Expressions are terms. More...
Public Member Functions | |
Expr | Simplify (Params p=null) |
Returns a simplified version of the expression. More... | |
Expr | Arg (uint i) |
The i'th argument of the expression. More... | |
void | Update (Expr[] args) |
Update the arguments of the expression using the arguments args The number of new arguments should coincide with the current number of arguments. More... | |
Expr | Substitute (Expr[] from, Expr[] to) |
Substitute every occurrence of from[i] in the expression with to[i] , for i smaller than num_exprs . More... | |
Expr | Substitute (Expr from, Expr to) |
Substitute every occurrence of from in the expression with to . More... | |
Expr | SubstituteVars (Expr[] to) |
Substitute the free variables in the expression with the expressions in to More... | |
new Expr | Translate (Context ctx) |
Translates (copies) the term to the Context ctx . More... | |
Expr | Dup () |
Create a duplicate of expression. This feature is to allow extending the life-time of expressions that were passed down as arguments by the user propagator callbacks. By default the life-time of arguments to callbacks is within the callback only. More... | |
override string | ToString () |
Returns a string representation of the expression. More... | |
Public Member Functions inherited from AST | |
override bool | Equals (object o) |
Object comparison. More... | |
virtual int | CompareTo (object other) |
Object Comparison. More... | |
override int | GetHashCode () |
The AST's hash code. More... | |
AST | Translate (Context ctx) |
Translates (copies) the AST to the Context ctx . More... | |
override string | ToString () |
A string representation of the AST. More... | |
string | SExpr () |
A string representation of the AST in s-expression notation. More... | |
Public Member Functions inherited from Z3Object | |
void | Dispose () |
Disposes of the underlying native Z3 object. More... | |
Protected Member Functions | |
Expr (Context ctx, IntPtr obj) | |
Constructor for Expr More... | |
Properties | |
FuncDecl | FuncDecl [get] |
The function declaration of the function that is applied in this expression. More... | |
Z3_lbool | BoolValue [get] |
Indicates whether the expression is the true or false expression or something else (Z3_L_UNDEF). More... | |
uint | NumArgs [get] |
The number of arguments of the expression. More... | |
Expr[] | Args [get] |
The arguments of the expression. More... | |
bool | IsNumeral [get] |
Indicates whether the term is a numeral More... | |
bool | IsWellSorted [get] |
Indicates whether the term is well-sorted. More... | |
Sort | Sort [get] |
The Sort of the term. More... | |
bool | IsConst [get] |
Indicates whether the term represents a constant. More... | |
bool | IsIntNum [get] |
Indicates whether the term is an integer numeral. More... | |
bool | IsRatNum [get] |
Indicates whether the term is a real numeral. More... | |
bool | IsAlgebraicNumber [get] |
Indicates whether the term is an algebraic number More... | |
bool | IsBool [get] |
Indicates whether the term has Boolean sort. More... | |
bool | IsTrue [get] |
Indicates whether the term is the constant true. More... | |
bool | IsFalse [get] |
Indicates whether the term is the constant false. More... | |
bool | IsEq [get] |
Indicates whether the term is an equality predicate. More... | |
bool | IsDistinct [get] |
Indicates whether the term is an n-ary distinct predicate (every argument is mutually distinct). More... | |
bool | IsITE [get] |
Indicates whether the term is a ternary if-then-else term More... | |
bool | IsAnd [get] |
Indicates whether the term is an n-ary conjunction More... | |
bool | IsOr [get] |
Indicates whether the term is an n-ary disjunction More... | |
bool | IsIff [get] |
Indicates whether the term is an if-and-only-if (Boolean equivalence, binary) More... | |
bool | IsXor [get] |
Indicates whether the term is an exclusive or More... | |
bool | IsNot [get] |
Indicates whether the term is a negation More... | |
bool | IsImplies [get] |
Indicates whether the term is an implication More... | |
bool | IsAtMost [get] |
Indicates whether the term is at-most More... | |
uint | AtMostBound [get] |
Retrieve bound of at-most More... | |
bool | IsAtLeast [get] |
Indicates whether the term is at-least More... | |
uint | AtLeastBound [get] |
Retrieve bound of at-least More... | |
bool | IsPbEq [get] |
Indicates whether the term is pbeq More... | |
bool | IsPbLe [get] |
