/*++
Copyright (c) 2006 Microsoft Corporation

Module Name:

    ast.h

Abstract:

    Expression DAG

Author:

    Leonardo de Moura (leonardo) 2006-09-18.

Revision History:

--*/
#ifndef AST_H_
#define AST_H_

#include "util/vector.h"
#include "util/hashtable.h"
#include "util/buffer.h"
#include "util/symbol.h"
#include "util/rational.h"
#include "util/hash.h"
#include "util/optional.h"
#include "util/trace.h"
#include "util/bit_vector.h"
#include "util/symbol_table.h"
#include "util/tptr.h"
#include "util/memory_manager.h"
#include "util/small_object_allocator.h"
#include "util/obj_ref.h"
#include "util/ref_vector.h"
#include "util/ref_buffer.h"
#include "util/obj_mark.h"
#include "util/obj_hashtable.h"
#include "util/id_gen.h"
#include "util/map.h"
#include "util/parray.h"
#include "util/dictionary.h"
#include "util/chashtable.h"
#include "util/z3_exception.h"
#include "util/dependency.h"
#include "util/rlimit.h"

#define RECYCLE_FREE_AST_INDICES

#ifdef _MSC_VER
#pragma warning(disable : 4200)
#pragma warning(disable : 4355)
#endif

class ast;
class ast_manager;

/**
   \brief Generic exception for AST related errors.

   We used to use fatal_error_msg to report errors inside plugins.
*/
class ast_exception : public default_exception {
public:
    ast_exception(char const * msg):default_exception(msg) {}
};

typedef int     family_id;
const family_id null_family_id = -1;

// -----------------------------------
//
// parameter
//
// -----------------------------------

/**
   \brief Interpreted function declarations and sorts may have parameters that are used
   to encode extra information associated with them.
*/
class parameter {
public:
    enum kind_t {
        PARAM_INT,
        PARAM_AST,
        PARAM_SYMBOL,
        PARAM_RATIONAL,
        PARAM_DOUBLE,
        // PARAM_EXTERNAL is used for handling decl_plugin specific parameters.
        // For example, it is used for handling mpf numbers in float_decl_plugin,
        // and irrational algebraic numbers in arith_decl_plugin.
        // PARAM_EXTERNAL is not supported by z3 low level input format. This format is legacy, so
        // this is not a big problem.
        // Remark: PARAM_EXTERNAL can only be used to decorate theory decls.
        PARAM_EXTERNAL
    };
private:
    kind_t m_kind;

    // It is not possible to use tag pointers, since symbols are already tagged.
    union {
        int          m_int;     // for PARAM_INT
        ast*         m_ast;     // for PARAM_AST
        void const*  m_symbol;  // for PARAM_SYMBOL
        rational*    m_rational; // for PARAM_RATIONAL
        double       m_dval;   // for PARAM_DOUBLE (remark: this is not used in float_decl_plugin)
        unsigned     m_ext_id; // for PARAM_EXTERNAL
    };

public:

    parameter(): m_kind(PARAM_INT), m_int(0) {}
    explicit parameter(int val): m_kind(PARAM_INT), m_int(val) {}
    explicit parameter(unsigned val): m_kind(PARAM_INT), m_int(val) {}
    explicit parameter(ast * p): m_kind(PARAM_AST), m_ast(p) {}
    explicit parameter(symbol const & s): m_kind(PARAM_SYMBOL), m_symbol(s.c_ptr()) {}
    explicit parameter(rational const & r): m_kind(PARAM_RATIONAL), m_rational(alloc(rational, r)) {}
    explicit parameter(double d):m_kind(PARAM_DOUBLE), m_dval(d) {}
    explicit parameter(const char *s):m_kind(PARAM_SYMBOL), m_symbol(symbol(s).c_ptr()) {}
    explicit parameter(unsigned ext_id, bool):m_kind(PARAM_EXTERNAL), m_ext_id(ext_id) {}
    parameter(parameter const&);

    ~parameter();

    parameter& operator=(parameter const& other);

    kind_t get_kind() const { return m_kind; }
    bool is_int() const { return m_kind == PARAM_INT; }
    bool is_ast() const { return m_kind == PARAM_AST; }
    bool is_symbol() const { return m_kind == PARAM_SYMBOL; }
    bool is_rational() const { return m_kind == PARAM_RATIONAL; }
    bool is_double() const { return m_kind == PARAM_DOUBLE; }
    bool is_external() const { return m_kind == PARAM_EXTERNAL; }

    bool is_int(int & i) const { return is_int() && (i = get_int(), true); }
    bool is_ast(ast * & a) const { return is_ast() && (a = get_ast(), true); }
    bool is_symbol(symbol & s) const { return is_symbol() && (s = get_symbol(), true); }
    bool is_rational(rational & r) const { return is_rational() && (r = get_rational(), true); }
    bool is_double(double & d) const { return is_double() && (d = get_double(), true); }
    bool is_external(unsigned & id) const { return is_external() && (id = get_ext_id(), true); }

    /**
       \brief This method is invoked when the parameter is
       attached to a function declaration or sort.
    */
    void init_eh(ast_manager & m);
    /**
       \brief This method is invoked before the function
       declaration or sort associated with the parameter is
       deleted.
    */
    void del_eh(ast_manager & m, family_id fid);

    int get_int() const { SASSERT(is_int()); return m_int; }
    ast * get_ast() const { SASSERT(is_ast()); return m_ast; }
    symbol get_symbol() const { SASSERT(is_symbol()); return symbol::mk_symbol_from_c_ptr(m_symbol); }
    rational const & get_rational() const { SASSERT(is_rational()); return *m_rational; }
    double get_double() const { SASSERT(is_double()); return m_dval; }
    unsigned get_ext_id() const { SASSERT(is_external()); return m_ext_id; }

    bool operator==(parameter const & p) const;
    bool operator!=(parameter const & p) const { return !operator==(p); }

    unsigned hash() const;

    std::ostream& display(std::ostream& out) const;
};

inline std::ostream& operator<<(std::ostream& out, parameter const & p) {
    return p.display(out);
}

void display_parameters(std::ostream & out, unsigned n, parameter const * p);

// -----------------------------------
//
// family_manager
//
// -----------------------------------

/**
   \brief Interpreted functions and sorts are grouped in families.
   Each family has an unique ID. This class models the mapping
   between symbols (family names) and the unique IDs.
*/
class family_manager {
    family_id               m_next_id;
    symbol_table<family_id> m_families;
    svector<symbol>         m_names;
public:
    family_manager():m_next_id(0) {}

    /**
       \brief Return the family_id for s, a new id is created if !has_family(s)

       If has_family(s), then this method is equivalent to get_family_id(s)
    */
    family_id mk_family_id(symbol const & s);

    /**
       \brief Return the family_id for s, return null_family_id if s was not registered in the manager.
    */
    family_id get_family_id(symbol const & s) const;

    bool has_family(symbol const & s) const;

    void get_dom(svector<symbol>& dom) const { m_families.get_dom(dom); }

    void get_range(svector<family_id> & range) const { m_families.get_range(range); }

    symbol const & get_name(family_id fid) const { return fid >= 0 && fid < static_cast<int>(m_names.size()) ? m_names[fid] : symbol::null; }

    bool has_family(family_id fid) const { return fid >= 0 && fid < static_cast<int>(m_names.size()); }
};

// -----------------------------------
//
// decl_info
//
// -----------------------------------

/**
   \brief Each interpreted function declaration or sort has a kind.
   Kinds are used to identify interpreted functions and sorts in a family.
*/
typedef int     decl_kind;
const decl_kind null_decl_kind = -1;

