z3++.h

Go to the documentation of this file.

/*++
Copyright (c) 2012 Microsoft Corporation
 
    Thin C++ layer on top of the Z3 C API.
    Main features:
      - Smart pointers for all Z3 objects.
      - Object-Oriented interface.
      - Operator overloading.
      - Exceptions for signaling Z3 errors
 
    The C API can be used simultaneously with the C++ layer.
    However, if you use the C API directly, you will have to check the error conditions manually.
    Of course, you can invoke the method check_error() of the context object.
Author:
 
    Leonardo (leonardo) 2012-03-28
 
Notes:
 
--*/
#pragma once
 
#include<cassert>
#include<ostream>
#include<string>
#include<memory>
#include<vector>
#include<z3.h>
#include<limits.h>
#include<functional>
 
#undef min
#undef max
 
namespace z3 {
 
    class exception;
    class config;
    class context;
    class symbol;
    class params;
    class param_descrs;
    class ast;
    class sort;
    class constructors;
    class constructor_list;
    class func_decl;
    class expr;
    class solver;
    class goal;
    class tactic;
    class simplifier;
    class probe;
    class model;
    class func_interp;
    class func_entry;
    class statistics;
    class apply_result;
    template<typename T> class cast_ast;
    template<typename T> class ast_vector_tpl;
    typedef ast_vector_tpl<ast>       ast_vector;
    typedef ast_vector_tpl<expr>      expr_vector;
    typedef ast_vector_tpl<sort>      sort_vector;
    typedef ast_vector_tpl<func_decl> func_decl_vector;
 
    inline void set_param(char const * param, char const * value) { Z3_global_param_set(param, value); }
    inline void set_param(char const * param, bool value) { Z3_global_param_set(param, value ? "true" : "false"); }
    inline void set_param(char const * param, int value) { auto str = std::to_string(value); Z3_global_param_set(param, str.c_str()); }
    inline void reset_params() { Z3_global_param_reset_all(); }
 
    class exception : public std::exception {
        std::string m_msg;
    public:
        virtual ~exception() throw() = default;
        exception(char const * msg):m_msg(msg) {}
        char const * msg() const { return m_msg.c_str(); }
        char const * what() const throw() { return m_msg.c_str(); }
        friend std::ostream & operator<<(std::ostream & out, exception const & e);
    };
    inline std::ostream & operator<<(std::ostream & out, exception const & e) { out << e.msg(); return out; }
 
#if !defined(Z3_THROW)
#if __cpp_exceptions || _CPPUNWIND || __EXCEPTIONS
#define Z3_THROW(x) throw x
#else
#define Z3_THROW(x) {}
#endif
#endif // !defined(Z3_THROW)
 
    class config {
        Z3_config    m_cfg;
        config(config const &) = delete;
        config & operator=(config const &) = delete;
    public:
        config() { m_cfg = Z3_mk_config(); }
        ~config() { Z3_del_config(m_cfg); }
        operator Z3_config() const { return m_cfg; }
        void set(char const * param, char const * value) { Z3_set_param_value(m_cfg, param, value); }
        void set(char const * param, bool value) { Z3_set_param_value(m_cfg, param, value ? "true" : "false"); }
        void set(char const * param, int value) {
            auto str = std::to_string(value);
            Z3_set_param_value(m_cfg, param, str.c_str());
        }
    };
 
    enum check_result {
        unsat, sat, unknown
    };
 
    enum rounding_mode {
        RNA,
        RNE,
        RTP,
        RTN,
        RTZ
    };
 
    inline check_result to_check_result(Z3_lbool l) {
        if (l == Z3_L_TRUE) return sat;
        else if (l == Z3_L_FALSE) return unsat;
        return unknown;
    }
 
 
 
    class context {
    private:
        friend class user_propagator_base;
        bool       m_enable_exceptions = true;
        rounding_mode m_rounding_mode;
        Z3_context m_ctx = nullptr;
        void init(config & c) {
            set_context(Z3_mk_context_rc(c));
        }
        void set_context(Z3_context ctx) {
            m_ctx = ctx;
            m_enable_exceptions = true;
            m_rounding_mode = RNE;
            Z3_set_error_handler(m_ctx, 0);
            Z3_set_ast_print_mode(m_ctx, Z3_PRINT_SMTLIB2_COMPLIANT);
        }
 
 
        context(context const &) = delete;
        context & operator=(context const &) = delete;
 
        context(Z3_context c) { set_context(c); }
        void detach() { m_ctx = nullptr; }
    public:
        context() { config c; init(c); }
        context(config & c) { init(c); }
        ~context() { if (m_ctx) Z3_del_context(m_ctx); }
        operator Z3_context() const { return m_ctx; }
 
        Z3_error_code check_error() const {
            Z3_error_code e = Z3_get_error_code(m_ctx);
            if (e != Z3_OK && enable_exceptions())
                Z3_THROW(exception(Z3_get_error_msg(m_ctx, e)));
            return e;
        }
 
        void check_parser_error() const {
            check_error();
        }
 
        void set_enable_exceptions(bool f) { m_enable_exceptions = f; }
 
        bool enable_exceptions() const { return m_enable_exceptions; }
 
        void set(char const * param, char const * value) { Z3_update_param_value(m_ctx, param, value); }
        void set(char const * param, bool value) { Z3_update_param_value(m_ctx, param, value ? "true" : "false"); }
        void set(char const * param, int value) {
            auto str = std::to_string(value);
            Z3_update_param_value(m_ctx, param, str.c_str());
        }
 
        void interrupt() { Z3_interrupt(m_ctx); }
 
        symbol str_symbol(char const * s);
        symbol int_symbol(int n);
        sort bool_sort();
        sort int_sort();
        sort real_sort();
        sort bv_sort(unsigned sz);
 
        sort char_sort();
        sort string_sort();
        sort seq_sort(sort& s);
        sort re_sort(sort& seq_sort);
        sort array_sort(sort d, sort r);
        sort array_sort(sort_vector const& d, sort r);
        sort fpa_sort(unsigned ebits, unsigned sbits);
        template<size_t precision>
        sort fpa_sort();
        sort fpa_rounding_mode_sort();
        void set_rounding_mode(rounding_mode rm);
        sort enumeration_sort(char const * name, unsigned n, char const * const * enum_names, func_decl_vector & cs, func_decl_vector & ts);
 
        func_decl tuple_sort(char const * name, unsigned n, char const * const * names, sort const* sorts, func_decl_vector & projs);
 
 
        sort datatype(symbol const& name, constructors const& cs);
 
        sort_vector datatypes(unsigned n, symbol const* names,
                              constructor_list *const* cons);
                       
 
        sort datatype_sort(symbol const& name);
 
            
        sort uninterpreted_sort(char const* name);
        sort uninterpreted_sort(symbol const& name);
 
        func_decl function(symbol const & name, unsigned arity, sort const * domain, sort const & range);
        func_decl function(char const * name, unsigned arity, sort const * domain, sort const & range);
        func_decl function(symbol const&  name, sort_vector const& domain, sort const& range);
        func_decl function(char const * name, sort_vector const& domain, sort const& range);
        func_decl function(char const * name, sort const & domain, sort const & range);
        func_decl function(char const * name, sort const & d1, sort const & d2, sort const & range);
        func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & range);
        func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & range);
        func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & d5, sort const & range);
 
        func_decl recfun(symbol const & name, unsigned arity, sort const * domain, sort const & range);
        func_decl recfun(symbol const & name, const sort_vector& domain, sort const & range);
        func_decl recfun(char const * name, sort_vector const& domain, sort const & range);
        func_decl recfun(char const * name, unsigned arity, sort const * domain, sort const & range);
        func_decl recfun(char const * name, sort const & domain, sort const & range);
        func_decl recfun(char const * name, sort const & d1, sort const & d2, sort const & range);
 
        void      recdef(func_decl decl, expr_vector const& args, expr const& body);
        func_decl user_propagate_function(symbol const& name, sort_vector const& domain, sort const& range);
 
        expr constant(symbol const & name, sort const & s);
        expr constant(char const * name, sort const & s);
        expr bool_const(char const * name);
        expr int_const(char const * name);
        expr real_const(char const * name);
        expr string_const(char const * name);
        expr bv_const(char const * name, unsigned sz);
        expr fpa_const(char const * name, unsigned ebits, unsigned sbits);
 
        template<size_t precision>
        expr fpa_const(char const * name);
 
        expr variable(unsigned index, sort const& s);
        
 
        expr fpa_rounding_mode();
 
        expr bool_val(bool b);
 
        expr int_val(int n);
        expr int_val(unsigned n);
        expr int_val(int64_t n);
        expr int_val(uint64_t n);
        expr int_val(char const * n);
 
        expr real_val(int n);
        expr real_val(unsigned n);
        expr real_val(int64_t n);
        expr real_val(uint64_t n);
        expr real_val(int64_t n, int64_t d);
        expr real_val(char const * n);
 
        expr bv_val(int n, unsigned sz);
        expr bv_val(unsigned n, unsigned sz);
        expr bv_val(int64_t n, unsigned sz);
        expr bv_val(uint64_t n, unsigned sz);
        expr bv_val(char const * n, unsigned sz);
        expr bv_val(unsigned n, bool const* bits);
 
        expr fpa_val(double n);
        expr fpa_val(float n);
        expr fpa_nan(sort const & s);
        expr fpa_inf(sort const & s, bool sgn);
 
        expr string_val(char const* s);
        expr string_val(char const* s, unsigned n);
        expr string_val(std::string const& s);
        expr string_val(std::u32string const& s);
 
        expr num_val(int n, sort const & s);
 
        expr_vector parse_string(char const* s);
        expr_vector parse_file(char const* file);
 
        expr_vector parse_string(char const* s, sort_vector const& sorts, func_decl_vector const& decls);
        expr_vector parse_file(char const* s, sort_vector const& sorts, func_decl_vector const& decls);
    };
 
 
    template<typename T>
    class array {
        std::unique_ptr<T[]> m_array;
        unsigned m_size;
        array(array const &) = delete;
        array & operator=(array const &) = delete;
    public:
        array(unsigned sz):m_array(new T[sz]),m_size(sz) {}
        template<typename T2>
        array(ast_vector_tpl<T2> const & v);
        void resize(unsigned sz) { m_array.reset(new T[sz]); m_size = sz; }
        unsigned size() const { return m_size; }
        T & operator[](int i) { assert(0 <= i); assert(static_cast<unsigned>(i) < m_size); return m_array[i]; }
        T const & operator[](int i) const { assert(0 <= i); assert(static_cast<unsigned>(i) < m_size); return m_array[i]; }
        T const * ptr() const { return m_array.get(); }
        T * ptr() { return m_array.get(); }
    };
 
    class object {
    protected:
        context * m_ctx;
    public:
        object(context & c):m_ctx(&c) {}
        virtual ~object() = default;
        context & ctx() const { return *m_ctx; }
        Z3_error_code check_error() const { return m_ctx->check_error(); }
        friend void check_context(object const & a, object const & b);
    };
    inline void check_context(object const & a, object const & b) { (void)a; (void)b; assert(a.m_ctx == b.m_ctx); }
 
    class symbol : public object {
        Z3_symbol m_sym;
    public:
        symbol(context & c, Z3_symbol s):object(c), m_sym(s) {}
        operator Z3_symbol() const { return m_sym; }
        Z3_symbol_kind kind() const { return Z3_get_symbol_kind(ctx(), m_sym); }
        std::string str() const { assert(kind() == Z3_STRING_SYMBOL); return Z3_get_symbol_string(ctx(), m_sym); }
        int to_int() const { assert(kind() == Z3_INT_SYMBOL); return Z3_get_symbol_int(ctx(), m_sym); }
        friend std::ostream & operator<<(std::ostream & out, symbol const & s);
    };
 
    inline std::ostream & operator<<(std::ostream & out, symbol const & s) {
        if (s.kind() == Z3_INT_SYMBOL)
            out << "k!" << s.to_int();
        else
            out << s.str();
        return out;
    }
 
 
    class param_descrs : public object {
        Z3_param_descrs m_descrs;
    public:
        param_descrs(context& c, Z3_param_descrs d): object(c), m_descrs(d) { Z3_param_descrs_inc_ref(c, d); }
        param_descrs(param_descrs const& o): object(o.ctx()), m_descrs(o.m_descrs) { Z3_param_descrs_inc_ref(ctx(), m_descrs); }
        param_descrs& operator=(param_descrs const& o) {
            Z3_param_descrs_inc_ref(o.ctx(), o.m_descrs);
            Z3_param_descrs_dec_ref(ctx(), m_descrs);
            m_descrs = o.m_descrs;
            object::operator=(o);
            return *this;
        }
        ~param_descrs() override { Z3_param_descrs_dec_ref(ctx(), m_descrs); }
        static param_descrs simplify_param_descrs(context& c) { return param_descrs(c, Z3_simplify_get_param_descrs(c)); }
        static param_descrs global_param_descrs(context& c) { return param_descrs(c, Z3_get_global_param_descrs(c)); }
 
        unsigned size() { return Z3_param_descrs_size(ctx(), m_descrs); }
        symbol name(unsigned i) { return symbol(ctx(), Z3_param_descrs_get_name(ctx(), m_descrs, i)); }
        Z3_param_kind kind(symbol const& s) { return Z3_param_descrs_get_kind(ctx(), m_descrs, s); }
        std::string documentation(symbol const& s) { char const* r = Z3_param_descrs_get_documentation(ctx(), m_descrs, s); check_error(); return r; }
        std::string to_string() const { return Z3_param_descrs_to_string(ctx(), m_descrs); }
    };
 
    inline std::ostream& operator<<(std::ostream & out, param_descrs const & d) { return out << d.to_string(); }
 
    class params : public object {
        Z3_params m_params;
    public:
        params(context & c):object(c) { m_params = Z3_mk_params(c); Z3_params_inc_ref(ctx(), m_params); }
        params(params const & s):object(s), m_params(s.m_params) { Z3_params_inc_ref(ctx(), m_params); }
        ~params() override { Z3_params_dec_ref(ctx(), m_params); }
        operator Z3_params() const { return m_params; }
        params & operator=(params const & s) {
            Z3_params_inc_ref(s.ctx(), s.m_params);
            Z3_params_dec_ref(ctx(), m_params);
            object::operator=(s);
            m_params = s.m_params;
            return *this;
        }
        void set(char const * k, bool b) { Z3_params_set_bool(ctx(), m_params, ctx().str_symbol(k), b); }
        void set(char const * k, unsigned n) { Z3_params_set_uint(ctx(), m_params, ctx().str_symbol(k), n); }
        void set(char const * k, double n) { Z3_params_set_double(ctx(), m_params, ctx().str_symbol(k), n); }
        void set(char const * k, symbol const & s) { Z3_params_set_symbol(ctx(), m_params, ctx().str_symbol(k), s); }
        void set(char const * k, char const* s) { Z3_params_set_symbol(ctx(), m_params, ctx().str_symbol(k), ctx().str_symbol(s)); }
        friend std::ostream & operator<<(std::ostream & out, params const & p);
    };
 
    inline std::ostream & operator<<(std::ostream & out, params const & p) {
        out << Z3_params_to_string(p.ctx(), p); return out;
    }
 
    class ast : public object {
    protected:
        Z3_ast    m_ast;
    public:
        ast(context & c):object(c), m_ast(0) {}
        ast(context & c, Z3_ast n):object(c), m_ast(n) { Z3_inc_ref(ctx(), m_ast); }
        ast(ast const & s) :object(s), m_ast(s.m_ast) { Z3_inc_ref(ctx(), m_ast); }
        ~ast() override { if (m_ast) { Z3_dec_ref(*m_ctx, m_ast); } }
        operator Z3_ast() const { return m_ast; }
        operator bool() const { return m_ast != 0; }
        ast & operator=(ast const & s) {
            Z3_inc_ref(s.ctx(), s.m_ast);
            if (m_ast)
                Z3_dec_ref(ctx(), m_ast);
            object::operator=(s);
            m_ast = s.m_ast;
            return *this;
        }
        Z3_ast_kind kind() const { Z3_ast_kind r = Z3_get_ast_kind(ctx(), m_ast); check_error(); return r; }
        unsigned hash() const { unsigned r = Z3_get_ast_hash(ctx(), m_ast); check_error(); return r; }
        friend std::ostream & operator<<(std::ostream & out, ast const & n);
        std::string to_string() const { return std::string(Z3_ast_to_string(ctx(), m_ast)); }
 
 
        friend bool eq(ast const & a, ast const & b);
    };
    inline std::ostream & operator<<(std::ostream & out, ast const & n) {
        out << Z3_ast_to_string(n.ctx(), n.m_ast); return out;
    }
 
    inline bool eq(ast const & a, ast const & b) { return Z3_is_eq_ast(a.ctx(), a, b); }
 
    template<typename T>
    class ast_vector_tpl : public object {
        Z3_ast_vector m_vector;
        void init(Z3_ast_vector v) { Z3_ast_vector_inc_ref(ctx(), v); m_vector = v; }
    public:
        ast_vector_tpl(context & c):object(c) { init(Z3_mk_ast_vector(c)); }
        ast_vector_tpl(context & c, Z3_ast_vector v):object(c) { init(v); }
        ast_vector_tpl(ast_vector_tpl const & s):object(s), m_vector(s.m_vector) { Z3_ast_vector_inc_ref(ctx(), m_vector); }
        ast_vector_tpl(context& c, ast_vector_tpl const& src): object(c) { init(Z3_ast_vector_translate(src.ctx(), src, c)); }
 
        ~ast_vector_tpl() override { Z3_ast_vector_dec_ref(ctx(), m_vector); }
        operator Z3_ast_vector() const { return m_vector; }
        unsigned size() const { return Z3_ast_vector_size(ctx(), m_vector); }
        T operator[](unsigned i) const { Z3_ast r = Z3_ast_vector_get(ctx(), m_vector, i); check_error(); return cast_ast<T>()(ctx(), r); }
        void push_back(T const & e) { Z3_ast_vector_push(ctx(), m_vector, e); check_error(); }
        void resize(unsigned sz) { Z3_ast_vector_resize(ctx(), m_vector, sz); check_error(); }
        T back() const { return operator[](size() - 1); }
        void pop_back() { assert(size() > 0); resize(size() - 1); }
        bool empty() const { return size() == 0; }
        ast_vector_tpl & operator=(ast_vector_tpl const & s) {
            Z3_ast_vector_inc_ref(s.ctx(), s.m_vector);
            Z3_ast_vector_dec_ref(ctx(), m_vector);
            object::operator=(s);
            m_vector = s.m_vector;
            return *this;
        }
        ast_vector_tpl& set(unsigned idx, ast& a) {
            Z3_ast_vector_set(ctx(), m_vector, idx, a);
            return *this;
        }
        /*
          Disabled pending C++98 build upgrade
        bool contains(T const& x) const {
            for (T y : *this) if (eq(x, y)) return true;
            return false;
        }
        */
 
        class iterator final {
            ast_vector_tpl const* m_vector;
            unsigned m_index;
        public:
            iterator(ast_vector_tpl const* v, unsigned i): m_vector(v), m_index(i) {}
 
            bool operator==(iterator const& other) const noexcept {
                return other.m_index == m_index;
            };
            bool operator!=(iterator const& other) const noexcept {
                return other.m_index != m_index;
            };
            iterator& operator++() noexcept {
                ++m_index;
                return *this;
            }
            void set(T& arg) {
                Z3_ast_vector_set(m_vector->ctx(), *m_vector, m_index, arg);
            }
            iterator operator++(int) noexcept { iterator tmp = *this; ++m_index; return tmp; }
            T * operator->() const { return &(operator*()); }
            T operator*() const { return (*m_vector)[m_index]; }
        };
        iterator begin() const noexcept { return iterator(this, 0); }
        iterator end() const { return iterator(this, size()); }
        friend std::ostream & operator<<(std::ostream & out, ast_vector_tpl const & v) { out << Z3_ast_vector_to_string(v.ctx(), v); return out; }
        std::string to_string() const { return std::string(Z3_ast_vector_to_string(ctx(), m_vector)); }
    };
 
 
    class sort : public ast {
    public:
        sort(context & c):ast(c) {}
        sort(context & c, Z3_sort s):ast(c, reinterpret_cast<Z3_ast>(s)) {}
        sort(context & c, Z3_ast a):ast(c, a) {}
        operator Z3_sort() const { return reinterpret_cast<Z3_sort>(m_ast); }
 
        unsigned id() const { unsigned r = Z3_get_sort_id(ctx(), *this); check_error(); return r; }
 