Indicates whether the term is pble More... | |
bool | IsPbGe [get] |
Indicates whether the term is pbge More... | |
bool | IsInt [get] |
Indicates whether the term is of integer sort. More... | |
bool | IsReal [get] |
Indicates whether the term is of sort real. More... | |
bool | IsArithmeticNumeral [get] |
Indicates whether the term is an arithmetic numeral. More... | |
bool | IsLE [get] |
Indicates whether the term is a less-than-or-equal More... | |
bool | IsGE [get] |
Indicates whether the term is a greater-than-or-equal More... | |
bool | IsLT [get] |
Indicates whether the term is a less-than More... | |
bool | IsGT [get] |
Indicates whether the term is a greater-than More... | |
bool | IsAdd [get] |
Indicates whether the term is addition (binary) More... | |
bool | IsSub [get] |
Indicates whether the term is subtraction (binary) More... | |
bool | IsUMinus [get] |
Indicates whether the term is a unary minus More... | |
bool | IsMul [get] |
Indicates whether the term is multiplication (binary) More... | |
bool | IsDiv [get] |
Indicates whether the term is division (binary) More... | |
bool | IsIDiv [get] |
Indicates whether the term is integer division (binary) More... | |
bool | IsRemainder [get] |
Indicates whether the term is remainder (binary) More... | |
bool | IsModulus [get] |
Indicates whether the term is modulus (binary) More... | |
bool | IsIntToReal [get] |
Indicates whether the term is a coercion of integer to real (unary) More... | |
bool | IsRealToInt [get] |
Indicates whether the term is a coercion of real to integer (unary) More... | |
bool | IsRealIsInt [get] |
Indicates whether the term is a check that tests whether a real is integral (unary) More... | |
bool | IsArray [get] |
Indicates whether the term is of an array sort. More... | |
bool | IsStore [get] |
Indicates whether the term is an array store. More... | |
bool | IsSelect [get] |
Indicates whether the term is an array select. More... | |
bool | IsConstantArray [get] |
Indicates whether the term is a constant array. More... | |
bool | IsDefaultArray [get] |
Indicates whether the term is a default array. More... | |
bool | IsArrayMap [get] |
Indicates whether the term is an array map. More... | |
bool | IsAsArray [get] |
Indicates whether the term is an as-array term. More... | |
bool | IsSetUnion [get] |
Indicates whether the term is set union More... | |
bool | IsSetIntersect [get] |
Indicates whether the term is set intersection More... | |
bool | IsSetDifference [get] |
Indicates whether the term is set difference More... | |
bool | IsSetComplement [get] |
Indicates whether the term is set complement More... | |
bool | IsSetSubset [get] |
Indicates whether the term is set subset More... | |
bool | IsBV [get] |
Indicates whether the terms is of bit-vector sort. More... | |
bool | IsBVNumeral [get] |
Indicates whether the term is a bit-vector numeral More... | |
bool | IsBVBitOne [get] |
Indicates whether the term is a one-bit bit-vector with value one More... | |
bool | IsBVBitZero [get] |
Indicates whether the term is a one-bit bit-vector with value zero More... | |
bool | IsBVUMinus [get] |
Indicates whether the term is a bit-vector unary minus More... | |
bool | IsBVAdd [get] |
Indicates whether the term is a bit-vector addition (binary) More... | |
bool | IsBVSub [get] |
Indicates whether the term is a bit-vector subtraction (binary) More... | |
bool | IsBVMul [get] |
Indicates whether the term is a bit-vector multiplication (binary) More... | |
bool | IsBVSDiv [get] |
Indicates whether the term is a bit-vector signed division (binary) More... | |
bool | IsBVUDiv [get] |
Indicates whether the term is a bit-vector unsigned division (binary) More... | |
bool | IsBVSRem [get] |
Indicates whether the term is a bit-vector signed remainder (binary) More... | |
bool | IsBVURem [get] |
Indicates whether the term is a bit-vector unsigned remainder (binary) More... | |
bool | IsBVSMod [get] |
Indicates whether the term is a bit-vector signed modulus More... | |
bool | IsBVULE [get] |
Indicates whether the term is an unsigned bit-vector less-than-or-equal More... | |
bool | IsBVSLE [get] |
Indicates whether the term is a signed bit-vector less-than-or-equal More... | |
bool | IsBVUGE [get] |
Indicates whether the term is an unsigned bit-vector greater-than-or-equal More... | |
bool | IsBVSGE [get] |
Indicates whether the term is a signed bit-vector greater-than-or-equal More... | |
bool | IsBVULT [get] |