/**
   \brief Interpreted function declarations and sorts are associated with
   a family id, kind, and parameters.
*/
class decl_info {
    family_id            m_family_id;
    decl_kind            m_kind;
    vector<parameter>    m_parameters;
public:
    bool                 m_private_parameters;
    decl_info(family_id family_id = null_family_id, decl_kind k = null_decl_kind,
              unsigned num_parameters = 0, parameter const * parameters = 0, bool private_params = false);

    decl_info(decl_info const& other);
    ~decl_info() {}

    void init_eh(ast_manager & m);
    void del_eh(ast_manager & m);

    family_id get_family_id() const { return m_family_id; }
    decl_kind get_decl_kind() const { return m_kind; }
    unsigned get_num_parameters() const { return m_parameters.size(); }
    parameter const & get_parameter(unsigned idx) const { return m_parameters[idx]; }
    parameter const * get_parameters() const { return m_parameters.begin(); }
    bool private_parameters() const { return m_private_parameters; }

    unsigned hash() const;
    bool operator==(decl_info const & info) const;
};

std::ostream & operator<<(std::ostream & out, decl_info const & info);

// -----------------------------------
//
// sort_size
//
// -----------------------------------

/**
   \brief Models the number of elements of a sort.
*/
class sort_size {
    enum kind_t {
        SS_FINITE,
        // For some sorts it may be too expensive to compute the
        // number of elements precisely (e.g., arrays).  In this
        // cases, we mark the sort as too big. That is, the number
        // of elements is at least bigger than 2^64.
        SS_FINITE_VERY_BIG,
        SS_INFINITE
    } m_kind;
    uint64 m_size; // It is only meaningful if m_kind == SS_FINITE
    sort_size(kind_t k, uint64 r):m_kind(k), m_size(r) {}
public:
    sort_size():m_kind(SS_INFINITE) {}
    sort_size(uint64 const & sz):m_kind(SS_FINITE), m_size(sz) {}
    sort_size(sort_size const& other): m_kind(other.m_kind), m_size(other.m_size) {}
    explicit sort_size(rational const& r) {
        if (r.is_uint64()) {
            m_kind = SS_FINITE;
            m_size = r.get_uint64();
        }
        else {
            m_kind = SS_FINITE_VERY_BIG;
            m_size = 0;
        }
    }
    static sort_size mk_infinite() { return sort_size(SS_INFINITE, 0); }
    static sort_size mk_very_big() { return sort_size(SS_FINITE_VERY_BIG, 0); }
    static sort_size mk_finite(uint64 r) { return sort_size(SS_FINITE, r); }

    bool is_infinite() const { return m_kind == SS_INFINITE; }
    bool is_very_big() const { return m_kind == SS_FINITE_VERY_BIG; }
    bool is_finite() const { return m_kind == SS_FINITE; }

    static bool is_very_big_base2(unsigned power) { return power >= 64; }

    uint64 size() const { SASSERT(is_finite()); return m_size; }
};

std::ostream& operator<<(std::ostream& out, sort_size const & ss);

// -----------------------------------
//
// sort_info
//
// -----------------------------------

/**
   \brief Extra information that may be attached to intepreted sorts.
*/
class sort_info : public decl_info {
    sort_size m_num_elements;
public:
    sort_info(family_id family_id = null_family_id, decl_kind k = null_decl_kind,
              unsigned num_parameters = 0, parameter const * parameters = 0, bool private_parameters = false):
        decl_info(family_id, k, num_parameters, parameters, private_parameters) {
    }

    sort_info(family_id family_id, decl_kind k, uint64 num_elements,
              unsigned num_parameters = 0, parameter const * parameters = 0, bool private_parameters = false):
        decl_info(family_id, k, num_parameters, parameters, private_parameters), m_num_elements(num_elements) {
    }

    sort_info(family_id family_id, decl_kind k, sort_size const& num_elements,
              unsigned num_parameters = 0, parameter const * parameters = 0, bool private_parameters = false):
        decl_info(family_id, k, num_parameters, parameters, private_parameters), m_num_elements(num_elements) {
    }
    sort_info(sort_info const& other) : decl_info(other), m_num_elements(other.m_num_elements) {
    }
    ~sort_info() {}

    bool is_infinite() const { return m_num_elements.is_infinite(); }
    bool is_very_big() const { return m_num_elements.is_very_big(); }
    sort_size const & get_num_elements() const { return m_num_elements; }
};

std::ostream & operator<<(std::ostream & out, sort_info const & info);

// -----------------------------------
//
// func_decl_info
//
// -----------------------------------

/**
   \brief Extra information that may be attached to interpreted function decls.
*/
struct func_decl_info : public decl_info {
    bool m_left_assoc:1;
    bool m_right_assoc:1;
    bool m_flat_associative:1;
    bool m_commutative:1;
    bool m_chainable:1;
    bool m_pairwise:1;
    bool m_injective:1;
    bool m_idempotent:1;
    bool m_skolem:1;

    func_decl_info(family_id family_id = null_family_id, decl_kind k = null_decl_kind, unsigned num_parameters = 0, parameter const * parameters = 0);
    ~func_decl_info() {}

    bool is_associative() const { return m_left_assoc && m_right_assoc; }
    bool is_left_associative() const { return m_left_assoc; }
    bool is_right_associative() const { return m_right_assoc; }
    bool is_flat_associative() const { return m_flat_associative; }
    bool is_commutative() const { return m_commutative; }
    bool is_chainable() const { return m_chainable; }
    bool is_pairwise() const { return m_pairwise; }
    bool is_injective() const { return m_injective; }
    bool is_idempotent() const { return m_idempotent; }
    bool is_skolem() const { return m_skolem; }

    void set_associative(bool flag = true) { m_left_assoc = flag; m_right_assoc = flag; }
    void set_left_associative(bool flag = true) { m_left_assoc = flag; }
    void set_right_associative(bool flag = true) { m_right_assoc = flag; }
    void set_flat_associative(bool flag = true) { m_flat_associative = flag; }
    void set_commutative(bool flag = true) { m_commutative = flag; }
    void set_chainable(bool flag = true) { m_chainable = flag; }
    void set_pairwise(bool flag = true) { m_pairwise = flag; }
    void set_injective(bool flag = true) { m_injective = flag; }
    void set_idempotent(bool flag = true) { m_idempotent = flag; }
    void set_skolem(bool flag = true) { m_skolem = flag; }

    bool operator==(func_decl_info const & info) const;

    // Return true if the func_decl_info is equivalent to the null one (i.e., it does not contain any useful info).
    bool is_null() const {
        return
            get_family_id() == null_family_id && !is_left_associative() && !is_right_associative() && !is_commutative() &&
            !is_chainable() && !is_pairwise() && !is_injective() && !is_idempotent() && !is_skolem();
    }
};

std::ostream & operator<<(std::ostream & out, func_decl_info const & info);

