y', s)
    >>> fpSub(rm, x, y)
    x - y
    >>> fpSub(rm, x, y).sort()
    FPSort(8, 24)
    """
    return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
 
 

Referenced by FPRef.__rsub__(), and FPRef.__sub__().

fpToFP()

def z3py.fpToFP	(		a1,
			a2 = None,
			a3 = None,
			ctx = None
	)

Create a Z3 floating-point conversion expression from other term sorts
to floating-point.

From a bit-vector term in IEEE 754-2008 format:
>>> x = FPVal(1.0, Float32())
>>> x_bv = fpToIEEEBV(x)
>>> simplify(fpToFP(x_bv, Float32()))
1

From a floating-point term with different precision:
>>> x = FPVal(1.0, Float32())
>>> x_db = fpToFP(RNE(), x, Float64())
>>> x_db.sort()
FPSort(11, 53)

From a real term:
>>> x_r = RealVal(1.5)
>>> simplify(fpToFP(RNE(), x_r, Float32()))
1.5

From a signed bit-vector term:
>>> x_signed = BitVecVal(-5, BitVecSort(32))
>>> simplify(fpToFP(RNE(), x_signed, Float32()))
-1.25*(2**2)

Definition at line 10489 of file z3py.py.

def fpToFP(a1, a2=None, a3=None, ctx=None):
    """Create a Z3 floating-point conversion expression from other term sorts
    to floating-point.
 
    From a bit-vector term in IEEE 754-2008 format:
    >>> x = FPVal(1.0, Float32())
    >>> x_bv = fpToIEEEBV(x)
    >>> simplify(fpToFP(x_bv, Float32()))
    1
 
    From a floating-point term with different precision:
    >>> x = FPVal(1.0, Float32())
    >>> x_db = fpToFP(RNE(), x, Float64())
    >>> x_db.sort()
    FPSort(11, 53)
 
    From a real term:
    >>> x_r = RealVal(1.5)
    >>> simplify(fpToFP(RNE(), x_r, Float32()))
    1.5
 
    From a signed bit-vector term:
    >>> x_signed = BitVecVal(-5, BitVecSort(32))
    >>> simplify(fpToFP(RNE(), x_signed, Float32()))
    -1.25*(2**2)
    """
    ctx = _get_ctx(ctx)
    if is_bv(a1) and is_fp_sort(a2):
        return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
    elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
        return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
    elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
        return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
    elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
        return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
    else:
        raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
 
 

fpToFPUnsigned()

def z3py.fpToFPUnsigned	(		rm,
			x,
			s,
			ctx = None
	)

Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression.

Definition at line 10619 of file z3py.py.

def fpToFPUnsigned(rm, x, s, ctx=None):
    """Create a Z3 floating-point conversion expression, from unsigned bit-vector to floating-point expression."""
    if z3_debug():
        _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
        _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
        _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
    ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
 
 

fpToIEEEBV()

def z3py.fpToIEEEBV	(		x,
			ctx = None
	)

\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.

The size of the resulting bit-vector is automatically determined.

Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
knows only one NaN and it will always produce the same bit-vector representation of
that NaN.

>>> x = FP('x', FPSort(8, 24))
>>> y = fpToIEEEBV(x)
>>> print(is_fp(x))
True
>>> print(is_bv(y))
True
>>> print(is_fp(y))
False
>>> print(is_bv(x))
False

Definition at line 10693 of file z3py.py.

def fpToIEEEBV(x, ctx=None):
    """\brief Conversion of a floating-point term into a bit-vector term in IEEE 754-2008 format.
 
    The size of the resulting bit-vector is automatically determined.
 
    Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
    knows only one NaN and it will always produce the same bit-vector representation of
    that NaN.
 
    >>> x = FP('x', FPSort(8, 24))
    >>> y = fpToIEEEBV(x)
    >>> print(is_fp(x))
    True
    >>> print(is_bv(y))
    True
    >>> print(is_fp(y))
    False
    >>> print(is_bv(x))
    False
    """
    if z3_debug():
        _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
    ctx = _get_ctx(ctx)
    return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
 
 

fpToReal()

def z3py.fpToReal	(		x,
			ctx = None
	)

Create a Z3 floating-point conversion expression, from floating-point expression to real.

>>> x = FP('x', FPSort(8, 24))
>>> y = fpToReal(x)
>>> print(is_fp(x))
True
>>> print(is_real(y))
True
>>> print(is_fp(y))
False
>>> print(is_real(x))
False

Definition at line 10673 of file z3py.py.

def fpToReal(x, ctx=None):
    """Create a Z3 floating-point conversion expression, from floating-point expression to real.
 
    >>> x = FP('x', FPSort(8, 24))
    >>> y = fpToReal(x)
    >>> print(is_fp(x))
    True
    >>> print(is_real(y))
    True
    >>> print(is_fp(y))
    False
    >>> print(is_real(x))
    False
    """
    if z3_debug():
        _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
    ctx = _get_ctx(ctx)
    return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
 
 

fpToSBV()

def z3py.fpToSBV	(		rm,
			x,
			s,
			ctx = None
	)

Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.

>>> x = FP('x', FPSort(8, 24))
>>> y = fpToSBV(RTZ(), x, BitVecSort(32))
>>> print(is_fp(x))
True
>>> print(is_bv(y))
True
>>> print(is_fp(y))
False
>>> print(is_bv(x))
False

Definition at line 10629 of file z3py.py.

def fpToSBV(rm, x, s, ctx=None):
    """Create a Z3 floating-point conversion expression, from floating-point expression to signed bit-vector.
 
    >>> x = FP('x', FPSort(8, 24))
    >>> y = fpToSBV(RTZ(), x, BitVecSort(32))
    >>> print(is_fp(x))
    True
    >>> print(is_bv(y))
    True
    >>> print(is_fp(y))
    False
    >>> print(is_bv(x))
    False
    """
    if z3_debug():
        _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
        _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
        _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
    ctx = _get_ctx(ctx)
    return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
 
 

fpToUBV()

def z3py.fpToUBV	(		rm,
			x,
			s,
			ctx = None
	)

Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.

>>> x = FP('x', FPSort(8, 24))
>>> y = fpToUBV(RTZ(), x, BitVecSort(32))
>>> print(is_fp(x))
True
>>> print(is_bv(y))
True
>>> print(is_fp(y))
False
>>> print(is_bv(x))
False

Definition at line 10651 of file z3py.py.

def fpToUBV(rm, x, s, ctx=None):
    """Create a Z3 floating-point conversion expression, from floating-point expression to unsigned bit-vector.
 
    >>> x = FP('x', FPSort(8, 24))
    >>> y = fpToUBV(RTZ(), x, BitVecSort(32))
    >>> print(is_fp(x))
    True
    >>> print(is_bv(y))
    True
    >>> print(is_fp(y))
    False
    >>> print(is_bv(x))
    False
    """
    if z3_debug():
        _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
        _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
        _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
    ctx = _get_ctx(ctx)
    return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
 
 

fpUnsignedToFP()

def z3py.fpUnsignedToFP	(		rm,
			v,
			sort,
			ctx = None
	)

Create a Z3 floating-point conversion expression that represents the
conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.

>>> x_signed = BitVecVal(-5, BitVecSort(32))
>>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
>>> x_fp
fpToFPUnsigned(RNE(), 4294967291)
>>> simplify(x_fp)
1*(2**32)

Definition at line 10601 of file z3py.py.

def fpUnsignedToFP(rm, v, sort, ctx=None):
    """Create a Z3 floating-point conversion expression that represents the
    conversion from an unsigned bit-vector term (encoding an integer) to a floating-point term.
 
    >>> x_signed = BitVecVal(-5, BitVecSort(32))
    >>> x_fp = fpUnsignedToFP(RNE(), x_signed, Float32())
    >>> x_fp
    fpToFPUnsigned(RNE(), 4294967291)
    >>> simplify(x_fp)
    1*(2**32)
    """
    _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
    _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
    _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
    ctx = _get_ctx(ctx)
    return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
 
 

FPVal()

def z3py.FPVal	(		sig,
			exp = None,
			fps = None,
			ctx = None
	)

Return a floating-point value of value `val` and sort `fps`.
If `ctx=None`, then the global context is used.

>>> v = FPVal(20.0, FPSort(8, 24))
>>> v
1.25*(2**4)
>>> print("0x%.8x" % v.exponent_as_long(False))
0x00000004
>>> v = FPVal(2.25, FPSort(8, 24))
>>> v
1.125*(2**1)
>>> v = FPVal(-2.25, FPSort(8, 24))
>>> v
-1.125*(2**1)
>>> FPVal(-0.0, FPSort(8, 24))
-0.0
>>> FPVal(0.0, FPSort(8, 24))
+0.0
>>> FPVal(+0.0, FPSort(8, 24))
+0.0

Definition at line 10026 of file z3py.py.

def FPVal(sig, exp=None, fps=None, ctx=None):
    """Return a floating-point value of value `val` and sort `fps`.
    If `ctx=None`, then the global context is used.
 
    >>> v = FPVal(20.0, FPSort(8, 24))
    >>> v
    1.25*(2**4)
    >>> print("0x%.8x" % v.exponent_as_long(False))
    0x00000004
    >>> v = FPVal(2.25, FPSort(8, 24))
    >>> v
    1.125*(2**1)
    >>> v = FPVal(-2.25, FPSort(8, 24))
    >>> v
    -1.125*(2**1)
    >>> FPVal(-0.0, FPSort(8, 24))
    -0.0
    >>> FPVal(0.0, FPSort(8, 24))
    +0.0
    >>> FPVal(+0.0, FPSort(8, 24))
    +0.0
    """
    ctx = _get_ctx(ctx)
    if is_fp_sort(exp):
        fps = exp
        exp = None
    elif fps is None:
        fps = _dflt_fps(ctx)
    _z3_assert(is_fp_sort(fps), "sort mismatch")
    if exp is None:
        exp = 0
    val = _to_float_str(sig)
    if val == "NaN" or val == "nan":
        return fpNaN(fps)
    elif val == "-0.0":
        return fpMinusZero(fps)
    elif val == "0.0" or val == "+0.0":
        return fpPlusZero(fps)
    elif val == "+oo" or val == "+inf" or val == "+Inf":
        return fpPlusInfinity(fps)
    elif val == "-oo" or val == "-inf" or val == "-Inf":
        return fpMinusInfinity(fps)
    else:
        return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
 
 

Referenced by set_default_fp_sort().

fpZero()

def z3py.fpZero	(		s,
			negative
	)

Create a Z3 floating-point +0.0 or -0.0 term.

Definition at line 10019 of file z3py.py.

def fpZero(s, negative):
    """Create a Z3 floating-point +0.0 or -0.0 term."""
    _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
    _z3_assert(isinstance(negative, bool), "expected Boolean flag")
    return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
 
 

FreshBool()

def z3py.FreshBool	(		prefix = "b",
			ctx = None
	)

Return a fresh Boolean constant in the given context using the given prefix.

If `ctx=None`, then the global context is used.

>>> b1 = FreshBool()
>>> b2 = FreshBool()
>>> eq(b1, b2)
False

Definition at line 1771 of file z3py.py.

def FreshBool(prefix="b", ctx=None):
    """Return a fresh Boolean constant in the given context using the given prefix.
 
    If `ctx=None`, then the global context is used.
 
    >>> b1 = FreshBool()
    >>> b2 = FreshBool()
    >>> eq(b1, b2)
    False
    """
    ctx = _get_ctx(ctx)
    return BoolRef(Z3_mk_fresh_const(ctx.ref(), prefix, BoolSort(ctx).ast), ctx)
 
 

FreshConst()

def z3py.FreshConst	(		sort,
			prefix = "c"
	)

Create a fresh constant of a specified sort

Definition at line 1464 of file z3py.py.

def FreshConst(sort, prefix="c"):
    """Create a fresh constant of a specified sort"""
    ctx = _get_ctx(sort.ctx)
    return _to_expr_ref(Z3_mk_fresh_const(ctx.ref(), prefix, sort.ast), ctx)
 
 

FreshFunction()

def z3py.FreshFunction

(

*

sig

)

Create a new fresh Z3 uninterpreted function with the given sorts.

Definition at line 886 of file z3py.py.

def FreshFunction(*sig):
    """Create a new fresh Z3 uninterpreted function with the given sorts.
    """
    sig = _get_args(sig)
    if z3_debug():
        _z3_assert(len(sig) > 0, "At least two arguments expected")
    arity = len(sig) - 1
    rng = sig[arity]
    if z3_debug():
        _z3_assert(is_sort(rng), "Z3 sort expected")
    dom = (z3.Sort * arity)()
    for i in range(arity):
        if z3_debug():
            _z3_assert(is_sort(sig[i]), "Z3 sort expected")
        dom[i] = sig[i].ast
    ctx = rng.ctx
    return FuncDeclRef(Z3_mk_fresh_func_decl(ctx.ref(), "f", arity, dom, rng.ast), ctx)
 
 

FreshInt()

def z3py.FreshInt	(		prefix = "x",
			ctx = None
	)

Return a fresh integer constant in the given context using the given prefix.

>>> x = FreshInt()
>>> y = FreshInt()
>>> eq(x, y)
False
>>> x.sort()
Int

Definition at line 3287 of file z3py.py.

def FreshInt(prefix="x", ctx=None):
    """Return a fresh integer constant in the given context using the given prefix.
 
    >>> x = FreshInt()
    >>> y = FreshInt()
    >>> eq(x, y)
    False
    >>> x.sort()
    Int
    """
    ctx = _get_ctx(ctx)
    return ArithRef(Z3_mk_fresh_const(ctx.ref(), prefix, IntSort(ctx).ast), ctx)
 
 

FreshReal()

def z3py.FreshReal	(		prefix = "b",
			ctx = None
	)

Return a fresh real constant in the given context using the given prefix.

>>> x = FreshReal()
>>> y = FreshReal()
>>> eq(x, y)
False
>>> x.sort()
Real

Definition at line 3344 of file z3py.py.

def FreshReal(prefix="b", ctx=None):
    """Return a fresh real constant in the given context using the given prefix.
 
    >>> x = FreshReal()
    >>> y = FreshReal()
    >>> eq(x, y)
    False
    >>> x.sort()
    Real
    """
    ctx = _get_ctx(ctx)
    return ArithRef(Z3_mk_fresh_const(ctx.ref(), prefix, RealSort(ctx).ast), ctx)
 
 

Full()

def z3py.Full

(

s

)

Create the regular expression that accepts the universal language
>>> e = Full(ReSort(SeqSort(IntSort())))
>>> print(e)
Full(ReSort(Seq(Int)))
>>> e1 = Full(ReSort(StringSort()))
>>> print(e1)
Full(ReSort(String))

Definition at line 10975 of file z3py.py.

def Full(s):
    """Create the regular expression that accepts the universal language
    >>> e = Full(ReSort(SeqSort(IntSort())))
    >>> print(e)
    Full(ReSort(Seq(Int)))
    >>> e1 = Full(ReSort(StringSort()))
    >>> print(e1)
    Full(ReSort(String))
    """
    if isinstance(s, ReSortRef):
        return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
    raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
 
 
 

FullSet()

def z3py.FullSet

(

s

)

Create the full set
>>> FullSet(IntSort())
K(Int, True)

Definition at line 4931 of file z3py.py.

def FullSet(s):
    """Create the full set
    >>> FullSet(IntSort())
    K(Int, True)
    """
    ctx = s.ctx
    return ArrayRef(Z3_mk_full_set(ctx.ref(), s.ast), ctx)
 
 

Function()

def z3py.Function	(		name,
		*	sig
	)

Create a new Z3 uninterpreted function with the given sorts.

>>> f = Function('f', IntSort(), IntSort())
>>> f(f(0))
f(f(0))

Definition at line 863 of file z3py.py.

def Function(name, *sig):
    """Create a new Z3 uninterpreted function with the given sorts.
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> f(f(0))
    f(f(0))
    """
    sig = _get_args(sig)
    if z3_debug():
        _z3_assert(len(sig) > 0, "At least two arguments expected")
    arity = len(sig) - 1
    rng = sig[arity]
    if z3_debug():
        _z3_assert(is_sort(rng), "Z3 sort expected")
    dom = (Sort * arity)()
    for i in range(arity):
        if z3_debug():
            _z3_assert(is_sort(sig[i]), "Z3 sort expected")
        dom[i] = sig[i].ast
    ctx = rng.ctx
    return FuncDeclRef(Z3_mk_func_decl(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
 
 

get_as_array_func()

def z3py.get_as_array_func

(

n

)

Return the function declaration f associated with a Z3 expression of the form (_ as-array f).

Definition at line 6699 of file z3py.py.

def get_as_array_func(n):
    """Return the function declaration f associated with a Z3 expression of the form (_ as-array f)."""
    if z3_debug():
        _z3_assert(is_as_array(n), "as-array Z3 expression expected.")
    return FuncDeclRef(Z3_get_as_array_func_decl(n.ctx.ref(), n.as_ast()), n.ctx)
 

Referenced by ModelRef.get_interp().

get_ctx()

def z3py.get_ctx

(

ctx

)

Definition at line 267 of file z3py.py.

def get_ctx(ctx):
    return _get_ctx(ctx)
 
 

get_default_fp_sort()

def z3py.get_default_fp_sort

(

ctx = None

)

Definition at line 9323 of file z3py.py.

def get_default_fp_sort(ctx=None):
    return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
 
 

Referenced by set_default_fp_sort().

get_default_rounding_mode()

def z3py.get_default_rounding_mode

(

ctx = None

)

Retrieves the global default rounding mode.

Definition at line 9290 of file z3py.py.

def get_default_rounding_mode(ctx=None):
    """Retrieves the global default rounding mode."""
    global _dflt_rounding_mode
    if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
        return RTZ(ctx)
    elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
        return RTN(ctx)
    elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
        return RTP(ctx)
    elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
        return RNE(ctx)
    elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
        return RNA(ctx)
 
 

Referenced by set_default_fp_sort().

get_full_version()

def z3py.get_full_version

(

)

Definition at line 101 of file z3py.py.

def get_full_version():
    return Z3_get_full_version()
 
 

get_map_func()

def z3py.get_map_func

(

a

)

Return the function declaration associated with a Z3 map array expression.

>>> f = Function('f', IntSort(), IntSort())
>>> b = Array('b', IntSort(), IntSort())
>>> a  = Map(f, b)
>>> eq(f, get_map_func(a))
True
>>> get_map_func(a)
f
>>> get_map_func(a)(0)
f(0)

Definition at line 4676 of file z3py.py.

def get_map_func(a):
    """Return the function declaration associated with a Z3 map array expression.
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> b = Array('b', IntSort(), IntSort())
    >>> a  = Map(f, b)
    >>> eq(f, get_map_func(a))
    True
    >>> get_map_func(a)
    f
    >>> get_map_func(a)(0)
    f(0)
    """
    if z3_debug():
        _z3_assert(is_map(a), "Z3 array map expression expected.")
    return FuncDeclRef(
        Z3_to_func_decl(
            a.ctx_ref(),
            Z3_get_decl_ast_parameter(a.ctx_ref(), a.decl().ast, 0),
        ),
        ctx=a.ctx,
    )
 
 

get_param()

def z3py.get_param

(

name

)

Return the value of a Z3 global (or module) parameter

>>> get_param('nlsat.reorder')
'true'

Definition at line 307 of file z3py.py.

def get_param(name):
    """Return the value of a Z3 global (or module) parameter
 
    >>> get_param('nlsat.reorder')
    'true'
    """
    ptr = (ctypes.c_char_p * 1)()
    if Z3_global_param_get(str(name), ptr):
        r = z3core._to_pystr(ptr[0])
        return r
    raise Z3Exception("failed to retrieve value for '%s'" % name)
 

get_var_index()

def z3py.get_var_index

(

a

)

Return the de-Bruijn index of the Z3 bounded variable `a`.

>>> x = Int('x')
>>> y = Int('y')
>>> is_var(x)
False
>>> is_const(x)
True
>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> # Z3 replaces x and y with bound variables when ForAll is executed.
>>> q = ForAll([x, y], f(x, y) == x + y)
>>> q.body()
f(Var(1), Var(0)) == Var(1) + Var(0)
>>> b = q.body()
>>> b.arg(0)
f(Var(1), Var(0))
>>> v1 = b.arg(0).arg(0)
>>> v2 = b.arg(0).arg(1)
>>> v1
Var(1)
>>> v2
Var(0)
>>> get_var_index(v1)
1
>>> get_var_index(v2)
0

Definition at line 1335 of file z3py.py.

def get_var_index(a):
    """Return the de-Bruijn index of the Z3 bounded variable `a`.
 
    >>> x = Int('x')
    >>> y = Int('y')
    >>> is_var(x)
    False
    >>> is_const(x)
    True
    >>> f = Function('f', IntSort(), IntSort(), IntSort())
    >>> # Z3 replaces x and y with bound variables when ForAll is executed.
    >>> q = ForAll([x, y], f(x, y) == x + y)
    >>> q.body()
    f(Var(1), Var(0)) == Var(1) + Var(0)
    >>> b = q.body()
    >>> b.arg(0)
    f(Var(1), Var(0))
    >>> v1 = b.arg(0).arg(0)
    >>> v2 = b.arg(0).arg(1)
    >>> v1
    Var(1)
    >>> v2
    Var(0)
    >>> get_var_index(v1)
    1
    >>> get_var_index(v2)
    0
    """
    if z3_debug():
        _z3_assert(is_var(a), "Z3 bound variable expected")
    return int(Z3_get_index_value(a.ctx.ref(), a.as_ast()))
 
 

get_version()

def z3py.get_version

(

)

Definition at line 92 of file z3py.py.

def get_version():
    major = ctypes.c_uint(0)
    minor = ctypes.c_uint(0)
    build = ctypes.c_uint(0)
    rev = ctypes.c_uint(0)
    Z3_get_version(major, minor, build, rev)
    return (major.value, minor.value, build.value, rev.value)
 
 

get_version_string()

def z3py.get_version_string

(

)

Definition at line 83 of file z3py.py.

def get_version_string():
    major = ctypes.c_uint(0)
    minor = ctypes.c_uint(0)
    build = ctypes.c_uint(0)
    rev = ctypes.c_uint(0)
    Z3_get_version(major, minor, build, rev)
    return "%s.%s.%s" % (major.value, minor.value, build.value)
 
 

help_simplify()

def z3py.help_simplify

(

)

Return a string describing all options available for Z3 `simplify` procedure.