Indicates whether the term is an unsigned bit-vector less-than More... | |
bool | IsBVSLT [get] |
Indicates whether the term is a signed bit-vector less-than More... | |
bool | IsBVUGT [get] |
Indicates whether the term is an unsigned bit-vector greater-than More... | |
bool | IsBVSGT [get] |
Indicates whether the term is a signed bit-vector greater-than More... | |
bool | IsBVAND [get] |
Indicates whether the term is a bit-wise AND More... | |
bool | IsBVOR [get] |
Indicates whether the term is a bit-wise OR More... | |
bool | IsBVNOT [get] |
Indicates whether the term is a bit-wise NOT More... | |
bool | IsBVXOR [get] |
Indicates whether the term is a bit-wise XOR More... | |
bool | IsBVNAND [get] |
Indicates whether the term is a bit-wise NAND More... | |
bool | IsBVNOR [get] |
Indicates whether the term is a bit-wise NOR More... | |
bool | IsBVXNOR [get] |
Indicates whether the term is a bit-wise XNOR More... | |
bool | IsBVConcat [get] |
Indicates whether the term is a bit-vector concatenation (binary) More... | |
bool | IsBVSignExtension [get] |
Indicates whether the term is a bit-vector sign extension More... | |
bool | IsBVZeroExtension [get] |
Indicates whether the term is a bit-vector zero extension More... | |
bool | IsBVExtract [get] |
Indicates whether the term is a bit-vector extraction More... | |
bool | IsBVRepeat [get] |
Indicates whether the term is a bit-vector repetition More... | |
bool | IsBVReduceOR [get] |
Indicates whether the term is a bit-vector reduce OR More... | |
bool | IsBVReduceAND [get] |
Indicates whether the term is a bit-vector reduce AND More... | |
bool | IsBVComp [get] |
Indicates whether the term is a bit-vector comparison More... | |
bool | IsBVShiftLeft [get] |
Indicates whether the term is a bit-vector shift left More... | |
bool | IsBVShiftRightLogical [get] |
Indicates whether the term is a bit-vector logical shift right More... | |
bool | IsBVShiftRightArithmetic [get] |
Indicates whether the term is a bit-vector arithmetic shift left More... | |
bool | IsBVRotateLeft [get] |
Indicates whether the term is a bit-vector rotate left More... | |
bool | IsBVRotateRight [get] |
Indicates whether the term is a bit-vector rotate right More... | |
bool | IsBVRotateLeftExtended [get] |
Indicates whether the term is a bit-vector rotate left (extended) More... | |
bool | IsBVRotateRightExtended [get] |
Indicates whether the term is a bit-vector rotate right (extended) More... | |
bool | IsIntToBV [get] |
Indicates whether the term is a coercion from integer to bit-vector More... | |
bool | IsBVToInt [get] |
Indicates whether the term is a coercion from bit-vector to integer More... | |
bool | IsBVCarry [get] |
Indicates whether the term is a bit-vector carry More... | |
bool | IsBVXOR3 [get] |
Indicates whether the term is a bit-vector ternary XOR More... | |
bool | IsLabel [get] |
Indicates whether the term is a label (used by the Boogie Verification condition generator). More... | |
bool | IsLabelLit [get] |
Indicates whether the term is a label literal (used by the Boogie Verification condition generator). More... | |
bool | IsString [get] |
Check whether expression is a string constant. More... | |
string | String [get] |
Retrieve string corresponding to string constant. More... | |
bool | IsConcat [get] |
Check whether expression is a concatenation. More... | |
bool | IsPrefix [get] |
Check whether expression is a prefix. More... | |
bool | IsSuffix [get] |
Check whether expression is a suffix. More... | |
bool | IsContains [get] |
Check whether expression is a contains. More... | |
bool | IsExtract [get] |
Check whether expression is an extract. More... | |
bool | IsReplace [get] |
Check whether expression is a replace. More... | |
bool | IsAt [get] |
Check whether expression is an at. More... | |
bool | IsLength [get] |
Check whether expression is a sequence length. More... | |
bool | IsIndex [get] |
Check whether expression is a sequence index. More... | |
bool | IsOEQ [get] |
Indicates whether the term is a binary equivalence modulo namings. More... | |
bool | IsProofTrue [get] |
Indicates whether the term is a Proof for the expression 'true'. More... | |
bool | IsProofAsserted [get] |
Indicates whether the term is a proof for a fact asserted by the user. More... | |
bool | IsProofGoal [get] |
Indicates whether the term is a proof for a fact (tagged as goal) asserted by the user. More... | |
bool | IsProofModusPonens [get] |