        Z3_sort_kind sort_kind() const { return Z3_get_sort_kind(*m_ctx, *this); }
        symbol name() const { Z3_symbol s = Z3_get_sort_name(ctx(), *this); check_error(); return symbol(ctx(), s); }
        bool is_bool() const { return sort_kind() == Z3_BOOL_SORT; }
        bool is_int() const { return sort_kind() == Z3_INT_SORT; }
        bool is_real() const { return sort_kind() == Z3_REAL_SORT; }
        bool is_arith() const { return is_int() || is_real(); }
        bool is_bv() const { return sort_kind() == Z3_BV_SORT; }
        bool is_array() const { return sort_kind() == Z3_ARRAY_SORT; }
        bool is_datatype() const { return sort_kind() == Z3_DATATYPE_SORT; }
        bool is_relation() const { return sort_kind() == Z3_RELATION_SORT; }
        bool is_seq() const { return sort_kind() == Z3_SEQ_SORT; }
        bool is_re() const { return sort_kind() == Z3_RE_SORT; }
        bool is_finite_domain() const { return sort_kind() == Z3_FINITE_DOMAIN_SORT; }
        bool is_fpa() const { return sort_kind() == Z3_FLOATING_POINT_SORT; }
 
        unsigned bv_size() const { assert(is_bv()); unsigned r = Z3_get_bv_sort_size(ctx(), *this); check_error(); return r; }
 
        unsigned fpa_ebits() const { assert(is_fpa()); unsigned r = Z3_fpa_get_ebits(ctx(), *this); check_error(); return r; }
 
        unsigned fpa_sbits() const { assert(is_fpa()); unsigned r = Z3_fpa_get_sbits(ctx(), *this); check_error(); return r; }
        sort array_domain() const { assert(is_array()); Z3_sort s = Z3_get_array_sort_domain(ctx(), *this); check_error(); return sort(ctx(), s); }
        sort array_range() const { assert(is_array()); Z3_sort s = Z3_get_array_sort_range(ctx(), *this); check_error(); return sort(ctx(), s); }
 
        friend std::ostream & operator<<(std::ostream & out, sort const & s) { return out << Z3_sort_to_string(s.ctx(), Z3_sort(s.m_ast)); }
 
        func_decl_vector constructors();
        func_decl_vector recognizers();
    };
 
 
    class func_decl : public ast {
    public:
        func_decl(context & c):ast(c) {}
        func_decl(context & c, Z3_func_decl n):ast(c, reinterpret_cast<Z3_ast>(n)) {}
        operator Z3_func_decl() const { return reinterpret_cast<Z3_func_decl>(m_ast); }
 
        unsigned id() const { unsigned r = Z3_get_func_decl_id(ctx(), *this); check_error(); return r; }
 
        unsigned arity() const { return Z3_get_arity(ctx(), *this); }
        sort domain(unsigned i) const { assert(i < arity()); Z3_sort r = Z3_get_domain(ctx(), *this, i); check_error(); return sort(ctx(), r); }
        sort range() const { Z3_sort r = Z3_get_range(ctx(), *this); check_error(); return sort(ctx(), r); }
        symbol name() const { Z3_symbol s = Z3_get_decl_name(ctx(), *this); check_error(); return symbol(ctx(), s); }
        Z3_decl_kind decl_kind() const { return Z3_get_decl_kind(ctx(), *this); }
        unsigned num_parameters() const { return Z3_get_decl_num_parameters(ctx(), *this); }
 
 
        func_decl transitive_closure(func_decl const&) {
            Z3_func_decl tc = Z3_mk_transitive_closure(ctx(), *this); check_error(); return func_decl(ctx(), tc); 
        }
 
        bool is_const() const { return arity() == 0; }
 
        expr operator()() const;
        expr operator()(unsigned n, expr const * args) const;
        expr operator()(expr_vector const& v) const;
        expr operator()(expr const & a) const;
        expr operator()(int a) const;
        expr operator()(expr const & a1, expr const & a2) const;
        expr operator()(expr const & a1, int a2) const;
        expr operator()(int a1, expr const & a2) const;
        expr operator()(expr const & a1, expr const & a2, expr const & a3) const;
        expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4) const;
        expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5) const;
 
        func_decl_vector accessors();
 
    };
 
    expr select(expr const & a, expr const& i);
    expr select(expr const & a, expr_vector const & i);
 
    class expr : public ast {
    public:
        expr(context & c):ast(c) {}
        expr(context & c, Z3_ast n):ast(c, reinterpret_cast<Z3_ast>(n)) {}
 
        sort get_sort() const { Z3_sort s = Z3_get_sort(*m_ctx, m_ast); check_error(); return sort(*m_ctx, s); }
 
        bool is_bool() const { return get_sort().is_bool(); }
        bool is_int() const { return get_sort().is_int(); }
        bool is_real() const { return get_sort().is_real(); }
        bool is_arith() const { return get_sort().is_arith(); }
        bool is_bv() const { return get_sort().is_bv(); }
        bool is_array() const { return get_sort().is_array(); }
        bool is_datatype() const { return get_sort().is_datatype(); }
        bool is_relation() const { return get_sort().is_relation(); }
        bool is_seq() const { return get_sort().is_seq(); }
        bool is_re() const { return get_sort().is_re(); }
 
        bool is_finite_domain() const { return get_sort().is_finite_domain(); }
        bool is_fpa() const { return get_sort().is_fpa(); }
 
        bool is_numeral() const { return kind() == Z3_NUMERAL_AST; }
        bool is_numeral_i64(int64_t& i) const { bool r = Z3_get_numeral_int64(ctx(), m_ast, &i); check_error(); return r;}
        bool is_numeral_u64(uint64_t& i) const { bool r = Z3_get_numeral_uint64(ctx(), m_ast, &i); check_error(); return r;}
        bool is_numeral_i(int& i) const { bool r = Z3_get_numeral_int(ctx(), m_ast, &i); check_error(); return r;}
        bool is_numeral_u(unsigned& i) const { bool r = Z3_get_numeral_uint(ctx(), m_ast, &i); check_error(); return r;}
        bool is_numeral(std::string& s) const { if (!is_numeral()) return false; s = Z3_get_numeral_string(ctx(), m_ast); check_error(); return true; }
        bool is_numeral(std::string& s, unsigned precision) const { if (!is_numeral()) return false; s = Z3_get_numeral_decimal_string(ctx(), m_ast, precision); check_error(); return true; }
        bool is_numeral(double& d) const { if (!is_numeral()) return false; d = Z3_get_numeral_double(ctx(), m_ast); check_error(); return true; }
        bool as_binary(std::string& s) const { if (!is_numeral()) return false; s = Z3_get_numeral_binary_string(ctx(), m_ast); check_error(); return true; }
 
        double as_double() const { double d = 0; is_numeral(d); return d; }
        uint64_t as_uint64() const { uint64_t r = 0; is_numeral_u64(r); return r; }
        int64_t as_int64() const { int64_t r = 0; is_numeral_i64(r); return r; }
        
 
        bool is_app() const { return kind() == Z3_APP_AST || kind() == Z3_NUMERAL_AST; }
        bool is_const() const { return is_app() && num_args() == 0; }
        bool is_quantifier() const { return kind() == Z3_QUANTIFIER_AST; }
 
        bool is_forall() const { return Z3_is_quantifier_forall(ctx(), m_ast); }
        bool is_exists() const { return Z3_is_quantifier_exists(ctx(), m_ast); }
        bool is_lambda() const { return Z3_is_lambda(ctx(), m_ast); }
        bool is_var() const { return kind() == Z3_VAR_AST; }
        bool is_algebraic() const { return Z3_is_algebraic_number(ctx(), m_ast); }
 
        bool is_well_sorted() const { bool r = Z3_is_well_sorted(ctx(), m_ast); check_error(); return r; }
 
        expr mk_is_inf() const {
            assert(is_fpa());
            Z3_ast r = Z3_mk_fpa_is_infinite(ctx(), m_ast);
            check_error();
            return expr(ctx(), r);
        }
 
        expr mk_is_nan() const {
            assert(is_fpa());
            Z3_ast r = Z3_mk_fpa_is_nan(ctx(), m_ast);
            check_error();
            return expr(ctx(), r);
        }
 
        expr mk_is_normal() const {
            assert(is_fpa());
            Z3_ast r = Z3_mk_fpa_is_normal(ctx(), m_ast);
            check_error();
            return expr(ctx(), r);
        }
 
        expr mk_is_subnormal() const {
            assert(is_fpa());
            Z3_ast r = Z3_mk_fpa_is_subnormal(ctx(), m_ast);
            check_error();
            return expr(ctx(), r);
        }
 
        expr mk_is_zero() const {
            assert(is_fpa());
            Z3_ast r = Z3_mk_fpa_is_zero(ctx(), m_ast);
            check_error();
            return expr(ctx(), r);
        }
 
        expr mk_to_ieee_bv() const {
            assert(is_fpa());
            Z3_ast r = Z3_mk_fpa_to_ieee_bv(ctx(), m_ast);
            check_error();
            return expr(ctx(), r);
        }
 
        expr mk_from_ieee_bv(sort const &s) const {
            assert(is_bv());
            Z3_ast r = Z3_mk_fpa_to_fp_bv(ctx(), m_ast, s);
            check_error();
            return expr(ctx(), r);
        }
 
        std::string get_decimal_string(int precision) const {
            assert(is_numeral() || is_algebraic());
            return std::string(Z3_get_numeral_decimal_string(ctx(), m_ast, precision));
        }
 
        expr algebraic_lower(unsigned precision) const { 
            assert(is_algebraic());      
            Z3_ast r = Z3_get_algebraic_number_lower(ctx(), m_ast, precision);
            check_error();
            return expr(ctx(), r);
        }
 
        expr algebraic_upper(unsigned precision) const { 
            assert(is_algebraic());      
            Z3_ast r = Z3_get_algebraic_number_upper(ctx(), m_ast, precision);
            check_error();
            return expr(ctx(), r);
        }
        
        expr_vector algebraic_poly() const {
            assert(is_algebraic());
            Z3_ast_vector r = Z3_algebraic_get_poly(ctx(), m_ast);
            check_error();
            return expr_vector(ctx(), r);
        }
 
        unsigned algebraic_i() const {
            assert(is_algebraic());
            unsigned i = Z3_algebraic_get_i(ctx(), m_ast);
            check_error();
            return i;
        }
 
        unsigned id() const { unsigned r = Z3_get_ast_id(ctx(), m_ast); check_error(); return r; }
 
        int get_numeral_int() const {
            int result = 0;
            if (!is_numeral_i(result)) {
                assert(ctx().enable_exceptions());
                if (!ctx().enable_exceptions()) return 0;
                Z3_THROW(exception("numeral does not fit in machine int"));
            }
            return result;
        }
 
        unsigned get_numeral_uint() const {
            assert(is_numeral());
            unsigned result = 0;
            if (!is_numeral_u(result)) {
                assert(ctx().enable_exceptions());
                if (!ctx().enable_exceptions()) return 0;
                Z3_THROW(exception("numeral does not fit in machine uint"));
            }
            return result;
        }
 
        int64_t get_numeral_int64() const {
            assert(is_numeral());
            int64_t result = 0;
            if (!is_numeral_i64(result)) {
                assert(ctx().enable_exceptions());
                if (!ctx().enable_exceptions()) return 0;
                Z3_THROW(exception("numeral does not fit in machine int64_t"));
            }
            return result;
        }
 
        uint64_t get_numeral_uint64() const {
            assert(is_numeral());
            uint64_t result = 0;
            if (!is_numeral_u64(result)) {
                assert(ctx().enable_exceptions());
                if (!ctx().enable_exceptions()) return 0;
                Z3_THROW(exception("numeral does not fit in machine uint64_t"));
            }
            return result;
        }
 
        Z3_lbool bool_value() const {
            return Z3_get_bool_value(ctx(), m_ast);
        }
 
        expr numerator() const {
            assert(is_numeral());
            Z3_ast r = Z3_get_numerator(ctx(), m_ast);
            check_error();
            return expr(ctx(),r);
        }
 
 
        expr denominator() const {
            assert(is_numeral());
            Z3_ast r = Z3_get_denominator(ctx(), m_ast);
            check_error();
            return expr(ctx(),r);
        }
 
 
        bool is_string_value() const { return Z3_is_string(ctx(), m_ast); }
 
        std::string get_string() const {            
            assert(is_string_value());
            char const* s = Z3_get_string(ctx(), m_ast);
            check_error();
            return std::string(s);
        }
 
        std::u32string get_u32string() const {
            assert(is_string_value());
            unsigned n = Z3_get_string_length(ctx(), m_ast);
            std::u32string s;
            s.resize(n);
            Z3_get_string_contents(ctx(), m_ast, n, (unsigned*)s.data());
            return s;
        }
 
        operator Z3_app() const { assert(is_app()); return reinterpret_cast<Z3_app>(m_ast); }
 
        func_decl decl() const { Z3_func_decl f = Z3_get_app_decl(ctx(), *this); check_error(); return func_decl(ctx(), f); }
        unsigned num_args() const { unsigned r = Z3_get_app_num_args(ctx(), *this); check_error(); return r; }
        expr arg(unsigned i) const { Z3_ast r = Z3_get_app_arg(ctx(), *this, i); check_error(); return expr(ctx(), r); }
        expr_vector args() const {
          expr_vector vec(ctx());
          unsigned argCnt = num_args();
          for (unsigned i = 0; i < argCnt; i++)
            vec.push_back(arg(i));
          return vec;
        }
 
        expr body() const { assert(is_quantifier()); Z3_ast r = Z3_get_quantifier_body(ctx(), *this); check_error(); return expr(ctx(), r); }
 
        friend expr operator!(expr const & a);
 
        friend expr operator&&(expr const & a, expr const & b);
 
 
        friend expr operator&&(expr const & a, bool b);
        friend expr operator&&(bool a, expr const & b);
 
        friend expr operator||(expr const & a, expr const & b);
        friend expr operator||(expr const & a, bool b);
 
        friend expr operator||(bool a, expr const & b);
 
        friend expr implies(expr const & a, expr const & b);
        friend expr implies(expr const & a, bool b);
        friend expr implies(bool a, expr const & b);
 
        friend expr mk_or(expr_vector const& args);
        friend expr mk_xor(expr_vector const& args);
        friend expr mk_and(expr_vector const& args);
 
        friend expr ite(expr const & c, expr const & t, expr const & e);
 
        bool is_true() const { return is_app() && Z3_OP_TRUE == decl().decl_kind(); }
        bool is_false() const { return is_app() && Z3_OP_FALSE == decl().decl_kind(); }
        bool is_not() const { return is_app() && Z3_OP_NOT == decl().decl_kind(); }
        bool is_and() const { return is_app() && Z3_OP_AND == decl().decl_kind(); }
        bool is_or() const  { return is_app() && Z3_OP_OR  == decl().decl_kind(); }
        bool is_xor() const { return is_app() && Z3_OP_XOR  == decl().decl_kind(); }
        bool is_implies() const { return is_app() && Z3_OP_IMPLIES  == decl().decl_kind(); }
        bool is_eq() const { return is_app() && Z3_OP_EQ == decl().decl_kind(); }
        bool is_ite() const { return is_app() && Z3_OP_ITE == decl().decl_kind(); }
        bool is_distinct() const { return is_app() && Z3_OP_DISTINCT == decl().decl_kind(); }
 
        friend expr distinct(expr_vector const& args);
        friend expr concat(expr const& a, expr const& b);
        friend expr concat(expr_vector const& args);
 
        friend expr operator==(expr const & a, expr const & b);
        friend expr operator==(expr const & a, int b);
        friend expr operator==(int a, expr const & b);
 
        friend expr operator!=(expr const & a, expr const & b);
        friend expr operator!=(expr const & a, int b);
        friend expr operator!=(int a, expr const & b);
 
        friend expr operator+(expr const & a, expr const & b);
        friend expr operator+(expr const & a, int b);
        friend expr operator+(int a, expr const & b);
        friend expr sum(expr_vector const& args);
 
        friend expr operator*(expr const & a, expr const & b);
        friend expr operator*(expr const & a, int b);
        friend expr operator*(int a, expr const & b);
 
        /*  \brief Power operator  */
        friend expr pw(expr const & a, expr const & b);
        friend expr pw(expr const & a, int b);
        friend expr pw(int a, expr const & b);
 
        /* \brief mod operator */
        friend expr mod(expr const& a, expr const& b);
        friend expr mod(expr const& a, int b);
        friend expr mod(int a, expr const& b);
 
        /* \brief rem operator */
        friend expr rem(expr const& a, expr const& b);
        friend expr rem(expr const& a, int b);
        friend expr rem(int a, expr const& b);
 
        friend expr is_int(expr const& e);
 
        friend expr operator/(expr const & a, expr const & b);
        friend expr operator/(expr const & a, int b);
        friend expr operator/(int a, expr const & b);
 
        friend expr operator-(expr const & a);
 
        friend expr operator-(expr const & a, expr const & b);
        friend expr operator-(expr const & a, int b);
        friend expr operator-(int a, expr const & b);
 
        friend expr operator<=(expr const & a, expr const & b);
        friend expr operator<=(expr const & a, int b);
        friend expr operator<=(int a, expr const & b);
 
 
        friend expr operator>=(expr const & a, expr const & b);
        friend expr operator>=(expr const & a, int b);
        friend expr operator>=(int a, expr const & b);
 
        friend expr operator<(expr const & a, expr const & b);
        friend expr operator<(expr const & a, int b);
        friend expr operator<(int a, expr const & b);
 
        friend expr operator>(expr const & a, expr const & b);
        friend expr operator>(expr const & a, int b);
        friend expr operator>(int a, expr const & b);
 
        friend expr pble(expr_vector const& es, int const * coeffs, int bound);
        friend expr pbge(expr_vector const& es, int const * coeffs, int bound);
        friend expr pbeq(expr_vector const& es, int const * coeffs, int bound);
        friend expr atmost(expr_vector const& es, unsigned bound);
        friend expr atleast(expr_vector const& es, unsigned bound);
 
        friend expr operator&(expr const & a, expr const & b);
        friend expr operator&(expr const & a, int b);
        friend expr operator&(int a, expr const & b);
 
        friend expr operator^(expr const & a, expr const & b);
        friend expr operator^(expr const & a, int b);
        friend expr operator^(int a, expr const & b);
 
        friend expr operator|(expr const & a, expr const & b);
        friend expr operator|(expr const & a, int b);
        friend expr operator|(int a, expr const & b);
        friend expr nand(expr const& a, expr const& b);
        friend expr nor(expr const& a, expr const& b);
        friend expr xnor(expr const& a, expr const& b);
 
        friend expr min(expr const& a, expr const& b);
        friend expr max(expr const& a, expr const& b);
 
        friend expr bv2int(expr const& a, bool is_signed); 
        friend expr int2bv(unsigned n, expr const& a);
        friend expr bvadd_no_overflow(expr const& a, expr const& b, bool is_signed);
        friend expr bvadd_no_underflow(expr const& a, expr const& b);
        friend expr bvsub_no_overflow(expr const& a, expr const& b);
        friend expr bvsub_no_underflow(expr const& a, expr const& b, bool is_signed);
        friend expr bvsdiv_no_overflow(expr const& a, expr const& b);
        friend expr bvneg_no_overflow(expr const& a);
        friend expr bvmul_no_overflow(expr const& a, expr const& b, bool is_signed);
        friend expr bvmul_no_underflow(expr const& a, expr const& b);
        
        expr rotate_left(unsigned i) const { Z3_ast r = Z3_mk_rotate_left(ctx(), i, *this); ctx().check_error(); return expr(ctx(), r); }
        expr rotate_right(unsigned i) const { Z3_ast r = Z3_mk_rotate_right(ctx(), i, *this); ctx().check_error(); return expr(ctx(), r); }
        expr repeat(unsigned i) const { Z3_ast r = Z3_mk_repeat(ctx(), i, *this); ctx().check_error(); return expr(ctx(), r); }
 
        friend expr bvredor(expr const & a);
        friend expr bvredand(expr const & a);
 
        friend expr abs(expr const & a);
        friend expr sqrt(expr const & a, expr const & rm);
        friend expr fp_eq(expr const & a, expr const & b);
 
        friend expr operator~(expr const & a);
        expr extract(unsigned hi, unsigned lo) const { Z3_ast r = Z3_mk_extract(ctx(), hi, lo, *this); ctx().check_error(); return expr(ctx(), r); }
        expr bit2bool(unsigned i) const { Z3_ast r = Z3_mk_bit2bool(ctx(), i, *this); ctx().check_error(); return expr(ctx(), r); }
        unsigned lo() const { assert (is_app() && Z3_get_decl_num_parameters(ctx(), decl()) == 2); return static_cast<unsigned>(Z3_get_decl_int_parameter(ctx(), decl(), 1)); }
        unsigned hi() const { assert (is_app() && Z3_get_decl_num_parameters(ctx(), decl()) == 2); return static_cast<unsigned>(Z3_get_decl_int_parameter(ctx(), decl(), 0)); }
 