Definition at line 8796 of file z3py.py.

def help_simplify():
    """Return a string describing all options available for Z3 `simplify` procedure."""
    print(Z3_simplify_get_help(main_ctx().ref()))
 
 

If()

def z3py.If	(		a,
			b,
			c,
			ctx = None
	)

Create a Z3 if-then-else expression.

>>> x = Int('x')
>>> y = Int('y')
>>> max = If(x > y, x, y)
>>> max
If(x > y, x, y)
>>> simplify(max)
If(x <= y, y, x)

Definition at line 1381 of file z3py.py.

def If(a, b, c, ctx=None):
    """Create a Z3 if-then-else expression.
 
    >>> x = Int('x')
    >>> y = Int('y')
    >>> max = If(x > y, x, y)
    >>> max
    If(x > y, x, y)
    >>> simplify(max)
    If(x <= y, y, x)
    """
    if isinstance(a, Probe) or isinstance(b, Tactic) or isinstance(c, Tactic):
        return Cond(a, b, c, ctx)
    else:
        ctx = _get_ctx(_ctx_from_ast_arg_list([a, b, c], ctx))
        s = BoolSort(ctx)
        a = s.cast(a)
        b, c = _coerce_exprs(b, c, ctx)
        if z3_debug():
            _z3_assert(a.ctx == b.ctx, "Context mismatch")
        return _to_expr_ref(Z3_mk_ite(ctx.ref(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
 
 

Referenced by BoolRef.__mul__(), ArithRef.__mul__(), and Abs().

Implies()

def z3py.Implies	(		a,
			b,
			ctx = None
	)

Create a Z3 implies expression.

>>> p, q = Bools('p q')
>>> Implies(p, q)
Implies(p, q)

Definition at line 1785 of file z3py.py.

def Implies(a, b, ctx=None):
    """Create a Z3 implies expression.
 
    >>> p, q = Bools('p q')
    >>> Implies(p, q)
    Implies(p, q)
    """
    ctx = _get_ctx(_ctx_from_ast_arg_list([a, b], ctx))
    s = BoolSort(ctx)
    a = s.cast(a)
    b = s.cast(b)
    return BoolRef(Z3_mk_implies(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
 
 

Referenced by Fixedpoint.add_rule(), and Fixedpoint.update_rule().

IndexOf()

def z3py.IndexOf	(		s,
			substr,
			offset = None
	)

Retrieve the index of substring within a string starting at a specified offset.
>>> simplify(IndexOf("abcabc", "bc", 0))
1
>>> simplify(IndexOf("abcabc", "bc", 2))
4

Definition at line 11059 of file z3py.py.

def IndexOf(s, substr, offset=None):
    """Retrieve the index of substring within a string starting at a specified offset.
    >>> simplify(IndexOf("abcabc", "bc", 0))
    1
    >>> simplify(IndexOf("abcabc", "bc", 2))
    4
    """
    if offset is None:
        offset = IntVal(0)
    ctx = None
    if is_expr(offset):
        ctx = offset.ctx
    ctx = _get_ctx2(s, substr, ctx)
    s = _coerce_seq(s, ctx)
    substr = _coerce_seq(substr, ctx)
    if _is_int(offset):
        offset = IntVal(offset, ctx)
    return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
 
 

InRe()

def z3py.InRe	(		s,
			re
	)

Create regular expression membership test
>>> re = Union(Re("a"),Re("b"))
>>> print (simplify(InRe("a", re)))
True
>>> print (simplify(InRe("b", re)))
True
>>> print (simplify(InRe("c", re)))
False

Definition at line 11172 of file z3py.py.

def InRe(s, re):
    """Create regular expression membership test
    >>> re = Union(Re("a"),Re("b"))
    >>> print (simplify(InRe("a", re)))
    True
    >>> print (simplify(InRe("b", re)))
    True
    >>> print (simplify(InRe("c", re)))
    False
    """
    s = _coerce_seq(s, re.ctx)
    return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
 
 

Int()

def z3py.Int	(		name,
			ctx = None
	)

Return an integer constant named `name`. If `ctx=None`, then the global context is used.

>>> x = Int('x')
>>> is_int(x)
True
>>> is_int(x + 1)
True

Definition at line 3248 of file z3py.py.

def Int(name, ctx=None):
    """Return an integer constant named `name`. If `ctx=None`, then the global context is used.
 
    >>> x = Int('x')
    >>> is_int(x)
    True
    >>> is_int(x + 1)
    True
    """
    ctx = _get_ctx(ctx)
    return ArithRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), IntSort(ctx).ast), ctx)
 
 

Referenced by Ints(), and IntVector().

Int2BV()

def z3py.Int2BV	(		a,
			num_bits
	)

Return the z3 expression Int2BV(a, num_bits).
It is a bit-vector of width num_bits and represents the
modulo of a by 2^num_bits

Definition at line 3996 of file z3py.py.

def Int2BV(a, num_bits):
    """Return the z3 expression Int2BV(a, num_bits).
    It is a bit-vector of width num_bits and represents the
    modulo of a by 2^num_bits
    """
    ctx = a.ctx
    return BitVecRef(Z3_mk_int2bv(ctx.ref(), num_bits, a.as_ast()), ctx)
 
 

Intersect()

def z3py.Intersect

(

*

args

)

Create intersection of regular expressions.
>>> re = Intersect(Re("a"), Re("b"), Re("c"))

Definition at line 11206 of file z3py.py.

def Intersect(*args):
    """Create intersection of regular expressions.
    >>> re = Intersect(Re("a"), Re("b"), Re("c"))
    """
    args = _get_args(args)
    sz = len(args)
    if z3_debug():
        _z3_assert(sz > 0, "At least one argument expected.")
        _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
    if sz == 1:
        return args[0]
    ctx = args[0].ctx
    v = (Ast * sz)()
    for i in range(sz):
        v[i] = args[i].as_ast()
    return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
 
 

Ints()

def z3py.Ints	(		names,
			ctx = None
	)

Return a tuple of Integer constants.

>>> x, y, z = Ints('x y z')
>>> Sum(x, y, z)
x + y + z

Definition at line 3261 of file z3py.py.

def Ints(names, ctx=None):
    """Return a tuple of Integer constants.
 
    >>> x, y, z = Ints('x y z')
    >>> Sum(x, y, z)
    x + y + z
    """
    ctx = _get_ctx(ctx)
    if isinstance(names, str):
        names = names.split(" ")
    return [Int(name, ctx) for name in names]
 
 

IntSort()

def z3py.IntSort

(

ctx = None

)

Return the integer sort in the given context. If `ctx=None`, then the global context is used.

>>> IntSort()
Int
>>> x = Const('x', IntSort())
>>> is_int(x)
True
>>> x.sort() == IntSort()
True
>>> x.sort() == BoolSort()
False

Definition at line 3138 of file z3py.py.

def IntSort(ctx=None):
    """Return the integer sort in the given context. If `ctx=None`, then the global context is used.
 
    >>> IntSort()
    Int
    >>> x = Const('x', IntSort())
    >>> is_int(x)
    True
    >>> x.sort() == IntSort()
    True
    >>> x.sort() == BoolSort()
    False
    """
    ctx = _get_ctx(ctx)
    return ArithSortRef(Z3_mk_int_sort(ctx.ref()), ctx)
 
 

Referenced by FreshInt(), Context.getIntSort(), Int(), IntVal(), and Context.mkIntSort().

IntToStr()

def z3py.IntToStr

(

s

)

Convert integer expression to string

Definition at line 11114 of file z3py.py.

def IntToStr(s):
    """Convert integer expression to string"""
    if not is_expr(s):
        s = _py2expr(s)
    return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
 
 

IntVal()

def z3py.IntVal	(		val,
			ctx = None
	)

Return a Z3 integer value. If `ctx=None`, then the global context is used.

>>> IntVal(1)
1
>>> IntVal("100")
100

Definition at line 3188 of file z3py.py.

def IntVal(val, ctx=None):
    """Return a Z3 integer value. If `ctx=None`, then the global context is used.
 
    >>> IntVal(1)
    1
    >>> IntVal("100")
    100
    """
    ctx = _get_ctx(ctx)
    return IntNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), IntSort(ctx).ast), ctx)
 
 

Referenced by SeqRef.__getitem__(), BoolRef.__mul__(), SeqRef.at(), AlgebraicNumRef.index(), and IndexOf().

IntVector()

def z3py.IntVector	(		prefix,
			sz,
			ctx = None
	)

Return a list of integer constants of size `sz`.

>>> X = IntVector('x', 3)
>>> X
[x__0, x__1, x__2]
>>> Sum(X)
x__0 + x__1 + x__2

Definition at line 3274 of file z3py.py.

def IntVector(prefix, sz, ctx=None):
    """Return a list of integer constants of size `sz`.
 
    >>> X = IntVector('x', 3)
    >>> X
    [x__0, x__1, x__2]
    >>> Sum(X)
    x__0 + x__1 + x__2
    """
    ctx = _get_ctx(ctx)
    return [Int("%s__%s" % (prefix, i), ctx) for i in range(sz)]
 
 

is_add()

def z3py.is_add

(

a

)

Return `True` if `a` is an expression of the form b + c.

>>> x, y = Ints('x y')
>>> is_add(x + y)
True
>>> is_add(x - y)
False

Definition at line 2792 of file z3py.py.

def is_add(a):
    """Return `True` if `a` is an expression of the form b + c.
 
    >>> x, y = Ints('x y')
    >>> is_add(x + y)
    True
    >>> is_add(x - y)
    False
    """
    return is_app_of(a, Z3_OP_ADD)
 
 

is_algebraic_value()

def z3py.is_algebraic_value

(

a

)

Return `True` if `a` is an algebraic value of sort Real.

>>> is_algebraic_value(RealVal("3/5"))
False
>>> n = simplify(Sqrt(2))
>>> n
1.4142135623?
>>> is_algebraic_value(n)
True

Definition at line 2778 of file z3py.py.

def is_algebraic_value(a):
    """Return `True` if `a` is an algebraic value of sort Real.
 
    >>> is_algebraic_value(RealVal("3/5"))
    False
    >>> n = simplify(Sqrt(2))
    >>> n
    1.4142135623?
    >>> is_algebraic_value(n)
    True
    """
    return is_arith(a) and a.is_real() and _is_algebraic(a.ctx, a.as_ast())
 
 

is_and()

def z3py.is_and

(

a

)

Return `True` if `a` is a Z3 and expression.

>>> p, q = Bools('p q')
>>> is_and(And(p, q))
True
>>> is_and(Or(p, q))
False

Definition at line 1621 of file z3py.py.

def is_and(a):
    """Return `True` if `a` is a Z3 and expression.
 
    >>> p, q = Bools('p q')
    >>> is_and(And(p, q))
    True
    >>> is_and(Or(p, q))
    False
    """
    return is_app_of(a, Z3_OP_AND)
 
 

is_app()

def z3py.is_app

(

a

)

Return `True` if `a` is a Z3 function application.

Note that, constants are function applications with 0 arguments.

>>> a = Int('a')
>>> is_app(a)
True
>>> is_app(a + 1)
True
>>> is_app(IntSort())
False
>>> is_app(1)
False
>>> is_app(IntVal(1))
True
>>> x = Int('x')
>>> is_app(ForAll(x, x >= 0))
False

Definition at line 1265 of file z3py.py.

def is_app(a):
    """Return `True` if `a` is a Z3 function application.
 
    Note that, constants are function applications with 0 arguments.
 
    >>> a = Int('a')
    >>> is_app(a)
    True
    >>> is_app(a + 1)
    True
    >>> is_app(IntSort())
    False
    >>> is_app(1)
    False
    >>> is_app(IntVal(1))
    True
    >>> x = Int('x')
    >>> is_app(ForAll(x, x >= 0))
    False
    """
    if not isinstance(a, ExprRef):
        return False
    k = _ast_kind(a.ctx, a)
    return k == Z3_NUMERAL_AST or k == Z3_APP_AST
 
 

Referenced by ExprRef.arg(), ExprRef.children(), ExprRef.decl(), is_app_of(), is_const(), is_quantifier(), Lambda(), ExprRef.num_args(), and RecAddDefinition().

is_app_of()

def z3py.is_app_of	(		a,
			k
	)

Return `True` if `a` is an application of the given kind `k`.

>>> x = Int('x')
>>> n = x + 1
>>> is_app_of(n, Z3_OP_ADD)
True
>>> is_app_of(n, Z3_OP_MUL)
False

Definition at line 1368 of file z3py.py.

def is_app_of(a, k):
    """Return `True` if `a` is an application of the given kind `k`.
 
    >>> x = Int('x')
    >>> n = x + 1
    >>> is_app_of(n, Z3_OP_ADD)
    True
    >>> is_app_of(n, Z3_OP_MUL)
    False
    """
    return is_app(a) and a.decl().kind() == k
 
 

Referenced by is_add(), is_and(), is_const_array(), is_default(), is_distinct(), is_div(), is_eq(), is_false(), is_ge(), is_gt(), is_idiv(), is_implies(), is_is_int(), is_K(), is_le(), is_lt(), is_map(), is_mod(), is_mul(), is_not(), is_or(), is_select(), is_store(), is_sub(), is_to_int(), is_to_real(), and is_true().

is_arith()

def z3py.is_arith

(

a

)

Return `True` if `a` is an arithmetical expression.

>>> x = Int('x')
>>> is_arith(x)
True
>>> is_arith(x + 1)
True
>>> is_arith(1)
False
>>> is_arith(IntVal(1))
True
>>> y = Real('y')
>>> is_arith(y)
True
>>> is_arith(y + 1)
True

Definition at line 2665 of file z3py.py.

def is_arith(a):
    """Return `True` if `a` is an arithmetical expression.
 
    >>> x = Int('x')
    >>> is_arith(x)
    True
    >>> is_arith(x + 1)
    True
    >>> is_arith(1)
    False
    >>> is_arith(IntVal(1))
    True
    >>> y = Real('y')
    >>> is_arith(y)
    True
    >>> is_arith(y + 1)
    True
    """
    return isinstance(a, ArithRef)
 
 

Referenced by is_algebraic_value(), is_int(), is_int_value(), is_rational_value(), and is_real().

is_arith_sort()

def z3py.is_arith_sort

(

s

)

Return `True` if s is an arithmetical sort (type).

>>> is_arith_sort(IntSort())
True
>>> is_arith_sort(RealSort())
True
>>> is_arith_sort(BoolSort())
False
>>> n = Int('x') + 1
>>> is_arith_sort(n.sort())
True

Definition at line 2364 of file z3py.py.

def is_arith_sort(s):
    """Return `True` if s is an arithmetical sort (type).
 
    >>> is_arith_sort(IntSort())
    True
    >>> is_arith_sort(RealSort())
    True
    >>> is_arith_sort(BoolSort())
    False
    >>> n = Int('x') + 1
    >>> is_arith_sort(n.sort())
    True
    """
    return isinstance(s, ArithSortRef)
 
 

Referenced by ArithSortRef.subsort().

is_array()

def z3py.is_array

(

a

)

Return `True` if `a` is a Z3 array expression.

>>> a = Array('a', IntSort(), IntSort())
>>> is_array(a)
True
>>> is_array(Store(a, 0, 1))
True
>>> is_array(a[0])
False

Definition at line 4611 of file z3py.py.

def is_array(a):
    """Return `True` if `a` is a Z3 array expression.
 
    >>> a = Array('a', IntSort(), IntSort())
    >>> is_array(a)
    True
    >>> is_array(Store(a, 0, 1))
    True
    >>> is_array(a[0])
    False
    """
    return isinstance(a, ArrayRef)
 
 

Referenced by Ext(), and Map().

is_array_sort()

def z3py.is_array_sort

(

a

)

Definition at line 4607 of file z3py.py.

def is_array_sort(a):
    return Z3_get_sort_kind(a.ctx.ref(), Z3_get_sort(a.ctx.ref(), a.ast)) == Z3_ARRAY_SORT
 
 

Referenced by Default(), Ext(), Select(), and Update().

is_as_array()

def z3py.is_as_array

(

n

)

Return true if n is a Z3 expression of the form (_ as-array f).

Definition at line 6694 of file z3py.py.

def is_as_array(n):
    """Return true if n is a Z3 expression of the form (_ as-array f)."""
    return isinstance(n, ExprRef) and Z3_is_as_array(n.ctx.ref(), n.as_ast())
 
 

Referenced by get_as_array_func(), and ModelRef.get_interp().

is_ast()

def z3py.is_ast

(

a

)

Return `True` if `a` is an AST node.

>>> is_ast(10)
False
>>> is_ast(IntVal(10))
True
>>> is_ast(Int('x'))
True
>>> is_ast(BoolSort())
True
>>> is_ast(Function('f', IntSort(), IntSort()))
True
>>> is_ast("x")
False
>>> is_ast(Solver())
False

Definition at line 451 of file z3py.py.

def is_ast(a):
    """Return `True` if `a` is an AST node.
 
    >>> is_ast(10)
    False
    >>> is_ast(IntVal(10))
    True
    >>> is_ast(Int('x'))
    True
    >>> is_ast(BoolSort())
    True
    >>> is_ast(Function('f', IntSort(), IntSort()))
    True
    >>> is_ast("x")
    False
    >>> is_ast(Solver())
    False
    """
    return isinstance(a, AstRef)
 
 

Referenced by eq(), AstRef.eq(), and ReSort().

is_bool()

def z3py.is_bool

(

a

)

Return `True` if `a` is a Z3 Boolean expression.

>>> p = Bool('p')
>>> is_bool(p)
True
>>> q = Bool('q')
>>> is_bool(And(p, q))
True
>>> x = Real('x')
>>> is_bool(x)
False
>>> is_bool(x == 0)
True

Definition at line 1571 of file z3py.py.

def is_bool(a):
    """Return `True` if `a` is a Z3 Boolean expression.
 
    >>> p = Bool('p')
    >>> is_bool(p)
    True
    >>> q = Bool('q')
    >>> is_bool(And(p, q))
    True
    >>> x = Real('x')
    >>> is_bool(x)
    False
    >>> is_bool(x == 0)
    True
    """
    return isinstance(a, BoolRef)
 
 

Referenced by is_quantifier(), and prove().

is_bv()

def z3py.is_bv

(

a

)

Return `True` if `a` is a Z3 bit-vector expression.

>>> b = BitVec('b', 32)
>>> is_bv(b)
True
>>> is_bv(b + 10)
True
>>> is_bv(Int('x'))
False

Definition at line 3944 of file z3py.py.

def is_bv(a):
    """Return `True` if `a` is a Z3 bit-vector expression.
 
    >>> b = BitVec('b', 32)
    >>> is_bv(b)
    True
    >>> is_bv(b + 10)
    True
    >>> is_bv(Int('x'))
    False
    """
    return isinstance(a, BitVecRef)
 
 

Referenced by BV2Int(), BVRedAnd(), BVRedOr(), BVSNegNoOverflow(), Concat(), Extract(), fpBVToFP(), fpFP(), fpSignedToFP(), fpToFP(), fpToFPUnsigned(), fpUnsignedToFP(), is_bv_value(), Product(), RepeatBitVec(), SignExt(), Sum(), and ZeroExt().

is_bv_sort()

def z3py.is_bv_sort

(

s

)

Return True if `s` is a Z3 bit-vector sort.

>>> is_bv_sort(BitVecSort(32))
True
>>> is_bv_sort(IntSort())
False

Definition at line 3476 of file z3py.py.

def is_bv_sort(s):
    """Return True if `s` is a Z3 bit-vector sort.
 
    >>> is_bv_sort(BitVecSort(32))
    True
    >>> is_bv_sort(IntSort())
    False
    """
    return isinstance(s, BitVecSortRef)
 
 

Referenced by BitVecVal(), fpToSBV(), fpToUBV(), and BitVecSortRef.subsort().

is_bv_value()

def z3py.is_bv_value

(

a

)

Return `True` if `a` is a Z3 bit-vector numeral value.

>>> b = BitVec('b', 32)
>>> is_bv_value(b)
False
>>> b = BitVecVal(10, 32)
>>> b
10
>>> is_bv_value(b)
True

Definition at line 3958 of file z3py.py.

def is_bv_value(a):
    """Return `True` if `a` is a Z3 bit-vector numeral value.
 
    >>> b = BitVec('b', 32)
    >>> is_bv_value(b)
    False
    >>> b = BitVecVal(10, 32)
    >>> b
    10
    >>> is_bv_value(b)
    True
    """
    return is_bv(a) and _is_numeral(a.ctx, a.as_ast())
 
 

is_const()

def z3py.is_const

(

a

)

Return `True` if `a` is Z3 constant/variable expression.

>>> a = Int('a')
>>> is_const(a)
True
>>> is_const(a + 1)
False
>>> is_const(1)
False
>>> is_const(IntVal(1))
True
>>> x = Int('x')
>>> is_const(ForAll(x, x >= 0))
False

Definition at line 1291 of file z3py.py.

def is_const(a):
    """Return `True` if `a` is Z3 constant/variable expression.
 
    >>> a = Int('a')
    >>> is_const(a)
    True
    >>> is_const(a + 1)
    False
    >>> is_const(1)
    False
    >>> is_const(IntVal(1))
    True
    >>> x = Int('x')
    >>> is_const(ForAll(x, x >= 0))
    False
    """
    return is_app(a) and a.num_args() == 0
 
 

Referenced by ModelRef.__getitem__(), Solver.assert_and_track(), Optimize.assert_and_track(), ModelRef.get_interp(), is_quantifier(), and prove().

is_const_array()

def z3py.is_const_array

(

a

)

Return `True` if `a` is a Z3 constant array.

>>> a = K(IntSort(), 10)
>>> is_const_array(a)
True
>>> a = Array('a', IntSort(), IntSort())
>>> is_const_array(a)
False

Definition at line 4625 of file z3py.py.

def is_const_array(a):
    """Return `True` if `a` is a Z3 constant array.
 
    >>> a = K(IntSort(), 10)
    >>> is_const_array(a)
    True
    >>> a = Array('a', IntSort(), IntSort())
    >>> is_const_array(a)
    False
    """
    return is_app_of(a, Z3_OP_CONST_ARRAY)
 
 

is_default()

def z3py.is_default

(

a

)

Return `True` if `a` is a Z3 default array expression.
>>> d = Default(K(IntSort(), 10))
>>> is_default(d)
True

Definition at line 4667 of file z3py.py.

def is_default(a):
    """Return `True` if `a` is a Z3 default array expression.
    >>> d = Default(K(IntSort(), 10))
    >>> is_default(d)
    True
    """
    return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
 
 

is_distinct()

def z3py.is_distinct

(

a

)

Return `True` if `a` is a Z3 distinct expression.