Indicates whether the term is proof via modus ponens More... | |
bool | IsProofReflexivity [get] |
Indicates whether the term is a proof for (R t t), where R is a reflexive relation. More... | |
bool | IsProofSymmetry [get] |
Indicates whether the term is proof by symmetricity of a relation More... | |
bool | IsProofTransitivity [get] |
Indicates whether the term is a proof by transitivity of a relation More... | |
bool | IsProofTransitivityStar [get] |
Indicates whether the term is a proof by condensed transitivity of a relation More... | |
bool | IsProofMonotonicity [get] |
Indicates whether the term is a monotonicity proof object. More... | |
bool | IsProofQuantIntro [get] |
Indicates whether the term is a quant-intro proof More... | |
bool | IsProofDistributivity [get] |
Indicates whether the term is a distributivity proof object. More... | |
bool | IsProofAndElimination [get] |
Indicates whether the term is a proof by elimination of AND More... | |
bool | IsProofOrElimination [get] |
Indicates whether the term is a proof by elimination of not-or More... | |
bool | IsProofRewrite [get] |
Indicates whether the term is a proof by rewriting More... | |
bool | IsProofRewriteStar [get] |
Indicates whether the term is a proof by rewriting More... | |
bool | IsProofPullQuant [get] |
Indicates whether the term is a proof for pulling quantifiers out. More... | |
bool | IsProofPushQuant [get] |
Indicates whether the term is a proof for pushing quantifiers in. More... | |
bool | IsProofElimUnusedVars [get] |
Indicates whether the term is a proof for elimination of unused variables. More... | |
bool | IsProofDER [get] |
Indicates whether the term is a proof for destructive equality resolution More... | |
bool | IsProofQuantInst [get] |
Indicates whether the term is a proof for quantifier instantiation More... | |
bool | IsProofHypothesis [get] |
Indicates whether the term is a hypothesis marker. More... | |
bool | IsProofLemma [get] |
Indicates whether the term is a proof by lemma More... | |
bool | IsProofUnitResolution [get] |
Indicates whether the term is a proof by unit resolution More... | |
bool | IsProofIFFTrue [get] |
Indicates whether the term is a proof by iff-true More... | |
bool | IsProofIFFFalse [get] |
Indicates whether the term is a proof by iff-false More... | |
bool | IsProofCommutativity [get] |
Indicates whether the term is a proof by commutativity More... | |
bool | IsProofDefAxiom [get] |
Indicates whether the term is a proof for Tseitin-like axioms More... | |
bool | IsProofDefIntro [get] |
Indicates whether the term is a proof for introduction of a name More... | |
bool | IsProofApplyDef [get] |
Indicates whether the term is a proof for application of a definition More... | |
bool | IsProofIFFOEQ [get] |
Indicates whether the term is a proof iff-oeq More... | |
bool | IsProofNNFPos [get] |
Indicates whether the term is a proof for a positive NNF step More... | |
bool | IsProofNNFNeg [get] |
Indicates whether the term is a proof for a negative NNF step More... | |
bool | IsProofSkolemize [get] |
Indicates whether the term is a proof for a Skolemization step More... | |
bool | IsProofModusPonensOEQ [get] |
Indicates whether the term is a proof by modus ponens for equi-satisfiability. More... | |
bool | IsProofTheoryLemma [get] |
Indicates whether the term is a proof for theory lemma More... | |
bool | IsRelation [get] |
Indicates whether the term is of relation sort. More... | |
bool | IsRelationStore [get] |
Indicates whether the term is an relation store More... | |
bool | IsEmptyRelation [get] |
Indicates whether the term is an empty relation More... | |
bool | IsIsEmptyRelation [get] |
Indicates whether the term is a test for the emptiness of a relation More... | |
bool | IsRelationalJoin [get] |
Indicates whether the term is a relational join More... | |
bool | IsRelationUnion [get] |
Indicates whether the term is the union or convex hull of two relations. More... | |
bool | IsRelationWiden [get] |
Indicates whether the term is the widening of two relations More... | |
bool | IsRelationProject [get] |
Indicates whether the term is a projection of columns (provided as numbers in the parameters). More... | |
bool | IsRelationFilter [get] |
Indicates whether the term is a relation filter More... | |
bool | IsRelationNegationFilter [get] |
Indicates whether the term is an intersection of a relation with the negation of another. More... | |
bool | IsRelationRename [get] |