        friend expr fma(expr const& a, expr const& b, expr const& c, expr const& rm);
 
        friend expr fpa_fp(expr const& sgn, expr const& exp, expr const& sig);
 
        friend expr fpa_to_sbv(expr const& t, unsigned sz);
 
        friend expr fpa_to_ubv(expr const& t, unsigned sz);
 
        friend expr sbv_to_fpa(expr const& t, sort s);
 
        friend expr ubv_to_fpa(expr const& t, sort s);
 
        friend expr fpa_to_fpa(expr const& t, sort s);
 
        friend expr round_fpa_to_closest_integer(expr const& t);
 
        expr extract(expr const& offset, expr const& length) const {
            check_context(*this, offset); check_context(offset, length);
            Z3_ast r = Z3_mk_seq_extract(ctx(), *this, offset, length); check_error(); return expr(ctx(), r);
        }
        expr replace(expr const& src, expr const& dst) const {
            check_context(*this, src); check_context(src, dst);
            Z3_ast r = Z3_mk_seq_replace(ctx(), *this, src, dst);
            check_error();
            return expr(ctx(), r);
        }
        expr unit() const {
            Z3_ast r = Z3_mk_seq_unit(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr contains(expr const& s) const {
            check_context(*this, s);
            Z3_ast r = Z3_mk_seq_contains(ctx(), *this, s);
            check_error();
            return expr(ctx(), r);
        }
        expr at(expr const& index) const {
            check_context(*this, index);
            Z3_ast r = Z3_mk_seq_at(ctx(), *this, index);
            check_error();
            return expr(ctx(), r);
        }
        expr nth(expr const& index) const {
            check_context(*this, index);
            Z3_ast r = Z3_mk_seq_nth(ctx(), *this, index);
            check_error();
            return expr(ctx(), r);
        }
        expr length() const {
            Z3_ast r = Z3_mk_seq_length(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr stoi() const {
            Z3_ast r = Z3_mk_str_to_int(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr itos() const {
            Z3_ast r = Z3_mk_int_to_str(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr ubvtos() const {
            Z3_ast r = Z3_mk_ubv_to_str(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr sbvtos() const {
            Z3_ast r = Z3_mk_sbv_to_str(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr char_to_int() const {
            Z3_ast r = Z3_mk_char_to_int(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr char_to_bv() const {
            Z3_ast r = Z3_mk_char_to_bv(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr char_from_bv() const {
            Z3_ast r = Z3_mk_char_from_bv(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
        expr is_digit() const {
            Z3_ast r = Z3_mk_char_is_digit(ctx(), *this);
            check_error();
            return expr(ctx(), r);
        }
 
        friend expr range(expr const& lo, expr const& hi);
        expr loop(unsigned lo) {
            Z3_ast r = Z3_mk_re_loop(ctx(), m_ast, lo, 0);
            check_error();
            return expr(ctx(), r);
        }
        expr loop(unsigned lo, unsigned hi) {
            Z3_ast r = Z3_mk_re_loop(ctx(), m_ast, lo, hi);
            check_error();
            return expr(ctx(), r);
        }
 
        expr operator[](expr const& index) const {
            assert(is_array() || is_seq());
            if (is_array()) {
                return select(*this, index);
            }
            return nth(index);            
        }
 
        expr operator[](expr_vector const& index) const {
            return select(*this, index);
        }
 
        expr simplify() const { Z3_ast r = Z3_simplify(ctx(), m_ast); check_error(); return expr(ctx(), r); }
        expr simplify(params const & p) const { Z3_ast r = Z3_simplify_ex(ctx(), m_ast, p); check_error(); return expr(ctx(), r); }
 
        expr substitute(expr_vector const& src, expr_vector const& dst);
 
        expr substitute(expr_vector const& dst);
 
        expr substitute(func_decl_vector const& funs, expr_vector const& bodies);
 
 
    class iterator {
            expr& e;
            unsigned i;
        public:
            iterator(expr& e, unsigned i): e(e), i(i) {}
            bool operator==(iterator const& other) const noexcept {
                return i == other.i;
            }
            bool operator!=(iterator const& other) const noexcept {
                return i != other.i;
            }
            expr operator*() const { return e.arg(i); }
            iterator& operator++() { ++i; return *this; }
            iterator operator++(int) { assert(false); return *this; }
        };
 
        iterator begin() { return iterator(*this, 0); }
        iterator end() { return iterator(*this, is_app() ? num_args() : 0); }
 
   };
 
#define _Z3_MK_BIN_(a, b, binop)                        \
    check_context(a, b);                                \
    Z3_ast r = binop(a.ctx(), a, b);                    \
    a.check_error();                                    \
    return expr(a.ctx(), r);                            \
 
 
    inline expr implies(expr const & a, expr const & b) {
        assert(a.is_bool() && b.is_bool());
        _Z3_MK_BIN_(a, b, Z3_mk_implies);
    }
    inline expr implies(expr const & a, bool b) { return implies(a, a.ctx().bool_val(b)); }
    inline expr implies(bool a, expr const & b) { return implies(b.ctx().bool_val(a), b); }
 
 
    inline expr pw(expr const & a, expr const & b) { _Z3_MK_BIN_(a, b, Z3_mk_power);   }
    inline expr pw(expr const & a, int b) { return pw(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr pw(int a, expr const & b) { return pw(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr mod(expr const& a, expr const& b) { 
        if (a.is_bv()) {
            _Z3_MK_BIN_(a, b, Z3_mk_bvsmod);   
        }
        else {
            _Z3_MK_BIN_(a, b, Z3_mk_mod);   
        }
    }
    inline expr mod(expr const & a, int b) { return mod(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr mod(int a, expr const & b) { return mod(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr operator%(expr const& a, expr const& b) { return mod(a, b); }
    inline expr operator%(expr const& a, int b) { return mod(a, b); }
    inline expr operator%(int a, expr const& b) { return mod(a, b); }
 
 
    inline expr rem(expr const& a, expr const& b) {
        if (a.is_fpa() && b.is_fpa()) {
            _Z3_MK_BIN_(a, b, Z3_mk_fpa_rem);
        } else {
            _Z3_MK_BIN_(a, b, Z3_mk_rem);
        }
    }
    inline expr rem(expr const & a, int b) { return rem(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr rem(int a, expr const & b) { return rem(b.ctx().num_val(a, b.get_sort()), b); }
 
#undef _Z3_MK_BIN_
 
#define _Z3_MK_UN_(a, mkun)                     \
    Z3_ast r = mkun(a.ctx(), a);                \
    a.check_error();                            \
    return expr(a.ctx(), r);                    \
 
 
    inline expr operator!(expr const & a) { assert(a.is_bool()); _Z3_MK_UN_(a, Z3_mk_not); }
 
    inline expr is_int(expr const& e) { _Z3_MK_UN_(e, Z3_mk_is_int); }
 
#undef _Z3_MK_UN_
 
    inline expr operator&&(expr const & a, expr const & b) {
        check_context(a, b);
        assert(a.is_bool() && b.is_bool());
        Z3_ast args[2] = { a, b };
        Z3_ast r = Z3_mk_and(a.ctx(), 2, args);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr operator&&(expr const & a, bool b) { return a && a.ctx().bool_val(b); }
    inline expr operator&&(bool a, expr const & b) { return b.ctx().bool_val(a) && b; }
 
    inline expr operator||(expr const & a, expr const & b) {
        check_context(a, b);
        assert(a.is_bool() && b.is_bool());
        Z3_ast args[2] = { a, b };
        Z3_ast r = Z3_mk_or(a.ctx(), 2, args);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr operator||(expr const & a, bool b) { return a || a.ctx().bool_val(b); }
 
    inline expr operator||(bool a, expr const & b) { return b.ctx().bool_val(a) || b; }
 
    inline expr operator==(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = Z3_mk_eq(a.ctx(), a, b);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator==(expr const & a, int b) { assert(a.is_arith() || a.is_bv() || a.is_fpa()); return a == a.ctx().num_val(b, a.get_sort()); }
    inline expr operator==(int a, expr const & b) { assert(b.is_arith() || b.is_bv() || b.is_fpa()); return b.ctx().num_val(a, b.get_sort()) == b; }
    inline expr operator==(expr const & a, double b) { assert(a.is_fpa()); return a == a.ctx().fpa_val(b); }
    inline expr operator==(double a, expr const & b) { assert(b.is_fpa()); return b.ctx().fpa_val(a) == b; }
 
    inline expr operator!=(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast args[2] = { a, b };
        Z3_ast r = Z3_mk_distinct(a.ctx(), 2, args);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator!=(expr const & a, int b) { assert(a.is_arith() || a.is_bv() || a.is_fpa()); return a != a.ctx().num_val(b, a.get_sort()); }
    inline expr operator!=(int a, expr const & b) { assert(b.is_arith() || b.is_bv() || b.is_fpa()); return b.ctx().num_val(a, b.get_sort()) != b; }
    inline expr operator!=(expr const & a, double b) { assert(a.is_fpa()); return a != a.ctx().fpa_val(b); }
    inline expr operator!=(double a, expr const & b) { assert(b.is_fpa()); return b.ctx().fpa_val(a) != b; }
 
    inline expr operator+(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            Z3_ast args[2] = { a, b };
            r = Z3_mk_add(a.ctx(), 2, args);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvadd(a.ctx(), a, b);
        }
        else if (a.is_seq() && b.is_seq()) {
            return concat(a, b);
        }
        else if (a.is_re() && b.is_re()) {
            Z3_ast _args[2] = { a, b };
            r = Z3_mk_re_union(a.ctx(), 2, _args);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_add(a.ctx(), a.ctx().fpa_rounding_mode(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator+(expr const & a, int b) { return a + a.ctx().num_val(b, a.get_sort()); }
    inline expr operator+(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) + b; }
 
    inline expr operator*(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            Z3_ast args[2] = { a, b };
            r = Z3_mk_mul(a.ctx(), 2, args);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvmul(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_mul(a.ctx(), a.ctx().fpa_rounding_mode(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator*(expr const & a, int b) { return a * a.ctx().num_val(b, a.get_sort()); }
    inline expr operator*(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) * b; }
 
 
    inline expr operator>=(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            r = Z3_mk_ge(a.ctx(), a, b);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvsge(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_geq(a.ctx(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr operator/(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            r = Z3_mk_div(a.ctx(), a, b);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvsdiv(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_div(a.ctx(), a.ctx().fpa_rounding_mode(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator/(expr const & a, int b) { return a / a.ctx().num_val(b, a.get_sort()); }
    inline expr operator/(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) / b; }
 
    inline expr operator-(expr const & a) {
        Z3_ast r = 0;
        if (a.is_arith()) {
            r = Z3_mk_unary_minus(a.ctx(), a);
        }
        else if (a.is_bv()) {
            r = Z3_mk_bvneg(a.ctx(), a);
        }
        else if (a.is_fpa()) {
            r = Z3_mk_fpa_neg(a.ctx(), a);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr operator-(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            Z3_ast args[2] = { a, b };
            r = Z3_mk_sub(a.ctx(), 2, args);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvsub(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_sub(a.ctx(), a.ctx().fpa_rounding_mode(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator-(expr const & a, int b) { return a - a.ctx().num_val(b, a.get_sort()); }
    inline expr operator-(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) - b; }
 
    inline expr operator<=(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            r = Z3_mk_le(a.ctx(), a, b);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvsle(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_leq(a.ctx(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator<=(expr const & a, int b) { return a <= a.ctx().num_val(b, a.get_sort()); }
    inline expr operator<=(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) <= b; }
 
    inline expr operator>=(expr const & a, int b) { return a >= a.ctx().num_val(b, a.get_sort()); }
    inline expr operator>=(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) >= b; }
 
    inline expr operator<(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            r = Z3_mk_lt(a.ctx(), a, b);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvslt(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_lt(a.ctx(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator<(expr const & a, int b) { return a < a.ctx().num_val(b, a.get_sort()); }
    inline expr operator<(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) < b; }
 
    inline expr operator>(expr const & a, expr const & b) {
        check_context(a, b);
        Z3_ast r = 0;
        if (a.is_arith() && b.is_arith()) {
            r = Z3_mk_gt(a.ctx(), a, b);
        }
        else if (a.is_bv() && b.is_bv()) {
            r = Z3_mk_bvsgt(a.ctx(), a, b);
        }
        else if (a.is_fpa() && b.is_fpa()) {
            r = Z3_mk_fpa_gt(a.ctx(), a, b);
        }
        else {
            // operator is not supported by given arguments.
            assert(false);
        }
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator>(expr const & a, int b) { return a > a.ctx().num_val(b, a.get_sort()); }
    inline expr operator>(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) > b; }
 
    inline expr operator&(expr const & a, expr const & b) { if (a.is_bool()) return a && b; check_context(a, b); Z3_ast r = Z3_mk_bvand(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); }
    inline expr operator&(expr const & a, int b) { return a & a.ctx().num_val(b, a.get_sort()); }
    inline expr operator&(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) & b; }
 
    inline expr operator^(expr const & a, expr const & b) { check_context(a, b); Z3_ast r = a.is_bool() ? Z3_mk_xor(a.ctx(), a, b) : Z3_mk_bvxor(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); }
    inline expr operator^(expr const & a, int b) { return a ^ a.ctx().num_val(b, a.get_sort()); }
    inline expr operator^(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) ^ b; }
 
    inline expr operator|(expr const & a, expr const & b) { if (a.is_bool()) return a || b; check_context(a, b); Z3_ast r = Z3_mk_bvor(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); }
    inline expr operator|(expr const & a, int b) { return a | a.ctx().num_val(b, a.get_sort()); }
    inline expr operator|(int a, expr const & b) { return b.ctx().num_val(a, b.get_sort()) | b; }
 
    inline expr nand(expr const& a, expr const& b) { if (a.is_bool()) return !(a && b); check_context(a, b); Z3_ast r = Z3_mk_bvnand(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); }
    inline expr nor(expr const& a, expr const& b) { if (a.is_bool()) return !(a || b); check_context(a, b); Z3_ast r = Z3_mk_bvnor(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); }
    inline expr xnor(expr const& a, expr const& b) { if (a.is_bool()) return !(a ^ b); check_context(a, b); Z3_ast r = Z3_mk_bvxnor(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); }
    inline expr min(expr const& a, expr const& b) { 
        check_context(a, b); 
        Z3_ast r;
        if (a.is_arith()) {
            r = Z3_mk_ite(a.ctx(), Z3_mk_ge(a.ctx(), a, b), b, a);
        }
        else if (a.is_bv()) {
            r = Z3_mk_ite(a.ctx(), Z3_mk_bvuge(a.ctx(), a, b), b, a);
        }
        else {
            assert(a.is_fpa());
            r = Z3_mk_fpa_min(a.ctx(), a, b); 
        }
        a.check_error();
        return expr(a.ctx(), r); 
    }
    inline expr max(expr const& a, expr const& b) { 
        check_context(a, b); 
        Z3_ast r;
        if (a.is_arith()) {
            r = Z3_mk_ite(a.ctx(), Z3_mk_ge(a.ctx(), a, b), a, b);
        }
        else if (a.is_bv()) {
            r = Z3_mk_ite(a.ctx(), Z3_mk_bvuge(a.ctx(), a, b), a, b);
        }
        else {
            assert(a.is_fpa());
            r = Z3_mk_fpa_max(a.ctx(), a, b); 
        }
        a.check_error();
        return expr(a.ctx(), r); 
    }
    inline expr bvredor(expr const & a) {
        assert(a.is_bv());
        Z3_ast r = Z3_mk_bvredor(a.ctx(), a);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr bvredand(expr const & a) {
        assert(a.is_bv());
        Z3_ast r = Z3_mk_bvredand(a.ctx(), a);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr abs(expr const & a) { 
        Z3_ast r;
        if (a.is_int()) {
            expr zero = a.ctx().int_val(0);
        expr ge = a >= zero;
        expr na = -a;
            r = Z3_mk_ite(a.ctx(), ge, a, na);      
        }
        else if (a.is_real()) {
            expr zero = a.ctx().real_val(0);
        expr ge = a >= zero;
        expr na = -a;
            r = Z3_mk_ite(a.ctx(), ge, a, na);
        }
        else {
            r = Z3_mk_fpa_abs(a.ctx(), a); 
        }
        a.check_error();
        return expr(a.ctx(), r); 
    }
    inline expr sqrt(expr const & a, expr const& rm) {
        check_context(a, rm);
        assert(a.is_fpa());
        Z3_ast r = Z3_mk_fpa_sqrt(a.ctx(), rm, a);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr fp_eq(expr const & a, expr const & b) {
        check_context(a, b);
        assert(a.is_fpa());
        Z3_ast r = Z3_mk_fpa_eq(a.ctx(), a, b);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr operator~(expr const & a) { Z3_ast r = Z3_mk_bvnot(a.ctx(), a); return expr(a.ctx(), r); }
 
    inline expr fma(expr const& a, expr const& b, expr const& c, expr const& rm) {
        check_context(a, b); check_context(a, c); check_context(a, rm);
        assert(a.is_fpa() && b.is_fpa() && c.is_fpa());
        Z3_ast r = Z3_mk_fpa_fma(a.ctx(), rm, a, b, c);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr fpa_fp(expr const& sgn, expr const& exp, expr const& sig) {
        check_context(sgn, exp); check_context(exp, sig);
        assert(sgn.is_bv() && exp.is_bv() && sig.is_bv());
        Z3_ast r = Z3_mk_fpa_fp(sgn.ctx(), sgn, exp, sig);
        sgn.check_error();
        return expr(sgn.ctx(), r);
    }
 
    inline expr fpa_to_sbv(expr const& t, unsigned sz) {
        assert(t.is_fpa());
        Z3_ast r = Z3_mk_fpa_to_sbv(t.ctx(), t.ctx().fpa_rounding_mode(), t, sz);
        t.check_error();
        return expr(t.ctx(), r);
    }
 
    inline expr fpa_to_ubv(expr const& t, unsigned sz) {
        assert(t.is_fpa());
        Z3_ast r = Z3_mk_fpa_to_ubv(t.ctx(), t.ctx().fpa_rounding_mode(), t, sz);
        t.check_error();
        return expr(t.ctx(), r);
    }
 
    inline expr sbv_to_fpa(expr const& t, sort s) {
        assert(t.is_bv());
        Z3_ast r = Z3_mk_fpa_to_fp_signed(t.ctx(), t.ctx().fpa_rounding_mode(), t, s);
        t.check_error();
        return expr(t.ctx(), r);
    }
 
    inline expr ubv_to_fpa(expr const& t, sort s) {
        assert(t.is_bv());
        Z3_ast r = Z3_mk_fpa_to_fp_unsigned(t.ctx(), t.ctx().fpa_rounding_mode(), t, s);
        t.check_error();
        return expr(t.ctx(), r);
    }
 
    inline expr fpa_to_fpa(expr const& t, sort s) {
        assert(t.is_fpa());
        Z3_ast r = Z3_mk_fpa_to_fp_float(t.ctx(), t.ctx().fpa_rounding_mode(), t, s);
        t.check_error();
        return expr(t.ctx(), r);
    }
 
    inline expr round_fpa_to_closest_integer(expr const& t) {
        assert(t.is_fpa());
        Z3_ast r = Z3_mk_fpa_round_to_integral(t.ctx(), t.ctx().fpa_rounding_mode(), t);
        t.check_error();
        return expr(t.ctx(), r);
    }
 
    inline expr ite(expr const & c, expr const & t, expr const & e) {
        check_context(c, t); check_context(c, e);
        assert(c.is_bool());
        Z3_ast r = Z3_mk_ite(c.ctx(), c, t, e);
        c.check_error();
        return expr(c.ctx(), r);
    }
 
 
    inline expr to_expr(context & c, Z3_ast a) {
        c.check_error();
        assert(Z3_get_ast_kind(c, a) == Z3_APP_AST ||
               Z3_get_ast_kind(c, a) == Z3_NUMERAL_AST ||
               Z3_get_ast_kind(c, a) == Z3_VAR_AST ||
               Z3_get_ast_kind(c, a) == Z3_QUANTIFIER_AST);
        return expr(c, a);
    }
 
    inline sort to_sort(context & c, Z3_sort s) {
        c.check_error();
        return sort(c, s);
    }
 
    inline func_decl to_func_decl(context & c, Z3_func_decl f) {
        c.check_error();
        return func_decl(c, f);
    }
 
    inline expr sle(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvsle(a.ctx(), a, b)); }
    inline expr sle(expr const & a, int b) { return sle(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr sle(int a, expr const & b) { return sle(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr slt(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvslt(a.ctx(), a, b)); }
    inline expr slt(expr const & a, int b) { return slt(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr slt(int a, expr const & b) { return slt(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr sge(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvsge(a.ctx(), a, b)); }
    inline expr sge(expr const & a, int b) { return sge(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr sge(int a, expr const & b) { return sge(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr sgt(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvsgt(a.ctx(), a, b)); }
    inline expr sgt(expr const & a, int b) { return sgt(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr sgt(int a, expr const & b) { return sgt(b.ctx().num_val(a, b.get_sort()), b); }
 