>>> x, y, z = Ints('x y z')
>>> is_distinct(x == y)
False
>>> is_distinct(Distinct(x, y, z))
True

Definition at line 1679 of file z3py.py.

def is_distinct(a):
    """Return `True` if `a` is a Z3 distinct expression.
 
    >>> x, y, z = Ints('x y z')
    >>> is_distinct(x == y)
    False
    >>> is_distinct(Distinct(x, y, z))
    True
    """
    return is_app_of(a, Z3_OP_DISTINCT)
 
 

is_div()

def z3py.is_div

(

a

)

Return `True` if `a` is an expression of the form b / c.

>>> x, y = Reals('x y')
>>> is_div(x / y)
True
>>> is_div(x + y)
False
>>> x, y = Ints('x y')
>>> is_div(x / y)
False
>>> is_idiv(x / y)
True

Definition at line 2828 of file z3py.py.

def is_div(a):
    """Return `True` if `a` is an expression of the form b / c.
 
    >>> x, y = Reals('x y')
    >>> is_div(x / y)
    True
    >>> is_div(x + y)
    False
    >>> x, y = Ints('x y')
    >>> is_div(x / y)
    False
    >>> is_idiv(x / y)
    True
    """
    return is_app_of(a, Z3_OP_DIV)
 
 

is_eq()

def z3py.is_eq

(

a

)

Return `True` if `a` is a Z3 equality expression.

>>> x, y = Ints('x y')
>>> is_eq(x == y)
True

Definition at line 1669 of file z3py.py.

def is_eq(a):
    """Return `True` if `a` is a Z3 equality expression.
 
    >>> x, y = Ints('x y')
    >>> is_eq(x == y)
    True
    """
    return is_app_of(a, Z3_OP_EQ)
 
 

Referenced by AstRef.__bool__().

is_expr()

def z3py.is_expr

(

a

)

Return `True` if `a` is a Z3 expression.

>>> a = Int('a')
>>> is_expr(a)
True
>>> is_expr(a + 1)
True
>>> is_expr(IntSort())
False
>>> is_expr(1)
False
>>> is_expr(IntVal(1))
True
>>> x = Int('x')
>>> is_expr(ForAll(x, x >= 0))
True
>>> is_expr(FPVal(1.0))
True

Definition at line 1242 of file z3py.py.

def is_expr(a):
    """Return `True` if `a` is a Z3 expression.
 
    >>> a = Int('a')
    >>> is_expr(a)
    True
    >>> is_expr(a + 1)
    True
    >>> is_expr(IntSort())
    False
    >>> is_expr(1)
    False
    >>> is_expr(IntVal(1))
    True
    >>> x = Int('x')
    >>> is_expr(ForAll(x, x >= 0))
    True
    >>> is_expr(FPVal(1.0))
    True
    """
    return isinstance(a, ExprRef)
 
 

Referenced by SeqRef.__gt__(), SortRef.cast(), BoolSortRef.cast(), ArithSortRef.cast(), BitVecSortRef.cast(), FPSortRef.cast(), Cbrt(), CharFromBv(), CharIsDigit(), Concat(), deserialize(), AlgebraicNumRef.index(), IndexOf(), IntToStr(), is_quantifier(), is_var(), K(), MultiPattern(), Replace(), simplify(), Sqrt(), StrFromCode(), StrToCode(), substitute(), substitute_funs(), substitute_vars(), and ModelRef.update_value().

is_false()

def z3py.is_false

(

a

)

Return `True` if `a` is the Z3 false expression.

>>> p = Bool('p')
>>> is_false(p)
False
>>> is_false(False)
False
>>> is_false(BoolVal(False))
True

Definition at line 1607 of file z3py.py.

def is_false(a):
    """Return `True` if `a` is the Z3 false expression.
 
    >>> p = Bool('p')
    >>> is_false(p)
    False
    >>> is_false(False)
    False
    >>> is_false(BoolVal(False))
    True
    """
    return is_app_of(a, Z3_OP_FALSE)
 
 

Referenced by AstRef.__bool__().

is_finite_domain()

def z3py.is_finite_domain

(

a

)

Return `True` if `a` is a Z3 finite-domain expression.

>>> s = FiniteDomainSort('S', 100)
>>> b = Const('b', s)
>>> is_finite_domain(b)
True
>>> is_finite_domain(Int('x'))
False

Definition at line 7747 of file z3py.py.

def is_finite_domain(a):
    """Return `True` if `a` is a Z3 finite-domain expression.
 
    >>> s = FiniteDomainSort('S', 100)
    >>> b = Const('b', s)
    >>> is_finite_domain(b)
    True
    >>> is_finite_domain(Int('x'))
    False
    """
    return isinstance(a, FiniteDomainRef)
 
 

Referenced by is_finite_domain_value().

is_finite_domain_sort()

def z3py.is_finite_domain_sort

(

s

)

Return True if `s` is a Z3 finite-domain sort.

>>> is_finite_domain_sort(FiniteDomainSort('S', 100))
True
>>> is_finite_domain_sort(IntSort())
False

Definition at line 7724 of file z3py.py.

def is_finite_domain_sort(s):
    """Return True if `s` is a Z3 finite-domain sort.
 
    >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
    True
    >>> is_finite_domain_sort(IntSort())
    False
    """
    return isinstance(s, FiniteDomainSortRef)
 
 

Referenced by FiniteDomainVal().

is_finite_domain_value()

def z3py.is_finite_domain_value

(

a

)

Return `True` if `a` is a Z3 finite-domain value.

>>> s = FiniteDomainSort('S', 100)
>>> b = Const('b', s)
>>> is_finite_domain_value(b)
False
>>> b = FiniteDomainVal(10, s)
>>> b
10
>>> is_finite_domain_value(b)
True

Definition at line 7801 of file z3py.py.

def is_finite_domain_value(a):
    """Return `True` if `a` is a Z3 finite-domain value.
 
    >>> s = FiniteDomainSort('S', 100)
    >>> b = Const('b', s)
    >>> is_finite_domain_value(b)
    False
    >>> b = FiniteDomainVal(10, s)
    >>> b
    10
    >>> is_finite_domain_value(b)
    True
    """
    return is_finite_domain(a) and _is_numeral(a.ctx, a.as_ast())
 
 

is_fp()

def z3py.is_fp

(

a

)

Return `True` if `a` is a Z3 floating-point expression.

>>> b = FP('b', FPSort(8, 24))
>>> is_fp(b)
True
>>> is_fp(b + 1.0)
True
>>> is_fp(Int('x'))
False

Definition at line 9872 of file z3py.py.

def is_fp(a):
    """Return `True` if `a` is a Z3 floating-point expression.
 
    >>> b = FP('b', FPSort(8, 24))
    >>> is_fp(b)
    True
    >>> is_fp(b + 1.0)
    True
    >>> is_fp(Int('x'))
    False
    """
    return isinstance(a, FPRef)
 
 

Referenced by fpFPToFP(), fpIsPositive(), fpNeg(), fpToFP(), fpToIEEEBV(), fpToReal(), fpToSBV(), fpToUBV(), is_fp_value(), and set_default_fp_sort().

is_fp_sort()

def z3py.is_fp_sort

(

s

)

Return True if `s` is a Z3 floating-point sort.

>>> is_fp_sort(FPSort(8, 24))
True
>>> is_fp_sort(IntSort())
False

Definition at line 9456 of file z3py.py.

def is_fp_sort(s):
    """Return True if `s` is a Z3 floating-point sort.
 
    >>> is_fp_sort(FPSort(8, 24))
    True
    >>> is_fp_sort(IntSort())
    False
    """
    return isinstance(s, FPSortRef)
 
 

Referenced by fpBVToFP(), fpFPToFP(), fpRealToFP(), fpSignedToFP(), fpToFP(), fpToFPUnsigned(), fpUnsignedToFP(), and FPVal().

is_fp_value()

def z3py.is_fp_value

(

a

)

Return `True` if `a` is a Z3 floating-point numeral value.

>>> b = FP('b', FPSort(8, 24))
>>> is_fp_value(b)
False
>>> b = FPVal(1.0, FPSort(8, 24))
>>> b
1
>>> is_fp_value(b)
True

Definition at line 9886 of file z3py.py.

def is_fp_value(a):
    """Return `True` if `a` is a Z3 floating-point numeral value.
 
    >>> b = FP('b', FPSort(8, 24))
    >>> is_fp_value(b)
    False
    >>> b = FPVal(1.0, FPSort(8, 24))
    >>> b
    1
    >>> is_fp_value(b)
    True
    """
    return is_fp(a) and _is_numeral(a.ctx, a.ast)
 
 

is_fprm()

def z3py.is_fprm

(

a

)

Return `True` if `a` is a Z3 floating-point rounding mode expression.

>>> rm = RNE()
>>> is_fprm(rm)
True
>>> rm = 1.0
>>> is_fprm(rm)
False

Definition at line 9716 of file z3py.py.

def is_fprm(a):
    """Return `True` if `a` is a Z3 floating-point rounding mode expression.
 
    >>> rm = RNE()
    >>> is_fprm(rm)
    True
    >>> rm = 1.0
    >>> is_fprm(rm)
    False
    """
    return isinstance(a, FPRMRef)
 
 

Referenced by fpFPToFP(), fpNeg(), fpRealToFP(), fpSignedToFP(), fpToFP(), fpToFPUnsigned(), fpToSBV(), fpToUBV(), fpUnsignedToFP(), and is_fprm_value().

is_fprm_sort()

def z3py.is_fprm_sort

(

s

)

Return True if `s` is a Z3 floating-point rounding mode sort.

>>> is_fprm_sort(FPSort(8, 24))
False
>>> is_fprm_sort(RNE().sort())
True

Definition at line 9467 of file z3py.py.

def is_fprm_sort(s):
    """Return True if `s` is a Z3 floating-point rounding mode sort.
 
    >>> is_fprm_sort(FPSort(8, 24))
    False
    >>> is_fprm_sort(RNE().sort())
    True
    """
    return isinstance(s, FPRMSortRef)
 
# FP Expressions
 
 

is_fprm_value()

def z3py.is_fprm_value

(

a

)

Return `True` if `a` is a Z3 floating-point rounding mode numeral value.

Definition at line 9729 of file z3py.py.

def is_fprm_value(a):
    """Return `True` if `a` is a Z3 floating-point rounding mode numeral value."""
    return is_fprm(a) and _is_numeral(a.ctx, a.ast)
 
# FP Numerals
 
 

Referenced by set_default_rounding_mode().

is_func_decl()

def z3py.is_func_decl

(

a

)

Return `True` if `a` is a Z3 function declaration.

>>> f = Function('f', IntSort(), IntSort())
>>> is_func_decl(f)
True
>>> x = Real('x')
>>> is_func_decl(x)
False

Definition at line 850 of file z3py.py.

def is_func_decl(a):
    """Return `True` if `a` is a Z3 function declaration.
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> is_func_decl(f)
    True
    >>> x = Real('x')
    >>> is_func_decl(x)
    False
    """
    return isinstance(a, FuncDeclRef)
 
 

Referenced by Map(), prove(), substitute_funs(), and ModelRef.update_value().

is_ge()

def z3py.is_ge

(

a

)

Return `True` if `a` is an expression of the form b >= c.

>>> x, y = Ints('x y')
>>> is_ge(x >= y)
True
>>> is_ge(x == y)
False

Definition at line 2893 of file z3py.py.

def is_ge(a):
    """Return `True` if `a` is an expression of the form b >= c.
 
    >>> x, y = Ints('x y')
    >>> is_ge(x >= y)
    True
    >>> is_ge(x == y)
    False
    """
    return is_app_of(a, Z3_OP_GE)
 
 

is_gt()

def z3py.is_gt

(

a

)

Return `True` if `a` is an expression of the form b > c.

>>> x, y = Ints('x y')
>>> is_gt(x > y)
True
>>> is_gt(x == y)
False

Definition at line 2905 of file z3py.py.

def is_gt(a):
    """Return `True` if `a` is an expression of the form b > c.
 
    >>> x, y = Ints('x y')
    >>> is_gt(x > y)
    True
    >>> is_gt(x == y)
    False
    """
    return is_app_of(a, Z3_OP_GT)
 
 

is_idiv()

def z3py.is_idiv

(

a

)

Return `True` if `a` is an expression of the form b div c.

>>> x, y = Ints('x y')
>>> is_idiv(x / y)
True
>>> is_idiv(x + y)
False

Definition at line 2845 of file z3py.py.

def is_idiv(a):
    """Return `True` if `a` is an expression of the form b div c.
 
    >>> x, y = Ints('x y')
    >>> is_idiv(x / y)
    True
    >>> is_idiv(x + y)
    False
    """
    return is_app_of(a, Z3_OP_IDIV)
 
 

is_implies()

def z3py.is_implies

(

a

)

Return `True` if `a` is a Z3 implication expression.

>>> p, q = Bools('p q')
>>> is_implies(Implies(p, q))
True
>>> is_implies(And(p, q))
False

Definition at line 1645 of file z3py.py.

def is_implies(a):
    """Return `True` if `a` is a Z3 implication expression.
 
    >>> p, q = Bools('p q')
    >>> is_implies(Implies(p, q))
    True
    >>> is_implies(And(p, q))
    False
    """
    return is_app_of(a, Z3_OP_IMPLIES)
 
 

is_int()

def z3py.is_int

(

a

)

Return `True` if `a` is an integer expression.

>>> x = Int('x')
>>> is_int(x + 1)
True
>>> is_int(1)
False
>>> is_int(IntVal(1))
True
>>> y = Real('y')
>>> is_int(y)
False
>>> is_int(y + 1)
False

Definition at line 2686 of file z3py.py.

def is_int(a):
    """Return `True` if `a` is an integer expression.
 
    >>> x = Int('x')
    >>> is_int(x + 1)
    True
    >>> is_int(1)
    False
    >>> is_int(IntVal(1))
    True
    >>> y = Real('y')
    >>> is_int(y)
    False
    >>> is_int(y + 1)
    False
    """
    return is_arith(a) and a.is_int()
 
 

is_int_value()

def z3py.is_int_value

(

a

)

Return `True` if `a` is an integer value of sort Int.

>>> is_int_value(IntVal(1))
True
>>> is_int_value(1)
False
>>> is_int_value(Int('x'))
False
>>> n = Int('x') + 1
>>> n
x + 1
>>> n.arg(1)
1
>>> is_int_value(n.arg(1))
True
>>> is_int_value(RealVal("1/3"))
False
>>> is_int_value(RealVal(1))
False

Definition at line 2732 of file z3py.py.

def is_int_value(a):
    """Return `True` if `a` is an integer value of sort Int.
 
    >>> is_int_value(IntVal(1))
    True
    >>> is_int_value(1)
    False
    >>> is_int_value(Int('x'))
    False
    >>> n = Int('x') + 1
    >>> n
    x + 1
    >>> n.arg(1)
    1
    >>> is_int_value(n.arg(1))
    True
    >>> is_int_value(RealVal("1/3"))
    False
    >>> is_int_value(RealVal(1))
    False
    """
    return is_arith(a) and a.is_int() and _is_numeral(a.ctx, a.as_ast())
 
 

is_is_int()

def z3py.is_is_int

(

a

)

Return `True` if `a` is an expression of the form IsInt(b).

>>> x = Real('x')
>>> is_is_int(IsInt(x))
True
>>> is_is_int(x)
False

Definition at line 2917 of file z3py.py.

def is_is_int(a):
    """Return `True` if `a` is an expression of the form IsInt(b).
 
    >>> x = Real('x')
    >>> is_is_int(IsInt(x))
    True
    >>> is_is_int(x)
    False
    """
    return is_app_of(a, Z3_OP_IS_INT)
 
 

is_K()

def z3py.is_K

(

a

)

Return `True` if `a` is a Z3 constant array.

>>> a = K(IntSort(), 10)
>>> is_K(a)
True
>>> a = Array('a', IntSort(), IntSort())
>>> is_K(a)
False

Definition at line 4638 of file z3py.py.

def is_K(a):
    """Return `True` if `a` is a Z3 constant array.
 
    >>> a = K(IntSort(), 10)
    >>> is_K(a)
    True
    >>> a = Array('a', IntSort(), IntSort())
    >>> is_K(a)
    False
    """
    return is_app_of(a, Z3_OP_CONST_ARRAY)
 
 

is_le()

def z3py.is_le

(

a

)

Return `True` if `a` is an expression of the form b <= c.

>>> x, y = Ints('x y')
>>> is_le(x <= y)
True
>>> is_le(x < y)
False

Definition at line 2869 of file z3py.py.

def is_le(a):
    """Return `True` if `a` is an expression of the form b <= c.
 
    >>> x, y = Ints('x y')
    >>> is_le(x <= y)
    True
    >>> is_le(x < y)
    False
    """
    return is_app_of(a, Z3_OP_LE)
 
 

is_lt()

def z3py.is_lt

(

a

)

Return `True` if `a` is an expression of the form b < c.

>>> x, y = Ints('x y')
>>> is_lt(x < y)
True
>>> is_lt(x == y)
False

Definition at line 2881 of file z3py.py.

def is_lt(a):
    """Return `True` if `a` is an expression of the form b < c.
 
    >>> x, y = Ints('x y')
    >>> is_lt(x < y)
    True
    >>> is_lt(x == y)
    False
    """
    return is_app_of(a, Z3_OP_LT)
 
 

is_map()

def z3py.is_map

(

a

)

Return `True` if `a` is a Z3 map array expression.

>>> f = Function('f', IntSort(), IntSort())
>>> b = Array('b', IntSort(), IntSort())
>>> a  = Map(f, b)
>>> a
Map(f, b)
>>> is_map(a)
True
>>> is_map(b)
False

Definition at line 4651 of file z3py.py.

def is_map(a):
    """Return `True` if `a` is a Z3 map array expression.
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> b = Array('b', IntSort(), IntSort())
    >>> a  = Map(f, b)
    >>> a
    Map(f, b)
    >>> is_map(a)
    True
    >>> is_map(b)
    False
    """
    return is_app_of(a, Z3_OP_ARRAY_MAP)
 
 

Referenced by get_map_func().

is_mod()

def z3py.is_mod

(

a

)

Return `True` if `a` is an expression of the form b % c.

>>> x, y = Ints('x y')
>>> is_mod(x % y)
True
>>> is_mod(x + y)
False

Definition at line 2857 of file z3py.py.

def is_mod(a):
    """Return `True` if `a` is an expression of the form b % c.
 
    >>> x, y = Ints('x y')
    >>> is_mod(x % y)
    True
    >>> is_mod(x + y)
    False
    """
    return is_app_of(a, Z3_OP_MOD)
 
 

is_mul()

def z3py.is_mul

(

a

)

Return `True` if `a` is an expression of the form b * c.

>>> x, y = Ints('x y')
>>> is_mul(x * y)
True
>>> is_mul(x - y)
False

Definition at line 2804 of file z3py.py.

def is_mul(a):
    """Return `True` if `a` is an expression of the form b * c.
 
    >>> x, y = Ints('x y')
    >>> is_mul(x * y)
    True
    >>> is_mul(x - y)
    False
    """
    return is_app_of(a, Z3_OP_MUL)
 
 

is_not()

def z3py.is_not

(

a

)

Return `True` if `a` is a Z3 not expression.

>>> p = Bool('p')
>>> is_not(p)
False
>>> is_not(Not(p))
True

Definition at line 1657 of file z3py.py.

def is_not(a):
    """Return `True` if `a` is a Z3 not expression.
 
    >>> p = Bool('p')
    >>> is_not(p)
    False
    >>> is_not(Not(p))
    True
    """
    return is_app_of(a, Z3_OP_NOT)
 
 

Referenced by mk_not().

is_or()

def z3py.is_or

(

a

)

Return `True` if `a` is a Z3 or expression.

>>> p, q = Bools('p q')
>>> is_or(Or(p, q))
True
>>> is_or(And(p, q))
False

Definition at line 1633 of file z3py.py.

def is_or(a):
    """Return `True` if `a` is a Z3 or expression.
 
    >>> p, q = Bools('p q')
    >>> is_or(Or(p, q))
    True
    >>> is_or(And(p, q))
    False
    """
    return is_app_of(a, Z3_OP_OR)
 
 

is_pattern()

def z3py.is_pattern

(

a

)

Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
>>> q
ForAll(x, f(x) == 0)
>>> q.num_patterns()
1
>>> is_pattern(q.pattern(0))
True
>>> q.pattern(0)
f(Var(0))

Definition at line 1933 of file z3py.py.

def is_pattern(a):
    """Return `True` if `a` is a Z3 pattern (hint for quantifier instantiation.
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> x = Int('x')
    >>> q = ForAll(x, f(x) == 0, patterns = [ f(x) ])
    >>> q
    ForAll(x, f(x) == 0)
    >>> q.num_patterns()
    1
    >>> is_pattern(q.pattern(0))
    True
    >>> q.pattern(0)
    f(Var(0))
    """
    return isinstance(a, PatternRef)
 
 

Referenced by is_quantifier(), and MultiPattern().

is_probe()

def z3py.is_probe

(

p

)

Return `True` if `p` is a Z3 probe.

>>> is_probe(Int('x'))
False
>>> is_probe(Probe('memory'))
True

Definition at line 8637 of file z3py.py.

def is_probe(p):
    """Return `True` if `p` is a Z3 probe.
 
    >>> is_probe(Int('x'))
    False
    >>> is_probe(Probe('memory'))
    True
    """
    return isinstance(p, Probe)
 
 

Referenced by eq(), mk_not(), and Not().

is_quantifier()

def z3py.is_quantifier

(

a

)

Return `True` if `a` is a Z3 quantifier.

>>> f = Function('f', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) == 0)
>>> is_quantifier(q)
True
>>> is_quantifier(f(x))
False

Definition at line 2173 of file z3py.py.

def is_quantifier(a):
    """Return `True` if `a` is a Z3 quantifier.
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> x = Int('x')
    >>> q = ForAll(x, f(x) == 0)
    >>> is_quantifier(q)
    True
    >>> is_quantifier(f(x))
    False
    """
    return isinstance(a, QuantifierRef)
 
 

is_rational_value()

def z3py.is_rational_value

(

a

)

Return `True` if `a` is rational value of sort Real.