Indicates whether the term is the renaming of a column in a relation More... | |
bool | IsRelationComplement [get] |
Indicates whether the term is the complement of a relation More... | |
bool | IsRelationSelect [get] |
Indicates whether the term is a relational select More... | |
bool | IsRelationClone [get] |
Indicates whether the term is a relational clone (copy) More... | |
bool | IsFiniteDomain [get] |
Indicates whether the term is of an array sort. More... | |
bool | IsFiniteDomainLT [get] |
Indicates whether the term is a less than predicate over a finite domain. More... | |
bool | IsFP [get] |
Indicates whether the terms is of floating-point sort. More... | |
bool | IsFPRM [get] |
Indicates whether the terms is of floating-point rounding mode sort. More... | |
bool | IsFPNumeral [get] |
Indicates whether the term is a floating-point numeral More... | |
bool | IsFPRMNumeral [get] |
Indicates whether the term is a floating-point rounding mode numeral More... | |
bool | IsFPRMRoundNearestTiesToEven [get] |
Indicates whether the term is the floating-point rounding numeral roundNearestTiesToEven More... | |
bool | IsFPRMRoundNearestTiesToAway [get] |
Indicates whether the term is the floating-point rounding numeral roundNearestTiesToAway More... | |
bool | IsFPRMRoundTowardNegative [get] |
Indicates whether the term is the floating-point rounding numeral roundTowardNegative More... | |
bool | IsFPRMRoundTowardPositive [get] |
Indicates whether the term is the floating-point rounding numeral roundTowardPositive More... | |
bool | IsFPRMRoundTowardZero [get] |
Indicates whether the term is the floating-point rounding numeral roundTowardZero More... | |
bool | IsFPRMExprRNE [get] |
Indicates whether the term is the floating-point rounding numeral roundNearestTiesToEven More... | |
bool | IsFPRMExprRNA [get] |
Indicates whether the term is the floating-point rounding numeral roundNearestTiesToAway More... | |
bool | IsFPRMExprRTN [get] |
Indicates whether the term is the floating-point rounding numeral roundTowardNegative More... | |
bool | IsFPRMExprRTP [get] |
Indicates whether the term is the floating-point rounding numeral roundTowardPositive More... | |
bool | IsFPRMExprRTZ [get] |
Indicates whether the term is the floating-point rounding numeral roundTowardZero More... | |
bool | IsFPRMExpr [get] |
Indicates whether the term is a floating-point rounding mode numeral More... | |
bool | IsFPPlusInfinity [get] |
Indicates whether the term is a floating-point +oo More... | |
bool | IsFPMinusInfinity [get] |
Indicates whether the term is a floating-point -oo More... | |
bool | IsFPNaN [get] |
Indicates whether the term is a floating-point NaN More... | |
bool | IsFPPlusZero [get] |
bool | IsFPMinusZero [get] |
Indicates whether the term is a floating-point -zero More... | |
bool | IsFPAdd [get] |
Indicates whether the term is a floating-point addition term More... | |
bool | IsFPSub [get] |
Indicates whether the term is a floating-point subtraction term More... | |
bool | IsFPNeg [get] |
Indicates whether the term is a floating-point negation term More... | |
bool | IsFPMul [get] |
Indicates whether the term is a floating-point multiplication term More... | |
bool | IsFPDiv [get] |
Indicates whether the term is a floating-point division term More... | |
bool | IsFPRem [get] |
Indicates whether the term is a floating-point remainder term More... | |
bool | IsFPAbs [get] |
Indicates whether the term is a floating-point term absolute value term More... | |
bool | IsFPMin [get] |
Indicates whether the term is a floating-point minimum term More... | |
bool | IsFPMax [get] |
Indicates whether the term is a floating-point maximum term More... | |
bool | IsFPFMA [get] |
Indicates whether the term is a floating-point fused multiply-add term More... | |
bool | IsFPSqrt [get] |
Indicates whether the term is a floating-point square root term More... | |
bool | IsFPRoundToIntegral [get] |
Indicates whether the term is a floating-point roundToIntegral term More... | |
bool | IsFPEq [get] |
Indicates whether the term is a floating-point equality term More... | |
bool | IsFPLt [get] |
Indicates whether the term is a floating-point less-than term More... | |
bool | IsFPGt [get] |
Indicates whether the term is a floating-point greater-than term More... | |
bool | IsFPLe [get] |
Indicates whether the term is a floating-point less-than or equal term More... | |
bool | IsFPGe [get] |