 
    inline expr ule(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvule(a.ctx(), a, b)); }
    inline expr ule(expr const & a, int b) { return ule(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr ule(int a, expr const & b) { return ule(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr ult(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvult(a.ctx(), a, b)); }
    inline expr ult(expr const & a, int b) { return ult(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr ult(int a, expr const & b) { return ult(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr uge(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvuge(a.ctx(), a, b)); }
    inline expr uge(expr const & a, int b) { return uge(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr uge(int a, expr const & b) { return uge(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr ugt(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvugt(a.ctx(), a, b)); }
    inline expr ugt(expr const & a, int b) { return ugt(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr ugt(int a, expr const & b) { return ugt(b.ctx().num_val(a, b.get_sort()), b); }
    inline expr udiv(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvudiv(a.ctx(), a, b)); }
    inline expr udiv(expr const & a, int b) { return udiv(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr udiv(int a, expr const & b) { return udiv(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr srem(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvsrem(a.ctx(), a, b)); }
    inline expr srem(expr const & a, int b) { return srem(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr srem(int a, expr const & b) { return srem(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr smod(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvsmod(a.ctx(), a, b)); }
    inline expr smod(expr const & a, int b) { return smod(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr smod(int a, expr const & b) { return smod(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr urem(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvurem(a.ctx(), a, b)); }
    inline expr urem(expr const & a, int b) { return urem(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr urem(int a, expr const & b) { return urem(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr shl(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvshl(a.ctx(), a, b)); }
    inline expr shl(expr const & a, int b) { return shl(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr shl(int a, expr const & b) { return shl(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr lshr(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvlshr(a.ctx(), a, b)); }
    inline expr lshr(expr const & a, int b) { return lshr(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr lshr(int a, expr const & b) { return lshr(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr ashr(expr const & a, expr const & b) { return to_expr(a.ctx(), Z3_mk_bvashr(a.ctx(), a, b)); }
    inline expr ashr(expr const & a, int b) { return ashr(a, a.ctx().num_val(b, a.get_sort())); }
    inline expr ashr(int a, expr const & b) { return ashr(b.ctx().num_val(a, b.get_sort()), b); }
 
    inline expr zext(expr const & a, unsigned i) { return to_expr(a.ctx(), Z3_mk_zero_ext(a.ctx(), i, a)); }
 
    inline expr bv2int(expr const& a, bool is_signed) { Z3_ast r = Z3_mk_bv2int(a.ctx(), a, is_signed); a.check_error(); return expr(a.ctx(), r); }
    inline expr int2bv(unsigned n, expr const& a) { Z3_ast r = Z3_mk_int2bv(a.ctx(), n, a); a.check_error(); return expr(a.ctx(), r); }
 
    inline expr bvadd_no_overflow(expr const& a, expr const& b, bool is_signed) { 
        check_context(a, b); Z3_ast r = Z3_mk_bvadd_no_overflow(a.ctx(), a, b, is_signed); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvadd_no_underflow(expr const& a, expr const& b) {
        check_context(a, b); Z3_ast r = Z3_mk_bvadd_no_underflow(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvsub_no_overflow(expr const& a, expr const& b) {
        check_context(a, b); Z3_ast r = Z3_mk_bvsub_no_overflow(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvsub_no_underflow(expr const& a, expr const& b, bool is_signed) {
        check_context(a, b); Z3_ast r = Z3_mk_bvsub_no_underflow(a.ctx(), a, b, is_signed); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvsdiv_no_overflow(expr const& a, expr const& b) {
        check_context(a, b); Z3_ast r = Z3_mk_bvsdiv_no_overflow(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvneg_no_overflow(expr const& a) {
        Z3_ast r = Z3_mk_bvneg_no_overflow(a.ctx(), a); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvmul_no_overflow(expr const& a, expr const& b, bool is_signed) {
        check_context(a, b); Z3_ast r = Z3_mk_bvmul_no_overflow(a.ctx(), a, b, is_signed); a.check_error(); return expr(a.ctx(), r); 
    }
    inline expr bvmul_no_underflow(expr const& a, expr const& b) {
        check_context(a, b); Z3_ast r = Z3_mk_bvmul_no_underflow(a.ctx(), a, b); a.check_error(); return expr(a.ctx(), r); 
    }
 
 
    inline expr sext(expr const & a, unsigned i) { return to_expr(a.ctx(), Z3_mk_sign_ext(a.ctx(), i, a)); }
 
    inline func_decl linear_order(sort const& a, unsigned index) {
        return to_func_decl(a.ctx(), Z3_mk_linear_order(a.ctx(), a, index));
    }
    inline func_decl partial_order(sort const& a, unsigned index) {
        return to_func_decl(a.ctx(), Z3_mk_partial_order(a.ctx(), a, index));
    }
    inline func_decl piecewise_linear_order(sort const& a, unsigned index) {
        return to_func_decl(a.ctx(), Z3_mk_piecewise_linear_order(a.ctx(), a, index));
    }
    inline func_decl tree_order(sort const& a, unsigned index) {
        return to_func_decl(a.ctx(), Z3_mk_tree_order(a.ctx(), a, index));
    }
 
    template<> class cast_ast<ast> {
    public:
        ast operator()(context & c, Z3_ast a) { return ast(c, a); }
    };
 
    template<> class cast_ast<expr> {
    public:
        expr operator()(context & c, Z3_ast a) {
            assert(Z3_get_ast_kind(c, a) == Z3_NUMERAL_AST ||
                   Z3_get_ast_kind(c, a) == Z3_APP_AST ||
                   Z3_get_ast_kind(c, a) == Z3_QUANTIFIER_AST ||
                   Z3_get_ast_kind(c, a) == Z3_VAR_AST);
            return expr(c, a);
        }
    };
 
    template<> class cast_ast<sort> {
    public:
        sort operator()(context & c, Z3_ast a) {
            assert(Z3_get_ast_kind(c, a) == Z3_SORT_AST);
            return sort(c, reinterpret_cast<Z3_sort>(a));
        }
    };
 
    template<> class cast_ast<func_decl> {
    public:
        func_decl operator()(context & c, Z3_ast a) {
            assert(Z3_get_ast_kind(c, a) == Z3_FUNC_DECL_AST);
            return func_decl(c, reinterpret_cast<Z3_func_decl>(a));
        }
    };
 
    template<typename T>
    template<typename T2>
    array<T>::array(ast_vector_tpl<T2> const & v):m_array(new T[v.size()]), m_size(v.size()) {
        for (unsigned i = 0; i < m_size; i++) {
            m_array[i] = v[i];
        }
    }
 
    // Basic functions for creating quantified formulas.
    // The C API should be used for creating quantifiers with patterns, weights, many variables, etc.
    inline expr forall(expr const & x, expr const & b) {
        check_context(x, b);
        Z3_app vars[] = {(Z3_app) x};
        Z3_ast r = Z3_mk_forall_const(b.ctx(), 0, 1, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr forall(expr const & x1, expr const & x2, expr const & b) {
        check_context(x1, b); check_context(x2, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2};
        Z3_ast r = Z3_mk_forall_const(b.ctx(), 0, 2, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr forall(expr const & x1, expr const & x2, expr const & x3, expr const & b) {
        check_context(x1, b); check_context(x2, b); check_context(x3, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2, (Z3_app) x3 };
        Z3_ast r = Z3_mk_forall_const(b.ctx(), 0, 3, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr forall(expr const & x1, expr const & x2, expr const & x3, expr const & x4, expr const & b) {
        check_context(x1, b); check_context(x2, b); check_context(x3, b); check_context(x4, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2, (Z3_app) x3, (Z3_app) x4 };
        Z3_ast r = Z3_mk_forall_const(b.ctx(), 0, 4, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr forall(expr_vector const & xs, expr const & b) {
        array<Z3_app> vars(xs);
        Z3_ast r = Z3_mk_forall_const(b.ctx(), 0, vars.size(), vars.ptr(), 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr exists(expr const & x, expr const & b) {
        check_context(x, b);
        Z3_app vars[] = {(Z3_app) x};
        Z3_ast r = Z3_mk_exists_const(b.ctx(), 0, 1, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr exists(expr const & x1, expr const & x2, expr const & b) {
        check_context(x1, b); check_context(x2, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2};
        Z3_ast r = Z3_mk_exists_const(b.ctx(), 0, 2, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr exists(expr const & x1, expr const & x2, expr const & x3, expr const & b) {
        check_context(x1, b); check_context(x2, b); check_context(x3, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2, (Z3_app) x3 };
        Z3_ast r = Z3_mk_exists_const(b.ctx(), 0, 3, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr exists(expr const & x1, expr const & x2, expr const & x3, expr const & x4, expr const & b) {
        check_context(x1, b); check_context(x2, b); check_context(x3, b); check_context(x4, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2, (Z3_app) x3, (Z3_app) x4 };
        Z3_ast r = Z3_mk_exists_const(b.ctx(), 0, 4, vars, 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr exists(expr_vector const & xs, expr const & b) {
        array<Z3_app> vars(xs);
        Z3_ast r = Z3_mk_exists_const(b.ctx(), 0, vars.size(), vars.ptr(), 0, 0, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr lambda(expr const & x, expr const & b) {
        check_context(x, b);
        Z3_app vars[] = {(Z3_app) x};
        Z3_ast r = Z3_mk_lambda_const(b.ctx(), 1, vars, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr lambda(expr const & x1, expr const & x2, expr const & b) {
        check_context(x1, b); check_context(x2, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2};
        Z3_ast r = Z3_mk_lambda_const(b.ctx(), 2, vars, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr lambda(expr const & x1, expr const & x2, expr const & x3, expr const & b) {
        check_context(x1, b); check_context(x2, b); check_context(x3, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2, (Z3_app) x3 };
        Z3_ast r = Z3_mk_lambda_const(b.ctx(), 3, vars, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr lambda(expr const & x1, expr const & x2, expr const & x3, expr const & x4, expr const & b) {
        check_context(x1, b); check_context(x2, b); check_context(x3, b); check_context(x4, b);
        Z3_app vars[] = {(Z3_app) x1, (Z3_app) x2, (Z3_app) x3, (Z3_app) x4 };
        Z3_ast r = Z3_mk_lambda_const(b.ctx(), 4, vars, b); b.check_error(); return expr(b.ctx(), r);
    }
    inline expr lambda(expr_vector const & xs, expr const & b) {
        array<Z3_app> vars(xs);
        Z3_ast r = Z3_mk_lambda_const(b.ctx(), vars.size(), vars.ptr(), b); b.check_error(); return expr(b.ctx(), r);
    }
 
    inline expr pble(expr_vector const& es, int const* coeffs, int bound) {
        assert(es.size() > 0);
        context& ctx = es[0u].ctx();
        array<Z3_ast> _es(es);
        Z3_ast r = Z3_mk_pble(ctx, _es.size(), _es.ptr(), coeffs, bound);
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr pbge(expr_vector const& es, int const* coeffs, int bound) {
        assert(es.size() > 0);
        context& ctx = es[0u].ctx();
        array<Z3_ast> _es(es);
        Z3_ast r = Z3_mk_pbge(ctx, _es.size(), _es.ptr(), coeffs, bound);
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr pbeq(expr_vector const& es, int const* coeffs, int bound) {
        assert(es.size() > 0);
        context& ctx = es[0u].ctx();
        array<Z3_ast> _es(es);
        Z3_ast r = Z3_mk_pbeq(ctx, _es.size(), _es.ptr(), coeffs, bound);
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr atmost(expr_vector const& es, unsigned bound) {
        assert(es.size() > 0);
        context& ctx = es[0u].ctx();
        array<Z3_ast> _es(es);
        Z3_ast r = Z3_mk_atmost(ctx, _es.size(), _es.ptr(), bound);
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr atleast(expr_vector const& es, unsigned bound) {
        assert(es.size() > 0);
        context& ctx = es[0u].ctx();
        array<Z3_ast> _es(es);
        Z3_ast r = Z3_mk_atleast(ctx, _es.size(), _es.ptr(), bound);
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr sum(expr_vector const& args) {
        assert(args.size() > 0);
        context& ctx = args[0u].ctx();
        array<Z3_ast> _args(args);
        Z3_ast r = Z3_mk_add(ctx, _args.size(), _args.ptr());
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr distinct(expr_vector const& args) {
        assert(args.size() > 0);
        context& ctx = args[0u].ctx();
        array<Z3_ast> _args(args);
        Z3_ast r = Z3_mk_distinct(ctx, _args.size(), _args.ptr());
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr concat(expr const& a, expr const& b) {
        check_context(a, b);
        Z3_ast r;
        if (Z3_is_seq_sort(a.ctx(), a.get_sort())) {
            Z3_ast _args[2] = { a, b };
            r = Z3_mk_seq_concat(a.ctx(), 2, _args);
        }
        else if (Z3_is_re_sort(a.ctx(), a.get_sort())) {
            Z3_ast _args[2] = { a, b };
            r = Z3_mk_re_concat(a.ctx(), 2, _args);
        }
        else {
            r = Z3_mk_concat(a.ctx(), a, b);
        }
        a.ctx().check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr concat(expr_vector const& args) {
        Z3_ast r;
        assert(args.size() > 0);
        if (args.size() == 1) {
            return args[0u];
        }
        context& ctx = args[0u].ctx();
        array<Z3_ast> _args(args);
        if (Z3_is_seq_sort(ctx, args[0u].get_sort())) {
            r = Z3_mk_seq_concat(ctx, _args.size(), _args.ptr());
        }
        else if (Z3_is_re_sort(ctx, args[0u].get_sort())) {
            r = Z3_mk_re_concat(ctx, _args.size(), _args.ptr());
        }
        else {
            r = _args[args.size()-1];
            for (unsigned i = args.size()-1; i > 0; ) {
                --i;
                r = Z3_mk_concat(ctx, _args[i], r);
                ctx.check_error();
            }
        }
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr map(expr const& f, expr const& list) {
        context& ctx = f.ctx();
        Z3_ast r = Z3_mk_seq_map(ctx, f, list);
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr mapi(expr const& f, expr const& i, expr const& list) {
        context& ctx = f.ctx();
        Z3_ast r = Z3_mk_seq_mapi(ctx, f, i, list);
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr foldl(expr const& f, expr const& a, expr const& list) {
        context& ctx = f.ctx();
        Z3_ast r = Z3_mk_seq_foldl(ctx, f, a, list);
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr foldli(expr const& f, expr const& i, expr const& a, expr const& list) {
        context& ctx = f.ctx();
        Z3_ast r = Z3_mk_seq_foldli(ctx, f, i, a, list);
        ctx.check_error();
        return expr(ctx, r);
    }
 
    inline expr mk_or(expr_vector const& args) {
        array<Z3_ast> _args(args);
        Z3_ast r = Z3_mk_or(args.ctx(), _args.size(), _args.ptr());
        args.check_error();
        return expr(args.ctx(), r);
    }
    inline expr mk_and(expr_vector const& args) {
        array<Z3_ast> _args(args);
        Z3_ast r = Z3_mk_and(args.ctx(), _args.size(), _args.ptr());
        args.check_error();
        return expr(args.ctx(), r);
    }
    inline expr mk_xor(expr_vector const& args) {
        if (args.empty())
            return args.ctx().bool_val(false);
        expr r = args[0u];
        for (unsigned i = 1; i < args.size(); ++i)
            r = r ^ args[i];
        return r;
    }
 
 
    class func_entry : public object {
        Z3_func_entry m_entry;
        void init(Z3_func_entry e) {
            m_entry = e;
            Z3_func_entry_inc_ref(ctx(), m_entry);
        }
    public:
        func_entry(context & c, Z3_func_entry e):object(c) { init(e); }
        func_entry(func_entry const & s):object(s) { init(s.m_entry); }
        ~func_entry() override { Z3_func_entry_dec_ref(ctx(), m_entry); }
        operator Z3_func_entry() const { return m_entry; }
        func_entry & operator=(func_entry const & s) {
            Z3_func_entry_inc_ref(s.ctx(), s.m_entry);
            Z3_func_entry_dec_ref(ctx(), m_entry);
            object::operator=(s);
            m_entry = s.m_entry;
            return *this;
        }
        expr value() const { Z3_ast r = Z3_func_entry_get_value(ctx(), m_entry); check_error(); return expr(ctx(), r); }
        unsigned num_args() const { unsigned r = Z3_func_entry_get_num_args(ctx(), m_entry); check_error(); return r; }
        expr arg(unsigned i) const { Z3_ast r = Z3_func_entry_get_arg(ctx(), m_entry, i); check_error(); return expr(ctx(), r); }
    };
 
    class func_interp : public object {
        Z3_func_interp m_interp;
        void init(Z3_func_interp e) {
            m_interp = e;
            Z3_func_interp_inc_ref(ctx(), m_interp);
        }
    public:
        func_interp(context & c, Z3_func_interp e):object(c) { init(e); }
        func_interp(func_interp const & s):object(s) { init(s.m_interp); }
        ~func_interp() override { Z3_func_interp_dec_ref(ctx(), m_interp); }
        operator Z3_func_interp() const { return m_interp; }
        func_interp & operator=(func_interp const & s) {
            Z3_func_interp_inc_ref(s.ctx(), s.m_interp);
            Z3_func_interp_dec_ref(ctx(), m_interp);
            object::operator=(s);
            m_interp = s.m_interp;
            return *this;
        }
        expr else_value() const { Z3_ast r = Z3_func_interp_get_else(ctx(), m_interp); check_error(); return expr(ctx(), r); }
        unsigned num_entries() const { unsigned r = Z3_func_interp_get_num_entries(ctx(), m_interp); check_error(); return r; }
        func_entry entry(unsigned i) const { Z3_func_entry e = Z3_func_interp_get_entry(ctx(), m_interp, i); check_error(); return func_entry(ctx(), e); }
        void add_entry(expr_vector const& args, expr& value) {
            Z3_func_interp_add_entry(ctx(), m_interp, args, value);
            check_error();
        }
        void set_else(expr& value) {
            Z3_func_interp_set_else(ctx(), m_interp, value);
            check_error();
        }
    };
 
    class model : public object {
        Z3_model m_model;
        void init(Z3_model m) {
            m_model = m;
            Z3_model_inc_ref(ctx(), m);
        }
    public:
        struct translate {};
        model(context & c):object(c) { init(Z3_mk_model(c)); }
        model(context & c, Z3_model m):object(c) { init(m); }
        model(model const & s):object(s) { init(s.m_model); }
        model(model& src, context& dst, translate) : object(dst) { init(Z3_model_translate(src.ctx(), src, dst)); }
        ~model() override { Z3_model_dec_ref(ctx(), m_model); }
        operator Z3_model() const { return m_model; }
        model & operator=(model const & s) {
            Z3_model_inc_ref(s.ctx(), s.m_model);
            Z3_model_dec_ref(ctx(), m_model);
            object::operator=(s);
            m_model = s.m_model;
            return *this;
        }
 
        expr eval(expr const & n, bool model_completion=false) const {
            check_context(*this, n);
            Z3_ast r = 0;
            bool status = Z3_model_eval(ctx(), m_model, n, model_completion, &r);
            check_error();
            if (status == false && ctx().enable_exceptions())
                Z3_THROW(exception("failed to evaluate expression"));
            return expr(ctx(), r);
        }
 
        unsigned num_consts() const { return Z3_model_get_num_consts(ctx(), m_model); }
        unsigned num_funcs() const { return Z3_model_get_num_funcs(ctx(), m_model); }
        func_decl get_const_decl(unsigned i) const { Z3_func_decl r = Z3_model_get_const_decl(ctx(), m_model, i); check_error(); return func_decl(ctx(), r); }
        func_decl get_func_decl(unsigned i) const { Z3_func_decl r = Z3_model_get_func_decl(ctx(), m_model, i); check_error(); return func_decl(ctx(), r); }
        unsigned size() const { return num_consts() + num_funcs(); }
        func_decl operator[](int i) const {
            assert(0 <= i);
            return static_cast<unsigned>(i) < num_consts() ? get_const_decl(i) : get_func_decl(i - num_consts());
        }
 
        // returns interpretation of constant declaration c.
        // If c is not assigned any value in the model it returns
        // an expression with a null ast reference.
        expr get_const_interp(func_decl c) const {
            check_context(*this, c);
            Z3_ast r = Z3_model_get_const_interp(ctx(), m_model, c);
            check_error();
            return expr(ctx(), r);
        }
        func_interp get_func_interp(func_decl f) const {
            check_context(*this, f);
            Z3_func_interp r = Z3_model_get_func_interp(ctx(), m_model, f);
            check_error();
            return func_interp(ctx(), r);
        }
 