>>> is_rational_value(RealVal(1))
True
>>> is_rational_value(RealVal("3/5"))
True
>>> is_rational_value(IntVal(1))
False
>>> is_rational_value(1)
False
>>> n = Real('x') + 1
>>> n.arg(1)
1
>>> is_rational_value(n.arg(1))
True
>>> is_rational_value(Real('x'))
False

Definition at line 2756 of file z3py.py.

def is_rational_value(a):
    """Return `True` if `a` is rational value of sort Real.
 
    >>> is_rational_value(RealVal(1))
    True
    >>> is_rational_value(RealVal("3/5"))
    True
    >>> is_rational_value(IntVal(1))
    False
    >>> is_rational_value(1)
    False
    >>> n = Real('x') + 1
    >>> n.arg(1)
    1
    >>> is_rational_value(n.arg(1))
    True
    >>> is_rational_value(Real('x'))
    False
    """
    return is_arith(a) and a.is_real() and _is_numeral(a.ctx, a.as_ast())
 
 

is_re()

def z3py.is_re

(

s

)

Definition at line 11168 of file z3py.py.

def is_re(s):
    return isinstance(s, ReRef)
 
 

Referenced by Concat(), Intersect(), and Union().

is_real()

def z3py.is_real

(

a

)

Return `True` if `a` is a real expression.

>>> x = Int('x')
>>> is_real(x + 1)
False
>>> y = Real('y')
>>> is_real(y)
True
>>> is_real(y + 1)
True
>>> is_real(1)
False
>>> is_real(RealVal(1))
True

Definition at line 2705 of file z3py.py.

def is_real(a):
    """Return `True` if `a` is a real expression.
 
    >>> x = Int('x')
    >>> is_real(x + 1)
    False
    >>> y = Real('y')
    >>> is_real(y)
    True
    >>> is_real(y + 1)
    True
    >>> is_real(1)
    False
    >>> is_real(RealVal(1))
    True
    """
    return is_arith(a) and a.is_real()
 
 

Referenced by fpRealToFP(), and fpToFP().

is_select()

def z3py.is_select

(

a

)

Return `True` if `a` is a Z3 array select application.

>>> a = Array('a', IntSort(), IntSort())
>>> is_select(a)
False
>>> i = Int('i')
>>> is_select(a[i])
True

Definition at line 4886 of file z3py.py.

def is_select(a):
    """Return `True` if `a` is a Z3 array select application.
 
    >>> a = Array('a', IntSort(), IntSort())
    >>> is_select(a)
    False
    >>> i = Int('i')
    >>> is_select(a[i])
    True
    """
    return is_app_of(a, Z3_OP_SELECT)
 
 

is_seq()

def z3py.is_seq

(

a

)

Return `True` if `a` is a Z3 sequence expression.
>>> print (is_seq(Unit(IntVal(0))))
True
>>> print (is_seq(StringVal("abc")))
True

Definition at line 10894 of file z3py.py.

def is_seq(a):
    """Return `True` if `a` is a Z3 sequence expression.
    >>> print (is_seq(Unit(IntVal(0))))
    True
    >>> print (is_seq(StringVal("abc")))
    True
    """
    return isinstance(a, SeqRef)
 
 

Referenced by CharIsDigit(), Concat(), and Extract().

is_sort()

def z3py.is_sort

(

s

)

Return `True` if `s` is a Z3 sort.

>>> is_sort(IntSort())
True
>>> is_sort(Int('x'))
False
>>> is_expr(Int('x'))
True

Definition at line 647 of file z3py.py.

def is_sort(s):
    """Return `True` if `s` is a Z3 sort.
 
    >>> is_sort(IntSort())
    True
    >>> is_sort(Int('x'))
    False
    >>> is_expr(Int('x'))
    True
    """
    return isinstance(s, SortRef)
 
 

Referenced by ArraySort(), CreateDatatypes(), FreshFunction(), Function(), IsSubset(), K(), PropagateFunction(), prove(), RecFunction(), and Var().

is_store()

def z3py.is_store

(

a

)

Return `True` if `a` is a Z3 array store application.

>>> a = Array('a', IntSort(), IntSort())
>>> is_store(a)
False
>>> is_store(Store(a, 0, 1))
True

Definition at line 4899 of file z3py.py.

def is_store(a):
    """Return `True` if `a` is a Z3 array store application.
 
    >>> a = Array('a', IntSort(), IntSort())
    >>> is_store(a)
    False
    >>> is_store(Store(a, 0, 1))
    True
    """
    return is_app_of(a, Z3_OP_STORE)
 

is_string()

def z3py.is_string

(

a

)

Return `True` if `a` is a Z3 string expression.
>>> print (is_string(StringVal("ab")))
True

Definition at line 10904 of file z3py.py.

def is_string(a):
    """Return `True` if `a` is a Z3 string expression.
    >>> print (is_string(StringVal("ab")))
    True
    """
    return isinstance(a, SeqRef) and a.is_string()
 
 

is_string_value()

def z3py.is_string_value

(

a

)

return 'True' if 'a' is a Z3 string constant expression.
>>> print (is_string_value(StringVal("a")))
True
>>> print (is_string_value(StringVal("a") + StringVal("b")))
False

Definition at line 10912 of file z3py.py.

def is_string_value(a):
    """return 'True' if 'a' is a Z3 string constant expression.
    >>> print (is_string_value(StringVal("a")))
    True
    >>> print (is_string_value(StringVal("a") + StringVal("b")))
    False
    """
    return isinstance(a, SeqRef) and a.is_string_value()
 

is_sub()

def z3py.is_sub

(

a

)

Return `True` if `a` is an expression of the form b - c.

>>> x, y = Ints('x y')
>>> is_sub(x - y)
True
>>> is_sub(x + y)
False

Definition at line 2816 of file z3py.py.

def is_sub(a):
    """Return `True` if `a` is an expression of the form b - c.
 
    >>> x, y = Ints('x y')
    >>> is_sub(x - y)
    True
    >>> is_sub(x + y)
    False
    """
    return is_app_of(a, Z3_OP_SUB)
 
 

is_to_int()

def z3py.is_to_int

(

a

)

Return `True` if `a` is an expression of the form ToInt(b).

>>> x = Real('x')
>>> n = ToInt(x)
>>> n
ToInt(x)
>>> is_to_int(n)
True
>>> is_to_int(x)
False

Definition at line 2944 of file z3py.py.

def is_to_int(a):
    """Return `True` if `a` is an expression of the form ToInt(b).
 
    >>> x = Real('x')
    >>> n = ToInt(x)
    >>> n
    ToInt(x)
    >>> is_to_int(n)
    True
    >>> is_to_int(x)
    False
    """
    return is_app_of(a, Z3_OP_TO_INT)
 
 

is_to_real()

def z3py.is_to_real

(

a

)

Return `True` if `a` is an expression of the form ToReal(b).

>>> x = Int('x')
>>> n = ToReal(x)
>>> n
ToReal(x)
>>> is_to_real(n)
True
>>> is_to_real(x)
False

Definition at line 2929 of file z3py.py.

def is_to_real(a):
    """Return `True` if `a` is an expression of the form ToReal(b).
 
    >>> x = Int('x')
    >>> n = ToReal(x)
    >>> n
    ToReal(x)
    >>> is_to_real(n)
    True
    >>> is_to_real(x)
    False
    """
    return is_app_of(a, Z3_OP_TO_REAL)
 
 

is_true()

def z3py.is_true

(

a

)

Return `True` if `a` is the Z3 true expression.

>>> p = Bool('p')
>>> is_true(p)
False
>>> is_true(simplify(p == p))
True
>>> x = Real('x')
>>> is_true(x == 0)
False
>>> # True is a Python Boolean expression
>>> is_true(True)
False

Definition at line 1589 of file z3py.py.

def is_true(a):
    """Return `True` if `a` is the Z3 true expression.
 
    >>> p = Bool('p')
    >>> is_true(p)
    False
    >>> is_true(simplify(p == p))
    True
    >>> x = Real('x')
    >>> is_true(x == 0)
    False
    >>> # True is a Python Boolean expression
    >>> is_true(True)
    False
    """
    return is_app_of(a, Z3_OP_TRUE)
 
 

Referenced by AstRef.__bool__().

is_var()

def z3py.is_var

(

a

)

Return `True` if `a` is variable.

Z3 uses de-Bruijn indices for representing bound variables in
quantifiers.

>>> x = Int('x')
>>> is_var(x)
False
>>> is_const(x)
True
>>> f = Function('f', IntSort(), IntSort())
>>> # Z3 replaces x with bound variables when ForAll is executed.
>>> q = ForAll(x, f(x) == x)
>>> b = q.body()
>>> b
f(Var(0)) == Var(0)
>>> b.arg(1)
Var(0)
>>> is_var(b.arg(1))
True

Definition at line 1310 of file z3py.py.

def is_var(a):
    """Return `True` if `a` is variable.
 
    Z3 uses de-Bruijn indices for representing bound variables in
    quantifiers.
 
    >>> x = Int('x')
    >>> is_var(x)
    False
    >>> is_const(x)
    True
    >>> f = Function('f', IntSort(), IntSort())
    >>> # Z3 replaces x with bound variables when ForAll is executed.
    >>> q = ForAll(x, f(x) == x)
    >>> b = q.body()
    >>> b
    f(Var(0)) == Var(0)
    >>> b.arg(1)
    Var(0)
    >>> is_var(b.arg(1))
    True
    """
    return is_expr(a) and _ast_kind(a.ctx, a) == Z3_VAR_AST
 
 

Referenced by get_var_index().

IsInt()

def z3py.IsInt

(

a

)

 Return the Z3 predicate IsInt(a).

>>> x = Real('x')
>>> IsInt(x + "1/2")
IsInt(x + 1/2)
>>> solve(IsInt(x + "1/2"), x > 0, x < 1)
[x = 1/2]
>>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
no solution

Definition at line 3394 of file z3py.py.

def IsInt(a):
    """ Return the Z3 predicate IsInt(a).
 
    >>> x = Real('x')
    >>> IsInt(x + "1/2")
    IsInt(x + 1/2)
    >>> solve(IsInt(x + "1/2"), x > 0, x < 1)
    [x = 1/2]
    >>> solve(IsInt(x + "1/2"), x > 0, x < 1, x != "1/2")
    no solution
    """
    if z3_debug():
        _z3_assert(a.is_real(), "Z3 real expression expected.")
    ctx = a.ctx
    return BoolRef(Z3_mk_is_int(ctx.ref(), a.as_ast()), ctx)
 
 

IsMember()

def z3py.IsMember	(		e,
			s
	)

 Check if e is a member of set s
>>> a = Const('a', SetSort(IntSort()))
>>> IsMember(1, a)
a[1]

Definition at line 5009 of file z3py.py.

def IsMember(e, s):
    """ Check if e is a member of set s
    >>> a = Const('a', SetSort(IntSort()))
    >>> IsMember(1, a)
    a[1]
    """
    ctx = _ctx_from_ast_arg_list([s, e])
    e = _py2expr(e, ctx)
    return BoolRef(Z3_mk_set_member(ctx.ref(), e.as_ast(), s.as_ast()), ctx)
 
 

IsSubset()

def z3py.IsSubset	(		a,
			b
	)

 Check if a is a subset of b
>>> a = Const('a', SetSort(IntSort()))
>>> b = Const('b', SetSort(IntSort()))
>>> IsSubset(a, b)
subset(a, b)

Definition at line 5020 of file z3py.py.

def IsSubset(a, b):
    """ Check if a is a subset of b
    >>> a = Const('a', SetSort(IntSort()))
    >>> b = Const('b', SetSort(IntSort()))
    >>> IsSubset(a, b)
    subset(a, b)
    """
    ctx = _ctx_from_ast_arg_list([a, b])
    return BoolRef(Z3_mk_set_subset(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
 
 

K()

def z3py.K	(		dom,
			v
	)

Return a Z3 constant array expression.

>>> a = K(IntSort(), 10)
>>> a
K(Int, 10)
>>> a.sort()
Array(Int, Int)
>>> i = Int('i')
>>> a[i]
K(Int, 10)[i]
>>> simplify(a[i])
10

Definition at line 4846 of file z3py.py.

def K(dom, v):
    """Return a Z3 constant array expression.
 
    >>> a = K(IntSort(), 10)
    >>> a
    K(Int, 10)
    >>> a.sort()
    Array(Int, Int)
    >>> i = Int('i')
    >>> a[i]
    K(Int, 10)[i]
    >>> simplify(a[i])
    10
    """
    if z3_debug():
        _z3_assert(is_sort(dom), "Z3 sort expected")
    ctx = dom.ctx
    if not is_expr(v):
        v = _py2expr(v, ctx)
    return ArrayRef(Z3_mk_const_array(ctx.ref(), dom.ast, v.as_ast()), ctx)
 
 

Referenced by ModelRef.get_interp().

Lambda()

def z3py.Lambda	(		vs,
			body
	)

Create a Z3 lambda expression.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> mem0 = Array('mem0', IntSort(), IntSort())
>>> lo, hi, e, i = Ints('lo hi e i')
>>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
>>> mem1
Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))

Definition at line 2261 of file z3py.py.

def Lambda(vs, body):
    """Create a Z3 lambda expression.
 
    >>> f = Function('f', IntSort(), IntSort(), IntSort())
    >>> mem0 = Array('mem0', IntSort(), IntSort())
    >>> lo, hi, e, i = Ints('lo hi e i')
    >>> mem1 = Lambda([i], If(And(lo <= i, i <= hi), e, mem0[i]))
    >>> mem1
    Lambda(i, If(And(lo <= i, i <= hi), e, mem0[i]))
    """
    ctx = body.ctx
    if is_app(vs):
        vs = [vs]
    num_vars = len(vs)
    _vs = (Ast * num_vars)()
    for i in range(num_vars):
        # TODO: Check if is constant
        _vs[i] = vs[i].as_ast()
    return QuantifierRef(Z3_mk_lambda_const(ctx.ref(), num_vars, _vs, body.as_ast()), ctx)
 

Referenced by Context.MkLambda().

LastIndexOf()

def z3py.LastIndexOf	(		s,
			substr
	)

Retrieve the last index of substring within a string

Definition at line 11079 of file z3py.py.

def LastIndexOf(s, substr):
    """Retrieve the last index of substring within a string"""
    ctx = None
    ctx = _get_ctx2(s, substr, ctx)
    s = _coerce_seq(s, ctx)
    substr = _coerce_seq(substr, ctx)
    return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
 
 

Length()

def z3py.Length

(

s

)

Obtain the length of a sequence 's'
>>> l = Length(StringVal("abc"))
>>> simplify(l)
3

Definition at line 11088 of file z3py.py.

def Length(s):
    """Obtain the length of a sequence 's'
    >>> l = Length(StringVal("abc"))
    >>> simplify(l)
    3
    """
    s = _coerce_seq(s)
    return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
 
 

Referenced by NativeContext.MkAdd(), NativeContext.MkAnd(), NativeContext.MkApp(), NativeContext.MkFreshFuncDecl(), NativeContext.MkFuncDecl(), NativeContext.MkMul(), NativeContext.MkOr(), NativeContext.MkSub(), and NativeContext.MkTupleSort().

LinearOrder()

def z3py.LinearOrder	(		a,
			index
	)

Definition at line 11310 of file z3py.py.

def LinearOrder(a, index):
    return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
 
 

Loop()

def z3py.Loop	(		re,
			lo,
			hi = 0
	)

Create the regular expression accepting between a lower and upper bound repetitions
>>> re = Loop(Re("a"), 1, 3)
>>> print(simplify(InRe("aa", re)))
True
>>> print(simplify(InRe("aaaa", re)))
False
>>> print(simplify(InRe("", re)))
False

Definition at line 11268 of file z3py.py.

def Loop(re, lo, hi=0):
    """Create the regular expression accepting between a lower and upper bound repetitions
    >>> re = Loop(Re("a"), 1, 3)
    >>> print(simplify(InRe("aa", re)))
    True
    >>> print(simplify(InRe("aaaa", re)))
    False
    >>> print(simplify(InRe("", re)))
    False
    """
    return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
 
 

LShR()

def z3py.LShR	(		a,
			b
	)

Create the Z3 expression logical right shift.

Use the operator >> for the arithmetical right shift.

>>> x, y = BitVecs('x y', 32)
>>> LShR(x, y)
LShR(x, y)
>>> (x >> y).sexpr()
'(bvashr x y)'
>>> LShR(x, y).sexpr()
'(bvlshr x y)'
>>> BitVecVal(4, 3)
4
>>> BitVecVal(4, 3).as_signed_long()
-4
>>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
-2
>>> simplify(BitVecVal(4, 3) >> 1)
6
>>> simplify(LShR(BitVecVal(4, 3), 1))
2
>>> simplify(BitVecVal(2, 3) >> 1)
1
>>> simplify(LShR(BitVecVal(2, 3), 1))
1

Definition at line 4299 of file z3py.py.

def LShR(a, b):
    """Create the Z3 expression logical right shift.
 
    Use the operator >> for the arithmetical right shift.
 
    >>> x, y = BitVecs('x y', 32)
    >>> LShR(x, y)
    LShR(x, y)
    >>> (x >> y).sexpr()
    '(bvashr x y)'
    >>> LShR(x, y).sexpr()
    '(bvlshr x y)'
    >>> BitVecVal(4, 3)
    4
    >>> BitVecVal(4, 3).as_signed_long()
    -4
    >>> simplify(BitVecVal(4, 3) >> 1).as_signed_long()
    -2
    >>> simplify(BitVecVal(4, 3) >> 1)
    6
    >>> simplify(LShR(BitVecVal(4, 3), 1))
    2
    >>> simplify(BitVecVal(2, 3) >> 1)
    1
    >>> simplify(LShR(BitVecVal(2, 3), 1))
    1
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BitVecRef(Z3_mk_bvlshr(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

main_ctx()

def z3py.main_ctx

(

)

Return a reference to the global Z3 context.

>>> x = Real('x')
>>> x.ctx == main_ctx()
True
>>> c = Context()
>>> c == main_ctx()
False
>>> x2 = Real('x', c)
>>> x2.ctx == c
True
>>> eq(x, x2)
False

Definition at line 239 of file z3py.py.

def main_ctx():
    """Return a reference to the global Z3 context.
 
    >>> x = Real('x')
    >>> x.ctx == main_ctx()
    True
    >>> c = Context()
    >>> c == main_ctx()
    False
    >>> x2 = Real('x', c)
    >>> x2.ctx == c
    True
    >>> eq(x, x2)
    False
    """
    global _main_ctx
    if _main_ctx is None:
        _main_ctx = Context()
    return _main_ctx
 
 

Referenced by CharIsDigit(), help_simplify(), and simplify_param_descrs().

Map()

def z3py.Map	(		f,
		*	args
	)

Return a Z3 map array expression.

>>> f = Function('f', IntSort(), IntSort(), IntSort())
>>> a1 = Array('a1', IntSort(), IntSort())
>>> a2 = Array('a2', IntSort(), IntSort())
>>> b  = Map(f, a1, a2)
>>> b
Map(f, a1, a2)
>>> prove(b[0] == f(a1[0], a2[0]))
proved

Definition at line 4823 of file z3py.py.

def Map(f, *args):
    """Return a Z3 map array expression.
 
    >>> f = Function('f', IntSort(), IntSort(), IntSort())
    >>> a1 = Array('a1', IntSort(), IntSort())
    >>> a2 = Array('a2', IntSort(), IntSort())
    >>> b  = Map(f, a1, a2)
    >>> b
    Map(f, a1, a2)
    >>> prove(b[0] == f(a1[0], a2[0]))
    proved
    """
    args = _get_args(args)
    if z3_debug():
        _z3_assert(len(args) > 0, "At least one Z3 array expression expected")
        _z3_assert(is_func_decl(f), "First argument must be a Z3 function declaration")
        _z3_assert(all([is_array(a) for a in args]), "Z3 array expected expected")
        _z3_assert(len(args) == f.arity(), "Number of arguments mismatch")
    _args, sz = _to_ast_array(args)
    ctx = f.ctx
    return ArrayRef(Z3_mk_map(ctx.ref(), f.ast, sz, _args), ctx)
 
 

Referenced by Context.Context().

mk_not()

def z3py.mk_not

(

a

)

Definition at line 1834 of file z3py.py.

def mk_not(a):
    if is_not(a):
        return a.arg(0)
    else:
        return Not(a)
 
 

Model()

def z3py.Model

(

ctx = None

)

Definition at line 6689 of file z3py.py.

def Model(ctx=None):
    ctx = _get_ctx(ctx)
    return ModelRef(Z3_mk_model(ctx.ref()), ctx)
 
 

Referenced by Goal.ConvertModel(), Goal.convertModel(), Optimize.getModel(), Solver.getModel(), and Optimize.set_on_model().

MultiPattern()

def z3py.MultiPattern

(

*

args

)

Create a Z3 multi-pattern using the given expressions `*args`

>>> f = Function('f', IntSort(), IntSort())
>>> g = Function('g', IntSort(), IntSort())
>>> x = Int('x')
>>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
>>> q
ForAll(x, f(x) != g(x))
>>> q.num_patterns()
1
>>> is_pattern(q.pattern(0))
True
>>> q.pattern(0)
MultiPattern(f(Var(0)), g(Var(0)))

Definition at line 1951 of file z3py.py.

def MultiPattern(*args):
    """Create a Z3 multi-pattern using the given expressions `*args`
 
    >>> f = Function('f', IntSort(), IntSort())
    >>> g = Function('g', IntSort(), IntSort())
    >>> x = Int('x')
    >>> q = ForAll(x, f(x) != g(x), patterns = [ MultiPattern(f(x), g(x)) ])
    >>> q
    ForAll(x, f(x) != g(x))
    >>> q.num_patterns()
    1
    >>> is_pattern(q.pattern(0))
    True
    >>> q.pattern(0)
    MultiPattern(f(Var(0)), g(Var(0)))
    """
    if z3_debug():
        _z3_assert(len(args) > 0, "At least one argument expected")
        _z3_assert(all([is_expr(a) for a in args]), "Z3 expressions expected")
    ctx = args[0].ctx
    args, sz = _to_ast_array(args)
    return PatternRef(Z3_mk_pattern(ctx.ref(), sz, args), ctx)
 
 

Not()

def z3py.Not	(		a,
			ctx = None
	)

Create a Z3 not expression or probe.

>>> p = Bool('p')
>>> Not(Not(p))
Not(Not(p))
>>> simplify(Not(Not(p)))
p

Definition at line 1815 of file z3py.py.

def Not(a, ctx=None):
    """Create a Z3 not expression or probe.
 