Indicates whether the term is a floating-point greater-than or equal term More... | |
bool | IsFPisNaN [get] |
Indicates whether the term is a floating-point isNaN predicate term More... | |
bool | IsFPisInf [get] |
Indicates whether the term is a floating-point isInf predicate term More... | |
bool | IsFPisZero [get] |
Indicates whether the term is a floating-point isZero predicate term More... | |
bool | IsFPisNormal [get] |
Indicates whether the term is a floating-point isNormal term More... | |
bool | IsFPisSubnormal [get] |
Indicates whether the term is a floating-point isSubnormal predicate term More... | |
bool | IsFPisNegative [get] |
Indicates whether the term is a floating-point isNegative predicate term More... | |
bool | IsFPisPositive [get] |
Indicates whether the term is a floating-point isPositive predicate term More... | |
bool | IsFPFP [get] |
Indicates whether the term is a floating-point constructor term More... | |
bool | IsFPToFp [get] |
Indicates whether the term is a floating-point conversion term More... | |
bool | IsFPToFpUnsigned [get] |
Indicates whether the term is a floating-point conversion from unsigned bit-vector term More... | |
bool | IsFPToUBV [get] |
Indicates whether the term is a floating-point conversion to unsigned bit-vector term More... | |
bool | IsFPToSBV [get] |
Indicates whether the term is a floating-point conversion to signed bit-vector term More... | |
bool | IsFPToReal [get] |
Indicates whether the term is a floating-point conversion to real term More... | |
bool | IsFPToIEEEBV [get] |
Indicates whether the term is a floating-point conversion to IEEE-754 bit-vector term More... | |
uint | Index [get] |
The de-Bruijn index of a bound variable. More... | |
Properties inherited from AST | |
uint | Id [get] |
A unique identifier for the AST (unique among all ASTs). More... | |
Z3_ast_kind | ASTKind [get] |
The kind of the AST. More... | |
bool | IsExpr [get] |
Indicates whether the AST is an Expr More... | |
bool | IsApp [get] |
Indicates whether the AST is an application More... | |
bool | IsVar [get] |
Indicates whether the AST is a BoundVariable More... | |
bool | IsQuantifier [get] |
Indicates whether the AST is a Quantifier More... | |
bool | IsSort [get] |
Indicates whether the AST is a Sort More... | |
bool | IsFuncDecl [get] |
Indicates whether the AST is a FunctionDeclaration More... | |
Properties inherited from Z3Object | |
Context | Context [get] |
Access Context object More... | |
Additional Inherited Members | |
Static Public Member Functions inherited from AST | |
static bool | operator== (AST a, AST b) |
Comparison operator. More... | |
static bool | operator!= (AST a, AST b) |
Comparison operator. More... | |
Constructor for Expr
|
inline |
|
inline |
Create a duplicate of expression. This feature is to allow extending the life-time of expressions that were passed down as arguments by the user propagator callbacks. By default the life-time of arguments to callbacks is within the callback only.
Returns a simplified version of the expression.
p | A set of parameters to configure the simplifier |
Substitute every occurrence of from
in the expression with to
.
Definition at line 139 of file Expr.cs.
Substitute every occurrence of from[i]
in the expression with to[i]
, for i
smaller than num_exprs
.
The result is the new expression. The arrays from
and to
must have size num_exprs
. For every i
smaller than num_exprs
, we must have that sort of from[i]
must be equal to sort of to[i]
.
Definition at line 121 of file Expr.cs.
Referenced by Expr.Substitute().
Substitute the free variables in the expression with the expressions in to
For every i
smaller than num_exprs
, the variable with de-Bruijn index i
is replaced with term to[i]
.
|
inline |
Translates (copies) the term to the Context ctx .
ctx | A context |
Definition at line 167 of file Expr.cs.
Referenced by Expr.Translate().
|
inline |
Update the arguments of the expression using the arguments args The number of new arguments should coincide with the current number of arguments.
Definition at line 102 of file Expr.cs.
|
get |
|
get |
Retrieve bound of at-least
Definition at line 348 of file Expr.cs.
|
get |
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The de-Bruijn index of a bound variable.
Bound variables are indexed by de-Bruijn indices. It is perhaps easiest to explain the meaning of de-Bruijn indices by indicating the compilation process from non-de-Bruijn formulas to de-Bruijn format.