        // returns true iff the model contains an interpretation
        // for function f.
        bool has_interp(func_decl f) const {
            check_context(*this, f);
            return Z3_model_has_interp(ctx(), m_model, f);
        }
 
        func_interp add_func_interp(func_decl& f, expr& else_val) {
            Z3_func_interp r = Z3_add_func_interp(ctx(), m_model, f, else_val);
            check_error();
            return func_interp(ctx(), r);
        }
 
        void add_const_interp(func_decl& f, expr& value) {
            Z3_add_const_interp(ctx(), m_model, f, value);
            check_error();
        }
 
        friend std::ostream & operator<<(std::ostream & out, model const & m);
 
        std::string to_string() const { return m_model ? std::string(Z3_model_to_string(ctx(), m_model)) : "null"; }
    };
    inline std::ostream & operator<<(std::ostream & out, model const & m) { return out << m.to_string(); }
 
    class stats : public object {
        Z3_stats m_stats;
        void init(Z3_stats e) {
            m_stats = e;
            Z3_stats_inc_ref(ctx(), m_stats);
        }
    public:
        stats(context & c):object(c), m_stats(0) {}
        stats(context & c, Z3_stats e):object(c) { init(e); }
        stats(stats const & s):object(s) { init(s.m_stats); }
        ~stats() override { if (m_stats) Z3_stats_dec_ref(ctx(), m_stats); }
        operator Z3_stats() const { return m_stats; }
        stats & operator=(stats const & s) {
            Z3_stats_inc_ref(s.ctx(), s.m_stats);
            if (m_stats) Z3_stats_dec_ref(ctx(), m_stats);
            object::operator=(s);
            m_stats = s.m_stats;
            return *this;
        }
        unsigned size() const { return Z3_stats_size(ctx(), m_stats); }
        std::string key(unsigned i) const { Z3_string s = Z3_stats_get_key(ctx(), m_stats, i); check_error(); return s; }
        bool is_uint(unsigned i) const { bool r = Z3_stats_is_uint(ctx(), m_stats, i); check_error(); return r; }
        bool is_double(unsigned i) const { bool r = Z3_stats_is_double(ctx(), m_stats, i); check_error(); return r; }
        unsigned uint_value(unsigned i) const { unsigned r = Z3_stats_get_uint_value(ctx(), m_stats, i); check_error(); return r; }
        double double_value(unsigned i) const { double r = Z3_stats_get_double_value(ctx(), m_stats, i); check_error(); return r; }
        friend std::ostream & operator<<(std::ostream & out, stats const & s);
    };
    inline std::ostream & operator<<(std::ostream & out, stats const & s) { out << Z3_stats_to_string(s.ctx(), s); return out; }
 
 
    inline std::ostream & operator<<(std::ostream & out, check_result r) {
        if (r == unsat) out << "unsat";
        else if (r == sat) out << "sat";
        else out << "unknown";
        return out;
    }
 
    class parameter {
        Z3_parameter_kind m_kind;
        func_decl         m_decl;
        unsigned          m_index;
        context& ctx() const { return m_decl.ctx(); }
        void check_error() const { ctx().check_error(); }
    public:
        parameter(func_decl const& d, unsigned idx) : m_decl(d), m_index(idx) { 
            if (ctx().enable_exceptions() && idx >= d.num_parameters())
                Z3_THROW(exception("parameter index is out of bounds"));
            m_kind = Z3_get_decl_parameter_kind(ctx(), d, idx); 
        }
        parameter(expr const& e, unsigned idx) : m_decl(e.decl()), m_index(idx) {
            if (ctx().enable_exceptions() && idx >= m_decl.num_parameters())
                Z3_THROW(exception("parameter index is out of bounds"));
            m_kind = Z3_get_decl_parameter_kind(ctx(), m_decl, idx);
        }
        Z3_parameter_kind kind() const { return m_kind; }
        expr get_expr() const { Z3_ast a = Z3_get_decl_ast_parameter(ctx(), m_decl, m_index); check_error(); return expr(ctx(), a); }
        sort get_sort() const { Z3_sort s = Z3_get_decl_sort_parameter(ctx(), m_decl, m_index); check_error(); return sort(ctx(), s); }
        func_decl get_decl() const { Z3_func_decl f = Z3_get_decl_func_decl_parameter(ctx(), m_decl, m_index); check_error(); return func_decl(ctx(), f); }
        symbol get_symbol() const { Z3_symbol s = Z3_get_decl_symbol_parameter(ctx(), m_decl, m_index); check_error(); return symbol(ctx(), s); }
        std::string get_rational() const { Z3_string s = Z3_get_decl_rational_parameter(ctx(), m_decl, m_index); check_error(); return s; }
        double get_double() const { double d = Z3_get_decl_double_parameter(ctx(), m_decl, m_index); check_error(); return d; }
        int get_int() const { int i = Z3_get_decl_int_parameter(ctx(), m_decl, m_index); check_error(); return i; }
    };
 
 
    class solver : public object {
        Z3_solver m_solver;
        void init(Z3_solver s) {
            m_solver = s;
            if (s)
                Z3_solver_inc_ref(ctx(), s);
        }
    public:
        struct simple {};
        struct translate {};
        solver(context & c):object(c) { init(Z3_mk_solver(c)); check_error(); }
        solver(context & c, simple):object(c) { init(Z3_mk_simple_solver(c)); check_error(); }
        solver(context & c, Z3_solver s):object(c) { init(s); }
        solver(context & c, char const * logic):object(c) { init(Z3_mk_solver_for_logic(c, c.str_symbol(logic))); check_error(); }
        solver(context & c, solver const& src, translate): object(c) { Z3_solver s = Z3_solver_translate(src.ctx(), src, c); check_error(); init(s); }
        solver(solver const & s):object(s) { init(s.m_solver); }
        solver(solver const& s, simplifier const& simp);
        ~solver() override { Z3_solver_dec_ref(ctx(), m_solver); }
        operator Z3_solver() const { return m_solver; }
        solver & operator=(solver const & s) {
            Z3_solver_inc_ref(s.ctx(), s.m_solver);
            Z3_solver_dec_ref(ctx(), m_solver);
            object::operator=(s);
            m_solver = s.m_solver;
            return *this;
        }
        void set(params const & p) { Z3_solver_set_params(ctx(), m_solver, p); check_error(); }
        void set(char const * k, bool v) { params p(ctx()); p.set(k, v); set(p); }
        void set(char const * k, unsigned v) { params p(ctx()); p.set(k, v); set(p); }
        void set(char const * k, double v) { params p(ctx()); p.set(k, v); set(p); }
        void set(char const * k, symbol const & v) { params p(ctx()); p.set(k, v); set(p); }
        void set(char const * k, char const* v) { params p(ctx()); p.set(k, v); set(p); }
        void push() { Z3_solver_push(ctx(), m_solver); check_error(); }
        void pop(unsigned n = 1) { Z3_solver_pop(ctx(), m_solver, n); check_error(); }
        void reset() { Z3_solver_reset(ctx(), m_solver); check_error(); }
        void add(expr const & e) { assert(e.is_bool()); Z3_solver_assert(ctx(), m_solver, e); check_error(); }
        void add(expr const & e, expr const & p) {
            assert(e.is_bool()); assert(p.is_bool()); assert(p.is_const());
            Z3_solver_assert_and_track(ctx(), m_solver, e, p);
            check_error();
        }
        void add(expr const & e, char const * p) {
            add(e, ctx().bool_const(p));
        }        
        void add(expr_vector const& v) { 
            check_context(*this, v); 
            for (unsigned i = 0; i < v.size(); ++i) 
                add(v[i]); 
        }
        void from_file(char const* file) { Z3_solver_from_file(ctx(), m_solver, file); ctx().check_parser_error(); }
        void from_string(char const* s) { Z3_solver_from_string(ctx(), m_solver, s); ctx().check_parser_error(); }
 
        check_result check() { Z3_lbool r = Z3_solver_check(ctx(), m_solver); check_error(); return to_check_result(r); }
        check_result check(unsigned n, expr * const assumptions) {
            array<Z3_ast> _assumptions(n);
            for (unsigned i = 0; i < n; i++) {
                check_context(*this, assumptions[i]);
                _assumptions[i] = assumptions[i];
            }
            Z3_lbool r = Z3_solver_check_assumptions(ctx(), m_solver, n, _assumptions.ptr());
            check_error();
            return to_check_result(r);
        }
        check_result check(expr_vector const& assumptions) {
            unsigned n = assumptions.size();
            array<Z3_ast> _assumptions(n);
            for (unsigned i = 0; i < n; i++) {
                check_context(*this, assumptions[i]);
                _assumptions[i] = assumptions[i];
            }
            Z3_lbool r = Z3_solver_check_assumptions(ctx(), m_solver, n, _assumptions.ptr());
            check_error();
            return to_check_result(r);
        }
        model get_model() const { Z3_model m = Z3_solver_get_model(ctx(), m_solver); check_error(); return model(ctx(), m); }
        check_result consequences(expr_vector& assumptions, expr_vector& vars, expr_vector& conseq) {
            Z3_lbool r = Z3_solver_get_consequences(ctx(), m_solver, assumptions, vars, conseq);
            check_error();
            return to_check_result(r);
        }
        std::string reason_unknown() const { Z3_string r = Z3_solver_get_reason_unknown(ctx(), m_solver); check_error(); return r; }
        stats statistics() const { Z3_stats r = Z3_solver_get_statistics(ctx(), m_solver); check_error(); return stats(ctx(), r); }
        expr_vector unsat_core() const { Z3_ast_vector r = Z3_solver_get_unsat_core(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); }
        expr_vector assertions() const { Z3_ast_vector r = Z3_solver_get_assertions(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); }
        expr_vector non_units() const { Z3_ast_vector r = Z3_solver_get_non_units(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); }
        expr_vector units() const { Z3_ast_vector r = Z3_solver_get_units(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); }
        expr_vector trail() const { Z3_ast_vector r = Z3_solver_get_trail(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); }
        expr_vector trail(array<unsigned>& levels) const { 
            Z3_ast_vector r = Z3_solver_get_trail(ctx(), m_solver); 
            check_error(); 
            expr_vector result(ctx(), r);
            unsigned sz = result.size();
            levels.resize(sz);
            Z3_solver_get_levels(ctx(), m_solver, r, sz, levels.ptr());
            check_error(); 
            return result; 
        }
        void set_initial_value(expr const& var, expr const& value) {
            Z3_solver_set_initial_value(ctx(), m_solver, var, value);
            check_error();
        }
        void set_initial_value(expr const& var, int i) {
            set_initial_value(var, ctx().num_val(i, var.get_sort()));
        }
        void set_initial_value(expr const& var, bool b) {
            set_initial_value(var, ctx().bool_val(b));            
        }
 
        expr proof() const { Z3_ast r = Z3_solver_get_proof(ctx(), m_solver); check_error(); return expr(ctx(), r); }
        friend std::ostream & operator<<(std::ostream & out, solver const & s);
 
        std::string to_smt2(char const* status = "unknown") {
            array<Z3_ast> es(assertions());
            Z3_ast const* fmls = es.ptr();
            Z3_ast fml = 0;
            unsigned sz = es.size();
            if (sz > 0) {
                --sz;
                fml = fmls[sz];
            }
            else {
                fml = ctx().bool_val(true);
            }
            return std::string(Z3_benchmark_to_smtlib_string(
                                   ctx(),
                                   "", "", status, "",
                                   sz,
                                   fmls,
                                   fml));
        }
 
        std::string dimacs(bool include_names = true) const { return std::string(Z3_solver_to_dimacs_string(ctx(), m_solver, include_names)); }
 
        param_descrs get_param_descrs() { return param_descrs(ctx(), Z3_solver_get_param_descrs(ctx(), m_solver)); }
 
 
        expr_vector cube(expr_vector& vars, unsigned cutoff) {
            Z3_ast_vector r = Z3_solver_cube(ctx(), m_solver, vars, cutoff);
            check_error();
            return expr_vector(ctx(), r);
        }
 
        class cube_iterator {
            solver&      m_solver;
            unsigned&    m_cutoff;
            expr_vector& m_vars;
            expr_vector  m_cube;
            bool         m_end;
            bool         m_empty;
 
            void inc() {
                assert(!m_end && !m_empty);
                m_cube = m_solver.cube(m_vars, m_cutoff);
                m_cutoff = 0xFFFFFFFF;
                if (m_cube.size() == 1 && m_cube[0u].is_false()) {
                    m_cube = z3::expr_vector(m_solver.ctx());
                    m_end = true;
                }
                else if (m_cube.empty()) {
                    m_empty = true;
                }
            }
        public:
            cube_iterator(solver& s, expr_vector& vars, unsigned& cutoff, bool end):
                m_solver(s),
                m_cutoff(cutoff),
                m_vars(vars),
                m_cube(s.ctx()),
                m_end(end),
                m_empty(false) {
                if (!m_end) {
                    inc();
                }
            }
 
            cube_iterator& operator++() {
                assert(!m_end);
                if (m_empty) {
                    m_end = true;
                }
                else {
                    inc();
                }
                return *this;
            }
            cube_iterator operator++(int) { assert(false); return *this; }
            expr_vector const * operator->() const { return &(operator*()); }
            expr_vector const& operator*() const noexcept { return m_cube; }
 
            bool operator==(cube_iterator const& other) const noexcept {
                return other.m_end == m_end;
            };
            bool operator!=(cube_iterator const& other) const noexcept {
                return other.m_end != m_end;
            };
 
        };
 
        class cube_generator {
            solver&      m_solver;
            unsigned     m_cutoff;
            expr_vector  m_default_vars;
            expr_vector& m_vars;
        public:
            cube_generator(solver& s):
                m_solver(s),
                m_cutoff(0xFFFFFFFF),
                m_default_vars(s.ctx()),
                m_vars(m_default_vars)
            {}
 
            cube_generator(solver& s, expr_vector& vars):
                m_solver(s),
                m_cutoff(0xFFFFFFFF),
                m_default_vars(s.ctx()),
                m_vars(vars)
            {}
 
            cube_iterator begin() { return cube_iterator(m_solver, m_vars, m_cutoff, false); }
            cube_iterator end() { return cube_iterator(m_solver, m_vars, m_cutoff, true); }
            void set_cutoff(unsigned c) noexcept { m_cutoff = c; }
        };
 
        cube_generator cubes() { return cube_generator(*this); }
        cube_generator cubes(expr_vector& vars) { return cube_generator(*this, vars); }
 
    };
    inline std::ostream & operator<<(std::ostream & out, solver const & s) { out << Z3_solver_to_string(s.ctx(), s); return out; }
 
    class goal : public object {
        Z3_goal m_goal;
        void init(Z3_goal s) {
            m_goal = s;
            Z3_goal_inc_ref(ctx(), s);
        }
    public:
        goal(context & c, bool models=true, bool unsat_cores=false, bool proofs=false):object(c) { init(Z3_mk_goal(c, models, unsat_cores, proofs)); }
        goal(context & c, Z3_goal s):object(c) { init(s); }
        goal(goal const & s):object(s) { init(s.m_goal); }
        ~goal() override { Z3_goal_dec_ref(ctx(), m_goal); }
        operator Z3_goal() const { return m_goal; }
        goal & operator=(goal const & s) {
            Z3_goal_inc_ref(s.ctx(), s.m_goal);
            Z3_goal_dec_ref(ctx(), m_goal);
            object::operator=(s);
            m_goal = s.m_goal;
            return *this;
        }
        void add(expr const & f) { check_context(*this, f); Z3_goal_assert(ctx(), m_goal, f); check_error(); }
        void add(expr_vector const& v) { check_context(*this, v); for (unsigned i = 0; i < v.size(); ++i) add(v[i]); }
        unsigned size() const { return Z3_goal_size(ctx(), m_goal); }
        expr operator[](int i) const { assert(0 <= i); Z3_ast r = Z3_goal_formula(ctx(), m_goal, i); check_error(); return expr(ctx(), r); }
        Z3_goal_prec precision() const { return Z3_goal_precision(ctx(), m_goal); }
        bool inconsistent() const { return Z3_goal_inconsistent(ctx(), m_goal); }
        unsigned depth() const { return Z3_goal_depth(ctx(), m_goal); }
        void reset() { Z3_goal_reset(ctx(), m_goal); }
        unsigned num_exprs() const { return Z3_goal_num_exprs(ctx(), m_goal); }
        bool is_decided_sat() const { return Z3_goal_is_decided_sat(ctx(), m_goal); }
        bool is_decided_unsat() const { return Z3_goal_is_decided_unsat(ctx(), m_goal); }
        model convert_model(model const & m) const {
            check_context(*this, m);
            Z3_model new_m = Z3_goal_convert_model(ctx(), m_goal, m);
            check_error();
            return model(ctx(), new_m);
        }
        model get_model() const {
            Z3_model new_m = Z3_goal_convert_model(ctx(), m_goal, 0);
            check_error();
            return model(ctx(), new_m);
        }
        expr as_expr() const {
            unsigned n = size();
            if (n == 0)
                return ctx().bool_val(true);
            else if (n == 1)
                return operator[](0u);
            else {
                array<Z3_ast> args(n);
                for (unsigned i = 0; i < n; i++)
                    args[i] = operator[](i);
                return expr(ctx(), Z3_mk_and(ctx(), n, args.ptr()));
            }
        }
        std::string dimacs(bool include_names = true) const { return std::string(Z3_goal_to_dimacs_string(ctx(), m_goal, include_names)); }
        friend std::ostream & operator<<(std::ostream & out, goal const & g);
    };
    inline std::ostream & operator<<(std::ostream & out, goal const & g) { out << Z3_goal_to_string(g.ctx(), g); return out; }
 
    class apply_result : public object {
        Z3_apply_result m_apply_result;
        void init(Z3_apply_result s) {
            m_apply_result = s;
            Z3_apply_result_inc_ref(ctx(), s);
        }
    public:
        apply_result(context & c, Z3_apply_result s):object(c) { init(s); }
        apply_result(apply_result const & s):object(s) { init(s.m_apply_result); }
        ~apply_result() override { Z3_apply_result_dec_ref(ctx(), m_apply_result); }
        operator Z3_apply_result() const { return m_apply_result; }
        apply_result & operator=(apply_result const & s) {
            Z3_apply_result_inc_ref(s.ctx(), s.m_apply_result);
            Z3_apply_result_dec_ref(ctx(), m_apply_result);
            object::operator=(s);
            m_apply_result = s.m_apply_result;
            return *this;
        }
        unsigned size() const { return Z3_apply_result_get_num_subgoals(ctx(), m_apply_result); }
        goal operator[](int i) const { assert(0 <= i); Z3_goal r = Z3_apply_result_get_subgoal(ctx(), m_apply_result, i); check_error(); return goal(ctx(), r); }
        friend std::ostream & operator<<(std::ostream & out, apply_result const & r);
    };
    inline std::ostream & operator<<(std::ostream & out, apply_result const & r) { out << Z3_apply_result_to_string(r.ctx(), r); return out; }
 
    class tactic : public object {
        Z3_tactic m_tactic;
        void init(Z3_tactic s) {
            m_tactic = s;
            Z3_tactic_inc_ref(ctx(), s);
        }
    public:
        tactic(context & c, char const * name):object(c) { Z3_tactic r = Z3_mk_tactic(c, name); check_error(); init(r); }
        tactic(context & c, Z3_tactic s):object(c) { init(s); }
        tactic(tactic const & s):object(s) { init(s.m_tactic); }
        ~tactic() override { Z3_tactic_dec_ref(ctx(), m_tactic); }
        operator Z3_tactic() const { return m_tactic; }
        tactic & operator=(tactic const & s) {
            Z3_tactic_inc_ref(s.ctx(), s.m_tactic);
            Z3_tactic_dec_ref(ctx(), m_tactic);
            object::operator=(s);
            m_tactic = s.m_tactic;
            return *this;
        }
        solver mk_solver() const { Z3_solver r = Z3_mk_solver_from_tactic(ctx(), m_tactic); check_error(); return solver(ctx(), r);  }
        apply_result apply(goal const & g) const {
            check_context(*this, g);
            Z3_apply_result r = Z3_tactic_apply(ctx(), m_tactic, g);
            check_error();
            return apply_result(ctx(), r);
        }
        apply_result operator()(goal const & g) const {
            return apply(g);
        }
        std::string help() const { char const * r = Z3_tactic_get_help(ctx(), m_tactic); check_error();  return r; }
        friend tactic operator&(tactic const & t1, tactic const & t2);
        friend tactic operator|(tactic const & t1, tactic const & t2);
        friend tactic repeat(tactic const & t, unsigned max);
        friend tactic with(tactic const & t, params const & p);
        friend tactic try_for(tactic const & t, unsigned ms);
        friend tactic par_or(unsigned n, tactic const* tactics);
        friend tactic par_and_then(tactic const& t1, tactic const& t2);
        param_descrs get_param_descrs() { return param_descrs(ctx(), Z3_tactic_get_param_descrs(ctx(), m_tactic)); }
    };
 