// -----------------------------------
//
// ast
//
// -----------------------------------

typedef enum { AST_APP, AST_VAR, AST_QUANTIFIER, AST_SORT, AST_FUNC_DECL } ast_kind;
char const * get_ast_kind_name(ast_kind k);

class shared_occs_mark;

class ast {
protected:
    friend class ast_manager;

    unsigned m_id;
    unsigned m_kind:16;
    // Warning: the marks should be used carefully, since they are shared.
    unsigned m_mark1:1;
    unsigned m_mark2:1;
    // Private mark used by shared_occs functor
    // Motivation for this field:
    //  - A mark cannot be used by more than one owner.
    //    So, it is only safe to use mark by "self-contained" code.
    //    They should be viewed as temporary information.
    //  - The functor shared_occs is used by some AST pretty printers.
    //  - So, a code that uses marks could not use the pretty printer if
    //    shared_occs used one of the public marks.
    //  - This was a constant source of assertion violations.
    unsigned m_mark_shared_occs:1;
    friend class shared_occs_mark;
    void mark_so(bool flag) { m_mark_shared_occs = flag; }
    void reset_mark_so() { m_mark_shared_occs = false; }
    bool is_marked_so() const { return m_mark_shared_occs; }
    unsigned m_ref_count;
    unsigned m_hash;
#ifdef Z3DEBUG
    // In debug mode, we store who is the owner of the mark.
    void *   m_mark1_owner;
    void *   m_mark2_owner;
#endif

    void inc_ref() {
        SASSERT(m_ref_count < UINT_MAX);
        m_ref_count ++;
    }

    void dec_ref() {
        SASSERT(m_ref_count > 0);
        m_ref_count --;
    }

    ast(ast_kind k):m_id(UINT_MAX), m_kind(k), m_mark1(false), m_mark2(false), m_mark_shared_occs(false), m_ref_count(0) {
        DEBUG_CODE({
            m_mark1_owner = 0;
            m_mark2_owner = 0;
        });
    }
public:
    unsigned get_id() const { return m_id; }
    unsigned get_ref_count() const { return m_ref_count; }
    ast_kind get_kind() const { return static_cast<ast_kind>(m_kind); }
    unsigned hash() const { return m_hash; }

#ifdef Z3DEBUG
    void mark1(bool flag, void * owner) { SASSERT(m_mark1_owner == 0 || m_mark1_owner == owner); m_mark1 = flag; m_mark1_owner = owner; }
    void mark2(bool flag, void * owner) { SASSERT(m_mark2_owner == 0 || m_mark2_owner == owner); m_mark2 = flag; m_mark2_owner = owner; }
    void reset_mark1(void * owner) { SASSERT(m_mark1_owner == 0 || m_mark1_owner == owner); m_mark1 = false; m_mark1_owner = 0; }
    void reset_mark2(void * owner) { SASSERT(m_mark2_owner == 0 || m_mark2_owner == owner); m_mark2 = false; m_mark2_owner = 0; }
    bool is_marked1(void * owner) const { SASSERT(m_mark1_owner == 0 || m_mark1_owner == owner); return m_mark1; }
    bool is_marked2(void * owner) const { SASSERT(m_mark2_owner == 0 || m_mark2_owner == owner); return m_mark2; }
#define AST_MARK1(A,F,O) A->mark1(F, O)
#define AST_MARK2(A,F,O) A->mark2(F, O)
#define AST_RESET_MARK1(A,O) A->reset_mark1(O)
#define AST_RESET_MARK2(A,O) A->reset_mark2(O)
#define AST_IS_MARKED1(A,O) A->is_marked1(O)
#define AST_IS_MARKED2(A,O) A->is_marked2(O)
#else
    void mark1(bool flag) { m_mark1 = flag; }
    void mark2(bool flag) { m_mark2 = flag; }
    void reset_mark1() { m_mark1 = false; }
    void reset_mark2() { m_mark2 = false; }
    bool is_marked1() const { return m_mark1; }
    bool is_marked2() const { return m_mark2; }
#define AST_MARK1(A,F,O) A->mark1(F)
#define AST_MARK2(A,F,O) A->mark2(F)
#define AST_RESET_MARK1(A,O) A->reset_mark1()
#define AST_RESET_MARK2(A,O) A->reset_mark2()
#define AST_IS_MARKED1(A,O) A->is_marked1()
#define AST_IS_MARKED2(A,O) A->is_marked2()
#endif
};

#define MATCH_TERNARY(_MATCHER_)                                                                                \
    bool _MATCHER_(expr const* n, expr*& a1, expr*& a2, expr *& a3) const {                                     \
        if (_MATCHER_(n) && to_app(n)->get_num_args() == 3) {                                                   \
            a1 = to_app(n)->get_arg(0); a2 = to_app(n)->get_arg(1); a3 = to_app(n)->get_arg(2); return true; }  \
        return false;                                                                                           \
    }

#define MATCH_BINARY(_MATCHER_)                                                                                                         \
    bool _MATCHER_(expr const* n, expr*& s, expr*& t) const {                                                                           \
        if (_MATCHER_(n) && to_app(n)->get_num_args() == 2) { s = to_app(n)->get_arg(0); t = to_app(n)->get_arg(1); return true; }      \
        return false;                                                                                                                   \
    }

#define MATCH_UNARY(_MATCHER_)                                                                          \
    bool _MATCHER_(expr const* n, expr*& s) const {                                                     \
        if (_MATCHER_(n) && to_app(n)->get_num_args() == 1) { s = to_app(n)->get_arg(0); return true; } \
        return false;                                                                                   \
    }

// -----------------------------------
//
// decl
//
// -----------------------------------

/**
   The ids of expressions and declarations are in different ranges.
*/
const unsigned c_first_decl_id = (1u << 31u);

/**
   \brief Superclass for function declarations and sorts.
*/
class decl : public ast {
protected:
    friend class ast_manager;

    symbol      m_name;
    decl_info * m_info;

    decl(ast_kind k, symbol const & name, decl_info * info):ast(k), m_name(name), m_info(info) {}
public:
    unsigned get_decl_id() const { SASSERT(get_id() >= c_first_decl_id); return get_id() - c_first_decl_id; }
    symbol const & get_name() const { return m_name; }
    decl_info * get_info() const { return m_info; }
    family_id get_family_id() const { return m_info == 0 ? null_family_id : m_info->get_family_id(); }
    decl_kind get_decl_kind() const { return m_info == 0 ? null_decl_kind : m_info->get_decl_kind(); }
    unsigned get_num_parameters() const { return m_info == 0 ? 0 : m_info->get_num_parameters(); }
    parameter const & get_parameter(unsigned idx) const { return m_info->get_parameter(idx); }
    parameter const * get_parameters() const { return m_info == 0 ? 0 : m_info->get_parameters(); }
    bool private_parameters() const { return m_info != 0 && m_info->private_parameters(); }
};

// -----------------------------------
//
// sort
//
// -----------------------------------

class sort : public decl {
    friend class ast_manager;

    static unsigned get_obj_size() { return sizeof(sort); }

    sort(symbol const & name, sort_info * info):decl(AST_SORT, name, info) {}
public:
    sort_info * get_info() const { return static_cast<sort_info*>(m_info); }
    bool is_infinite() const { return get_info() == 0 || get_info()->is_infinite(); }
    bool is_very_big() const { return get_info() == 0 || get_info()->is_very_big(); }
    bool is_sort_of(family_id fid, decl_kind k) const { return get_family_id() == fid && get_decl_kind() == k; }
    sort_size const & get_num_elements() const { return get_info()->get_num_elements(); }
    unsigned get_size() const { return get_obj_size(); }
};