The last line is significant: the index of a bound variable is different depending on the scope in which it appears. The deeper x appears, the higher is its index.
Definition at line 1815 of file Expr.cs.
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Indicates whether the term is addition (binary)
Definition at line 412 of file Expr.cs.
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Indicates whether the term is of an array sort.
Definition at line 469 of file Expr.cs.
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Indicates whether the terms is of bit-vector sort.
Definition at line 548 of file Expr.cs.
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Indicates whether the term represents a constant.
Definition at line 222 of file Expr.cs.
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Indicates whether the term is of an array sort.
Definition at line 1504 of file Expr.cs.
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Indicates whether the terms is of floating-point sort.
Definition at line 1523 of file Expr.cs.
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Indicates whether the term is a floating-point numeral
Definition at line 1539 of file Expr.cs.
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Indicates whether the terms is of floating-point rounding mode sort.
Definition at line 1531 of file Expr.cs.
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Indicates whether the term is a floating-point rounding mode numeral
Definition at line 1544 of file Expr.cs.
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Indicates whether the term is of integer sort.
Definition at line 371 of file Expr.cs.
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Indicates whether the term is an integer numeral.
Definition at line 232 of file Expr.cs.
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Indicates whether the term is a proof for Tseitin-like axioms
Proof object used to justify Tseitin's like axioms:
(or (not (and p q)) p) (or (not (and p q)) q) (or (not (and p q r)) p) (or (not (and p q r)) q) (or (not (and p q r)) r) ... (or (and p q) (not p) (not q)) (or (not (or p q)) p q) (or (or p q) (not p)) (or (or p q) (not q)) (or (not (iff p q)) (not p) q) (or (not (iff p q)) p (not q)) (or (iff p q) (not p) (not q)) (or (iff p q) p q) (or (not (ite a b c)) (not a) b) (or (not (ite a b c)) a c) (or (ite a b c) (not a) (not b)) (or (ite a b c) a (not c)) (or (not (not a)) (not a)) (or (not a) a)
This proof object has no antecedents. Note: all axioms are propositional tautologies. Note also that 'and' and 'or' can take multiple arguments. You can recover the propositional tautologies by unfolding the Boolean connectives in the axioms a small bounded number of steps (=3).
Definition at line 1237 of file Expr.cs.
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Indicates whether the term is a proof for introduction of a name
Introduces a name for a formula/term. Suppose e is an expression with free variables x, and def-intro introduces the name n(x). The possible cases are:
When e is of Boolean type:
or:
when e only occurs positively.
When e is of the form (ite cond th el):
Otherwise: [def-intro]: (= n e)
Definition at line 1260 of file Expr.cs.
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Indicates whether the term is a proof for destructive equality resolution
A proof for destructive equality resolution: (iff (forall (x) (or (not (= x t)) P[x])) P[t]) if x does not occur in t.
This proof object has no antecedents.
Several variables can be eliminated simultaneously.
Definition at line 1131 of file Expr.cs.
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Indicates whether the term is a distributivity proof object.
Given that f (= or) distributes over g (= and), produces a proof for (= (f a (g c d)) (g (f a c) (f a d))) If f and g are associative, this proof also justifies the following equality: (= (f (g a b) (g c d)) (g (f a c) (f a d) (f b c) (f b d))) where each f and g can have arbitrary number of arguments.
This proof object has no antecedents. Remark. This rule is used by the CNF conversion pass and instantiated by f = or, and g = and.
Definition at line 1031 of file Expr.cs.
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Indicates whether the term is a proof for elimination of unused variables.
A proof for (iff (forall (x_1 ... x_n y_1 ... y_m) p[x_1 ... x_n]) (forall (x_1 ... x_n) p[x_1 ... x_n]))
It is used to justify the elimination of unused variables. This proof object has no antecedents.
Definition at line 1117 of file Expr.cs.
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Indicates whether the term is a proof for a negative NNF step
Proof for a (negative) NNF step. Examples:
T1: (not s_1) ~ r_1 ... Tn: (not s_n) ~ r_n
and T1: (not s_1) ~ r_1 ... Tn: (not s_n) ~ r_n
and T1: (not s_1) ~ r_1 T2: (not s_2) ~ r_2 T3: s_1 ~ r_1' T4: s_2 ~ r_2'
(and (or r_1 r_2) (or r_1' r_2')))
Definition at line 1332 of file Expr.cs.