    inline tactic operator&(tactic const & t1, tactic const & t2) {
        check_context(t1, t2);
        Z3_tactic r = Z3_tactic_and_then(t1.ctx(), t1, t2);
        t1.check_error();
        return tactic(t1.ctx(), r);
    }
 
    inline tactic operator|(tactic const & t1, tactic const & t2) {
        check_context(t1, t2);
        Z3_tactic r = Z3_tactic_or_else(t1.ctx(), t1, t2);
        t1.check_error();
        return tactic(t1.ctx(), r);
    }
 
    inline tactic repeat(tactic const & t, unsigned max=UINT_MAX) {
        Z3_tactic r = Z3_tactic_repeat(t.ctx(), t, max);
        t.check_error();
        return tactic(t.ctx(), r);
    }
 
    inline tactic with(tactic const & t, params const & p) {
        Z3_tactic r = Z3_tactic_using_params(t.ctx(), t, p);
        t.check_error();
        return tactic(t.ctx(), r);
    }
    inline tactic try_for(tactic const & t, unsigned ms) {
        Z3_tactic r = Z3_tactic_try_for(t.ctx(), t, ms);
        t.check_error();
        return tactic(t.ctx(), r);
    }
    inline tactic par_or(unsigned n, tactic const* tactics) {
        if (n == 0) {
            Z3_THROW(exception("a non-zero number of tactics need to be passed to par_or"));
        }
        array<Z3_tactic> buffer(n);
        for (unsigned i = 0; i < n; ++i) buffer[i] = tactics[i];
        return tactic(tactics[0u].ctx(), Z3_tactic_par_or(tactics[0u].ctx(), n, buffer.ptr()));
    }
 
    inline tactic par_and_then(tactic const & t1, tactic const & t2) {
        check_context(t1, t2);
        Z3_tactic r = Z3_tactic_par_and_then(t1.ctx(), t1, t2);
        t1.check_error();
        return tactic(t1.ctx(), r);
    }
 
    class simplifier : public object {
        Z3_simplifier m_simplifier;
        void init(Z3_simplifier s) {
            m_simplifier = s;
            Z3_simplifier_inc_ref(ctx(), s);
        }
    public:
        simplifier(context & c, char const * name):object(c) { Z3_simplifier r = Z3_mk_simplifier(c, name); check_error(); init(r); }
        simplifier(context & c, Z3_simplifier s):object(c) { init(s); }
        simplifier(simplifier const & s):object(s) { init(s.m_simplifier); }
        ~simplifier() override { Z3_simplifier_dec_ref(ctx(), m_simplifier); }
        operator Z3_simplifier() const { return m_simplifier; }
        simplifier & operator=(simplifier const & s) {
            Z3_simplifier_inc_ref(s.ctx(), s.m_simplifier);
            Z3_simplifier_dec_ref(ctx(), m_simplifier);
            object::operator=(s);
            m_simplifier = s.m_simplifier;
            return *this;
        }
        std::string help() const { char const * r = Z3_simplifier_get_help(ctx(), m_simplifier); check_error();  return r; }
        friend simplifier operator&(simplifier const & t1, simplifier const & t2);
        friend simplifier with(simplifier const & t, params const & p);
        param_descrs get_param_descrs() { return param_descrs(ctx(), Z3_simplifier_get_param_descrs(ctx(), m_simplifier)); }
    };
 
    inline solver::solver(solver const& s, simplifier const& simp):object(s) { init(Z3_solver_add_simplifier(s.ctx(), s, simp)); }
 
 
    inline simplifier operator&(simplifier const & t1, simplifier const & t2) {
        check_context(t1, t2);
        Z3_simplifier r = Z3_simplifier_and_then(t1.ctx(), t1, t2);
        t1.check_error();
        return simplifier(t1.ctx(), r);
    }
 
    inline simplifier with(simplifier const & t, params const & p) {
        Z3_simplifier r = Z3_simplifier_using_params(t.ctx(), t, p);
        t.check_error();
        return simplifier(t.ctx(), r);
    }
 
    class probe : public object {
        Z3_probe m_probe;
        void init(Z3_probe s) {
            m_probe = s;
            Z3_probe_inc_ref(ctx(), s);
        }
    public:
        probe(context & c, char const * name):object(c) { Z3_probe r = Z3_mk_probe(c, name); check_error(); init(r); }
        probe(context & c, double val):object(c) { Z3_probe r = Z3_probe_const(c, val); check_error(); init(r); }
        probe(context & c, Z3_probe s):object(c) { init(s); }
        probe(probe const & s):object(s) { init(s.m_probe); }
        ~probe() override { Z3_probe_dec_ref(ctx(), m_probe); }
        operator Z3_probe() const { return m_probe; }
        probe & operator=(probe const & s) {
            Z3_probe_inc_ref(s.ctx(), s.m_probe);
            Z3_probe_dec_ref(ctx(), m_probe);
            object::operator=(s);
            m_probe = s.m_probe;
            return *this;
        }
        double apply(goal const & g) const { double r = Z3_probe_apply(ctx(), m_probe, g); check_error(); return r; }
        double operator()(goal const & g) const { return apply(g); }
        friend probe operator<=(probe const & p1, probe const & p2);
        friend probe operator<=(probe const & p1, double p2);
        friend probe operator<=(double p1, probe const & p2);
        friend probe operator>=(probe const & p1, probe const & p2);
        friend probe operator>=(probe const & p1, double p2);
        friend probe operator>=(double p1, probe const & p2);
        friend probe operator<(probe const & p1, probe const & p2);
        friend probe operator<(probe const & p1, double p2);
        friend probe operator<(double p1, probe const & p2);
        friend probe operator>(probe const & p1, probe const & p2);
        friend probe operator>(probe const & p1, double p2);
        friend probe operator>(double p1, probe const & p2);
        friend probe operator==(probe const & p1, probe const & p2);
        friend probe operator==(probe const & p1, double p2);
        friend probe operator==(double p1, probe const & p2);
        friend probe operator&&(probe const & p1, probe const & p2);
        friend probe operator||(probe const & p1, probe const & p2);
        friend probe operator!(probe const & p);
    };
 
    inline probe operator<=(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_le(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator<=(probe const & p1, double p2) { return p1 <= probe(p1.ctx(), p2); }
    inline probe operator<=(double p1, probe const & p2) { return probe(p2.ctx(), p1) <= p2; }
    inline probe operator>=(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_ge(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator>=(probe const & p1, double p2) { return p1 >= probe(p1.ctx(), p2); }
    inline probe operator>=(double p1, probe const & p2) { return probe(p2.ctx(), p1) >= p2; }
    inline probe operator<(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_lt(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator<(probe const & p1, double p2) { return p1 < probe(p1.ctx(), p2); }
    inline probe operator<(double p1, probe const & p2) { return probe(p2.ctx(), p1) < p2; }
    inline probe operator>(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_gt(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator>(probe const & p1, double p2) { return p1 > probe(p1.ctx(), p2); }
    inline probe operator>(double p1, probe const & p2) { return probe(p2.ctx(), p1) > p2; }
    inline probe operator==(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_eq(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator==(probe const & p1, double p2) { return p1 == probe(p1.ctx(), p2); }
    inline probe operator==(double p1, probe const & p2) { return probe(p2.ctx(), p1) == p2; }
    inline probe operator&&(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_and(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator||(probe const & p1, probe const & p2) {
        check_context(p1, p2); Z3_probe r = Z3_probe_or(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r);
    }
    inline probe operator!(probe const & p) {
        Z3_probe r = Z3_probe_not(p.ctx(), p); p.check_error(); return probe(p.ctx(), r);
    }
 
    class optimize : public object {
        Z3_optimize m_opt;
 
    public:
        class handle final {
            unsigned m_h;
        public:
            handle(unsigned h): m_h(h) {}
            unsigned h() const { return m_h; }
        };
        optimize(context& c):object(c) { m_opt = Z3_mk_optimize(c); Z3_optimize_inc_ref(c, m_opt); }
        optimize(optimize const & o):object(o), m_opt(o.m_opt) {
            Z3_optimize_inc_ref(o.ctx(), o.m_opt);
        }
        optimize(context& c, optimize& src):object(c) {
            m_opt = Z3_mk_optimize(c); 
            Z3_optimize_inc_ref(c, m_opt);
            add(expr_vector(c, src.assertions()));
            expr_vector v(c, src.objectives());
            for (expr_vector::iterator it = v.begin(); it != v.end(); ++it) minimize(*it);
        }
        optimize& operator=(optimize const& o) {
            Z3_optimize_inc_ref(o.ctx(), o.m_opt);
            Z3_optimize_dec_ref(ctx(), m_opt);
            m_opt = o.m_opt;
            object::operator=(o);
            return *this;
        }
        ~optimize() override { Z3_optimize_dec_ref(ctx(), m_opt); }
        operator Z3_optimize() const { return m_opt; }
        void add(expr const& e) {
            assert(e.is_bool());
            Z3_optimize_assert(ctx(), m_opt, e);
        }
        void add(expr_vector const& es) {
            for (expr_vector::iterator it = es.begin(); it != es.end(); ++it) add(*it);
        }
        void add(expr const& e, expr const& t) {
            assert(e.is_bool());
            Z3_optimize_assert_and_track(ctx(), m_opt, e, t);
        }
        void add(expr const& e, char const* p) {
            assert(e.is_bool());
            add(e, ctx().bool_const(p));
        }
        handle add_soft(expr const& e, unsigned weight) {
            assert(e.is_bool());
            auto str = std::to_string(weight);
            return handle(Z3_optimize_assert_soft(ctx(), m_opt, e, str.c_str(), 0));
        }
        handle add_soft(expr const& e, char const* weight) {
            assert(e.is_bool());
            return handle(Z3_optimize_assert_soft(ctx(), m_opt, e, weight, 0));
        }
        handle add(expr const& e, unsigned weight) {
            return add_soft(e, weight);
        }
        void set_initial_value(expr const& var, expr const& value) {
            Z3_optimize_set_initial_value(ctx(), m_opt, var, value);
            check_error();
        }
        void set_initial_value(expr const& var, int i) {
            set_initial_value(var, ctx().num_val(i, var.get_sort()));
        }
        void set_initial_value(expr const& var, bool b) {
            set_initial_value(var, ctx().bool_val(b));            
        }
 
        handle maximize(expr const& e) {
            return handle(Z3_optimize_maximize(ctx(), m_opt, e));
        }
        handle minimize(expr const& e) {
            return handle(Z3_optimize_minimize(ctx(), m_opt, e));
        }
        void push() {
            Z3_optimize_push(ctx(), m_opt);
        }
        void pop() {
            Z3_optimize_pop(ctx(), m_opt);
        }
        check_result check() { Z3_lbool r = Z3_optimize_check(ctx(), m_opt, 0, 0); check_error(); return to_check_result(r); }
        check_result check(expr_vector const& asms) {
            unsigned n = asms.size();
            array<Z3_ast> _asms(n);
            for (unsigned i = 0; i < n; i++) {
                check_context(*this, asms[i]);
                _asms[i] = asms[i];
            }
            Z3_lbool r = Z3_optimize_check(ctx(), m_opt, n, _asms.ptr());
            check_error();
            return to_check_result(r);
        }
        model get_model() const { Z3_model m = Z3_optimize_get_model(ctx(), m_opt); check_error(); return model(ctx(), m); }
        expr_vector unsat_core() const { Z3_ast_vector r = Z3_optimize_get_unsat_core(ctx(), m_opt); check_error(); return expr_vector(ctx(), r); }
        void set(params const & p) { Z3_optimize_set_params(ctx(), m_opt, p); check_error(); }
        expr lower(handle const& h) {
            Z3_ast r = Z3_optimize_get_lower(ctx(), m_opt, h.h());
            check_error();
            return expr(ctx(), r);
        }
        expr upper(handle const& h) {
            Z3_ast r = Z3_optimize_get_upper(ctx(), m_opt, h.h());
            check_error();
            return expr(ctx(), r);
        }
        expr_vector assertions() const { Z3_ast_vector r = Z3_optimize_get_assertions(ctx(), m_opt); check_error(); return expr_vector(ctx(), r); }
        expr_vector objectives() const { Z3_ast_vector r = Z3_optimize_get_objectives(ctx(), m_opt); check_error(); return expr_vector(ctx(), r); }
        stats statistics() const { Z3_stats r = Z3_optimize_get_statistics(ctx(), m_opt); check_error(); return stats(ctx(), r); }
        friend std::ostream & operator<<(std::ostream & out, optimize const & s);
        void from_file(char const* filename) { Z3_optimize_from_file(ctx(), m_opt, filename); check_error(); }
        void from_string(char const* constraints) { Z3_optimize_from_string(ctx(), m_opt, constraints); check_error(); }
        std::string help() const { char const * r = Z3_optimize_get_help(ctx(), m_opt); check_error();  return r; }
    };
    inline std::ostream & operator<<(std::ostream & out, optimize const & s) { out << Z3_optimize_to_string(s.ctx(), s.m_opt); return out; }
 
    class fixedpoint : public object {
        Z3_fixedpoint m_fp;
    public:
        fixedpoint(context& c):object(c) { m_fp = Z3_mk_fixedpoint(c); Z3_fixedpoint_inc_ref(c, m_fp); }
        fixedpoint(fixedpoint const & o):object(o), m_fp(o.m_fp) { Z3_fixedpoint_inc_ref(ctx(), m_fp); }
        ~fixedpoint() override { Z3_fixedpoint_dec_ref(ctx(), m_fp); }
        fixedpoint & operator=(fixedpoint const & o) {
            Z3_fixedpoint_inc_ref(o.ctx(), o.m_fp);
            Z3_fixedpoint_dec_ref(ctx(), m_fp);
            m_fp = o.m_fp;
            object::operator=(o);
            return *this;
        }
        operator Z3_fixedpoint() const { return m_fp; }
        expr_vector from_string(char const* s) { 
            Z3_ast_vector r = Z3_fixedpoint_from_string(ctx(), m_fp, s); 
            check_error(); 
            return expr_vector(ctx(), r);
        }
        expr_vector from_file(char const* s) { 
            Z3_ast_vector r = Z3_fixedpoint_from_file(ctx(), m_fp, s); 
            check_error(); 
            return expr_vector(ctx(), r);
        }
        void add_rule(expr& rule, symbol const& name) { Z3_fixedpoint_add_rule(ctx(), m_fp, rule, name); check_error(); }
        void add_fact(func_decl& f, unsigned * args) { Z3_fixedpoint_add_fact(ctx(), m_fp, f, f.arity(), args); check_error(); }
        check_result query(expr& q) { Z3_lbool r = Z3_fixedpoint_query(ctx(), m_fp, q); check_error(); return to_check_result(r); }
        check_result query(func_decl_vector& relations) {
            array<Z3_func_decl> rs(relations);
            Z3_lbool r = Z3_fixedpoint_query_relations(ctx(), m_fp, rs.size(), rs.ptr());
            check_error();
            return to_check_result(r);
        }
        expr get_answer() { Z3_ast r = Z3_fixedpoint_get_answer(ctx(), m_fp); check_error(); return expr(ctx(), r); }
        std::string reason_unknown() { return Z3_fixedpoint_get_reason_unknown(ctx(), m_fp); }
        void update_rule(expr& rule, symbol const& name) { Z3_fixedpoint_update_rule(ctx(), m_fp, rule, name); check_error(); }
        unsigned get_num_levels(func_decl& p) { unsigned r = Z3_fixedpoint_get_num_levels(ctx(), m_fp, p); check_error(); return r; }
        expr get_cover_delta(int level, func_decl& p) {
            Z3_ast r = Z3_fixedpoint_get_cover_delta(ctx(), m_fp, level, p);
            check_error();
            return expr(ctx(), r);
        }
        void add_cover(int level, func_decl& p, expr& property) { Z3_fixedpoint_add_cover(ctx(), m_fp, level, p, property); check_error();  }
        stats statistics() const { Z3_stats r = Z3_fixedpoint_get_statistics(ctx(), m_fp); check_error(); return stats(ctx(), r); }
        void register_relation(func_decl& p) { Z3_fixedpoint_register_relation(ctx(), m_fp, p); }
        expr_vector assertions() const { Z3_ast_vector r = Z3_fixedpoint_get_assertions(ctx(), m_fp); check_error(); return expr_vector(ctx(), r); }
        expr_vector rules() const { Z3_ast_vector r = Z3_fixedpoint_get_rules(ctx(), m_fp); check_error(); return expr_vector(ctx(), r); }
        void set(params const & p) { Z3_fixedpoint_set_params(ctx(), m_fp, p); check_error(); }
        std::string help() const { return Z3_fixedpoint_get_help(ctx(), m_fp); }
        param_descrs get_param_descrs() { return param_descrs(ctx(), Z3_fixedpoint_get_param_descrs(ctx(), m_fp)); }
        std::string to_string() { return Z3_fixedpoint_to_string(ctx(), m_fp, 0, 0); }
        std::string to_string(expr_vector const& queries) {
            array<Z3_ast> qs(queries);
            return Z3_fixedpoint_to_string(ctx(), m_fp, qs.size(), qs.ptr());
        }
    };
    inline std::ostream & operator<<(std::ostream & out, fixedpoint const & f) { return out << Z3_fixedpoint_to_string(f.ctx(), f, 0, 0); }
 
    inline tactic fail_if(probe const & p) {
        Z3_tactic r = Z3_tactic_fail_if(p.ctx(), p);
        p.check_error();
        return tactic(p.ctx(), r);
    }
    inline tactic when(probe const & p, tactic const & t) {
        check_context(p, t);
        Z3_tactic r = Z3_tactic_when(t.ctx(), p, t);
        t.check_error();
        return tactic(t.ctx(), r);
    }
    inline tactic cond(probe const & p, tactic const & t1, tactic const & t2) {
        check_context(p, t1); check_context(p, t2);
        Z3_tactic r = Z3_tactic_cond(t1.ctx(), p, t1, t2);
        t1.check_error();
        return tactic(t1.ctx(), r);
    }
 
    inline symbol context::str_symbol(char const * s) { Z3_symbol r = Z3_mk_string_symbol(m_ctx, s); check_error(); return symbol(*this, r); }
    inline symbol context::int_symbol(int n) { Z3_symbol r = Z3_mk_int_symbol(m_ctx, n); check_error(); return symbol(*this, r); }
 
    inline sort context::bool_sort() { Z3_sort s = Z3_mk_bool_sort(m_ctx); check_error(); return sort(*this, s); }
    inline sort context::int_sort() { Z3_sort s = Z3_mk_int_sort(m_ctx); check_error(); return sort(*this, s); }
    inline sort context::real_sort() { Z3_sort s = Z3_mk_real_sort(m_ctx); check_error(); return sort(*this, s); }
    inline sort context::bv_sort(unsigned sz) { Z3_sort s = Z3_mk_bv_sort(m_ctx, sz); check_error(); return sort(*this, s); }
    inline sort context::string_sort() { Z3_sort s = Z3_mk_string_sort(m_ctx); check_error(); return sort(*this, s); }
    inline sort context::char_sort() { Z3_sort s = Z3_mk_char_sort(m_ctx); check_error(); return sort(*this, s); }
    inline sort context::seq_sort(sort& s) { Z3_sort r = Z3_mk_seq_sort(m_ctx, s); check_error(); return sort(*this, r); }
    inline sort context::re_sort(sort& s) { Z3_sort r = Z3_mk_re_sort(m_ctx, s); check_error(); return sort(*this, r); }
    inline sort context::fpa_sort(unsigned ebits, unsigned sbits) { Z3_sort s = Z3_mk_fpa_sort(m_ctx, ebits, sbits); check_error(); return sort(*this, s); }
 
    template<>
    inline sort context::fpa_sort<16>() { return fpa_sort(5, 11); }
 
    template<>
    inline sort context::fpa_sort<32>() { return fpa_sort(8, 24); }
 
    template<>
    inline sort context::fpa_sort<64>() { return fpa_sort(11, 53); }
 
    template<>
    inline sort context::fpa_sort<128>() { return fpa_sort(15, 113); }
 
    inline sort context::fpa_rounding_mode_sort() { Z3_sort r = Z3_mk_fpa_rounding_mode_sort(m_ctx); check_error(); return sort(*this, r); }
 
    inline sort context::array_sort(sort d, sort r) { Z3_sort s = Z3_mk_array_sort(m_ctx, d, r); check_error(); return sort(*this, s); }
    inline sort context::array_sort(sort_vector const& d, sort r) {
        array<Z3_sort> dom(d);
        Z3_sort s = Z3_mk_array_sort_n(m_ctx, dom.size(), dom.ptr(), r); check_error(); return sort(*this, s);
    }
    inline sort context::enumeration_sort(char const * name, unsigned n, char const * const * enum_names, func_decl_vector & cs, func_decl_vector & ts) {
        array<Z3_symbol> _enum_names(n);
        for (unsigned i = 0; i < n; i++) { _enum_names[i] = Z3_mk_string_symbol(*this, enum_names[i]); }
        array<Z3_func_decl> _cs(n);
        array<Z3_func_decl> _ts(n);
        Z3_symbol _name = Z3_mk_string_symbol(*this, name);
        sort s = to_sort(*this, Z3_mk_enumeration_sort(*this, _name, n, _enum_names.ptr(), _cs.ptr(), _ts.ptr()));
        check_error();
        for (unsigned i = 0; i < n; i++) { cs.push_back(func_decl(*this, _cs[i])); ts.push_back(func_decl(*this, _ts[i])); }
        return s;
    }
    inline func_decl context::tuple_sort(char const * name, unsigned n, char const * const * names, sort const* sorts, func_decl_vector & projs) {
        array<Z3_symbol> _names(n);
        array<Z3_sort> _sorts(n);
        for (unsigned i = 0; i < n; i++) { _names[i] = Z3_mk_string_symbol(*this, names[i]); _sorts[i] = sorts[i]; }
        array<Z3_func_decl> _projs(n);
        Z3_symbol _name = Z3_mk_string_symbol(*this, name);
        Z3_func_decl tuple;
        sort _ignore_s = to_sort(*this, Z3_mk_tuple_sort(*this, _name, n, _names.ptr(), _sorts.ptr(), &tuple, _projs.ptr()));
        check_error();
        for (unsigned i = 0; i < n; i++) { projs.push_back(func_decl(*this, _projs[i])); }
        return func_decl(*this, tuple);
    }
 
    class constructor_list {
        context& ctx;
        Z3_constructor_list clist;
    public:
        constructor_list(constructors const& cs);
        ~constructor_list() { Z3_del_constructor_list(ctx, clist); }
        operator Z3_constructor_list() const { return clist; }
    };
    
    class constructors {
        friend class constructor_list;
        context&       ctx;
        std::vector<Z3_constructor> cons;
        std::vector<unsigned> num_fields;
    public:
        constructors(context& ctx): ctx(ctx) {}
                