    >>> p = Bool('p')
    >>> Not(Not(p))
    Not(Not(p))
    >>> simplify(Not(Not(p)))
    p
    """
    ctx = _get_ctx(_ctx_from_ast_arg_list([a], ctx))
    if is_probe(a):
        # Not is also used to build probes
        return Probe(Z3_probe_not(ctx.ref(), a.probe), ctx)
    else:
        s = BoolSort(ctx)
        a = s.cast(a)
        return BoolRef(Z3_mk_not(ctx.ref(), a.as_ast()), ctx)
 
 

Referenced by fpNEQ(), mk_not(), and prove().

on_clause_eh()

def z3py.on_clause_eh	(		ctx,
			p,
			clause
	)

Definition at line 11350 of file z3py.py.

def on_clause_eh(ctx, p, clause):
    onc = _my_hacky_class
    p = _to_expr_ref(to_Ast(p), onc.ctx)
    clause = AstVector(to_AstVectorObj(clause), onc.ctx)
    onc.on_clause(p, clause)
    

Referenced by on_clause.on_clause().

open_log()

def z3py.open_log

(

fname

)

Log interaction to a file. This function must be invoked immediately after init(). 

Definition at line 114 of file z3py.py.

def open_log(fname):
    """Log interaction to a file. This function must be invoked immediately after init(). """
    Z3_open_log(fname)
 
 

Option()

def z3py.Option

(

re

)

Create the regular expression that optionally accepts the argument.
>>> re = Option(Re("a"))
>>> print(simplify(InRe("a", re)))
True
>>> print(simplify(InRe("", re)))
True
>>> print(simplify(InRe("aa", re)))
False

Definition at line 11237 of file z3py.py.

def Option(re):
    """Create the regular expression that optionally accepts the argument.
    >>> re = Option(Re("a"))
    >>> print(simplify(InRe("a", re)))
    True
    >>> print(simplify(InRe("", re)))
    True
    >>> print(simplify(InRe("aa", re)))
    False
    """
    return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
 
 

Or()

def z3py.Or

(

*

args

)

Create a Z3 or-expression or or-probe.

>>> p, q, r = Bools('p q r')
>>> Or(p, q, r)
Or(p, q, r)
>>> P = BoolVector('p', 5)
>>> Or(P)
Or(p__0, p__1, p__2, p__3, p__4)

Definition at line 1882 of file z3py.py.

def Or(*args):
    """Create a Z3 or-expression or or-probe.
 
    >>> p, q, r = Bools('p q r')
    >>> Or(p, q, r)
    Or(p, q, r)
    >>> P = BoolVector('p', 5)
    >>> Or(P)
    Or(p__0, p__1, p__2, p__3, p__4)
    """
    last_arg = None
    if len(args) > 0:
        last_arg = args[len(args) - 1]
    if isinstance(last_arg, Context):
        ctx = args[len(args) - 1]
        args = args[:len(args) - 1]
    elif len(args) == 1 and isinstance(args[0], AstVector):
        ctx = args[0].ctx
        args = [a for a in args[0]]
    else:
        ctx = None
    args = _get_args(args)
    ctx = _get_ctx(_ctx_from_ast_arg_list(args, ctx))
    if z3_debug():
        _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression or probe")
    if _has_probe(args):
        return _probe_or(args, ctx)
    else:
        args = _coerce_expr_list(args, ctx)
        _args, sz = _to_ast_array(args)
        return BoolRef(Z3_mk_or(ctx.ref(), sz, _args), ctx)
 

Referenced by ApplyResult.as_expr().

OrElse()

def z3py.OrElse	(	*	ts,
		**	ks
	)

Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).

>>> x = Int('x')
>>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
>>> # Tactic split-clause fails if there is no clause in the given goal.
>>> t(x == 0)
[[x == 0]]
>>> t(Or(x == 0, x == 1))
[[x == 0], [x == 1]]

Definition at line 8330 of file z3py.py.

def OrElse(*ts, **ks):
    """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
 
    >>> x = Int('x')
    >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
    >>> # Tactic split-clause fails if there is no clause in the given goal.
    >>> t(x == 0)
    [[x == 0]]
    >>> t(Or(x == 0, x == 1))
    [[x == 0], [x == 1]]
    """
    if z3_debug():
        _z3_assert(len(ts) >= 2, "At least two arguments expected")
    ctx = ks.get("ctx", None)
    num = len(ts)
    r = ts[0]
    for i in range(num - 1):
        r = _or_else(r, ts[i + 1], ctx)
    return r
 
 

ParAndThen()

def z3py.ParAndThen	(		t1,
			t2,
			ctx = None
	)

Alias for ParThen(t1, t2, ctx).

Definition at line 8386 of file z3py.py.

def ParAndThen(t1, t2, ctx=None):
    """Alias for ParThen(t1, t2, ctx)."""
    return ParThen(t1, t2, ctx)
 
 

ParOr()

def z3py.ParOr	(	*	ts,
		**	ks
	)

Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).

>>> x = Int('x')
>>> t = ParOr(Tactic('simplify'), Tactic('fail'))
>>> t(x + 1 == 2)
[[x == 1]]

Definition at line 8351 of file z3py.py.

def ParOr(*ts, **ks):
    """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
 
    >>> x = Int('x')
    >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
    >>> t(x + 1 == 2)
    [[x == 1]]
    """
    if z3_debug():
        _z3_assert(len(ts) >= 2, "At least two arguments expected")
    ctx = _get_ctx(ks.get("ctx", None))
    ts = [_to_tactic(t, ctx) for t in ts]
    sz = len(ts)
    _args = (TacticObj * sz)()
    for i in range(sz):
        _args[i] = ts[i].tactic
    return Tactic(Z3_tactic_par_or(ctx.ref(), sz, _args), ctx)
 
 

parse_smt2_file()

def z3py.parse_smt2_file	(		f,
			sorts = {},
			decls = {},
			ctx = None
	)

Parse a file in SMT 2.0 format using the given sorts and decls.

This function is similar to parse_smt2_string().

Definition at line 9266 of file z3py.py.

def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
    """Parse a file in SMT 2.0 format using the given sorts and decls.
 
    This function is similar to parse_smt2_string().
    """
    ctx = _get_ctx(ctx)
    ssz, snames, ssorts = _dict2sarray(sorts, ctx)
    dsz, dnames, ddecls = _dict2darray(decls, ctx)
    return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
 
 

parse_smt2_string()

def z3py.parse_smt2_string	(		s,
			sorts = {},
			decls = {},
			ctx = None
	)

Parse a string in SMT 2.0 format using the given sorts and decls.

The arguments sorts and decls are Python dictionaries used to initialize
the symbol table used for the SMT 2.0 parser.

>>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
[x > 0, x < 10]
>>> x, y = Ints('x y')
>>> f = Function('f', IntSort(), IntSort())
>>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
[x + f(y) > 0]
>>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
[a > 0]

Definition at line 9245 of file z3py.py.

def parse_smt2_string(s, sorts={}, decls={}, ctx=None):
    """Parse a string in SMT 2.0 format using the given sorts and decls.
 
    The arguments sorts and decls are Python dictionaries used to initialize
    the symbol table used for the SMT 2.0 parser.
 
    >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
    [x > 0, x < 10]
    >>> x, y = Ints('x y')
    >>> f = Function('f', IntSort(), IntSort())
    >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
    [x + f(y) > 0]
    >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
    [a > 0]
    """
    ctx = _get_ctx(ctx)
    ssz, snames, ssorts = _dict2sarray(sorts, ctx)
    dsz, dnames, ddecls = _dict2darray(decls, ctx)
    return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
 
 

ParThen()

def z3py.ParThen	(		t1,
			t2,
			ctx = None
	)

Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
The subgoals are processed in parallel.

>>> x, y = Ints('x y')
>>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
>>> t(And(Or(x == 1, x == 2), y == x + 1))
[[x == 1, y == 2], [x == 2, y == 3]]

Definition at line 8370 of file z3py.py.

def ParThen(t1, t2, ctx=None):
    """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
    The subgoals are processed in parallel.
 
    >>> x, y = Ints('x y')
    >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
    >>> t(And(Or(x == 1, x == 2), y == x + 1))
    [[x == 1, y == 2], [x == 2, y == 3]]
    """
    t1 = _to_tactic(t1, ctx)
    t2 = _to_tactic(t2, ctx)
    if z3_debug():
        _z3_assert(t1.ctx == t2.ctx, "Context mismatch")
    return Tactic(Z3_tactic_par_and_then(t1.ctx.ref(), t1.tactic, t2.tactic), t1.ctx)
 
 

Referenced by ParAndThen().

PartialOrder()

def z3py.PartialOrder	(		a,
			index
	)

Definition at line 11306 of file z3py.py.

def PartialOrder(a, index):
    return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
 
 

PbEq()

def z3py.PbEq	(		args,
			k,
			ctx = None
	)

Create a Pseudo-Boolean inequality k constraint.

>>> a, b, c = Bools('a b c')
>>> f = PbEq(((a,1),(b,3),(c,2)), 3)

Definition at line 9022 of file z3py.py.

def PbEq(args, k, ctx=None):
    """Create a Pseudo-Boolean inequality k constraint.
 
    >>> a, b, c = Bools('a b c')
    >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
    """
    _z3_check_cint_overflow(k, "k")
    ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
    return BoolRef(Z3_mk_pbeq(ctx.ref(), sz, _args, _coeffs, k), ctx)
 
 

PbGe()

def z3py.PbGe	(		args,
			k
	)

Create a Pseudo-Boolean inequality k constraint.

>>> a, b, c = Bools('a b c')
>>> f = PbGe(((a,1),(b,3),(c,2)), 3)

Definition at line 9011 of file z3py.py.

def PbGe(args, k):
    """Create a Pseudo-Boolean inequality k constraint.
 
    >>> a, b, c = Bools('a b c')
    >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
    """
    _z3_check_cint_overflow(k, "k")
    ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
    return BoolRef(Z3_mk_pbge(ctx.ref(), sz, _args, _coeffs, k), ctx)
 
 

PbLe()

def z3py.PbLe	(		args,
			k
	)

Create a Pseudo-Boolean inequality k constraint.

>>> a, b, c = Bools('a b c')
>>> f = PbLe(((a,1),(b,3),(c,2)), 3)

Definition at line 9000 of file z3py.py.

def PbLe(args, k):
    """Create a Pseudo-Boolean inequality k constraint.
 
    >>> a, b, c = Bools('a b c')
    >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
    """
    _z3_check_cint_overflow(k, "k")
    ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
    return BoolRef(Z3_mk_pble(ctx.ref(), sz, _args, _coeffs, k), ctx)
 
 

PiecewiseLinearOrder()

def z3py.PiecewiseLinearOrder	(		a,
			index
	)

Definition at line 11318 of file z3py.py.

def PiecewiseLinearOrder(a, index):
    return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
 
 

Plus()

def z3py.Plus

(

re

)

Create the regular expression accepting one or more repetitions of argument.
>>> re = Plus(Re("a"))
>>> print(simplify(InRe("aa", re)))
True
>>> print(simplify(InRe("ab", re)))
False
>>> print(simplify(InRe("", re)))
False

Definition at line 11224 of file z3py.py.

def Plus(re):
    """Create the regular expression accepting one or more repetitions of argument.
    >>> re = Plus(Re("a"))
    >>> print(simplify(InRe("aa", re)))
    True
    >>> print(simplify(InRe("ab", re)))
    False
    >>> print(simplify(InRe("", re)))
    False
    """
    return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
 
 

PrefixOf()

def z3py.PrefixOf	(		a,
			b
	)

Check if 'a' is a prefix of 'b'
>>> s1 = PrefixOf("ab", "abc")
>>> simplify(s1)
True
>>> s2 = PrefixOf("bc", "abc")
>>> simplify(s2)
False

Definition at line 10995 of file z3py.py.

def PrefixOf(a, b):
    """Check if 'a' is a prefix of 'b'
    >>> s1 = PrefixOf("ab", "abc")
    >>> simplify(s1)
    True
    >>> s2 = PrefixOf("bc", "abc")
    >>> simplify(s2)
    False
    """
    ctx = _get_ctx2(a, b)
    a = _coerce_seq(a, ctx)
    b = _coerce_seq(b, ctx)
    return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

probe_description()

def z3py.probe_description	(		name,
			ctx = None
	)

Return a short description for the probe named `name`.

>>> d = probe_description('memory')

Definition at line 8666 of file z3py.py.

def probe_description(name, ctx=None):
    """Return a short description for the probe named `name`.
 
    >>> d = probe_description('memory')
    """
    ctx = _get_ctx(ctx)
    return Z3_probe_get_descr(ctx.ref(), name)
 
 

Referenced by describe_probes().

probes()

def z3py.probes

(

ctx = None

)

Return a list of all available probes in Z3.

>>> l = probes()
>>> l.count('memory') == 1
True

Definition at line 8655 of file z3py.py.

def probes(ctx=None):
    """Return a list of all available probes in Z3.
 
    >>> l = probes()
    >>> l.count('memory') == 1
    True
    """
    ctx = _get_ctx(ctx)
    return [Z3_get_probe_name(ctx.ref(), i) for i in range(Z3_get_num_probes(ctx.ref()))]
 
 

Referenced by describe_probes().

Product()

def z3py.Product

(

*

args

)

Create the product of the Z3 expressions.

>>> a, b, c = Ints('a b c')
>>> Product(a, b, c)
a*b*c
>>> Product([a, b, c])
a*b*c
>>> A = IntVector('a', 5)
>>> Product(A)
a__0*a__1*a__2*a__3*a__4

Definition at line 8907 of file z3py.py.

def Product(*args):
    """Create the product of the Z3 expressions.
 
    >>> a, b, c = Ints('a b c')
    >>> Product(a, b, c)
    a*b*c
    >>> Product([a, b, c])
    a*b*c
    >>> A = IntVector('a', 5)
    >>> Product(A)
    a__0*a__1*a__2*a__3*a__4
    """
    args = _get_args(args)
    if len(args) == 0:
        return 1
    ctx = _ctx_from_ast_arg_list(args)
    if ctx is None:
        return _reduce(lambda a, b: a * b, args, 1)
    args = _coerce_expr_list(args, ctx)
    if is_bv(args[0]):
        return _reduce(lambda a, b: a * b, args, 1)
    else:
        _args, sz = _to_ast_array(args)
        return ArithRef(Z3_mk_mul(ctx.ref(), sz, _args), ctx)
 

PropagateFunction()

def z3py.PropagateFunction	(		name,
		*	sig
	)

Create a function that gets tracked by user propagator.
   Every term headed by this function symbol is tracked.
   If a term is fixed and the fixed callback is registered a
   callback is invoked that the term headed by this function is fixed.

Definition at line 11501 of file z3py.py.

def PropagateFunction(name, *sig):
    """Create a function that gets tracked by user propagator.
       Every term headed by this function symbol is tracked.
       If a term is fixed and the fixed callback is registered a
       callback is invoked that the term headed by this function is fixed.
    """
    sig = _get_args(sig)
    if z3_debug():
        _z3_assert(len(sig) > 0, "At least two arguments expected")
    arity = len(sig) - 1
    rng = sig[arity]
    if z3_debug():
        _z3_assert(is_sort(rng), "Z3 sort expected")
    dom = (Sort * arity)()
    for i in range(arity):
        if z3_debug():
            _z3_assert(is_sort(sig[i]), "Z3 sort expected")
        dom[i] = sig[i].ast
    ctx = rng.ctx
    return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
 
    
 

prove()

def z3py.prove	(		claim,
			show = False,
		**	keywords
	)

Try to prove the given claim.

This is a simple function for creating demonstrations.  It tries to prove
`claim` by showing the negation is unsatisfiable.

>>> p, q = Bools('p q')
>>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
proved

Definition at line 9094 of file z3py.py.

def prove(claim, show=False, **keywords):
    """Try to prove the given claim.
 
    This is a simple function for creating demonstrations.  It tries to prove
    `claim` by showing the negation is unsatisfiable.
 
    >>> p, q = Bools('p q')
    >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
    proved
    """
    if z3_debug():
        _z3_assert(is_bool(claim), "Z3 Boolean expression expected")
    s = Solver()
    s.set(**keywords)
    s.add(Not(claim))
    if show:
        print(s)
    r = s.check()
    if r == unsat:
        print("proved")
    elif r == unknown:
        print("failed to prove")
        print(s.model())
    else:
        print("counterexample")
        print(s.model())
 
 

Q()

def z3py.Q	(		a,
			b,
			ctx = None
	)

Return a Z3 rational a/b.

If `ctx=None`, then the global context is used.

>>> Q(3,5)
3/5
>>> Q(3,5).sort()
Real

Definition at line 3235 of file z3py.py.

def Q(a, b, ctx=None):
    """Return a Z3 rational a/b.
 
    If `ctx=None`, then the global context is used.
 
    >>> Q(3,5)
    3/5
    >>> Q(3,5).sort()
    Real
    """
    return simplify(RatVal(a, b, ctx=ctx))
 
 

Range()

def z3py.Range	(		lo,
			hi,
			ctx = None
	)

Create the range regular expression over two sequences of length 1
>>> range = Range("a","z")
>>> print(simplify(InRe("b", range)))
True
>>> print(simplify(InRe("bb", range)))
False

Definition at line 11281 of file z3py.py.

def Range(lo, hi, ctx=None):
    """Create the range regular expression over two sequences of length 1
    >>> range = Range("a","z")
    >>> print(simplify(InRe("b", range)))
    True
    >>> print(simplify(InRe("bb", range)))
    False
    """
    lo = _coerce_seq(lo, ctx)
    hi = _coerce_seq(hi, ctx)
    return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
 

RatVal()

def z3py.RatVal	(		a,
			b,
			ctx = None
	)

Return a Z3 rational a/b.

If `ctx=None`, then the global context is used.

>>> RatVal(3,5)
3/5
>>> RatVal(3,5).sort()
Real

Definition at line 3219 of file z3py.py.

def RatVal(a, b, ctx=None):
    """Return a Z3 rational a/b.
 
    If `ctx=None`, then the global context is used.
 
    >>> RatVal(3,5)
    3/5
    >>> RatVal(3,5).sort()
    Real
    """
    if z3_debug():
        _z3_assert(_is_int(a) or isinstance(a, str), "First argument cannot be converted into an integer")
        _z3_assert(_is_int(b) or isinstance(b, str), "Second argument cannot be converted into an integer")
    return simplify(RealVal(a, ctx) / RealVal(b, ctx))
 
 

Referenced by Q().

Re()

def z3py.Re	(		s,
			ctx = None
	)

The regular expression that accepts sequence 's'
>>> s1 = Re("ab")
>>> s2 = Re(StringVal("ab"))
>>> s3 = Re(Unit(BoolVal(True)))

Definition at line 11133 of file z3py.py.

def Re(s, ctx=None):
    """The regular expression that accepts sequence 's'
    >>> s1 = Re("ab")
    >>> s2 = Re(StringVal("ab"))
    >>> s3 = Re(Unit(BoolVal(True)))
    """
    s = _coerce_seq(s, ctx)
    return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
 
 
# Regular expressions
 

Real()

def z3py.Real	(		name,
			ctx = None
	)

Return a real constant named `name`. If `ctx=None`, then the global context is used.

>>> x = Real('x')
>>> is_real(x)
True
>>> is_real(x + 1)
True

Definition at line 3301 of file z3py.py.

def Real(name, ctx=None):
    """Return a real constant named `name`. If `ctx=None`, then the global context is used.
 
    >>> x = Real('x')
    >>> is_real(x)
    True
    >>> is_real(x + 1)
    True
    """
    ctx = _get_ctx(ctx)
    return ArithRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), RealSort(ctx).ast), ctx)
 
 

Referenced by Reals(), and RealVector().

Reals()

def z3py.Reals	(		names,
			ctx = None
	)

Return a tuple of real constants.

>>> x, y, z = Reals('x y z')
>>> Sum(x, y, z)
x + y + z
>>> Sum(x, y, z).sort()
Real

Definition at line 3314 of file z3py.py.

def Reals(names, ctx=None):
    """Return a tuple of real constants.
 
    >>> x, y, z = Reals('x y z')
    >>> Sum(x, y, z)
    x + y + z
    >>> Sum(x, y, z).sort()
    Real
    """
    ctx = _get_ctx(ctx)
    if isinstance(names, str):
        names = names.split(" ")
    return [Real(name, ctx) for name in names]
 
 

RealSort()

def z3py.RealSort

(

ctx = None

)

Return the real sort in the given context. If `ctx=None`, then the global context is used.

>>> RealSort()
Real
>>> x = Const('x', RealSort())
>>> is_real(x)
True
>>> is_int(x)
False
>>> x.sort() == RealSort()
True

Definition at line 3155 of file z3py.py.

def RealSort(ctx=None):
    """Return the real sort in the given context. If `ctx=None`, then the global context is used.
 
    >>> RealSort()
    Real
    >>> x = Const('x', RealSort())
    >>> is_real(x)
    True
    >>> is_int(x)
    False
    >>> x.sort() == RealSort()
    True
    """
    ctx = _get_ctx(ctx)
    return ArithSortRef(Z3_mk_real_sort(ctx.ref()), ctx)
 
 

Referenced by FreshReal(), Context.getRealSort(), Context.mkRealSort(), Real(), RealVal(), and RealVar().

RealVal()

def z3py.RealVal	(		val,
			ctx = None
	)

Return a Z3 real value.

`val` may be a Python int, long, float or string representing a number in decimal or rational notation.
If `ctx=None`, then the global context is used.

>>> RealVal(1)
1
>>> RealVal(1).sort()
Real
>>> RealVal("3/5")
3/5
>>> RealVal("1.5")
3/2

Definition at line 3200 of file z3py.py.

def RealVal(val, ctx=None):
    """Return a Z3 real value.
 
    `val` may be a Python int, long, float or string representing a number in decimal or rational notation.
    If `ctx=None`, then the global context is used.
 
    >>> RealVal(1)
    1
    >>> RealVal(1).sort()
    Real
    >>> RealVal("3/5")
    3/5
    >>> RealVal("1.5")
    3/2
    """
    ctx = _get_ctx(ctx)
    return RatNumRef(Z3_mk_numeral(ctx.ref(), str(val), RealSort(ctx).ast), ctx)
 
 

Referenced by Cbrt(), deserialize(), AlgebraicNumRef.index(), RatVal(), and Sqrt().

RealVar()

def z3py.RealVar	(		idx,
			ctx = None
	)

Create a real free variable. Free variables are used to create quantified formulas.
They are also used to create polynomials.