// -----------------------------------
//
// func_decl
//
// -----------------------------------

class func_decl : public decl {
    friend class ast_manager;

    unsigned         m_arity;
    sort *           m_range;
    sort *           m_domain[0];

    static unsigned get_obj_size(unsigned arity) { return sizeof(func_decl) + arity * sizeof(sort *); }

    func_decl(symbol const & name, unsigned arity, sort * const * domain, sort * range, func_decl_info * info);
public:
    func_decl_info * get_info() const { return static_cast<func_decl_info*>(m_info); }
    bool is_associative() const { return get_info() != 0 && get_info()->is_associative(); }
    bool is_left_associative() const { return get_info() != 0 && get_info()->is_left_associative(); }
    bool is_right_associative() const { return get_info() != 0 && get_info()->is_right_associative(); }
    bool is_flat_associative() const { return get_info() != 0 && get_info()->is_flat_associative(); }
    bool is_commutative() const { return get_info() != 0 && get_info()->is_commutative(); }
    bool is_chainable() const { return get_info() != 0 && get_info()->is_chainable(); }
    bool is_pairwise() const { return get_info() != 0 && get_info()->is_pairwise(); }
    bool is_injective() const { return get_info() != 0 && get_info()->is_injective(); }
    bool is_skolem() const { return get_info() != 0 && get_info()->is_skolem(); }
    bool is_idempotent() const { return get_info() != 0 && get_info()->is_idempotent(); }
    unsigned get_arity() const { return m_arity; }
    sort * get_domain(unsigned idx) const { SASSERT(idx < get_arity()); return m_domain[idx]; }
    sort * const * get_domain() const { return m_domain; }
    sort * get_range() const { return m_range; }
    unsigned get_size() const { return get_obj_size(m_arity); }
};

// -----------------------------------
//
// expression
//
// -----------------------------------

/**
   \brief Superclass for applications, variables and quantifiers.
*/
class expr : public ast {
protected:
    friend class ast_manager;

    expr(ast_kind k):ast(k) {}
public:
};

// -----------------------------------
//
// application
//
// -----------------------------------

#define APP_DEPTH_NUM_BITS 16
const unsigned c_max_depth = ((1 << APP_DEPTH_NUM_BITS) - 1);
struct app_flags {
    unsigned     m_depth:APP_DEPTH_NUM_BITS;  // if app is to deep, it doesn't matter.
    unsigned     m_ground:1;   // application does not have free variables or nested quantifiers.
    unsigned     m_has_quantifiers:1; // application has nested quantifiers.
    unsigned     m_has_labels:1; // application has nested labels.
};

class app : public expr {
    friend class ast_manager;

    func_decl *  m_decl;
    unsigned     m_num_args;
    expr *       m_args[0];

    static app_flags g_constant_flags;

    // remark: store term depth in the end of the app. the depth is only stored if the num_args > 0
    static unsigned get_obj_size(unsigned num_args) {
        return num_args == 0 ? sizeof(app) : sizeof(app) + num_args * sizeof(expr *) + sizeof(app_flags);
    }

    friend class tmp_app;

    app_flags * flags() const { return m_num_args == 0 ? &g_constant_flags : reinterpret_cast<app_flags*>(const_cast<expr**>(m_args + m_num_args)); }

    app(func_decl * decl, unsigned num_args, expr * const * args);
public:
    func_decl * get_decl() const { return m_decl; }
    family_id get_family_id() const { return get_decl()->get_family_id(); }
    decl_kind get_decl_kind() const { return get_decl()->get_decl_kind(); }
    bool is_app_of(family_id fid, decl_kind k) const { return get_family_id() == fid && get_decl_kind() == k; }
    unsigned get_num_args() const { return m_num_args; }
    expr * get_arg(unsigned idx) const { SASSERT(idx < m_num_args); return m_args[idx]; }
    expr * const * get_args() const { return m_args; }
    unsigned get_size() const { return get_obj_size(get_num_args()); }
    expr * const * begin() const { return m_args; }
    expr * const * end() const { return m_args + m_num_args; }

    unsigned get_depth() const { return flags()->m_depth; }
    bool is_ground() const { return flags()->m_ground; }
    bool has_quantifiers() const { return flags()->m_has_quantifiers; }
    bool has_labels() const { return flags()->m_has_labels; }
};

// -----------------------------------
//
// temporary application: little hack to avoid
// the creation of temporary expressions to just
// check the presence of the expression in
// some container/index.
//
// -----------------------------------

class tmp_app {
    unsigned m_num_args;
    char *   m_data;
public:
    tmp_app(unsigned num_args):
        m_num_args(num_args) {
        unsigned sz = app::get_obj_size(num_args);
        m_data = alloc_svect(char, sz);
        memset(m_data, 0, sz);
        get_app()->m_num_args = m_num_args;
    }

    ~tmp_app() {
        dealloc_svect(m_data);
    }

    app * get_app() {
        return reinterpret_cast<app*>(m_data);
    }

    expr ** get_args() {
        return get_app()->m_args;
    }

    void set_decl(func_decl * d) {
        get_app()->m_decl = d;
    }

    void set_num_args(unsigned num_args) {
        get_app()->m_num_args = num_args;
    }

    void set_arg(unsigned idx, expr * arg) {
        get_args()[idx] = arg;
        SASSERT(get_app()->get_arg(idx) == arg);
    }

    void copy(app * source) {
        SASSERT(source->get_num_args() <= m_num_args);
        new (m_data) app(source->get_decl(), source->get_num_args(), source->get_args());
        SASSERT(get_app()->get_decl() == source->get_decl());
        SASSERT(get_app()->get_arg(0) == source->get_arg(0));
        SASSERT(get_app()->get_arg(1) == source->get_arg(1));
    }

    void copy_swapping_args(app * source) {
        SASSERT(source->get_num_args() == 2 && m_num_args >= 2);
        expr * args[2] = { source->get_arg(1), source->get_arg(0) };
        new (m_data) app(source->get_decl(), 2, args);
        SASSERT(get_app()->get_decl() == source->get_decl());
        SASSERT(get_app()->get_arg(0) == source->get_arg(1));
        SASSERT(get_app()->get_arg(1) == source->get_arg(0));
    }
};

// -----------------------------------
//
// variables
//
// -----------------------------------

class var : public expr {
    friend class ast_manager;

    unsigned     m_idx;
    sort *       m_sort;

    static unsigned get_obj_size() { return sizeof(var); }

    var(unsigned idx, sort * s):expr(AST_VAR), m_idx(idx), m_sort(s) {}
public:
    unsigned get_idx() const { return m_idx; }
    sort * get_sort() const { return m_sort; }
    unsigned get_size() const { return get_obj_size(); }
};

// -----------------------------------
//
// quantifier
//
// -----------------------------------

class quantifier : public expr {
    friend class ast_manager;
    bool                m_forall;
    unsigned            m_num_decls;
    expr *              m_expr;
    unsigned            m_depth;
    // extra fields
    int                 m_weight;
    bool                m_has_unused_vars;
    bool                m_has_labels;
    symbol              m_qid;
    symbol              m_skid;
    unsigned            m_num_patterns;
    unsigned            m_num_no_patterns;
    char                m_patterns_decls[0];

    static unsigned get_obj_size(unsigned num_decls, unsigned num_patterns, unsigned num_no_patterns) {
        return sizeof(quantifier) + num_decls * (sizeof(sort *) + sizeof(symbol)) + (num_patterns + num_no_patterns) * sizeof(expr*);
    }

    quantifier(bool forall, unsigned num_decls, sort * const * decl_sorts, symbol const * decl_names, expr * body,
               int weight, symbol const & qid, symbol const & skid, unsigned num_patterns, expr * const * patterns,
               unsigned num_no_patterns, expr * const * no_patterns);
public:
    bool is_forall() const { return m_forall; }
    bool is_exists() const { return !m_forall; }
    unsigned get_num_decls() const { return m_num_decls; }
    sort * const * get_decl_sorts() const { return reinterpret_cast<sort * const *>(m_patterns_decls); }
    symbol const * get_decl_names() const { return reinterpret_cast<symbol const *>(get_decl_sorts() + m_num_decls); }
    sort * get_decl_sort(unsigned idx) const { return get_decl_sorts()[idx]; }
    symbol const & get_decl_name(unsigned idx) const { return get_decl_names()[idx]; }
    expr * get_expr() const { return m_expr; }