        ~constructors() {
            for (auto con : cons)
                Z3_del_constructor(ctx, con);           
        }
 
        void add(symbol const& name, symbol const& rec, unsigned n, symbol const* names, sort const* fields) {
            array<unsigned> sort_refs(n);
            array<Z3_sort> sorts(n);
            array<Z3_symbol> _names(n);            
            for (unsigned i = 0; i < n; ++i) sorts[i] = fields[i], _names[i] = names[i];
            cons.push_back(Z3_mk_constructor(ctx, name, rec, n, _names.ptr(), sorts.ptr(), sort_refs.ptr()));
            num_fields.push_back(n);
        }
 
        Z3_constructor operator[](unsigned i) const { return cons[i]; }
 
        unsigned size() const { return (unsigned)cons.size(); }
        
        void query(unsigned i, func_decl& constructor, func_decl& test, func_decl_vector& accs) {
            Z3_func_decl _constructor;
            Z3_func_decl _test;
            array<Z3_func_decl> accessors(num_fields[i]);
            accs.resize(0);
            Z3_query_constructor(ctx,
                                 cons[i],
                                 num_fields[i],
                                 &_constructor,
                                 &_test,
                                 accessors.ptr());
            constructor = func_decl(ctx, _constructor);
 
            test = func_decl(ctx, _test);
            for (unsigned j = 0; j < num_fields[i]; ++j)
                accs.push_back(func_decl(ctx, accessors[j]));
        }
    };
    
    inline constructor_list::constructor_list(constructors const& cs): ctx(cs.ctx) {
        array<Z3_constructor> cons(cs.size());
        for (unsigned i = 0; i < cs.size(); ++i)
            cons[i] = cs[i];
        clist = Z3_mk_constructor_list(ctx, cs.size(), cons.ptr());
    }
 
    inline sort context::datatype(symbol const& name, constructors const& cs) {
        array<Z3_constructor> _cs(cs.size());
        for (unsigned i = 0; i < cs.size(); ++i) _cs[i] = cs[i];
        Z3_sort s = Z3_mk_datatype(*this, name, cs.size(), _cs.ptr());
        check_error();
        return sort(*this, s);
    }
 
    inline sort_vector context::datatypes(
        unsigned n, symbol const* names,
        constructor_list *const* cons) {
        sort_vector result(*this);
        array<Z3_symbol> _names(n);
        array<Z3_sort> _sorts(n);
        array<Z3_constructor_list> _cons(n);
        for (unsigned i = 0; i < n; ++i)
            _names[i] = names[i], _cons[i] = *cons[i];
        Z3_mk_datatypes(*this, n, _names.ptr(), _sorts.ptr(), _cons.ptr());
        for (unsigned i = 0; i < n; ++i)
            result.push_back(sort(*this, _sorts[i]));
        return result;
    }
 
 
    inline sort context::datatype_sort(symbol const& name) {
        Z3_sort s = Z3_mk_datatype_sort(*this, name);
        check_error();
        return sort(*this, s);            
    }
 
 
    inline sort context::uninterpreted_sort(char const* name) {
        Z3_symbol _name = Z3_mk_string_symbol(*this, name);
        return to_sort(*this, Z3_mk_uninterpreted_sort(*this, _name));
    }
    inline sort context::uninterpreted_sort(symbol const& name) {
        return to_sort(*this, Z3_mk_uninterpreted_sort(*this, name));
    }
 
    inline func_decl context::function(symbol const & name, unsigned arity, sort const * domain, sort const & range) {
        array<Z3_sort> args(arity);
        for (unsigned i = 0; i < arity; i++) {
            check_context(domain[i], range);
            args[i] = domain[i];
        }
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, name, arity, args.ptr(), range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::function(char const * name, unsigned arity, sort const * domain, sort const & range) {
        return function(range.ctx().str_symbol(name), arity, domain, range);
    }
 
    inline func_decl context::function(symbol const& name, sort_vector const& domain, sort const& range) {
        array<Z3_sort> args(domain.size());
        for (unsigned i = 0; i < domain.size(); i++) {
            check_context(domain[i], range);
            args[i] = domain[i];
        }
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, name, domain.size(), args.ptr(), range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::function(char const * name, sort_vector const& domain, sort const& range) {
        return function(range.ctx().str_symbol(name), domain, range);
    }
 
 
    inline func_decl context::function(char const * name, sort const & domain, sort const & range) {
        check_context(domain, range);
        Z3_sort args[1] = { domain };
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, str_symbol(name), 1, args, range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & range) {
        check_context(d1, range); check_context(d2, range);
        Z3_sort args[2] = { d1, d2 };
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, str_symbol(name), 2, args, range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & range) {
        check_context(d1, range); check_context(d2, range); check_context(d3, range);
        Z3_sort args[3] = { d1, d2, d3 };
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, str_symbol(name), 3, args, range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & range) {
        check_context(d1, range); check_context(d2, range); check_context(d3, range); check_context(d4, range);
        Z3_sort args[4] = { d1, d2, d3, d4 };
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, str_symbol(name), 4, args, range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & d5, sort const & range) {
        check_context(d1, range); check_context(d2, range); check_context(d3, range); check_context(d4, range); check_context(d5, range);
        Z3_sort args[5] = { d1, d2, d3, d4, d5 };
        Z3_func_decl f = Z3_mk_func_decl(m_ctx, str_symbol(name), 5, args, range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::recfun(symbol const & name, unsigned arity, sort const * domain, sort const & range) {
        array<Z3_sort> args(arity);
        for (unsigned i = 0; i < arity; i++) {
            check_context(domain[i], range);
            args[i] = domain[i];
        }
        Z3_func_decl f = Z3_mk_rec_func_decl(m_ctx, name, arity, args.ptr(), range);
        check_error();
        return func_decl(*this, f);
 
    }
 
    inline func_decl context::recfun(symbol const & name, sort_vector const& domain, sort const & range) {
        check_context(domain, range);
        array<Z3_sort> domain1(domain);
        Z3_func_decl f = Z3_mk_rec_func_decl(m_ctx, name, domain1.size(), domain1.ptr(), range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline func_decl context::recfun(char const * name, sort_vector const& domain, sort const & range) {
        return recfun(str_symbol(name), domain, range);
 
    }
 
    inline func_decl context::recfun(char const * name, unsigned arity, sort const * domain, sort const & range) {
        return recfun(str_symbol(name), arity, domain, range);
    }
 
    inline func_decl context::recfun(char const * name, sort const& d1, sort const & range) {
        return recfun(str_symbol(name), 1, &d1, range);
    }
 
    inline func_decl context::recfun(char const * name, sort const& d1, sort const& d2, sort const & range) {
        sort dom[2] = { d1, d2 };
        return recfun(str_symbol(name), 2, dom, range);
    }
 
    inline void context::recdef(func_decl f, expr_vector const& args, expr const& body) {
        check_context(f, args); check_context(f, body);
        array<Z3_ast> vars(args);
        Z3_add_rec_def(f.ctx(), f, vars.size(), vars.ptr(), body);
    }
 
    inline func_decl context::user_propagate_function(symbol const& name, sort_vector const& domain, sort const& range) {
        check_context(domain, range);
        array<Z3_sort> domain1(domain);
        Z3_func_decl f = Z3_solver_propagate_declare(range.ctx(), name, domain1.size(), domain1.ptr(), range);
        check_error();
        return func_decl(*this, f);
    }
 
    inline expr context::constant(symbol const & name, sort const & s) {
        Z3_ast r = Z3_mk_const(m_ctx, name, s);
        check_error();
        return expr(*this, r);
    }
    inline expr context::constant(char const * name, sort const & s) { return constant(str_symbol(name), s); }
    inline expr context::variable(unsigned idx, sort const& s) { 
        Z3_ast r = Z3_mk_bound(m_ctx, idx, s);
        check_error();
        return expr(*this, r);
    }
    inline expr context::bool_const(char const * name) { return constant(name, bool_sort()); }
    inline expr context::int_const(char const * name) { return constant(name, int_sort()); }
    inline expr context::real_const(char const * name) { return constant(name, real_sort()); }
    inline expr context::string_const(char const * name) { return constant(name, string_sort()); }
    inline expr context::bv_const(char const * name, unsigned sz) { return constant(name, bv_sort(sz)); }
    inline expr context::fpa_const(char const * name, unsigned ebits, unsigned sbits) { return constant(name, fpa_sort(ebits, sbits)); }
 
    template<size_t precision>
    inline expr context::fpa_const(char const * name) { return constant(name, fpa_sort<precision>()); }
 
    inline void context::set_rounding_mode(rounding_mode rm) { m_rounding_mode = rm; }
 
    inline expr context::fpa_rounding_mode() {
        switch (m_rounding_mode) {
        case RNA: return expr(*this, Z3_mk_fpa_rna(m_ctx));
        case RNE: return expr(*this, Z3_mk_fpa_rne(m_ctx));
        case RTP: return expr(*this, Z3_mk_fpa_rtp(m_ctx));
        case RTN: return expr(*this, Z3_mk_fpa_rtn(m_ctx));
        case RTZ: return expr(*this, Z3_mk_fpa_rtz(m_ctx));
        default: return expr(*this);
        }
    }
 
    inline expr context::bool_val(bool b) { return b ? expr(*this, Z3_mk_true(m_ctx)) : expr(*this, Z3_mk_false(m_ctx)); }
 
    inline expr context::int_val(int n) { Z3_ast r = Z3_mk_int(m_ctx, n, int_sort()); check_error(); return expr(*this, r); }
    inline expr context::int_val(unsigned n) { Z3_ast r = Z3_mk_unsigned_int(m_ctx, n, int_sort()); check_error(); return expr(*this, r); }
    inline expr context::int_val(int64_t n) { Z3_ast r = Z3_mk_int64(m_ctx, n, int_sort()); check_error(); return expr(*this, r); }
    inline expr context::int_val(uint64_t n) { Z3_ast r = Z3_mk_unsigned_int64(m_ctx, n, int_sort()); check_error(); return expr(*this, r); }
    inline expr context::int_val(char const * n) { Z3_ast r = Z3_mk_numeral(m_ctx, n, int_sort()); check_error(); return expr(*this, r); }
 
    inline expr context::real_val(int64_t n, int64_t d) { Z3_ast r = Z3_mk_real_int64(m_ctx, n, d); check_error(); return expr(*this, r); }
    inline expr context::real_val(int n) { Z3_ast r = Z3_mk_int(m_ctx, n, real_sort()); check_error(); return expr(*this, r); }
    inline expr context::real_val(unsigned n) { Z3_ast r = Z3_mk_unsigned_int(m_ctx, n, real_sort()); check_error(); return expr(*this, r); }
    inline expr context::real_val(int64_t n) { Z3_ast r = Z3_mk_int64(m_ctx, n, real_sort()); check_error(); return expr(*this, r); }
    inline expr context::real_val(uint64_t n) { Z3_ast r = Z3_mk_unsigned_int64(m_ctx, n, real_sort()); check_error(); return expr(*this, r); }
    inline expr context::real_val(char const * n) { Z3_ast r = Z3_mk_numeral(m_ctx, n, real_sort()); check_error(); return expr(*this, r); }
 
    inline expr context::bv_val(int n, unsigned sz) { sort s = bv_sort(sz); Z3_ast r = Z3_mk_int(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::bv_val(unsigned n, unsigned sz) { sort s = bv_sort(sz); Z3_ast r = Z3_mk_unsigned_int(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::bv_val(int64_t n, unsigned sz) { sort s = bv_sort(sz); Z3_ast r = Z3_mk_int64(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::bv_val(uint64_t n, unsigned sz) { sort s = bv_sort(sz); Z3_ast r = Z3_mk_unsigned_int64(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::bv_val(char const * n, unsigned sz) { sort s = bv_sort(sz); Z3_ast r = Z3_mk_numeral(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::bv_val(unsigned n, bool const* bits) {
        array<bool> _bits(n);
        for (unsigned i = 0; i < n; ++i) _bits[i] = bits[i] ? 1 : 0;
        Z3_ast r = Z3_mk_bv_numeral(m_ctx, n, _bits.ptr()); check_error(); return expr(*this, r);
    }
 
    inline expr context::fpa_val(double n) { sort s = fpa_sort<64>(); Z3_ast r = Z3_mk_fpa_numeral_double(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::fpa_val(float n) { sort s = fpa_sort<32>(); Z3_ast r = Z3_mk_fpa_numeral_float(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::fpa_nan(sort const & s) { Z3_ast r = Z3_mk_fpa_nan(m_ctx, s); check_error(); return expr(*this, r); }
    inline expr context::fpa_inf(sort const & s, bool sgn) { Z3_ast r = Z3_mk_fpa_inf(m_ctx, s, sgn); check_error(); return expr(*this, r); }
 
    inline expr context::string_val(char const* s, unsigned n) { Z3_ast r = Z3_mk_lstring(m_ctx, n, s); check_error(); return expr(*this, r); }
    inline expr context::string_val(char const* s) { Z3_ast r = Z3_mk_string(m_ctx, s); check_error(); return expr(*this, r); }
    inline expr context::string_val(std::string const& s) { Z3_ast r = Z3_mk_string(m_ctx, s.c_str()); check_error(); return expr(*this, r); }
    inline expr context::string_val(std::u32string const& s) { Z3_ast r = Z3_mk_u32string(m_ctx, (unsigned)s.size(), (unsigned const*)s.c_str()); check_error(); return expr(*this, r); }
 
    inline expr context::num_val(int n, sort const & s) { Z3_ast r = Z3_mk_int(m_ctx, n, s); check_error(); return expr(*this, r); }
 
    inline expr func_decl::operator()(unsigned n, expr const * args) const {
        array<Z3_ast> _args(n);
        for (unsigned i = 0; i < n; i++) {
            check_context(*this, args[i]);
            _args[i] = args[i];
        }
        Z3_ast r = Z3_mk_app(ctx(), *this, n, _args.ptr());
        check_error();
        return expr(ctx(), r);
 
    }
    inline expr func_decl::operator()(expr_vector const& args) const {
        array<Z3_ast> _args(args.size());
        for (unsigned i = 0; i < args.size(); i++) {
            check_context(*this, args[i]);
            _args[i] = args[i];
        }
        Z3_ast r = Z3_mk_app(ctx(), *this, args.size(), _args.ptr());
        check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()() const {
        Z3_ast r = Z3_mk_app(ctx(), *this, 0, 0);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(expr const & a) const {
        check_context(*this, a);
        Z3_ast args[1] = { a };
        Z3_ast r = Z3_mk_app(ctx(), *this, 1, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(int a) const {
        Z3_ast args[1] = { ctx().num_val(a, domain(0)) };
        Z3_ast r = Z3_mk_app(ctx(), *this, 1, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(expr const & a1, expr const & a2) const {
        check_context(*this, a1); check_context(*this, a2);
        Z3_ast args[2] = { a1, a2 };
        Z3_ast r = Z3_mk_app(ctx(), *this, 2, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(expr const & a1, int a2) const {
        check_context(*this, a1);
        Z3_ast args[2] = { a1, ctx().num_val(a2, domain(1)) };
        Z3_ast r = Z3_mk_app(ctx(), *this, 2, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(int a1, expr const & a2) const {
        check_context(*this, a2);
        Z3_ast args[2] = { ctx().num_val(a1, domain(0)), a2 };
        Z3_ast r = Z3_mk_app(ctx(), *this, 2, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(expr const & a1, expr const & a2, expr const & a3) const {
        check_context(*this, a1); check_context(*this, a2); check_context(*this, a3);
        Z3_ast args[3] = { a1, a2, a3 };
        Z3_ast r = Z3_mk_app(ctx(), *this, 3, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4) const {
        check_context(*this, a1); check_context(*this, a2); check_context(*this, a3); check_context(*this, a4);
        Z3_ast args[4] = { a1, a2, a3, a4 };
        Z3_ast r = Z3_mk_app(ctx(), *this, 4, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
    inline expr func_decl::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5) const {
        check_context(*this, a1); check_context(*this, a2); check_context(*this, a3); check_context(*this, a4); check_context(*this, a5);
        Z3_ast args[5] = { a1, a2, a3, a4, a5 };
        Z3_ast r = Z3_mk_app(ctx(), *this, 5, args);
        ctx().check_error();
        return expr(ctx(), r);
    }
 
    inline expr to_real(expr const & a) { Z3_ast r = Z3_mk_int2real(a.ctx(), a); a.check_error(); return expr(a.ctx(), r); }
 
    inline func_decl function(symbol const & name, unsigned arity, sort const * domain, sort const & range) {
        return range.ctx().function(name, arity, domain, range);
    }
    inline func_decl function(char const * name, unsigned arity, sort const * domain, sort const & range) {
        return range.ctx().function(name, arity, domain, range);
    }
    inline func_decl function(char const * name, sort const & domain, sort const & range) {
        return range.ctx().function(name, domain, range);
    }
    inline func_decl function(char const * name, sort const & d1, sort const & d2, sort const & range) {
        return range.ctx().function(name, d1, d2, range);
    }
    inline func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & range) {
        return range.ctx().function(name, d1, d2, d3, range);
    }
    inline func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & range) {
        return range.ctx().function(name, d1, d2, d3, d4, range);
    }
    inline func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & d5, sort const & range) {
        return range.ctx().function(name, d1, d2, d3, d4, d5, range);
    }
    inline func_decl function(char const* name, sort_vector const& domain, sort const& range) {
        return range.ctx().function(name, domain, range);
    }
    inline func_decl function(std::string const& name, sort_vector const& domain, sort const& range) {
        return range.ctx().function(name.c_str(), domain, range);
    }
 
    inline func_decl recfun(symbol const & name, unsigned arity, sort const * domain, sort const & range) {
        return range.ctx().recfun(name, arity, domain, range);
    }
    inline func_decl recfun(char const * name, unsigned arity, sort const * domain, sort const & range) {
        return range.ctx().recfun(name, arity, domain, range);
    }
    inline func_decl recfun(char const * name, sort const& d1, sort const & range) {
        return range.ctx().recfun(name, d1, range);
    }
    inline func_decl recfun(char const * name, sort const& d1, sort const& d2, sort const & range) {
        return range.ctx().recfun(name, d1, d2, range);
    }
 
    inline expr select(expr const & a, expr const & i) {
        check_context(a, i);
        Z3_ast r = Z3_mk_select(a.ctx(), a, i);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr select(expr const & a, int i) {
        return select(a, a.ctx().num_val(i, a.get_sort().array_domain()));
    }
    inline expr select(expr const & a, expr_vector const & i) {
        check_context(a, i);
        array<Z3_ast> idxs(i);
        Z3_ast r = Z3_mk_select_n(a.ctx(), a, idxs.size(), idxs.ptr());
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr store(expr const & a, expr const & i, expr const & v) {
        check_context(a, i); check_context(a, v);
        Z3_ast r = Z3_mk_store(a.ctx(), a, i, v);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr store(expr const & a, int i, expr const & v) { return store(a, a.ctx().num_val(i, a.get_sort().array_domain()), v); }
    inline expr store(expr const & a, expr i, int v) { return store(a, i, a.ctx().num_val(v, a.get_sort().array_range())); }
    inline expr store(expr const & a, int i, int v) {
        return store(a, a.ctx().num_val(i, a.get_sort().array_domain()), a.ctx().num_val(v, a.get_sort().array_range()));
    }
    inline expr store(expr const & a, expr_vector const & i, expr const & v) {
        check_context(a, i); check_context(a, v);
        array<Z3_ast> idxs(i);
        Z3_ast r = Z3_mk_store_n(a.ctx(), a, idxs.size(), idxs.ptr(), v);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr as_array(func_decl & f) {
        Z3_ast r = Z3_mk_as_array(f.ctx(), f);
        f.check_error();
        return expr(f.ctx(), r);
    }
 