>>> RealVar(0)
Var(0)

Definition at line 1485 of file z3py.py.

def RealVar(idx, ctx=None):
    """
    Create a real free variable. Free variables are used to create quantified formulas.
    They are also used to create polynomials.
 
    >>> RealVar(0)
    Var(0)
    """
    return Var(idx, RealSort(ctx))
 
 

Referenced by RealVarVector().

RealVarVector()

def z3py.RealVarVector	(		n,
			ctx = None
	)

Create a list of Real free variables.
The variables have ids: 0, 1, ..., n-1

>>> x0, x1, x2, x3 = RealVarVector(4)
>>> x2
Var(2)

Definition at line 1496 of file z3py.py.

def RealVarVector(n, ctx=None):
    """
    Create a list of Real free variables.
    The variables have ids: 0, 1, ..., n-1
 
    >>> x0, x1, x2, x3 = RealVarVector(4)
    >>> x2
    Var(2)
    """
    return [RealVar(i, ctx) for i in range(n)]
 

RealVector()

def z3py.RealVector	(		prefix,
			sz,
			ctx = None
	)

Return a list of real constants of size `sz`.

>>> X = RealVector('x', 3)
>>> X
[x__0, x__1, x__2]
>>> Sum(X)
x__0 + x__1 + x__2
>>> Sum(X).sort()
Real

Definition at line 3329 of file z3py.py.

def RealVector(prefix, sz, ctx=None):
    """Return a list of real constants of size `sz`.
 
    >>> X = RealVector('x', 3)
    >>> X
    [x__0, x__1, x__2]
    >>> Sum(X)
    x__0 + x__1 + x__2
    >>> Sum(X).sort()
    Real
    """
    ctx = _get_ctx(ctx)
    return [Real("%s__%s" % (prefix, i), ctx) for i in range(sz)]
 
 

RecAddDefinition()

def z3py.RecAddDefinition	(		f,
			args,
			body
	)

Set the body of a recursive function.
   Recursive definitions can be simplified if they are applied to ground
   arguments.
>>> ctx = Context()
>>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
>>> n = Int('n', ctx)
>>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
>>> simplify(fac(5))
120
>>> s = Solver(ctx=ctx)
>>> s.add(fac(n) < 3)
>>> s.check()
sat
>>> s.model().eval(fac(5))
120

Definition at line 927 of file z3py.py.

def RecAddDefinition(f, args, body):
    """Set the body of a recursive function.
       Recursive definitions can be simplified if they are applied to ground
       arguments.
    >>> ctx = Context()
    >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
    >>> n = Int('n', ctx)
    >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
    >>> simplify(fac(5))
    120
    >>> s = Solver(ctx=ctx)
    >>> s.add(fac(n) < 3)
    >>> s.check()
    sat
    >>> s.model().eval(fac(5))
    120
    """
    if is_app(args):
        args = [args]
    ctx = body.ctx
    args = _get_args(args)
    n = len(args)
    _args = (Ast * n)()
    for i in range(n):
        _args[i] = args[i].ast
    Z3_add_rec_def(ctx.ref(), f.ast, n, _args, body.ast)
 

RecFunction()

def z3py.RecFunction	(		name,
		*	sig
	)

Create a new Z3 recursive with the given sorts.

Definition at line 909 of file z3py.py.

def RecFunction(name, *sig):
    """Create a new Z3 recursive with the given sorts."""
    sig = _get_args(sig)
    if z3_debug():
        _z3_assert(len(sig) > 0, "At least two arguments expected")
    arity = len(sig) - 1
    rng = sig[arity]
    if z3_debug():
        _z3_assert(is_sort(rng), "Z3 sort expected")
    dom = (Sort * arity)()
    for i in range(arity):
        if z3_debug():
            _z3_assert(is_sort(sig[i]), "Z3 sort expected")
        dom[i] = sig[i].ast
    ctx = rng.ctx
    return FuncDeclRef(Z3_mk_rec_func_decl(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
 
 

Repeat()

def z3py.Repeat	(		t,
			max = 4294967295,
			ctx = None
	)

Return a tactic that keeps applying `t` until the goal is not modified anymore
or the maximum number of iterations `max` is reached.

>>> x, y = Ints('x y')
>>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
>>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
>>> r = t(c)
>>> for subgoal in r: print(subgoal)
[x == 0, y == 0, x > y]
[x == 0, y == 1, x > y]
[x == 1, y == 0, x > y]
[x == 1, y == 1, x > y]
>>> t = Then(t, Tactic('propagate-values'))
>>> t(c)
[[x == 1, y == 0]]

Definition at line 8419 of file z3py.py.

def Repeat(t, max=4294967295, ctx=None):
    """Return a tactic that keeps applying `t` until the goal is not modified anymore
    or the maximum number of iterations `max` is reached.
 
    >>> x, y = Ints('x y')
    >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
    >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
    >>> r = t(c)
    >>> for subgoal in r: print(subgoal)
    [x == 0, y == 0, x > y]
    [x == 0, y == 1, x > y]
    [x == 1, y == 0, x > y]
    [x == 1, y == 1, x > y]
    >>> t = Then(t, Tactic('propagate-values'))
    >>> t(c)
    [[x == 1, y == 0]]
    """
    t = _to_tactic(t, ctx)
    return Tactic(Z3_tactic_repeat(t.ctx.ref(), t.tactic, max), t.ctx)
 
 

RepeatBitVec()

def z3py.RepeatBitVec	(		n,
			a
	)

Return an expression representing `n` copies of `a`.

>>> x = BitVec('x', 8)
>>> n = RepeatBitVec(4, x)
>>> n
RepeatBitVec(4, x)
>>> n.size()
32
>>> v0 = BitVecVal(10, 4)
>>> print("%.x" % v0.as_long())
a
>>> v = simplify(RepeatBitVec(4, v0))
>>> v.size()
16
>>> print("%.x" % v.as_long())
aaaa

Definition at line 4421 of file z3py.py.

def RepeatBitVec(n, a):
    """Return an expression representing `n` copies of `a`.
 
    >>> x = BitVec('x', 8)
    >>> n = RepeatBitVec(4, x)
    >>> n
    RepeatBitVec(4, x)
    >>> n.size()
    32
    >>> v0 = BitVecVal(10, 4)
    >>> print("%.x" % v0.as_long())
    a
    >>> v = simplify(RepeatBitVec(4, v0))
    >>> v.size()
    16
    >>> print("%.x" % v.as_long())
    aaaa
    """
    if z3_debug():
        _z3_assert(_is_int(n), "First argument must be an integer")
        _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
    return BitVecRef(Z3_mk_repeat(a.ctx_ref(), n, a.as_ast()), a.ctx)
 
 

Replace()

def z3py.Replace	(		s,
			src,
			dst
	)

Replace the first occurrence of 'src' by 'dst' in 's'
>>> r = Replace("aaa", "a", "b")
>>> simplify(r)
"baa"

Definition at line 11044 of file z3py.py.

def Replace(s, src, dst):
    """Replace the first occurrence of 'src' by 'dst' in 's'
    >>> r = Replace("aaa", "a", "b")
    >>> simplify(r)
    "baa"
    """
    ctx = _get_ctx2(dst, s)
    if ctx is None and is_expr(src):
        ctx = src.ctx
    src = _coerce_seq(src, ctx)
    dst = _coerce_seq(dst, ctx)
    s = _coerce_seq(s, ctx)
    return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
 
 

reset_params()

def z3py.reset_params

(

)

Reset all global (or module) parameters.

Definition at line 295 of file z3py.py.

def reset_params():
    """Reset all global (or module) parameters.
    """
    Z3_global_param_reset_all()
 
 

ReSort()

def z3py.ReSort

(

s

)

Definition at line 11152 of file z3py.py.

def ReSort(s):
    if is_ast(s):
        return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
    if s is None or isinstance(s, Context):
        ctx = _get_ctx(s)
        return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
    raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
 
 

Referenced by Context.MkReSort().

RNA()

def z3py.RNA

(

ctx = None

)

Definition at line 9681 of file z3py.py.

def RNA(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
 
 

Referenced by get_default_rounding_mode().

RNE()

def z3py.RNE

(

ctx = None

)

Definition at line 9671 of file z3py.py.

def RNE(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
 
 

Referenced by get_default_rounding_mode().

RotateLeft()

def z3py.RotateLeft	(		a,
			b
	)

Return an expression representing `a` rotated to the left `b` times.

>>> a, b = BitVecs('a b', 16)
>>> RotateLeft(a, b)
RotateLeft(a, b)
>>> simplify(RotateLeft(a, 0))
a
>>> simplify(RotateLeft(a, 16))
a

Definition at line 4331 of file z3py.py.

def RotateLeft(a, b):
    """Return an expression representing `a` rotated to the left `b` times.
 
    >>> a, b = BitVecs('a b', 16)
    >>> RotateLeft(a, b)
    RotateLeft(a, b)
    >>> simplify(RotateLeft(a, 0))
    a
    >>> simplify(RotateLeft(a, 16))
    a
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BitVecRef(Z3_mk_ext_rotate_left(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

RotateRight()

def z3py.RotateRight	(		a,
			b
	)

Return an expression representing `a` rotated to the right `b` times.

>>> a, b = BitVecs('a b', 16)
>>> RotateRight(a, b)
RotateRight(a, b)
>>> simplify(RotateRight(a, 0))
a
>>> simplify(RotateRight(a, 16))
a

Definition at line 4347 of file z3py.py.

def RotateRight(a, b):
    """Return an expression representing `a` rotated to the right `b` times.
 
    >>> a, b = BitVecs('a b', 16)
    >>> RotateRight(a, b)
    RotateRight(a, b)
    >>> simplify(RotateRight(a, 0))
    a
    >>> simplify(RotateRight(a, 16))
    a
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BitVecRef(Z3_mk_ext_rotate_right(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

RoundNearestTiesToAway()

def z3py.RoundNearestTiesToAway

(

ctx = None

)

Definition at line 9676 of file z3py.py.

def RoundNearestTiesToAway(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
 
 

RoundNearestTiesToEven()

def z3py.RoundNearestTiesToEven

(

ctx = None

)

Definition at line 9666 of file z3py.py.

def RoundNearestTiesToEven(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
 
 

RoundTowardNegative()

def z3py.RoundTowardNegative

(

ctx = None

)

Definition at line 9696 of file z3py.py.

def RoundTowardNegative(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
 
 

RoundTowardPositive()

def z3py.RoundTowardPositive

(

ctx = None

)

Definition at line 9686 of file z3py.py.

def RoundTowardPositive(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
 
 

RoundTowardZero()

def z3py.RoundTowardZero

(

ctx = None

)

Definition at line 9706 of file z3py.py.

def RoundTowardZero(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
 
 

RTN()

def z3py.RTN

(

ctx = None

)

Definition at line 9701 of file z3py.py.

def RTN(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
 
 

Referenced by get_default_rounding_mode().

RTP()

def z3py.RTP

(

ctx = None

)

Definition at line 9691 of file z3py.py.

def RTP(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
 
 

Referenced by get_default_rounding_mode().

RTZ()

def z3py.RTZ

(

ctx = None

)

Definition at line 9711 of file z3py.py.

def RTZ(ctx=None):
    ctx = _get_ctx(ctx)
    return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
 
 

Referenced by get_default_rounding_mode().

Select()

def z3py.Select	(		a,
		*	args
	)

Return a Z3 select array expression.

>>> a = Array('a', IntSort(), IntSort())
>>> i = Int('i')
>>> Select(a, i)
a[i]
>>> eq(Select(a, i), a[i])
True

Definition at line 4807 of file z3py.py.

def Select(a, *args):
    """Return a Z3 select array expression.
 
    >>> a = Array('a', IntSort(), IntSort())
    >>> i = Int('i')
    >>> Select(a, i)
    a[i]
    >>> eq(Select(a, i), a[i])
    True
    """
    args = _get_args(args)
    if z3_debug():
        _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
    return a[args]
 
 

SeqSort()

def z3py.SeqSort

(

s

)

Create a sequence sort over elements provided in the argument
>>> s = SeqSort(IntSort())
>>> s == Unit(IntVal(1)).sort()
True

Definition at line 10765 of file z3py.py.

def SeqSort(s):
    """Create a sequence sort over elements provided in the argument
    >>> s = SeqSort(IntSort())
    >>> s == Unit(IntVal(1)).sort()
    True
    """
    return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
 
 

Referenced by Context.MkSeqSort().

set_default_fp_sort()

def z3py.set_default_fp_sort	(		ebits,
			sbits,
			ctx = None
	)

Definition at line 9327 of file z3py.py.

def set_default_fp_sort(ebits, sbits, ctx=None):
    global _dflt_fpsort_ebits
    global _dflt_fpsort_sbits
    _dflt_fpsort_ebits = ebits
    _dflt_fpsort_sbits = sbits
 
 

set_default_rounding_mode()

def z3py.set_default_rounding_mode	(		rm,
			ctx = None
	)

Definition at line 9314 of file z3py.py.

def set_default_rounding_mode(rm, ctx=None):
    global _dflt_rounding_mode
    if is_fprm_value(rm):
        _dflt_rounding_mode = rm.decl().kind()
    else:
        _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
        _dflt_rounding_mode = rm
 
 

set_option()

def z3py.set_option	(	*	args,
		**	kws
	)

Alias for 'set_param' for backward compatibility.

Definition at line 301 of file z3py.py.

def set_option(*args, **kws):
    """Alias for 'set_param' for backward compatibility.
    """
    return set_param(*args, **kws)
 
 

set_param()

def z3py.set_param	(	*	args,
		**	kws
	)

Set Z3 global (or module) parameters.

>>> set_param(precision=10)

Definition at line 271 of file z3py.py.

def set_param(*args, **kws):
    """Set Z3 global (or module) parameters.
 
    >>> set_param(precision=10)
    """
    if z3_debug():
        _z3_assert(len(args) % 2 == 0, "Argument list must have an even number of elements.")
    new_kws = {}
    for k in kws:
        v = kws[k]
        if not set_pp_option(k, v):
            new_kws[k] = v
    for key in new_kws:
        value = new_kws[key]
        Z3_global_param_set(str(key).upper(), _to_param_value(value))
    prev = None
    for a in args:
        if prev is None:
            prev = a
        else:
            Z3_global_param_set(str(prev), _to_param_value(a))
            prev = None
 
 

Referenced by set_option().

SetAdd()

def z3py.SetAdd	(		s,
			e
	)

 Add element e to set s
>>> a = Const('a', SetSort(IntSort()))
>>> SetAdd(a, 1)
Store(a, 1, True)

Definition at line 4966 of file z3py.py.

def SetAdd(s, e):
    """ Add element e to set s
    >>> a = Const('a', SetSort(IntSort()))
    >>> SetAdd(a, 1)
    Store(a, 1, True)
    """
    ctx = _ctx_from_ast_arg_list([s, e])
    e = _py2expr(e, ctx)
    return ArrayRef(Z3_mk_set_add(ctx.ref(), s.as_ast(), e.as_ast()), ctx)
 
 

SetComplement()

def z3py.SetComplement

(

s

)

 The complement of set s
>>> a = Const('a', SetSort(IntSort()))
>>> SetComplement(a)
complement(a)

Definition at line 4988 of file z3py.py.

def SetComplement(s):
    """ The complement of set s
    >>> a = Const('a', SetSort(IntSort()))
    >>> SetComplement(a)
    complement(a)
    """
    ctx = s.ctx
    return ArrayRef(Z3_mk_set_complement(ctx.ref(), s.as_ast()), ctx)
 
 

SetDel()

def z3py.SetDel	(		s,
			e
	)

 Remove element e to set s
>>> a = Const('a', SetSort(IntSort()))
>>> SetDel(a, 1)
Store(a, 1, False)

Definition at line 4977 of file z3py.py.

def SetDel(s, e):
    """ Remove element e to set s
    >>> a = Const('a', SetSort(IntSort()))
    >>> SetDel(a, 1)
    Store(a, 1, False)
    """
    ctx = _ctx_from_ast_arg_list([s, e])
    e = _py2expr(e, ctx)
    return ArrayRef(Z3_mk_set_del(ctx.ref(), s.as_ast(), e.as_ast()), ctx)
 
 

SetDifference()

def z3py.SetDifference	(		a,
			b
	)

 The set difference of a and b
>>> a = Const('a', SetSort(IntSort()))
>>> b = Const('b', SetSort(IntSort()))
>>> SetDifference(a, b)
setminus(a, b)

Definition at line 4998 of file z3py.py.

def SetDifference(a, b):
    """ The set difference of a and b
    >>> a = Const('a', SetSort(IntSort()))
    >>> b = Const('b', SetSort(IntSort()))
    >>> SetDifference(a, b)
    setminus(a, b)
    """
    ctx = _ctx_from_ast_arg_list([a, b])
    return ArrayRef(Z3_mk_set_difference(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
 
 

SetHasSize()

def z3py.SetHasSize	(		a,
			k
	)

Definition at line 4880 of file z3py.py.

def SetHasSize(a, k):
    ctx = a.ctx
    k = _py2expr(k, ctx)
    return _to_expr_ref(Z3_mk_set_has_size(ctx.ref(), a.as_ast(), k.as_ast()), ctx)
 
 

SetIntersect()

def z3py.SetIntersect

(

*

args

)

 Take the union of sets
>>> a = Const('a', SetSort(IntSort()))
>>> b = Const('b', SetSort(IntSort()))
>>> SetIntersect(a, b)
intersection(a, b)

Definition at line 4953 of file z3py.py.

def SetIntersect(*args):
    """ Take the union of sets
    >>> a = Const('a', SetSort(IntSort()))
    >>> b = Const('b', SetSort(IntSort()))
    >>> SetIntersect(a, b)
    intersection(a, b)
    """
    args = _get_args(args)
    ctx = _ctx_from_ast_arg_list(args)
    _args, sz = _to_ast_array(args)
    return ArrayRef(Z3_mk_set_intersect(ctx.ref(), sz, _args), ctx)
 
 

SetSort()

def z3py.SetSort

(

s

)

Sets.

 Create a set sort over element sort s

Definition at line 4917 of file z3py.py.

def SetSort(s):
    """ Create a set sort over element sort s"""
    return ArraySort(s, BoolSort())
 
 

Referenced by Context.MkSetSort().

SetUnion()

def z3py.SetUnion

(

*

args

)

 Take the union of sets
>>> a = Const('a', SetSort(IntSort()))
>>> b = Const('b', SetSort(IntSort()))
>>> SetUnion(a, b)
union(a, b)

Definition at line 4940 of file z3py.py.

def SetUnion(*args):
    """ Take the union of sets
    >>> a = Const('a', SetSort(IntSort()))
    >>> b = Const('b', SetSort(IntSort()))
    >>> SetUnion(a, b)
    union(a, b)
    """
    args = _get_args(args)
    ctx = _ctx_from_ast_arg_list(args)
    _args, sz = _to_ast_array(args)
    return ArrayRef(Z3_mk_set_union(ctx.ref(), sz, _args), ctx)
 
 

SignExt()

def z3py.SignExt	(		n,
			a
	)

Return a bit-vector expression with `n` extra sign-bits.

>>> x = BitVec('x', 16)
>>> n = SignExt(8, x)
>>> n.size()
24
>>> n
SignExt(8, x)
>>> n.sort()
BitVec(24)
>>> v0 = BitVecVal(2, 2)
>>> v0
2
>>> v0.size()
2
>>> v  = simplify(SignExt(6, v0))
>>> v
254
>>> v.size()
8
>>> print("%.x" % v.as_long())
fe

Definition at line 4363 of file z3py.py.

def SignExt(n, a):
    """Return a bit-vector expression with `n` extra sign-bits.
 
    >>> x = BitVec('x', 16)
    >>> n = SignExt(8, x)
    >>> n.size()
    24
    >>> n
    SignExt(8, x)
    >>> n.sort()
    BitVec(24)
    >>> v0 = BitVecVal(2, 2)
    >>> v0
    2
    >>> v0.size()
    2
    >>> v  = simplify(SignExt(6, v0))
    >>> v
    254
    >>> v.size()
    8
    >>> print("%.x" % v.as_long())
    fe
    """
    if z3_debug():
        _z3_assert(_is_int(n), "First argument must be an integer")
        _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
    return BitVecRef(Z3_mk_sign_ext(a.ctx_ref(), n, a.as_ast()), a.ctx)
 
 

SimpleSolver()

def z3py.SimpleSolver	(		ctx = None,
			logFile = None
	)

Return a simple general purpose solver with limited amount of preprocessing.

>>> s = SimpleSolver()
>>> x = Int('x')
>>> s.add(x > 0)
>>> s.check()
sat

Definition at line 7419 of file z3py.py.

def SimpleSolver(ctx=None, logFile=None):
    """Return a simple general purpose solver with limited amount of preprocessing.
 
    >>> s = SimpleSolver()
    >>> x = Int('x')
    >>> s.add(x > 0)
    >>> s.check()
    sat
    """
    ctx = _get_ctx(ctx)
    return Solver(Z3_mk_simple_solver(ctx.ref()), ctx, logFile)
 

simplify()

def z3py.simplify	(		a,
		*	arguments,
		**	keywords
	)

Utils.

Simplify the expression `a` using the given options.

This function has many options. Use `help_simplify` to obtain the complete list.

>>> x = Int('x')
>>> y = Int('y')
>>> simplify(x + 1 + y + x + 1)
2 + 2*x + y
>>> simplify((x + 1)*(y + 1), som=True)
1 + x + y + x*y
>>> simplify(Distinct(x, y, 1), blast_distinct=True)
And(Not(x == y), Not(x == 1), Not(y == 1))
>>> simplify(And(x == 0, y == 1), elim_and=True)
Not(Or(Not(x == 0), Not(y == 1)))

Definition at line 8771 of file z3py.py.

def simplify(a, *arguments, **keywords):
    """Simplify the expression `a` using the given options.
 
    This function has many options. Use `help_simplify` to obtain the complete list.
 
    >>> x = Int('x')
    >>> y = Int('y')
    >>> simplify(x + 1 + y + x + 1)
    2 + 2*x + y
    >>> simplify((x + 1)*(y + 1), som=True)
    1 + x + y + x*y
    >>> simplify(Distinct(x, y, 1), blast_distinct=True)
    And(Not(x == y), Not(x == 1), Not(y == 1))
    >>> simplify(And(x == 0, y == 1), elim_and=True)
    Not(Or(Not(x == 0), Not(y == 1)))
    """
    if z3_debug():
        _z3_assert(is_expr(a), "Z3 expression expected")
    if len(arguments) > 0 or len(keywords) > 0:
        p = args2params(arguments, keywords, a.ctx)
        return _to_expr_ref(Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
    else:
        return _to_expr_ref(Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
 
 

Referenced by Q(), RatVal(), and Expr< R extends Sort >.simplify().

simplify_param_descrs()

def z3py.simplify_param_descrs

(

)

Return the set of parameter descriptions for Z3 `simplify` procedure.