    unsigned get_depth() const { return m_depth; }

    int get_weight() const { return m_weight; }
    symbol const & get_qid() const { return m_qid; }
    symbol const & get_skid() const { return m_skid; }
    unsigned get_num_patterns() const { return m_num_patterns; }
    expr * const * get_patterns() const { return reinterpret_cast<expr * const *>(get_decl_names() + m_num_decls); }
    expr * get_pattern(unsigned idx) const { return get_patterns()[idx]; }
    unsigned get_num_no_patterns() const { return m_num_no_patterns; }
    expr * const * get_no_patterns() const { return reinterpret_cast<expr * const *>(get_decl_names() + m_num_decls); }
    expr * get_no_pattern(unsigned idx) const { return get_no_patterns()[idx]; }
    bool has_patterns() const { return m_num_patterns > 0 || m_num_no_patterns > 0; }
    unsigned get_size() const { return get_obj_size(m_num_decls, m_num_patterns, m_num_no_patterns); }

    bool may_have_unused_vars() const { return m_has_unused_vars; }
    void set_no_unused_vars() { m_has_unused_vars = false; }

    bool has_labels() const { return m_has_labels; }

    unsigned get_num_children() const { return 1 + get_num_patterns() + get_num_no_patterns(); }
    expr * get_child(unsigned idx) const {
        SASSERT(idx < get_num_children());
        if (idx == 0)
            return get_expr();
        else if (idx <= get_num_patterns())
            return get_pattern(idx - 1);
        else
            return get_no_pattern(idx - get_num_patterns() - 1);
    }
};

// -----------------------------------
//
// AST recognisers
//
// -----------------------------------

inline bool is_decl(ast const * n)       { ast_kind k = n->get_kind(); return k == AST_FUNC_DECL || k == AST_SORT; }
inline bool is_sort(ast const * n)       { return n->get_kind() == AST_SORT; }
inline bool is_func_decl(ast const * n)  { return n->get_kind() == AST_FUNC_DECL; }
inline bool is_expr(ast const * n)       { return !is_decl(n); }
inline bool is_app(ast const * n)        { return n->get_kind() == AST_APP; }
inline bool is_var(ast const * n)        { return n->get_kind() == AST_VAR; }
inline bool is_var(ast const * n, unsigned& idx) { return is_var(n) && (idx = static_cast<var const*>(n)->get_idx(), true); }
inline bool is_quantifier(ast const * n) { return n->get_kind() == AST_QUANTIFIER; }
inline bool is_forall(ast const * n)     { return is_quantifier(n) && static_cast<quantifier const *>(n)->is_forall(); }
inline bool is_exists(ast const * n)     { return is_quantifier(n) && static_cast<quantifier const *>(n)->is_exists(); }

// -----------------------------------
//
// AST coercions
//
// -----------------------------------

inline decl *       to_decl(ast * n)       { SASSERT(is_decl(n)); return static_cast<decl *>(n); }
inline sort *       to_sort(ast * n)       { SASSERT(is_sort(n)); return static_cast<sort *>(n); }
inline func_decl *  to_func_decl(ast * n)  { SASSERT(is_func_decl(n)); return static_cast<func_decl *>(n); }
inline expr *       to_expr(ast * n)       { SASSERT(is_expr(n)); return static_cast<expr *>(n); }
inline app *        to_app(ast * n)        { SASSERT(is_app(n)); return static_cast<app *>(n); }
inline var *        to_var(ast * n)        { SASSERT(is_var(n)); return static_cast<var *>(n); }
inline quantifier * to_quantifier(ast * n) { SASSERT(is_quantifier(n)); return static_cast<quantifier *>(n); }

inline decl const *       to_decl(ast const * n)       { SASSERT(is_decl(n)); return static_cast<decl const *>(n); }
inline sort const *       to_sort(ast const * n)       { SASSERT(is_sort(n)); return static_cast<sort const *>(n); }
inline func_decl const *  to_func_decl(ast const * n)  { SASSERT(is_func_decl(n)); return static_cast<func_decl const *>(n); }
inline expr const *       to_expr(ast const * n)       { SASSERT(is_expr(n)); return static_cast<expr const *>(n); }
inline app const *        to_app(ast const * n)        { SASSERT(is_app(n)); return static_cast<app const *>(n); }
inline var const *        to_var(ast const * n)        { SASSERT(is_var(n)); return static_cast<var const *>(n); }
inline quantifier const * to_quantifier(ast const * n) { SASSERT(is_quantifier(n)); return static_cast<quantifier const *>(n); }

// -----------------------------------
//
// AST hash-consing
//
// -----------------------------------

unsigned get_node_hash(ast const * n);
bool compare_nodes(ast const * n1, ast const * n2);
unsigned get_node_size(ast const * n);
unsigned get_asts_hash(unsigned sz, ast * const* ns, unsigned init);
unsigned get_apps_hash(unsigned sz, app * const* ns, unsigned init);
unsigned get_exprs_hash(unsigned sz, expr * const* ns, unsigned init);
unsigned get_sorts_hash(unsigned sz, sort * const* ns, unsigned init);
unsigned get_decl_hash(unsigned sz, func_decl* const* ns, unsigned init);

// This is the internal comparison functor for hash-consing AST nodes.
struct ast_eq_proc {
    bool operator()(ast const * n1, ast const * n2) const {
        return n1->hash() == n2->hash() && compare_nodes(n1, n2);
    }
};

class ast_table : public chashtable<ast*, obj_ptr_hash<ast>, ast_eq_proc> {
public:
    void erase(ast * n);
};

// -----------------------------------
//
// decl_plugin
//
// -----------------------------------

/**
   \brief Auxiliary data-structure used to initialize the parser symbol tables.
*/
struct builtin_name {
    decl_kind m_kind;
    symbol    m_name;
    builtin_name(char const * name, decl_kind k) : m_kind(k), m_name(name) {}
};

/**
   \brief Each family of intepreted function declarations and sorts must provide a plugin
   to build sorts and decls of the family.
*/
class decl_plugin {
protected:
    ast_manager * m_manager;
    family_id     m_family_id;

    virtual void set_manager(ast_manager * m, family_id id) {
        SASSERT(m_manager == 0);
        m_manager   = m;
        m_family_id = id;
    }

    friend class ast_manager;

public:
    decl_plugin():m_manager(0), m_family_id(null_family_id) {}

    virtual ~decl_plugin() {}
    virtual void finalize() {}


    virtual decl_plugin * mk_fresh() = 0;

    family_id get_family_id() const { return m_family_id; }

    virtual sort * mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters) = 0;

    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned arity, sort * const * domain, sort * range) = 0;

    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const* parameters,
                                     unsigned num_args, expr * const * args, sort * range);

    /**
       \brief Return true if the plugin can decide whether two
       interpreted constants are equal or not.

       For all a, b:
          If is_value(a) and is_value(b)
          Then,
               are_equal(a, b) != are_distinct(a, b)

       The may be much more expensive than checking a pointer.

       We need this because some plugin values are too expensive too canonize.
    */
    virtual bool is_value(app * a) const { return false; }

    /**
       \brief Return true if \c a is a unique plugin value.
       The following property should hold for unique theory values:

       For all a, b:
          If is_unique_value(a) and is_unique_value(b)
          Then,
              a == b (pointer equality)
              IFF
              the interpretations of these theory terms are equal.