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Indicates whether the term is a proof for a positive NNF step
Proof for a (positive) NNF step. Example:
T1: (not s_1) ~ r_1 T2: (not s_2) ~ r_2 T3: s_1 ~ r_1' T4: s_2 ~ r_2'
(and (or r_1 r_2') (or r_1' r_2)))
The negation normal form steps NNF_POS and NNF_NEG are used in the following cases: (a) When creating the NNF of a positive force quantifier. The quantifier is retained (unless the bound variables are eliminated). Example T1: q ~ q_new
(b) When recursively creating NNF over Boolean formulas, where the top-level connective is changed during NNF conversion. The relevant Boolean connectives for NNF_POS are 'implies', 'iff', 'xor', 'ite'. NNF_NEG furthermore handles the case where negation is pushed over Boolean connectives 'and' and 'or'.
Definition at line 1307 of file Expr.cs.
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Indicates whether the term is a proof for pushing quantifiers in.
A proof for: (iff (forall (x_1 ... x_m) (and p_1[x_1 ... x_m] ... p_n[x_1 ... x_m])) (and (forall (x_1 ... x_m) p_1[x_1 ... x_m]) ... (forall (x_1 ... x_m) p_n[x_1 ... x_m]))) This proof object has no antecedents
Definition at line 1105 of file Expr.cs.
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Indicates whether the term is a proof for (R t t), where R is a reflexive relation.
This proof object has no antecedents. The only reflexive relations that are used are equivalence modulo namings, equality and equivalence. That is, R is either '~', '=' or 'iff'.
Definition at line 945 of file Expr.cs.
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Indicates whether the term is a proof by rewriting
A proof for a local rewriting step (= t s). The head function symbol of t is interpreted.
This proof object has no antecedents. The conclusion of a rewrite rule is either an equality (= t s), an equivalence (iff t s), or equi-satisfiability (~ t s). Remark: if f is bool, then = is iff.
Examples: (= (+ x 0) x) (= (+ x 1 2) (+ 3 x)) (iff (or x false) x)
Definition at line 1070 of file Expr.cs.
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Indicates whether the term is a proof by rewriting
A proof for rewriting an expression t into an expression s. This proof object can have n antecedents. The antecedents are proofs for equalities used as substitution rules. The object is used in a few cases:
Definition at line 1083 of file Expr.cs.
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Indicates whether the term is a proof for theory lemma
Generic proof for theory lemmas.
The theory lemma function comes with one or more parameters. The first parameter indicates the name of the theory. For the theory of arithmetic, additional parameters provide hints for checking the theory lemma. The hints for arithmetic are:
Definition at line 1375 of file Expr.cs.
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Indicates whether the term is a proof by condensed transitivity of a relation
Condensed transitivity proof. It combines several symmetry and transitivity proofs. Example: T1: (R a b) T2: (R c b) T3: (R c d) [trans* T1 T2 T3]: (R a d) R must be a symmetric and transitive relation.
Assuming that this proof object is a proof for (R s t), then a proof checker must check if it is possible to prove (R s t) using the antecedents, symmetry and transitivity. That is, if there is a path from s to t, if we view every antecedent (R a b) as an edge between a and b.
Definition at line 989 of file Expr.cs.
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Indicates whether the term is a real numeral.
Definition at line 242 of file Expr.cs.
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Indicates whether the term is of sort real.
Definition at line 379 of file Expr.cs.
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Indicates whether the term is a relational clone (copy)
Create a fresh copy (clone) of a relation. The function is logically the identity, but in the context of a register machine allows for terms of kind
to perform destructive updates to the first argument.
Definition at line 1497 of file Expr.cs.
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Indicates whether the term is a relation filter
Filter (restrict) a relation with respect to a predicate. The first argument is a relation. The second argument is a predicate with free de-Bruijn indices corresponding to the columns of the relation. So the first column in the relation has index 0.
Definition at line 1445 of file Expr.cs.
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Indicates whether the term is an intersection of a relation with the negation of another.
Intersect the first relation with respect to negation of the second relation (the function takes two arguments). Logically, the specification can be described by a function
target = filter_by_negation(pos, neg, columns)
where columns are pairs c1, d1, .., cN, dN of columns from pos and neg, such that target are elements in x in pos, such that there is no y in neg that agrees with x on the columns c1, d1, .., cN, dN.
Definition at line 1461 of file Expr.cs.
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The number of arguments of the expression.
Definition at line 69 of file Expr.cs.
Referenced by Expr.Update().