Definition at line 8801 of file z3py.py.

def simplify_param_descrs():
    """Return the set of parameter descriptions for Z3 `simplify` procedure."""
    return ParamDescrsRef(Z3_simplify_get_param_descrs(main_ctx().ref()), main_ctx())
 
 

solve()

def z3py.solve	(	*	args,
		**	keywords
	)

Solve the constraints `*args`.

This is a simple function for creating demonstrations. It creates a solver,
configure it using the options in `keywords`, adds the constraints
in `args`, and invokes check.

>>> a = Int('a')
>>> solve(a > 0, a < 2)
[a = 1]

Definition at line 9033 of file z3py.py.

def solve(*args, **keywords):
    """Solve the constraints `*args`.
 
    This is a simple function for creating demonstrations. It creates a solver,
    configure it using the options in `keywords`, adds the constraints
    in `args`, and invokes check.
 
    >>> a = Int('a')
    >>> solve(a > 0, a < 2)
    [a = 1]
    """
    show = keywords.pop("show", False)
    s = Solver()
    s.set(**keywords)
    s.add(*args)
    if show:
        print(s)
    r = s.check()
    if r == unsat:
        print("no solution")
    elif r == unknown:
        print("failed to solve")
        try:
            print(s.model())
        except Z3Exception:
            return
    else:
        print(s.model())
 
 

solve_using()

def z3py.solve_using	(		s,
		*	args,
		**	keywords
	)

Solve the constraints `*args` using solver `s`.

This is a simple function for creating demonstrations. It is similar to `solve`,
but it uses the given solver `s`.
It configures solver `s` using the options in `keywords`, adds the constraints
in `args`, and invokes check.

Definition at line 9063 of file z3py.py.

def solve_using(s, *args, **keywords):
    """Solve the constraints `*args` using solver `s`.
 
    This is a simple function for creating demonstrations. It is similar to `solve`,
    but it uses the given solver `s`.
    It configures solver `s` using the options in `keywords`, adds the constraints
    in `args`, and invokes check.
    """
    show = keywords.pop("show", False)
    if z3_debug():
        _z3_assert(isinstance(s, Solver), "Solver object expected")
    s.set(**keywords)
    s.add(*args)
    if show:
        print("Problem:")
        print(s)
    r = s.check()
    if r == unsat:
        print("no solution")
    elif r == unknown:
        print("failed to solve")
        try:
            print(s.model())
        except Z3Exception:
            return
    else:
        if show:
            print("Solution:")
        print(s.model())
 
 

SolverFor()

def z3py.SolverFor	(		logic,
			ctx = None,
			logFile = None
	)

Create a solver customized for the given logic.

The parameter `logic` is a string. It should be contains
the name of a SMT-LIB logic.
See http://www.smtlib.org/ for the name of all available logics.

>>> s = SolverFor("QF_LIA")
>>> x = Int('x')
>>> s.add(x > 0)
>>> s.add(x < 2)
>>> s.check()
sat
>>> s.model()
[x = 1]

Definition at line 7398 of file z3py.py.

def SolverFor(logic, ctx=None, logFile=None):
    """Create a solver customized for the given logic.
 
    The parameter `logic` is a string. It should be contains
    the name of a SMT-LIB logic.
    See http://www.smtlib.org/ for the name of all available logics.
 
    >>> s = SolverFor("QF_LIA")
    >>> x = Int('x')
    >>> s.add(x > 0)
    >>> s.add(x < 2)
    >>> s.check()
    sat
    >>> s.model()
    [x = 1]
    """
    ctx = _get_ctx(ctx)
    logic = to_symbol(logic)
    return Solver(Z3_mk_solver_for_logic(ctx.ref(), logic), ctx, logFile)
 
 

Sqrt()

def z3py.Sqrt	(		a,
			ctx = None
	)

 Return a Z3 expression which represents the square root of a.

>>> x = Real('x')
>>> Sqrt(x)
x**(1/2)

Definition at line 3411 of file z3py.py.

def Sqrt(a, ctx=None):
    """ Return a Z3 expression which represents the square root of a.
 
    >>> x = Real('x')
    >>> Sqrt(x)
    x**(1/2)
    """
    if not is_expr(a):
        ctx = _get_ctx(ctx)
        a = RealVal(a, ctx)
    return a ** "1/2"
 
 

SRem()

def z3py.SRem	(		a,
			b
	)

Create the Z3 expression signed remainder.

Use the operator % for signed modulus, and URem() for unsigned remainder.

>>> x = BitVec('x', 32)
>>> y = BitVec('y', 32)
>>> SRem(x, y)
SRem(x, y)
>>> SRem(x, y).sort()
BitVec(32)
>>> (x % y).sexpr()
'(bvsmod x y)'
>>> SRem(x, y).sexpr()
'(bvsrem x y)'

Definition at line 4278 of file z3py.py.

def SRem(a, b):
    """Create the Z3 expression signed remainder.
 
    Use the operator % for signed modulus, and URem() for unsigned remainder.
 
    >>> x = BitVec('x', 32)
    >>> y = BitVec('y', 32)
    >>> SRem(x, y)
    SRem(x, y)
    >>> SRem(x, y).sort()
    BitVec(32)
    >>> (x % y).sexpr()
    '(bvsmod x y)'
    >>> SRem(x, y).sexpr()
    '(bvsrem x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BitVecRef(Z3_mk_bvsrem(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

Star()

def z3py.Star

(

re

)

Create the regular expression accepting zero or more repetitions of argument.
>>> re = Star(Re("a"))
>>> print(simplify(InRe("aa", re)))
True
>>> print(simplify(InRe("ab", re)))
False
>>> print(simplify(InRe("", re)))
True

Definition at line 11255 of file z3py.py.

def Star(re):
    """Create the regular expression accepting zero or more repetitions of argument.
    >>> re = Star(Re("a"))
    >>> print(simplify(InRe("aa", re)))
    True
    >>> print(simplify(InRe("ab", re)))
    False
    >>> print(simplify(InRe("", re)))
    True
    """
    return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
 
 

Store()

def z3py.Store	(		a,
		*	args
	)

Return a Z3 store array expression.

>>> a    = Array('a', IntSort(), IntSort())
>>> i, v = Ints('i v')
>>> s    = Store(a, i, v)
>>> s.sort()
Array(Int, Int)
>>> prove(s[i] == v)
proved
>>> j    = Int('j')
>>> prove(Implies(i != j, s[j] == a[j]))
proved

Definition at line 4790 of file z3py.py.

def Store(a, *args):
    """Return a Z3 store array expression.
 
    >>> a    = Array('a', IntSort(), IntSort())
    >>> i, v = Ints('i v')
    >>> s    = Store(a, i, v)
    >>> s.sort()
    Array(Int, Int)
    >>> prove(s[i] == v)
    proved
    >>> j    = Int('j')
    >>> prove(Implies(i != j, s[j] == a[j]))
    proved
    """
    return Update(a, args)
 
 

Referenced by ModelRef.get_interp().

StrFromCode()

def z3py.StrFromCode

(

c

)

Convert code to a string

Definition at line 11127 of file z3py.py.

def StrFromCode(c):
    """Convert code to a string"""
    if not is_expr(c):
        c = _py2expr(c)
    return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
    

String()

def z3py.String	(		name,
			ctx = None
	)

Return a string constant named `name`. If `ctx=None`, then the global context is used.

>>> x = String('x')

Definition at line 10928 of file z3py.py.

def String(name, ctx=None):
    """Return a string constant named `name`. If `ctx=None`, then the global context is used.
 
    >>> x = String('x')
    """
    ctx = _get_ctx(ctx)
    return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
 
 

Referenced by Context.Context(), Statistics.getEntries(), Statistics.getKeys(), Context.getProbeNames(), Context.getTacticNames(), Context.mkString(), Strings(), and FuncInterp< R extends Sort >.toString().

Strings()

def z3py.Strings	(		names,
			ctx = None
	)

Return a tuple of String constants. 

Definition at line 10937 of file z3py.py.

def Strings(names, ctx=None):
    """Return a tuple of String constants. """
    ctx = _get_ctx(ctx)
    if isinstance(names, str):
        names = names.split(" ")
    return [String(name, ctx) for name in names]
 
 

StringSort()

def z3py.StringSort

(

ctx = None

)

Create a string sort
>>> s = StringSort()
>>> print(s)
String

Definition at line 10746 of file z3py.py.

def StringSort(ctx=None):
    """Create a string sort
    >>> s = StringSort()
    >>> print(s)
    String
    """
    ctx = _get_ctx(ctx)
    return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
 

Referenced by String().

StringVal()

def z3py.StringVal	(		s,
			ctx = None
	)

create a string expression

Definition at line 10921 of file z3py.py.

def StringVal(s, ctx=None):
    """create a string expression"""
    s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
    ctx = _get_ctx(ctx)
    return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
 
 

Referenced by CharIsDigit(), deserialize(), Extract(), and AlgebraicNumRef.index().

StrToCode()

def z3py.StrToCode

(

s

)

Convert a unit length string to integer code

Definition at line 11121 of file z3py.py.

def StrToCode(s):
    """Convert a unit length string to integer code"""
    if not is_expr(s):
        s = _py2expr(s)
    return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
 

StrToInt()

def z3py.StrToInt

(

s

)

Convert string expression to integer
>>> a = StrToInt("1")
>>> simplify(1 == a)
True
>>> b = StrToInt("2")
>>> simplify(1 == b)
False
>>> c = StrToInt(IntToStr(2))
>>> simplify(1 == c)
False

Definition at line 11098 of file z3py.py.

def StrToInt(s):
    """Convert string expression to integer
    >>> a = StrToInt("1")
    >>> simplify(1 == a)
    True
    >>> b = StrToInt("2")
    >>> simplify(1 == b)
    False
    >>> c = StrToInt(IntToStr(2))
    >>> simplify(1 == c)
    False
    """
    s = _coerce_seq(s)
    return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
 
 

SubSeq()

def z3py.SubSeq	(		s,
			offset,
			length
	)

Extract substring or subsequence starting at offset

Definition at line 10950 of file z3py.py.

def SubSeq(s, offset, length):
    """Extract substring or subsequence starting at offset"""
    return Extract(s, offset, length)
 
 

substitute()

def z3py.substitute	(		t,
		*	m
	)

Apply substitution m on t, m is a list of pairs of the form (from, to).
Every occurrence in t of from is replaced with to.

>>> x = Int('x')
>>> y = Int('y')
>>> substitute(x + 1, (x, y + 1))
y + 1 + 1
>>> f = Function('f', IntSort(), IntSort())
>>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
1 + 1

Definition at line 8806 of file z3py.py.

def substitute(t, *m):
    """Apply substitution m on t, m is a list of pairs of the form (from, to).
    Every occurrence in t of from is replaced with to.
 
    >>> x = Int('x')
    >>> y = Int('y')
    >>> substitute(x + 1, (x, y + 1))
    y + 1 + 1
    >>> f = Function('f', IntSort(), IntSort())
    >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
    1 + 1
    """
    if isinstance(m, tuple):
        m1 = _get_args(m)
        if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
            m = m1
    if z3_debug():
        _z3_assert(is_expr(t), "Z3 expression expected")
        _z3_assert(
            all([isinstance(p, tuple) and is_expr(p[0]) and is_expr(p[1]) for p in m]),
            "Z3 invalid substitution, expression pairs expected.")
        _z3_assert(
            all([p[0].sort().eq(p[1].sort()) for p in m]),
            'Z3 invalid substitution, mismatching "from" and "to" sorts.')
    num = len(m)
    _from = (Ast * num)()
    _to = (Ast * num)()
    for i in range(num):
        _from[i] = m[i][0].as_ast()
        _to[i] = m[i][1].as_ast()
    return _to_expr_ref(Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
 
 

Referenced by Expr< R extends Sort >.substitute().

substitute_funs()

def z3py.substitute_funs	(		t,
		*	m
	)

Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
Every occurrence in to of the function from is replaced with the expression to.
The expression to can have free variables, that refer to the arguments of from.
For examples, see 

Definition at line 8859 of file z3py.py.

def substitute_funs(t, *m):
    """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
    Every occurrence in to of the function from is replaced with the expression to.
    The expression to can have free variables, that refer to the arguments of from.
    For examples, see 
    """
    if isinstance(m, tuple):
        m1 = _get_args(m)
        if isinstance(m1, list) and all(isinstance(p, tuple) for p in m1):
            m = m1
    if z3_debug():
        _z3_assert(is_expr(t), "Z3 expression expected")
        _z3_assert(all([isinstance(p, tuple) and is_func_decl(p[0]) and is_expr(p[1]) for p in m]), "Z3 invalid substitution, funcion pairs expected.")
    num = len(m)
    _from = (FuncDecl * num)()
    _to = (Ast * num)()
    for i in range(num):
        _from[i] = m[i][0].as_func_decl()
        _to[i] = m[i][1].as_ast()
    return _to_expr_ref(Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
 
 

substitute_vars()

def z3py.substitute_vars	(		t,
		*	m
	)

Substitute the free variables in t with the expression in m.

>>> v0 = Var(0, IntSort())
>>> v1 = Var(1, IntSort())
>>> x  = Int('x')
>>> f  = Function('f', IntSort(), IntSort(), IntSort())
>>> # replace v0 with x+1 and v1 with x
>>> substitute_vars(f(v0, v1), x + 1, x)
f(x + 1, x)

Definition at line 8839 of file z3py.py.

def substitute_vars(t, *m):
    """Substitute the free variables in t with the expression in m.
 
    >>> v0 = Var(0, IntSort())
    >>> v1 = Var(1, IntSort())
    >>> x  = Int('x')
    >>> f  = Function('f', IntSort(), IntSort(), IntSort())
    >>> # replace v0 with x+1 and v1 with x
    >>> substitute_vars(f(v0, v1), x + 1, x)
    f(x + 1, x)
    """
    if z3_debug():
        _z3_assert(is_expr(t), "Z3 expression expected")
        _z3_assert(all([is_expr(n) for n in m]), "Z3 invalid substitution, list of expressions expected.")
    num = len(m)
    _to = (Ast * num)()
    for i in range(num):
        _to[i] = m[i].as_ast()
    return _to_expr_ref(Z3_substitute_vars(t.ctx.ref(), t.as_ast(), num, _to), t.ctx)
 

SubString()

def z3py.SubString	(		s,
			offset,
			length
	)

Extract substring or subsequence starting at offset

Definition at line 10945 of file z3py.py.

def SubString(s, offset, length):
    """Extract substring or subsequence starting at offset"""
    return Extract(s, offset, length)
 
 

SuffixOf()

def z3py.SuffixOf	(		a,
			b
	)

Check if 'a' is a suffix of 'b'
>>> s1 = SuffixOf("ab", "abc")
>>> simplify(s1)
False
>>> s2 = SuffixOf("bc", "abc")
>>> simplify(s2)
True

Definition at line 11010 of file z3py.py.

def SuffixOf(a, b):
    """Check if 'a' is a suffix of 'b'
    >>> s1 = SuffixOf("ab", "abc")
    >>> simplify(s1)
    False
    >>> s2 = SuffixOf("bc", "abc")
    >>> simplify(s2)
    True
    """
    ctx = _get_ctx2(a, b)
    a = _coerce_seq(a, ctx)
    b = _coerce_seq(b, ctx)
    return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

Sum()

def z3py.Sum

(

*

args

)

Create the sum of the Z3 expressions.

>>> a, b, c = Ints('a b c')
>>> Sum(a, b, c)
a + b + c
>>> Sum([a, b, c])
a + b + c
>>> A = IntVector('a', 5)
>>> Sum(A)
a__0 + a__1 + a__2 + a__3 + a__4

Definition at line 8881 of file z3py.py.

def Sum(*args):
    """Create the sum of the Z3 expressions.
 
    >>> a, b, c = Ints('a b c')
    >>> Sum(a, b, c)
    a + b + c
    >>> Sum([a, b, c])
    a + b + c
    >>> A = IntVector('a', 5)
    >>> Sum(A)
    a__0 + a__1 + a__2 + a__3 + a__4
    """
    args = _get_args(args)
    if len(args) == 0:
        return 0
    ctx = _ctx_from_ast_arg_list(args)
    if ctx is None:
        return _reduce(lambda a, b: a + b, args, 0)
    args = _coerce_expr_list(args, ctx)
    if is_bv(args[0]):
        return _reduce(lambda a, b: a + b, args, 0)
    else:
        _args, sz = _to_ast_array(args)
        return ArithRef(Z3_mk_add(ctx.ref(), sz, _args), ctx)
 
 

tactic_description()

def z3py.tactic_description	(		name,
			ctx = None
	)

Return a short description for the tactic named `name`.

>>> d = tactic_description('simplify')

Definition at line 8460 of file z3py.py.

def tactic_description(name, ctx=None):
    """Return a short description for the tactic named `name`.
 
    >>> d = tactic_description('simplify')
    """
    ctx = _get_ctx(ctx)
    return Z3_tactic_get_descr(ctx.ref(), name)
 
 

Referenced by describe_tactics().

tactics()

def z3py.tactics

(

ctx = None

)

Return a list of all available tactics in Z3.

>>> l = tactics()
>>> l.count('simplify') == 1
True

Definition at line 8449 of file z3py.py.

def tactics(ctx=None):
    """Return a list of all available tactics in Z3.
 
    >>> l = tactics()
    >>> l.count('simplify') == 1
    True
    """
    ctx = _get_ctx(ctx)
    return [Z3_get_tactic_name(ctx.ref(), i) for i in range(Z3_get_num_tactics(ctx.ref()))]
 
 

Referenced by describe_tactics().

Then()

def z3py.Then	(	*	ts,
		**	ks
	)

Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).

>>> x, y = Ints('x y')
>>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
>>> t(And(x == 0, y > x + 1))
[[Not(y <= 1)]]
>>> t(And(x == 0, y > x + 1)).as_expr()
Not(y <= 1)

Definition at line 8317 of file z3py.py.

def Then(*ts, **ks):
    """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
 
    >>> x, y = Ints('x y')
    >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
    >>> t(And(x == 0, y > x + 1))
    [[Not(y <= 1)]]
    >>> t(And(x == 0, y > x + 1)).as_expr()
    Not(y <= 1)
    """
    return AndThen(*ts, **ks)
 
 

to_Ast()

def z3py.to_Ast

(

ptr

)

Definition at line 11329 of file z3py.py.

def to_Ast(ptr,):
    ast = Ast(ptr)
    super(ctypes.c_void_p, ast).__init__(ptr)
    return ast
 

Referenced by on_clause_eh(), user_prop_created(), user_prop_decide(), user_prop_diseq(), user_prop_eq(), and user_prop_fixed().

to_AstVectorObj()

def z3py.to_AstVectorObj

(

ptr

)

Definition at line 11339 of file z3py.py.

def to_AstVectorObj(ptr,):
    v = AstVectorObj(ptr)
    super(ctypes.c_void_p, v).__init__(ptr)    
    return v
 
# NB. my-hacky-class only works for a single instance of OnClause
# it should be replaced with a proper correlation between OnClause
# and object references that can be passed over the FFI.
# for UserPropagator we use a global dictionary, which isn't great code.
 

Referenced by on_clause_eh().

to_ContextObj()

def z3py.to_ContextObj

(

ptr

)

Definition at line 11334 of file z3py.py.

def to_ContextObj(ptr,):
    ctx = ContextObj(ptr)
    super(ctypes.c_void_p, ctx).__init__(ptr)
    return ctx
 

Referenced by user_prop_fresh().

to_symbol()

def z3py.to_symbol	(		s,
			ctx = None
	)

Convert an integer or string into a Z3 symbol.

Definition at line 124 of file z3py.py.

def to_symbol(s, ctx=None):
    """Convert an integer or string into a Z3 symbol."""
    if _is_int(s):
        return Z3_mk_int_symbol(_get_ctx(ctx).ref(), s)
    else:
        return Z3_mk_string_symbol(_get_ctx(ctx).ref(), s)
 
 

Referenced by Fixedpoint.add_rule(), Optimize.add_soft(), Array(), BitVec(), Bool(), Const(), CreateDatatypes(), DatatypeSort(), DeclareSort(), EnumSort(), FiniteDomainSort(), FP(), Function(), ParamDescrsRef.get_documentation(), ParamDescrsRef.get_kind(), Int(), is_quantifier(), PropagateFunction(), prove(), Real(), RecFunction(), ParamsRef.set(), Fixedpoint.set_predicate_representation(), SolverFor(), String(), and Fixedpoint.update_rule().

ToInt()

def z3py.ToInt

(

a

)

 Return the Z3 expression ToInt(a).

>>> x = Real('x')
>>> x.sort()
Real
>>> n = ToInt(x)
>>> n
ToInt(x)
>>> n.sort()
Int

Definition at line 3376 of file z3py.py.

def ToInt(a):
    """ Return the Z3 expression ToInt(a).
 
    >>> x = Real('x')
    >>> x.sort()
    Real
    >>> n = ToInt(x)
    >>> n
    ToInt(x)
    >>> n.sort()
    Int
    """
    if z3_debug():
        _z3_assert(a.is_real(), "Z3 real expression expected.")
    ctx = a.ctx
    return ArithRef(Z3_mk_real2int(ctx.ref(), a.as_ast()), ctx)
 
 

ToReal()

def z3py.ToReal

(

a

)

 Return the Z3 expression ToReal(a).

>>> x = Int('x')
>>> x.sort()
Int
>>> n = ToReal(x)
>>> n
ToReal(x)
>>> n.sort()
Real

Definition at line 3358 of file z3py.py.

def ToReal(a):
    """ Return the Z3 expression ToReal(a).
 
    >>> x = Int('x')
    >>> x.sort()
    Int
    >>> n = ToReal(x)
    >>> n
    ToReal(x)
    >>> n.sort()
    Real
    """
    if z3_debug():
        _z3_assert(a.is_int(), "Z3 integer expression expected.")
    ctx = a.ctx
    return ArithRef(Z3_mk_int2real(ctx.ref(), a.as_ast()), ctx)
 
 

TransitiveClosure()

def z3py.TransitiveClosure

(

f

)

Given a binary relation R, such that the two arguments have the same sort
create the transitive closure relation R+.
The transitive closure R+ is a new relation.