       \remark This is a stronger version of is_value.
    */
    virtual bool is_unique_value(app * a) const { return false; }

    virtual bool are_equal(app * a, app * b) const { return a == b; }

    virtual bool are_distinct(app * a, app * b) const { return a != b && is_unique_value(a) && is_unique_value(b); }

    virtual void get_op_names(svector<builtin_name> & op_names, symbol const & logic = symbol()) {}

    virtual void get_sort_names(svector<builtin_name> & sort_names, symbol const & logic = symbol()) {}

    virtual expr * get_some_value(sort * s) { return 0; }

    // Return true if the interpreted sort s does not depend on uninterpreted sorts.
    // This may be the case, for example, for array and datatype sorts.
    virtual bool is_fully_interp(sort const * s) const { return true; }

    // Event handlers for deleting/translating PARAM_EXTERNAL
    virtual void del(parameter const & p) {}
    virtual parameter translate(parameter const & p, decl_plugin & target) { UNREACHABLE(); return p; }

    virtual bool is_considered_uninterpreted(func_decl * f) { return false; }
};

// -----------------------------------
//
// basic_decl_plugin (i.e., builtin plugin)
//
// -----------------------------------

enum basic_sort_kind {
    BOOL_SORT,
    PROOF_SORT
};

enum basic_op_kind {
    OP_TRUE, OP_FALSE, OP_EQ, OP_DISTINCT, OP_ITE, OP_AND, OP_OR, OP_IFF, OP_XOR, OP_NOT, OP_IMPLIES, OP_OEQ, OP_INTERP, LAST_BASIC_OP,

    PR_UNDEF, PR_TRUE, PR_ASSERTED, PR_GOAL, PR_MODUS_PONENS, PR_REFLEXIVITY, PR_SYMMETRY, PR_TRANSITIVITY, PR_TRANSITIVITY_STAR, PR_MONOTONICITY, PR_QUANT_INTRO,
    PR_DISTRIBUTIVITY, PR_AND_ELIM, PR_NOT_OR_ELIM, PR_REWRITE, PR_REWRITE_STAR, PR_PULL_QUANT,
    PR_PULL_QUANT_STAR, PR_PUSH_QUANT, PR_ELIM_UNUSED_VARS, PR_DER, PR_QUANT_INST,

    PR_HYPOTHESIS, PR_LEMMA, PR_UNIT_RESOLUTION, PR_IFF_TRUE, PR_IFF_FALSE, PR_COMMUTATIVITY, PR_DEF_AXIOM,

    PR_DEF_INTRO, PR_APPLY_DEF, PR_IFF_OEQ, PR_NNF_POS, PR_NNF_NEG, PR_NNF_STAR, PR_SKOLEMIZE, PR_CNF_STAR,
    PR_MODUS_PONENS_OEQ, PR_TH_LEMMA, PR_HYPER_RESOLVE, LAST_BASIC_PR
};

class basic_decl_plugin : public decl_plugin {
protected:
    sort *      m_bool_sort;
    func_decl * m_true_decl;
    func_decl * m_false_decl;
    func_decl * m_and_decl;
    func_decl * m_or_decl;
    func_decl * m_iff_decl;
    func_decl * m_xor_decl;
    func_decl * m_not_decl;
    func_decl * m_interp_decl;
    func_decl * m_implies_decl;
    ptr_vector<func_decl> m_eq_decls;  // cached eqs
    ptr_vector<func_decl> m_ite_decls; // cached ites

    ptr_vector<func_decl> m_oeq_decls;  // cached obsevational eqs
    sort *      m_proof_sort;
    func_decl * m_undef_decl;
    func_decl * m_true_pr_decl;
    func_decl * m_asserted_decl;
    func_decl * m_goal_decl;
    func_decl * m_modus_ponens_decl;
    func_decl * m_reflexivity_decl;
    func_decl * m_symmetry_decl;
    func_decl * m_transitivity_decl;
    func_decl * m_quant_intro_decl;
    func_decl * m_and_elim_decl;
    func_decl * m_not_or_elim_decl;
    func_decl * m_rewrite_decl;
    func_decl * m_pull_quant_decl;
    func_decl * m_pull_quant_star_decl;
    func_decl * m_push_quant_decl;
    func_decl * m_elim_unused_vars_decl;
    func_decl * m_der_decl;
    func_decl * m_quant_inst_decl;
    ptr_vector<func_decl> m_monotonicity_decls;
    ptr_vector<func_decl> m_transitivity_star_decls;
    ptr_vector<func_decl> m_distributivity_decls;
    ptr_vector<func_decl> m_assoc_flat_decls;
    ptr_vector<func_decl> m_rewrite_star_decls;

    func_decl * m_hypothesis_decl;
    func_decl * m_iff_true_decl;
    func_decl * m_iff_false_decl;
    func_decl * m_commutativity_decl;
    func_decl * m_def_axiom_decl;
    func_decl * m_lemma_decl;
    ptr_vector<func_decl> m_unit_resolution_decls;

    func_decl * m_def_intro_decl;
    func_decl * m_iff_oeq_decl;
    func_decl * m_skolemize_decl;
    func_decl * m_mp_oeq_decl;
    ptr_vector<func_decl> m_apply_def_decls;
    ptr_vector<func_decl> m_nnf_pos_decls;
    ptr_vector<func_decl> m_nnf_neg_decls;
    ptr_vector<func_decl> m_nnf_star_decls;
    ptr_vector<func_decl> m_cnf_star_decls;

    ptr_vector<func_decl> m_th_lemma_decls;
    func_decl * m_hyper_res_decl0;

    static bool is_proof(decl_kind k) { return k > LAST_BASIC_OP; }
    bool check_proof_sorts(basic_op_kind k, unsigned arity, sort * const * domain) const;
    bool check_proof_args(basic_op_kind k, unsigned num_args, expr * const * args) const;
    func_decl * mk_bool_op_decl(char const * name, basic_op_kind k, unsigned num_args = 0,
                                bool asooc = false, bool comm = false, bool idempotent = false, bool flat_associative = false, bool chainable = false);
    func_decl * mk_implies_decl();
    func_decl * mk_proof_decl(char const * name, basic_op_kind k, unsigned num_parents);
    func_decl * mk_proof_decl(char const * name, basic_op_kind k, unsigned num_parents, func_decl*& fn);
    func_decl * mk_proof_decl(char const * name, basic_op_kind k, unsigned num_parents, ptr_vector<func_decl> & cache);
    func_decl * mk_compressed_proof_decl(char const * name, basic_op_kind k, unsigned num_parents);
    func_decl * mk_proof_decl(basic_op_kind k, unsigned num_parents);
    func_decl * mk_proof_decl(basic_op_kind k, unsigned num_parameters, parameter const* params, unsigned num_parents);
    func_decl * mk_proof_decl(
        char const * name, basic_op_kind k,
        unsigned num_parameters, parameter const* params, unsigned num_parents);


    virtual void set_manager(ast_manager * m, family_id id);
    func_decl * mk_eq_decl_core(char const * name, decl_kind k, sort * s, ptr_vector<func_decl> & cache);
    func_decl * mk_ite_decl(sort * s);
    sort* join(sort* s1, sort* s2);
    sort* join(unsigned n, sort*const* srts);
    sort* join(unsigned n, expr*const* es);
public:
    basic_decl_plugin();

    virtual ~basic_decl_plugin() {}
    virtual void finalize();

    virtual decl_plugin * mk_fresh() {
        return alloc(basic_decl_plugin);
    }

    virtual sort * mk_sort(decl_kind k, unsigned num_parameters, parameter const* parameters);