#define MK_EXPR1(_fn, _arg)                     \
    Z3_ast r = _fn(_arg.ctx(), _arg);           \
    _arg.check_error();                         \
    return expr(_arg.ctx(), r);
 
#define MK_EXPR2(_fn, _arg1, _arg2)             \
    check_context(_arg1, _arg2);                \
    Z3_ast r = _fn(_arg1.ctx(), _arg1, _arg2);  \
    _arg1.check_error();                        \
    return expr(_arg1.ctx(), r);
 
    inline expr const_array(sort const & d, expr const & v) {
        MK_EXPR2(Z3_mk_const_array, d, v);
    }
 
    inline expr empty_set(sort const& s) {
        MK_EXPR1(Z3_mk_empty_set, s);
    }
 
    inline expr full_set(sort const& s) {
        MK_EXPR1(Z3_mk_full_set, s);
    }
 
    inline expr set_add(expr const& s, expr const& e) {
        MK_EXPR2(Z3_mk_set_add, s, e);
    }
 
    inline expr set_del(expr const& s, expr const& e) {
        MK_EXPR2(Z3_mk_set_del, s, e);
    }
 
    inline expr set_union(expr const& a, expr const& b) {
        check_context(a, b);
        Z3_ast es[2] = { a, b };
        Z3_ast r = Z3_mk_set_union(a.ctx(), 2, es);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr set_intersect(expr const& a, expr const& b) {
        check_context(a, b);
        Z3_ast es[2] = { a, b };
        Z3_ast r = Z3_mk_set_intersect(a.ctx(), 2, es);
        a.check_error();
        return expr(a.ctx(), r);
    }
 
    inline expr set_difference(expr const& a, expr const& b) {
        MK_EXPR2(Z3_mk_set_difference, a, b);
    }
 
    inline expr set_complement(expr const& a) {
        MK_EXPR1(Z3_mk_set_complement, a);
    }
 
    inline expr set_member(expr const& s, expr const& e) {
        MK_EXPR2(Z3_mk_set_member, s, e);
    }
 
    inline expr set_subset(expr const& a, expr const& b) {
        MK_EXPR2(Z3_mk_set_subset, a, b);
    }
 
    // sequence and regular expression operations.
    // union is +
    // concat is overloaded to handle sequences and regular expressions
 
    inline expr empty(sort const& s) {
        Z3_ast r = Z3_mk_seq_empty(s.ctx(), s);
        s.check_error();
        return expr(s.ctx(), r);
    }
    inline expr suffixof(expr const& a, expr const& b) {
        check_context(a, b);
        Z3_ast r = Z3_mk_seq_suffix(a.ctx(), a, b);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr prefixof(expr const& a, expr const& b) {
        check_context(a, b);
        Z3_ast r = Z3_mk_seq_prefix(a.ctx(), a, b);
        a.check_error();
        return expr(a.ctx(), r);
    }
    inline expr indexof(expr const& s, expr const& substr, expr const& offset) {
        check_context(s, substr); check_context(s, offset);
        Z3_ast r = Z3_mk_seq_index(s.ctx(), s, substr, offset);
        s.check_error();
        return expr(s.ctx(), r);
    }
    inline expr last_indexof(expr const& s, expr const& substr) {
        check_context(s, substr); 
        Z3_ast r = Z3_mk_seq_last_index(s.ctx(), s, substr);
        s.check_error();
        return expr(s.ctx(), r);
    }
    inline expr to_re(expr const& s) {
        MK_EXPR1(Z3_mk_seq_to_re, s);
    }
    inline expr in_re(expr const& s, expr const& re) {
        MK_EXPR2(Z3_mk_seq_in_re, s, re);
    }
    inline expr plus(expr const& re) {
        MK_EXPR1(Z3_mk_re_plus, re);
    }
    inline expr option(expr const& re) {
        MK_EXPR1(Z3_mk_re_option, re);
    }
    inline expr star(expr const& re) {
        MK_EXPR1(Z3_mk_re_star, re);
    }
    inline expr re_empty(sort const& s) {
        Z3_ast r = Z3_mk_re_empty(s.ctx(), s);
        s.check_error();
        return expr(s.ctx(), r);
    }
    inline expr re_full(sort const& s) {
        Z3_ast r = Z3_mk_re_full(s.ctx(), s);
        s.check_error();
        return expr(s.ctx(), r);
    }
    inline expr re_intersect(expr_vector const& args) {
        assert(args.size() > 0);
        context& ctx = args[0u].ctx();
        array<Z3_ast> _args(args);
        Z3_ast r = Z3_mk_re_intersect(ctx, _args.size(), _args.ptr());
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr re_diff(expr const& a, expr const& b) {
        check_context(a, b);
        context& ctx = a.ctx();
        Z3_ast r = Z3_mk_re_diff(ctx, a, b);
        ctx.check_error();
        return expr(ctx, r);
    }
    inline expr re_complement(expr const& a) {
        MK_EXPR1(Z3_mk_re_complement, a);
    }
    inline expr range(expr const& lo, expr const& hi) {
        check_context(lo, hi);
        Z3_ast r = Z3_mk_re_range(lo.ctx(), lo, hi);
        lo.check_error();
        return expr(lo.ctx(), r);
    }
 
 
 
 
 
    inline expr_vector context::parse_string(char const* s) {
        Z3_ast_vector r = Z3_parse_smtlib2_string(*this, s, 0, 0, 0, 0, 0, 0);
        check_error();
        return expr_vector(*this, r);
 
    }
    inline expr_vector context::parse_file(char const* s) {
        Z3_ast_vector r = Z3_parse_smtlib2_file(*this, s, 0, 0, 0, 0, 0, 0);
        check_error();
        return expr_vector(*this, r);
    }
 
    inline expr_vector context::parse_string(char const* s, sort_vector const& sorts, func_decl_vector const& decls) {
        array<Z3_symbol> sort_names(sorts.size());
        array<Z3_symbol> decl_names(decls.size());
        array<Z3_sort>   sorts1(sorts);
        array<Z3_func_decl> decls1(decls);
        for (unsigned i = 0; i < sorts.size(); ++i) {
            sort_names[i] = sorts[i].name();
        }
        for (unsigned i = 0; i < decls.size(); ++i) {
            decl_names[i] = decls[i].name();
        }
 
        Z3_ast_vector r = Z3_parse_smtlib2_string(*this, s, sorts.size(), sort_names.ptr(), sorts1.ptr(), decls.size(), decl_names.ptr(), decls1.ptr());
        check_error();
        return expr_vector(*this, r);
    }
 
    inline expr_vector context::parse_file(char const* s, sort_vector const& sorts, func_decl_vector const& decls) {
        array<Z3_symbol> sort_names(sorts.size());
        array<Z3_symbol> decl_names(decls.size());
        array<Z3_sort>   sorts1(sorts);
        array<Z3_func_decl> decls1(decls);
        for (unsigned i = 0; i < sorts.size(); ++i) {
            sort_names[i] = sorts[i].name();
        }
        for (unsigned i = 0; i < decls.size(); ++i) {
            decl_names[i] = decls[i].name();
        }
        Z3_ast_vector r = Z3_parse_smtlib2_file(*this, s, sorts.size(), sort_names.ptr(), sorts1.ptr(), decls.size(), decl_names.ptr(), decls1.ptr());
        check_error();
        return expr_vector(*this, r);
    }
 
    inline func_decl_vector sort::constructors() {
        assert(is_datatype()); 
        func_decl_vector cs(ctx());
        unsigned n = Z3_get_datatype_sort_num_constructors(ctx(), *this);
        for (unsigned i = 0; i < n; ++i) 
            cs.push_back(func_decl(ctx(), Z3_get_datatype_sort_constructor(ctx(), *this, i)));
        return cs;
    }
 
    inline func_decl_vector sort::recognizers() {
        assert(is_datatype()); 
        func_decl_vector rs(ctx());
        unsigned n = Z3_get_datatype_sort_num_constructors(ctx(), *this);
        for (unsigned i = 0; i < n; ++i) 
            rs.push_back(func_decl(ctx(), Z3_get_datatype_sort_recognizer(ctx(), *this, i)));
        return rs;
    }
 
    inline func_decl_vector func_decl::accessors() {
        sort s = range();
        assert(s.is_datatype());
        unsigned n = Z3_get_datatype_sort_num_constructors(ctx(), s);
        unsigned idx = 0;
        for (; idx < n; ++idx) {
            func_decl f(ctx(), Z3_get_datatype_sort_constructor(ctx(), s, idx));
            if (id() == f.id())
                break;
        }
        assert(idx < n);
        n = arity();
        func_decl_vector as(ctx());
        for (unsigned i = 0; i < n; ++i) 
            as.push_back(func_decl(ctx(), Z3_get_datatype_sort_constructor_accessor(ctx(), s, idx, i)));
        return as;
    }
 
 
    inline expr expr::substitute(expr_vector const& src, expr_vector const& dst) {
        assert(src.size() == dst.size());
        array<Z3_ast> _src(src.size());
        array<Z3_ast> _dst(dst.size());
        for (unsigned i = 0; i < src.size(); ++i) {
            _src[i] = src[i];
            _dst[i] = dst[i];
        }
        Z3_ast r = Z3_substitute(ctx(), m_ast, src.size(), _src.ptr(), _dst.ptr());
        check_error();
        return expr(ctx(), r);
    }
 
    inline expr expr::substitute(expr_vector const& dst) {
        array<Z3_ast> _dst(dst.size());
        for (unsigned i = 0; i < dst.size(); ++i) {
            _dst[i] = dst[i];
        }
        Z3_ast r = Z3_substitute_vars(ctx(), m_ast, dst.size(), _dst.ptr());
        check_error();
        return expr(ctx(), r);
    }
 
    inline expr expr::substitute(func_decl_vector const& funs, expr_vector const& dst) {
        array<Z3_ast> _dst(dst.size());
        array<Z3_func_decl> _funs(funs.size());
        if (dst.size() != funs.size()) {
            Z3_THROW(exception("length of argument lists don't align"));
            return expr(ctx(), nullptr);
        }
        for (unsigned i = 0; i < dst.size(); ++i) {
            _dst[i] = dst[i];
            _funs[i] = funs[i];
        }
        Z3_ast r = Z3_substitute_funs(ctx(), m_ast, dst.size(), _funs.ptr(), _dst.ptr());
        check_error();
        return expr(ctx(), r);
    }
 
    typedef std::function<void(expr const& proof, std::vector<unsigned> const& deps, expr_vector const& clause)> on_clause_eh_t;
 
    class on_clause {
        context& c;
        on_clause_eh_t m_on_clause;
 
        static void _on_clause_eh(void* _ctx, Z3_ast _proof, unsigned n, unsigned const* dep, Z3_ast_vector _literals) {
            on_clause* ctx = static_cast<on_clause*>(_ctx);
            expr_vector lits(ctx->c, _literals);
            expr proof(ctx->c, _proof);
            std::vector<unsigned> deps;
            for (unsigned i = 0; i < n; ++i)
                deps.push_back(dep[i]);
            ctx->m_on_clause(proof, deps, lits);
        }
    public:
        on_clause(solver& s, on_clause_eh_t& on_clause_eh): c(s.ctx()) {
            m_on_clause = on_clause_eh;
            Z3_solver_register_on_clause(c, s, this, _on_clause_eh);
            c.check_error();
        }        
    };
 
    class user_propagator_base {
 
        typedef std::function<void(expr const&, expr const&)> fixed_eh_t;
        typedef std::function<void(void)> final_eh_t;
        typedef std::function<void(expr const&, expr const&)> eq_eh_t;
        typedef std::function<void(expr const&)> created_eh_t;
        typedef std::function<void(expr, unsigned, bool)> decide_eh_t;
 
        final_eh_t m_final_eh;
        eq_eh_t    m_eq_eh;
        fixed_eh_t m_fixed_eh;
        created_eh_t m_created_eh;
        decide_eh_t m_decide_eh;
        solver*    s;
        context*   c;
        std::vector<z3::context*> subcontexts;
 
        Z3_solver_callback cb { nullptr };
 
        struct scoped_cb {
            user_propagator_base& p;
            scoped_cb(void* _p, Z3_solver_callback cb):p(*static_cast<user_propagator_base*>(_p)) {
                p.cb = cb;
            }
            ~scoped_cb() {
                p.cb = nullptr;
            }
        };
 
        static void push_eh(void* _p, Z3_solver_callback cb) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            scoped_cb _cb(p, cb);
            static_cast<user_propagator_base*>(p)->push();
        }
 
        static void pop_eh(void* _p, Z3_solver_callback cb, unsigned num_scopes) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            scoped_cb _cb(p, cb);
            static_cast<user_propagator_base*>(_p)->pop(num_scopes);
        }
 
        static void* fresh_eh(void* _p, Z3_context ctx) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            context* c = new context(ctx);
            p->subcontexts.push_back(c);
            return p->fresh(*c);
        }
 
        static void fixed_eh(void* _p, Z3_solver_callback cb, Z3_ast _var, Z3_ast _value) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            scoped_cb _cb(p, cb);
            expr value(p->ctx(), _value);
            expr var(p->ctx(), _var);
            p->m_fixed_eh(var, value);
        }
 
        static void eq_eh(void* _p, Z3_solver_callback cb, Z3_ast _x, Z3_ast _y) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            scoped_cb _cb(p, cb);
            expr x(p->ctx(), _x), y(p->ctx(), _y);
            p->m_eq_eh(x, y);
        }
 
        static void final_eh(void* p, Z3_solver_callback cb) {
            scoped_cb _cb(p, cb);
            static_cast<user_propagator_base*>(p)->m_final_eh(); 
        }
 
        static void created_eh(void* _p, Z3_solver_callback cb, Z3_ast _e) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            scoped_cb _cb(p, cb);
            expr e(p->ctx(), _e);
            p->m_created_eh(e);
        }
        
        static void decide_eh(void* _p, Z3_solver_callback cb, Z3_ast _val, unsigned bit, bool is_pos) {
            user_propagator_base* p = static_cast<user_propagator_base*>(_p);
            scoped_cb _cb(p, cb);
            expr val(p->ctx(), _val);
            p->m_decide_eh(val, bit, is_pos);
        }
        
    public:
        user_propagator_base(context& c) : s(nullptr), c(&c) {}
        
        user_propagator_base(solver* s): s(s), c(nullptr) {
            Z3_solver_propagate_init(ctx(), *s, this, push_eh, pop_eh, fresh_eh);
        }
 
        virtual void push() = 0;
        virtual void pop(unsigned num_scopes) = 0;
 
        virtual ~user_propagator_base() {
            for (auto& subcontext : subcontexts) {
                subcontext->detach(); // detach first; the subcontexts will be freed internally!
                delete subcontext;
            }
        }
 
        context& ctx() {
            return c ? *c : s->ctx();
        }
 
        virtual user_propagator_base* fresh(context& ctx) = 0;
 
        void register_fixed(fixed_eh_t& f) {
            m_fixed_eh = f;
            if (s) {
                Z3_solver_propagate_fixed(ctx(), *s, fixed_eh);
            }
        }
 
        void register_fixed() {
            m_fixed_eh = [this](expr const &id, expr const &e) {
                fixed(id, e);
            };
            if (s) {
                Z3_solver_propagate_fixed(ctx(), *s, fixed_eh);
            }
        }
 
        void register_eq(eq_eh_t& f) {
            m_eq_eh = f;
            if (s) {
                Z3_solver_propagate_eq(ctx(), *s, eq_eh);
            }
        }
 
        void register_eq() {
            m_eq_eh = [this](expr const& x, expr const& y) {
                eq(x, y);
            };
            if (s) {
                Z3_solver_propagate_eq(ctx(), *s, eq_eh);
            }
        }
 
        void register_final(final_eh_t& f) {
            m_final_eh = f;
            if (s) {
                Z3_solver_propagate_final(ctx(), *s, final_eh);
            }
        }
 
        void register_final() {
            m_final_eh = [this]() {
                final();
            };
            if (s) {
                Z3_solver_propagate_final(ctx(), *s, final_eh);
            }
        }
 
        void register_created(created_eh_t& c) {
            m_created_eh = c;
            if (s) {
                Z3_solver_propagate_created(ctx(), *s, created_eh);
            }
        }
 
        void register_created() {
            m_created_eh = [this](expr const& e) {
                created(e);
            };
            if (s) {
                Z3_solver_propagate_created(ctx(), *s, created_eh);
            }
        }
        
        void register_decide(decide_eh_t& c) {
            m_decide_eh = c;
            if (s) {
                Z3_solver_propagate_decide(ctx(), *s, decide_eh);
            }
        }
 
        void register_decide() {
            m_decide_eh = [this](expr val, unsigned bit, bool is_pos) {
                decide(val, bit, is_pos);
            };
            if (s) {
                Z3_solver_propagate_decide(ctx(), *s, decide_eh);
            }
        }
 
        virtual void fixed(expr const& /*id*/, expr const& /*e*/) { }
 
        virtual void eq(expr const& /*x*/, expr const& /*y*/) { }
 
        virtual void final() { }
 
        virtual void created(expr const& /*e*/) {}
        
        virtual void decide(expr const& /*val*/, unsigned /*bit*/, bool /*is_pos*/) {}
 
        bool next_split(expr const& e, unsigned idx, Z3_lbool phase) {
            assert(cb);
            return Z3_solver_next_split(ctx(), cb, e, idx, phase);
        }
 
        void add(expr const& e) {
            if (cb)
                Z3_solver_propagate_register_cb(ctx(), cb, e);
            else if (s)
                Z3_solver_propagate_register(ctx(), *s, e);
            else
                assert(false);
        }
 
        void conflict(expr_vector const& fixed) {
            assert(cb);
            expr conseq = ctx().bool_val(false);
            array<Z3_ast> _fixed(fixed);
            Z3_solver_propagate_consequence(ctx(), cb, fixed.size(), _fixed.ptr(), 0, nullptr, nullptr, conseq);
        }
 
        void conflict(expr_vector const& fixed, expr_vector const& lhs, expr_vector const& rhs) {
            assert(cb);
            assert(lhs.size() == rhs.size());
            expr conseq = ctx().bool_val(false);
            array<Z3_ast> _fixed(fixed);
            array<Z3_ast> _lhs(lhs);
            array<Z3_ast> _rhs(rhs);
            Z3_solver_propagate_consequence(ctx(), cb, fixed.size(), _fixed.ptr(), lhs.size(), _lhs.ptr(), _rhs.ptr(), conseq);
        }
 
        bool propagate(expr_vector const& fixed, expr const& conseq) {
            assert(cb);
            assert((Z3_context)conseq.ctx() == (Z3_context)ctx());
            array<Z3_ast> _fixed(fixed);
            return Z3_solver_propagate_consequence(ctx(), cb, _fixed.size(), _fixed.ptr(), 0, nullptr, nullptr, conseq);
        }
 
        bool propagate(expr_vector const& fixed,
                       expr_vector const& lhs, expr_vector const& rhs,
                       expr const& conseq) {
            assert(cb);
            assert((Z3_context)conseq.ctx() == (Z3_context)ctx());
            assert(lhs.size() == rhs.size());
            array<Z3_ast> _fixed(fixed);
            array<Z3_ast> _lhs(lhs);
            array<Z3_ast> _rhs(rhs);
            
            return Z3_solver_propagate_consequence(ctx(), cb, _fixed.size(), _fixed.ptr(), lhs.size(), _lhs.ptr(), _rhs.ptr(), conseq);
        }
    };
 
}
 
#undef Z3_THROW