Definition at line 11322 of file z3py.py.

def TransitiveClosure(f):
    """Given a binary relation R, such that the two arguments have the same sort
    create the transitive closure relation R+.
    The transitive closure R+ is a new relation.
    """
    return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
 

TreeOrder()

def z3py.TreeOrder	(		a,
			index
	)

Definition at line 11314 of file z3py.py.

def TreeOrder(a, index):
    return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
 
 

TryFor()

def z3py.TryFor	(		t,
			ms,
			ctx = None
	)

Return a tactic that applies `t` to a given goal for `ms` milliseconds.

If `t` does not terminate in `ms` milliseconds, then it fails.

Definition at line 8440 of file z3py.py.

def TryFor(t, ms, ctx=None):
    """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
 
    If `t` does not terminate in `ms` milliseconds, then it fails.
    """
    t = _to_tactic(t, ctx)
    return Tactic(Z3_tactic_try_for(t.ctx.ref(), t.tactic, ms), t.ctx)
 
 

TupleSort()

def z3py.TupleSort	(		name,
			sorts,
			ctx = None
	)

Create a named tuple sort base on a set of underlying sorts
Example:
    >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])

Definition at line 5363 of file z3py.py.

def TupleSort(name, sorts, ctx=None):
    """Create a named tuple sort base on a set of underlying sorts
    Example:
        >>> pair, mk_pair, (first, second) = TupleSort("pair", [IntSort(), StringSort()])
    """
    tuple = Datatype(name, ctx)
    projects = [("project%d" % i, sorts[i]) for i in range(len(sorts))]
    tuple.declare(name, *projects)
    tuple = tuple.create()
    return tuple, tuple.constructor(0), [tuple.accessor(0, i) for i in range(len(sorts))]
 
 

Referenced by Context.MkTupleSort(), and Context.mkTupleSort().

UDiv()

def z3py.UDiv	(		a,
			b
	)

Create the Z3 expression (unsigned) division `self / other`.

Use the operator / for signed division.

>>> x = BitVec('x', 32)
>>> y = BitVec('y', 32)
>>> UDiv(x, y)
UDiv(x, y)
>>> UDiv(x, y).sort()
BitVec(32)
>>> (x / y).sexpr()
'(bvsdiv x y)'
>>> UDiv(x, y).sexpr()
'(bvudiv x y)'

Definition at line 4236 of file z3py.py.

def UDiv(a, b):
    """Create the Z3 expression (unsigned) division `self / other`.
 
    Use the operator / for signed division.
 
    >>> x = BitVec('x', 32)
    >>> y = BitVec('y', 32)
    >>> UDiv(x, y)
    UDiv(x, y)
    >>> UDiv(x, y).sort()
    BitVec(32)
    >>> (x / y).sexpr()
    '(bvsdiv x y)'
    >>> UDiv(x, y).sexpr()
    '(bvudiv x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BitVecRef(Z3_mk_bvudiv(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

UGE()

def z3py.UGE	(		a,
			b
	)

Create the Z3 expression (unsigned) `other >= self`.

Use the operator >= for signed greater than or equal to.

>>> x, y = BitVecs('x y', 32)
>>> UGE(x, y)
UGE(x, y)
>>> (x >= y).sexpr()
'(bvsge x y)'
>>> UGE(x, y).sexpr()
'(bvuge x y)'

Definition at line 4200 of file z3py.py.

def UGE(a, b):
    """Create the Z3 expression (unsigned) `other >= self`.
 
    Use the operator >= for signed greater than or equal to.
 
    >>> x, y = BitVecs('x y', 32)
    >>> UGE(x, y)
    UGE(x, y)
    >>> (x >= y).sexpr()
    '(bvsge x y)'
    >>> UGE(x, y).sexpr()
    '(bvuge x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvuge(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

UGT()

def z3py.UGT	(		a,
			b
	)

Create the Z3 expression (unsigned) `other > self`.

Use the operator > for signed greater than.

>>> x, y = BitVecs('x y', 32)
>>> UGT(x, y)
UGT(x, y)
>>> (x > y).sexpr()
'(bvsgt x y)'
>>> UGT(x, y).sexpr()
'(bvugt x y)'

Definition at line 4218 of file z3py.py.

def UGT(a, b):
    """Create the Z3 expression (unsigned) `other > self`.
 
    Use the operator > for signed greater than.
 
    >>> x, y = BitVecs('x y', 32)
    >>> UGT(x, y)
    UGT(x, y)
    >>> (x > y).sexpr()
    '(bvsgt x y)'
    >>> UGT(x, y).sexpr()
    '(bvugt x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvugt(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

ULE()

def z3py.ULE	(		a,
			b
	)

Create the Z3 expression (unsigned) `other <= self`.

Use the operator <= for signed less than or equal to.

>>> x, y = BitVecs('x y', 32)
>>> ULE(x, y)
ULE(x, y)
>>> (x <= y).sexpr()
'(bvsle x y)'
>>> ULE(x, y).sexpr()
'(bvule x y)'

Definition at line 4164 of file z3py.py.

def ULE(a, b):
    """Create the Z3 expression (unsigned) `other <= self`.
 
    Use the operator <= for signed less than or equal to.
 
    >>> x, y = BitVecs('x y', 32)
    >>> ULE(x, y)
    ULE(x, y)
    >>> (x <= y).sexpr()
    '(bvsle x y)'
    >>> ULE(x, y).sexpr()
    '(bvule x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvule(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

ULT()

def z3py.ULT	(		a,
			b
	)

Create the Z3 expression (unsigned) `other < self`.

Use the operator < for signed less than.

>>> x, y = BitVecs('x y', 32)
>>> ULT(x, y)
ULT(x, y)
>>> (x < y).sexpr()
'(bvslt x y)'
>>> ULT(x, y).sexpr()
'(bvult x y)'

Definition at line 4182 of file z3py.py.

def ULT(a, b):
    """Create the Z3 expression (unsigned) `other < self`.
 
    Use the operator < for signed less than.
 
    >>> x, y = BitVecs('x y', 32)
    >>> ULT(x, y)
    ULT(x, y)
    >>> (x < y).sexpr()
    '(bvslt x y)'
    >>> ULT(x, y).sexpr()
    '(bvult x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BoolRef(Z3_mk_bvult(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

Union()

def z3py.Union

(

*

args

)

Create union of regular expressions.
>>> re = Union(Re("a"), Re("b"), Re("c"))
>>> print (simplify(InRe("d", re)))
False

Definition at line 11186 of file z3py.py.

def Union(*args):
    """Create union of regular expressions.
    >>> re = Union(Re("a"), Re("b"), Re("c"))
    >>> print (simplify(InRe("d", re)))
    False
    """
    args = _get_args(args)
    sz = len(args)
    if z3_debug():
        _z3_assert(sz > 0, "At least one argument expected.")
        _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
    if sz == 1:
        return args[0]
    ctx = args[0].ctx
    v = (Ast * sz)()
    for i in range(sz):
        v[i] = args[i].as_ast()
    return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
 
 

Referenced by ReRef.__add__().

Unit()

def z3py.Unit

(

a

)

Create a singleton sequence

Definition at line 10990 of file z3py.py.

def Unit(a):
    """Create a singleton sequence"""
    return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
 
 

Update()

def z3py.Update	(		a,
		*	args
	)

Return a Z3 store array expression.

>>> a    = Array('a', IntSort(), IntSort())
>>> i, v = Ints('i v')
>>> s    = Update(a, i, v)
>>> s.sort()
Array(Int, Int)
>>> prove(s[i] == v)
proved
>>> j    = Int('j')
>>> prove(Implies(i != j, s[j] == a[j]))
proved

Definition at line 4747 of file z3py.py.

def Update(a, *args):
    """Return a Z3 store array expression.
 
    >>> a    = Array('a', IntSort(), IntSort())
    >>> i, v = Ints('i v')
    >>> s    = Update(a, i, v)
    >>> s.sort()
    Array(Int, Int)
    >>> prove(s[i] == v)
    proved
    >>> j    = Int('j')
    >>> prove(Implies(i != j, s[j] == a[j]))
    proved
    """
    if z3_debug():
        _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
    args = _get_args(args)
    ctx = a.ctx
    if len(args) <= 1:
        raise Z3Exception("array update requires index and value arguments")
    if len(args) == 2:
        i = args[0]
        v = args[1]
        i = a.sort().domain().cast(i)
        v = a.sort().range().cast(v)
        return _to_expr_ref(Z3_mk_store(ctx.ref(), a.as_ast(), i.as_ast(), v.as_ast()), ctx)
    v = a.sort().range().cast(args[-1])
    idxs = [a.sort().domain_n(i).cast(args[i]) for i in range(len(args)-1)]
    _args, sz = _to_ast_array(idxs)
    return _to_expr_ref(Z3_mk_store_n(ctx.ref(), a.as_ast(), sz, _args, v.as_ast()), ctx)
 
 

Referenced by Store().

URem()

def z3py.URem	(		a,
			b
	)

Create the Z3 expression (unsigned) remainder `self % other`.

Use the operator % for signed modulus, and SRem() for signed remainder.

>>> x = BitVec('x', 32)
>>> y = BitVec('y', 32)
>>> URem(x, y)
URem(x, y)
>>> URem(x, y).sort()
BitVec(32)
>>> (x % y).sexpr()
'(bvsmod x y)'
>>> URem(x, y).sexpr()
'(bvurem x y)'

Definition at line 4257 of file z3py.py.

def URem(a, b):
    """Create the Z3 expression (unsigned) remainder `self % other`.
 
    Use the operator % for signed modulus, and SRem() for signed remainder.
 
    >>> x = BitVec('x', 32)
    >>> y = BitVec('y', 32)
    >>> URem(x, y)
    URem(x, y)
    >>> URem(x, y).sort()
    BitVec(32)
    >>> (x % y).sexpr()
    '(bvsmod x y)'
    >>> URem(x, y).sexpr()
    '(bvurem x y)'
    """
    _check_bv_args(a, b)
    a, b = _coerce_exprs(a, b)
    return BitVecRef(Z3_mk_bvurem(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
 
 

user_prop_created()

def z3py.user_prop_created	(		ctx,
			cb,
			id
	)

Definition at line 11448 of file z3py.py.

def user_prop_created(ctx, cb, id):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    id = _to_expr_ref(to_Ast(id), prop.ctx())
    prop.created(id)
    prop.cb = None
    

user_prop_decide()

def z3py.user_prop_decide	(		ctx,
			cb,
			t_ref,
			idx_ref,
			phase_ref
	)

Definition at line 11479 of file z3py.py.

def user_prop_decide(ctx, cb, t_ref, idx_ref, phase_ref):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
    t, idx, phase = prop.decide(t, idx, phase)
    t_ref = t
    idx_ref = idx
    phase_ref = phase
    prop.cb = None
    
 

user_prop_diseq()

def z3py.user_prop_diseq	(		ctx,
			cb,
			x,
			y
	)

Definition at line 11469 of file z3py.py.

def user_prop_diseq(ctx, cb, x, y):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    x = _to_expr_ref(to_Ast(x), prop.ctx())
    y = _to_expr_ref(to_Ast(y), prop.ctx())
    prop.diseq(x, y)
    prop.cb = None
 
# TODO The decision callback is not fully implemented.
# It needs to handle the ast*, unsigned* idx, and Z3_lbool* 

user_prop_eq()

def z3py.user_prop_eq	(		ctx,
			cb,
			x,
			y
	)

Definition at line 11461 of file z3py.py.

def user_prop_eq(ctx, cb, x, y):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    x = _to_expr_ref(to_Ast(x), prop.ctx())
    y = _to_expr_ref(to_Ast(y), prop.ctx())
    prop.eq(x, y)
    prop.cb = None
 

user_prop_final()

def z3py.user_prop_final	(		ctx,
			cb
	)

Definition at line 11455 of file z3py.py.

def user_prop_final(ctx, cb):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    prop.final()
    prop.cb = None
 

user_prop_fixed()

def z3py.user_prop_fixed	(		ctx,
			cb,
			id,
			value
	)

Definition at line 11440 of file z3py.py.

def user_prop_fixed(ctx, cb, id, value):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    id = _to_expr_ref(to_Ast(id), prop.ctx())
    value = _to_expr_ref(to_Ast(value), prop.ctx())
    prop.fixed(id, value)
    prop.cb = None
 

user_prop_fresh()

def z3py.user_prop_fresh	(		ctx,
			_new_ctx
	)

Definition at line 11426 of file z3py.py.

def user_prop_fresh(ctx, _new_ctx):
    _prop_closures.set_threaded()
    prop = _prop_closures.get(ctx)
    nctx = Context()
    Z3_del_context(nctx.ctx)
    new_ctx = to_ContextObj(_new_ctx)
    nctx.ctx = new_ctx
    nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
    nctx.owner = False
    new_prop = prop.fresh(nctx)
    _prop_closures.set(new_prop.id, new_prop)
    return new_prop.id
 
 

user_prop_pop()

def z3py.user_prop_pop	(		ctx,
			cb,
			num_scopes
	)

Definition at line 11420 of file z3py.py.

def user_prop_pop(ctx, cb, num_scopes):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    prop.pop(num_scopes)
 
 

user_prop_push()

def z3py.user_prop_push	(		ctx,
			cb
	)

Definition at line 11414 of file z3py.py.

def user_prop_push(ctx, cb):
    prop = _prop_closures.get(ctx)
    prop.cb = cb
    prop.push()
 
 

Var()

def z3py.Var	(		idx,
			s
	)

Create a Z3 free variable. Free variables are used to create quantified formulas.
A free variable with index n is bound when it occurs within the scope of n+1 quantified
declarations.

>>> Var(0, IntSort())
Var(0)
>>> eq(Var(0, IntSort()), Var(0, BoolSort()))
False

Definition at line 1470 of file z3py.py.

def Var(idx, s):
    """Create a Z3 free variable. Free variables are used to create quantified formulas.
    A free variable with index n is bound when it occurs within the scope of n+1 quantified
    declarations.
    
    >>> Var(0, IntSort())
    Var(0)
    >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
    False
    """
    if z3_debug():
        _z3_assert(is_sort(s), "Z3 sort expected")
    return _to_expr_ref(Z3_mk_bound(s.ctx_ref(), idx, s.ast), s.ctx)
 
 

Referenced by RealVar().

When()

def z3py.When	(		p,
			t,
			ctx = None
	)

Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
Otherwise, it returns the input goal unmodified.

>>> t = When(Probe('size') > 2, Tactic('simplify'))
>>> x, y = Ints('x y')
>>> g = Goal()
>>> g.add(x > 0)
>>> g.add(y > 0)
>>> t(g)
[[x > 0, y > 0]]
>>> g.add(x == y + 1)
>>> t(g)
[[Not(x <= 0), Not(y <= 0), x == 1 + y]]

Definition at line 8734 of file z3py.py.

def When(p, t, ctx=None):
    """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
    Otherwise, it returns the input goal unmodified.
 
    >>> t = When(Probe('size') > 2, Tactic('simplify'))
    >>> x, y = Ints('x y')
    >>> g = Goal()
    >>> g.add(x > 0)
    >>> g.add(y > 0)
    >>> t(g)
    [[x > 0, y > 0]]
    >>> g.add(x == y + 1)
    >>> t(g)
    [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
    """
    p = _to_probe(p, ctx)
    t = _to_tactic(t, ctx)
    return Tactic(Z3_tactic_when(t.ctx.ref(), p.probe, t.tactic), t.ctx)
 
 

With()

def z3py.With	(		t,
		*	args,
		**	keys
	)

Return a tactic that applies tactic `t` using the given configuration options.

>>> x, y = Ints('x y')
>>> t = With(Tactic('simplify'), som=True)
>>> t((x + 1)*(y + 2) == 0)
[[2*x + y + x*y == -2]]

Definition at line 8391 of file z3py.py.

def With(t, *args, **keys):
    """Return a tactic that applies tactic `t` using the given configuration options.
 
    >>> x, y = Ints('x y')
    >>> t = With(Tactic('simplify'), som=True)
    >>> t((x + 1)*(y + 2) == 0)
    [[2*x + y + x*y == -2]]
    """
    ctx = keys.pop("ctx", None)
    t = _to_tactic(t, ctx)
    p = args2params(args, keys, t.ctx)
    return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
 
 

WithParams()

def z3py.WithParams	(		t,
			p
	)

Return a tactic that applies tactic `t` using the given configuration options.

>>> x, y = Ints('x y')
>>> p = ParamsRef()
>>> p.set("som", True)
>>> t = WithParams(Tactic('simplify'), p)
>>> t((x + 1)*(y + 2) == 0)
[[2*x + y + x*y == -2]]

Definition at line 8405 of file z3py.py.

def WithParams(t, p):
    """Return a tactic that applies tactic `t` using the given configuration options.
 
    >>> x, y = Ints('x y')
    >>> p = ParamsRef()
    >>> p.set("som", True)
    >>> t = WithParams(Tactic('simplify'), p)
    >>> t((x + 1)*(y + 2) == 0)
    [[2*x + y + x*y == -2]]
    """
    t = _to_tactic(t, None)
    return Tactic(Z3_tactic_using_params(t.ctx.ref(), t.tactic, p.params), t.ctx)
 
 

Xor()

def z3py.Xor	(		a,
			b,
			ctx = None
	)

Create a Z3 Xor expression.

>>> p, q = Bools('p q')
>>> Xor(p, q)
Xor(p, q)
>>> simplify(Xor(p, q))
Not(p == q)

Definition at line 1799 of file z3py.py.

def Xor(a, b, ctx=None):
    """Create a Z3 Xor expression.
 
    >>> p, q = Bools('p q')
    >>> Xor(p, q)
    Xor(p, q)
    >>> simplify(Xor(p, q))
    Not(p == q)
    """
    ctx = _get_ctx(_ctx_from_ast_arg_list([a, b], ctx))
    s = BoolSort(ctx)
    a = s.cast(a)
    b = s.cast(b)
    return BoolRef(Z3_mk_xor(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
 
 

z3_debug()

def z3py.z3_debug

(

)

Definition at line 62 of file z3py.py.

def z3_debug():
    global Z3_DEBUG
    return Z3_DEBUG
 
 

Referenced by FuncDeclRef.__call__(), Probe.__call__(), QuantifierRef.__getitem__(), ModelRef.__getitem__(), Context.__init__(), Goal.__init__(), ArithRef.__mod__(), ArithRef.__rmod__(), DatatypeSortRef.accessor(), And(), AndThen(), Tactic.apply(), ExprRef.arg(), args2params(), ArraySort(), IntNumRef.as_long(), AtLeast(), AtMost(), BV2Int(), BVRedAnd(), BVRedOr(), BVSNegNoOverflow(), SortRef.cast(), BoolSortRef.cast(), ArithSortRef.cast(), BitVecSortRef.cast(), FPSortRef.cast(), Concat(), Const(), DatatypeSortRef.constructor(), Goal.convert_model(), CreateDatatypes(), ExprRef.decl(), Datatype.declare(), Datatype.declare_core(), Default(), describe_probes(), deserialize(), Distinct(), FuncDeclRef.domain(), EnumSort(), eq(), AstRef.eq(), Ext(), Extract(), FiniteDomainVal(), fpIsPositive(), fpNeg(), FPSort(), fpToFPUnsigned(), fpToIEEEBV(), fpToReal(), fpToSBV(), fpToUBV(), FreshFunction(), Function(), get_as_array_func(), ModelRef.get_interp(), get_map_func(), ModelRef.get_universe(), get_var_index(), If(), AlgebraicNumRef.index(), Intersect(), is_quantifier(), is_sort(), IsInt(), K(), Map(), MultiPattern(), QuantifierRef.no_pattern(), ExprRef.num_args(), Or(), OrElse(), Tactic.param_descrs(), ParOr(), ParThen(), QuantifierRef.pattern(), PropagateFunction(), prove(), RatVal(), RealSort(), RecFunction(), DatatypeSortRef.recognizer(), RepeatBitVec(), Select(), ParamsRef.set(), set_param(), SignExt(), simplify(), solve_using(), substitute(), substitute_funs(), substitute_vars(), ToInt(), ToReal(), AstRef.translate(), Goal.translate(), ModelRef.translate(), Solver.translate(), Union(), Update(), Var(), QuantifierRef.var_name(), QuantifierRef.var_sort(), and ZeroExt().

z3_error_handler()

def z3py.z3_error_handler	(		c,
			e
	)

Definition at line 174 of file z3py.py.

def z3_error_handler(c, e):
    # Do nothing error handler, just avoid exit(0)
    # The wrappers in z3core.py will raise a Z3Exception if an error is detected
    return
 
 

ZeroExt()

def z3py.ZeroExt	(		n,
			a
	)

Return a bit-vector expression with `n` extra zero-bits.

>>> x = BitVec('x', 16)
>>> n = ZeroExt(8, x)
>>> n.size()
24
>>> n
ZeroExt(8, x)
>>> n.sort()
BitVec(24)
>>> v0 = BitVecVal(2, 2)
>>> v0
2
>>> v0.size()
2
>>> v  = simplify(ZeroExt(6, v0))
>>> v
2
>>> v.size()
8

Definition at line 4393 of file z3py.py.

def ZeroExt(n, a):
    """Return a bit-vector expression with `n` extra zero-bits.
 
    >>> x = BitVec('x', 16)
    >>> n = ZeroExt(8, x)
    >>> n.size()
    24
    >>> n
    ZeroExt(8, x)
    >>> n.sort()
    BitVec(24)
    >>> v0 = BitVecVal(2, 2)
    >>> v0
    2
    >>> v0.size()
    2
    >>> v  = simplify(ZeroExt(6, v0))
    >>> v
    2
    >>> v.size()
    8
    """
    if z3_debug():
        _z3_assert(_is_int(n), "First argument must be an integer")
        _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
    return BitVecRef(Z3_mk_zero_ext(a.ctx_ref(), n, a.as_ast()), a.ctx)
 
 

Variable Documentation

sat

sat = CheckSatResult(Z3_L_TRUE)

Definition at line 6892 of file z3py.py.

unknown

unknown = CheckSatResult(Z3_L_UNDEF)

Definition at line 6894 of file z3py.py.

unsat

unsat = CheckSatResult(Z3_L_FALSE)

Definition at line 6893 of file z3py.py.

Z3_DEBUG

Z3_DEBUG = __debug__

Definition at line 59 of file z3py.py.