    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned arity, sort * const * domain, sort * range);

    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned num_args, expr * const * args, sort * range);

    virtual void get_op_names(svector<builtin_name> & op_names, symbol const & logic);

    virtual void get_sort_names(svector<builtin_name> & sort_names, symbol const & logic);

    virtual bool is_value(app* a) const;

    virtual bool is_unique_value(app* a) const;

    sort * mk_bool_sort() const { return m_bool_sort; }
    sort * mk_proof_sort() const { return m_proof_sort; }

    virtual expr * get_some_value(sort * s);
};

typedef app proof; /* a proof is just an applicaton */

// -----------------------------------
//
// label_decl_plugin
//
// -----------------------------------

enum label_op_kind {
    OP_LABEL,
    OP_LABEL_LIT
};

/**
   \brief Labels are identity functions used to mark sub-expressions.
*/
class label_decl_plugin : public decl_plugin {
    symbol m_lblpos;
    symbol m_lblneg;
    symbol m_lbllit;

    virtual void set_manager(ast_manager * m, family_id id);

public:
    label_decl_plugin();
    virtual ~label_decl_plugin();

    virtual decl_plugin * mk_fresh() { return alloc(label_decl_plugin); }

    virtual sort * mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters);

    /**
       contract: when label
       parameter[0] (int):      0 - if the label is negative, 1 - if positive.
       parameter[1] (symbol):   label's tag.
       ...
       parameter[n-1] (symbol): label's tag.

       contract: when label literal (they are always positive)
       parameter[0] (symbol):   label's tag
       ...
       parameter[n-1] (symbol): label's tag.
    */
    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned arity, sort * const * domain, sort * range);
};

// -----------------------------------
//
// pattern_decl_plugin
//
// -----------------------------------

enum pattern_op_kind {
    OP_PATTERN
};

/**
   \brief Patterns are used to group expressions. These expressions are using during E-matching for
   heurisitic quantifier instantiation.
*/
class pattern_decl_plugin : public decl_plugin {
public:
    virtual decl_plugin * mk_fresh() { return alloc(pattern_decl_plugin); }

    virtual sort * mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters);

    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned arity, sort * const * domain, sort * range);
};

// -----------------------------------
//
// model_value_plugin
//
// -----------------------------------

enum model_value_op_kind {
    OP_MODEL_VALUE
};

/**
   \brief Values are used during model construction. All values are
   assumed to be different.  Users should not use them, since they may
   introduce unsoundess if the sort of a value is finite.

   Moreover, values should never be internalized in a logical context.

   However, values can be used during evaluation (i.e., simplification).

   \remark Model values can be viewed as the partion ids in Z3 1.x.
*/
class model_value_decl_plugin : public decl_plugin {
public:
    model_value_decl_plugin() {}

    virtual decl_plugin * mk_fresh() { return alloc(model_value_decl_plugin); }

    virtual sort * mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters);

    /**
       contract:
       parameter[0]: (integer) value idx
       parameter[1]: (ast)     sort of the value.
    */
    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned arity, sort * const * domain, sort * range);

    virtual bool is_value(app* n) const;

    virtual bool is_unique_value(app* a) const;
};

// -----------------------------------
//
// user_sort_plugin for supporting user declared sorts in SMT2
//
// -----------------------------------

class user_sort_plugin : public decl_plugin {
    svector<symbol> m_sort_names;
    dictionary<int> m_name2decl_kind;
public:
    user_sort_plugin() {}

    virtual sort * mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters);
    virtual func_decl * mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                     unsigned arity, sort * const * domain, sort * range);
    decl_kind register_name(symbol s);
    virtual decl_plugin * mk_fresh();
};


// -----------------------------------
//
// Auxiliary functions
//
// -----------------------------------

// Return true if n is an application of d.
inline bool is_app_of(expr const * n, func_decl const * d) { return n->get_kind() == AST_APP && to_app(n)->get_decl() == d; }
inline bool is_app_of(expr const * n, family_id fid, decl_kind k) { return n->get_kind() == AST_APP && to_app(n)->is_app_of(fid, k); }
inline bool is_sort_of(sort const * s, family_id fid, decl_kind k) { return s->is_sort_of(fid, k); }
inline bool is_uninterp_const(expr const * n) { return n->get_kind() == AST_APP && to_app(n)->get_num_args() == 0 && to_app(n)->get_family_id() == null_family_id; }
inline bool is_uninterp(expr const * n) { return n->get_kind() == AST_APP && to_app(n)->get_family_id() == null_family_id; }
inline bool is_decl_of(func_decl const * d, family_id fid, decl_kind k) { return d->get_family_id() == fid && d->get_decl_kind() == k; }
inline bool is_ground(expr const * n) { return is_app(n) && to_app(n)->is_ground(); }
inline bool is_non_ground(expr const * n) { return ( ! is_ground(n)); }

inline unsigned get_depth(expr const * n) {
    if (is_app(n)) return to_app(n)->get_depth();
    else if (is_quantifier(n)) return to_quantifier(n)->get_depth();
    else return 1;
}

inline bool has_quantifiers(expr const * n) {
    return is_app(n) ? to_app(n)->has_quantifiers() : is_quantifier(n);
}

inline bool has_labels(expr const * n) {
    if (is_app(n)) return to_app(n)->has_labels();
    else if (is_quantifier(n)) return to_quantifier(n)->has_labels();
    else return false;
}

sort * get_sort(expr const * n);

class basic_recognizers {
    family_id m_fid;
public:
    basic_recognizers(family_id fid):m_fid(fid) {}
    bool is_bool(sort const * s) const { return is_sort_of(s, m_fid, BOOL_SORT); }
    bool is_bool(expr const * n) const { return is_bool(get_sort(n)); }
    bool is_or(expr const * n) const { return is_app_of(n, m_fid, OP_OR); }
    bool is_implies(expr const * n) const { return is_app_of(n, m_fid, OP_IMPLIES); }
    bool is_and(expr const * n) const { return is_app_of(n, m_fid, OP_AND); }
    bool is_not(expr const * n) const { return is_app_of(n, m_fid, OP_NOT); }
    bool is_eq(expr const * n) const { return is_app_of(n, m_fid, OP_EQ); }
    bool is_oeq(expr const * n) const { return is_app_of(n, m_fid, OP_OEQ); }
    bool is_distinct(expr const * n) const { return is_app_of(n, m_fid, OP_DISTINCT); }
    bool is_iff(expr const * n) const { return is_app_of(n, m_fid, OP_IFF); }
    bool is_xor(expr const * n) const { return is_app_of(n, m_fid, OP_XOR); }
    bool is_ite(expr const * n) const { return is_app_of(n, m_fid, OP_ITE); }
    bool is_term_ite(expr const * n) const { return is_ite(n) && !is_bool(n); }
    bool is_true(expr const * n) const { return is_app_of(n, m_fid, OP_TRUE); }
    bool is_false(expr const * n) const { return is_app_of(n, m_fid, OP_FALSE); }
    bool is_complement_core(expr const * n1, expr const * n2) const {
        return (is_true(n1) && is_false(n2)) || (is_not(n1) && to_app(n1)->get_arg(0) == n2);
    }
    bool is_complement(expr const * n1, expr const * n2) const { return is_complement_core(n1, n2) || is_complement_core(n2, n1); }
    bool is_or(func_decl const * d) const { return is_decl_of(d, m_fid, OP_OR); }
    bool is_implies(func_decl const * d) const { return is_decl_of(d, m_fid, OP_IMPLIES); }
    bool is_and(func_decl const * d) const { return is_decl_of(d, m_fid, OP_AND); }
    bool is_not(func_decl const * d) const { return is_decl_of(d, m_fid, OP_NOT); }
    bool is_eq(func_decl const * d) const { return is_decl_of(d, m_fid, OP_EQ); }
    bool is_iff(func_decl const * d) const { return is_decl_of(d, m_fid, OP_IFF); }
    bool is_xor(func_decl const * d) const { return is_decl_of(d, m_fid, OP_XOR); }
    bool is_ite(func_decl const * d) const { return is_decl_of(d, m_fid, OP_ITE); }
    bool is_term_ite(func_decl const * d) const { return is_ite(d) && !is_bool(d->get_range()); }
    bool is_distinct(func_decl const * d) const { return is_decl_of(d, m_fid, OP_DISTINCT); }

    MATCH_UNARY(is_not);
    MATCH_BINARY(is_eq);
    MATCH_BINARY(is_iff);
    MATCH_BINARY(is_implies);
    MATCH_BINARY(is_and);
    MATCH_BINARY(is_or);
    MATCH_BINARY(is_xor);
    MATCH_TERNARY(is_and);
    MATCH_TERNARY(is_or);

    bool is_ite(expr const * n, expr * & t1, expr * & t2, expr * & t3) const;
};

// -----------------------------------
//
// Get Some Value functor
//
// Functor for returning some value
// of the given sort.
//
// -----------------------------------
class some_value_proc {
public:
    virtual expr * operator()(sort * s) = 0;
};

// -----------------------------------
//
// Proof generation mode
//
// -----------------------------------

enum proof_gen_mode {
    PGM_DISABLED,
    PGM_COARSE,
    PGM_FINE
};

// -----------------------------------
//
// ast_manager
//
// -----------------------------------

class ast_manager {
    friend class basic_decl_plugin;
protected:
    struct config {
        typedef ast_manager              value_manager;
        typedef small_object_allocator   allocator;
        static const bool ref_count        = true;
    };

    struct array_config : public config {
        static const bool preserve_roots   = true;
        static const unsigned max_trail_sz = 16;
        static const unsigned factor       = 2;
    };

    struct expr_array_config : public array_config {
        typedef expr *                   value;
    };

    typedef parray_manager<expr_array_config> expr_array_manager;

    struct expr_dependency_config : public config {
        typedef expr *                   value;
    };

    typedef dependency_manager<expr_dependency_config> expr_dependency_manager;

public:
    typedef expr_array_manager::ref expr_array;
    typedef expr_dependency_manager::dependency expr_dependency;

protected:
    struct expr_dependency_array_config : public array_config {
        typedef expr_dependency *        value;
    };

    typedef parray_manager<expr_dependency_array_config> expr_dependency_array_manager;

public:
    typedef expr_dependency_array_manager::ref expr_dependency_array;

    void show_id_gen();

protected:
    reslimit                  m_limit;
    small_object_allocator    m_alloc;
    family_manager            m_family_manager;
    expr_array_manager        m_expr_array_manager;
    expr_dependency_manager   m_expr_dependency_manager;
    expr_dependency_array_manager m_expr_dependency_array_manager;
    ptr_vector<decl_plugin>   m_plugins;
    proof_gen_mode            m_proof_mode;
    bool                      m_int_real_coercions; // If true, use hack that automatically introduces to_int/to_real when needed.
    family_id                 m_basic_family_id;
    family_id                 m_label_family_id;
    family_id                 m_pattern_family_id;
    family_id                 m_model_value_family_id;
    family_id                 m_user_sort_family_id;
    family_id                 m_arith_family_id;
    ast_table                 m_ast_table;
    id_gen                    m_expr_id_gen;
    id_gen                    m_decl_id_gen;
    sort *                    m_bool_sort;
    sort *                    m_proof_sort;
    app *                     m_true;
    app *                     m_false;
    proof *                   m_undef_proof;
    unsigned                  m_fresh_id;
    bool                      m_debug_ref_count;
    u_map<unsigned>           m_debug_free_indices;
    std::fstream*             m_trace_stream;
    bool                      m_trace_stream_owner;
#ifdef Z3DEBUG
    bool slow_not_contains(ast const * n);
#endif
    ast_manager *             m_format_manager; // hack for isolating format objects in a different manager.
    symbol                    m_rec_fun;

    void init();

    bool coercion_needed(func_decl * decl, unsigned num_args, expr * const * args);

    void check_args(func_decl* f, unsigned n, expr* const* es);


public:
    ast_manager(proof_gen_mode = PGM_DISABLED, char const * trace_file = 0, bool is_format_manager = false);
    ast_manager(proof_gen_mode, std::fstream * trace_stream, bool is_format_manager = false);
    ast_manager(ast_manager const & src, bool disable_proofs = false);
    ~ast_manager();

    // propagate cancellation signal to decl_plugins

    bool has_trace_stream() const { return m_trace_stream != 0; }
    std::ostream & trace_stream() { SASSERT(has_trace_stream()); return *m_trace_stream; }

    void enable_int_real_coercions(bool f) { m_int_real_coercions = f; }
    bool int_real_coercions() const { return m_int_real_coercions; }

    // Return true if s1 and s2 are equal, or coercions are enabled, and s1 and s2 are compatible.
    bool compatible_sorts(sort * s1, sort * s2) const;

    // For debugging purposes
    void display_free_ids(std::ostream & out) { m_expr_id_gen.display_free_ids(out); out << "\n"; m_decl_id_gen.display_free_ids(out); }

    void compact_memory();

    void compress_ids();

    // Equivalent to throw ast_exception(msg)
    void raise_exception(char const * msg);

    bool is_format_manager() const { return m_format_manager == 0; }

    ast_manager & get_format_manager() { return is_format_manager() ? *this : *m_format_manager; }

    void copy_families_plugins(ast_manager const & from);

    small_object_allocator & get_allocator() { return m_alloc; }

    family_id mk_family_id(symbol const & s) { return m_family_manager.mk_family_id(s); }
    family_id mk_family_id(char const * s) { return mk_family_id(symbol(s)); }

    family_id get_family_id(symbol const & s) const { return m_family_manager.get_family_id(s); }
    family_id get_family_id(char const * s) const { return get_family_id(symbol(s)); }

    symbol const & get_family_name(family_id fid) const { return m_family_manager.get_name(fid); }

    bool is_builtin_family_id(family_id fid) const {
        return
            fid == null_family_id ||
            fid == m_basic_family_id ||
            fid == m_label_family_id ||
            fid == m_pattern_family_id ||
            fid == m_model_value_family_id ||
            fid == m_user_sort_family_id;
    }

    reslimit& limit() { return m_limit; }
    bool canceled() { return !limit().inc(); }

    void register_plugin(symbol const & s, decl_plugin * plugin);

    void register_plugin(family_id id, decl_plugin * plugin);

    decl_plugin * get_plugin(family_id fid) const;

    bool has_plugin(family_id fid) const { return get_plugin(fid) != 0; }

    bool has_plugin(symbol const & s) const { return m_family_manager.has_family(s) && has_plugin(m_family_manager.get_family_id(s)); }

    void get_dom(svector<symbol> & dom) const { m_family_manager.get_dom(dom); }

    void get_range(svector<family_id> & range) const { m_family_manager.get_range(range); }

    family_id get_basic_family_id() const { return m_basic_family_id; }

    basic_decl_plugin * get_basic_decl_plugin() const { return static_cast<basic_decl_plugin*>(get_plugin(m_basic_family_id)); }

    family_id get_user_sort_family_id() const { return m_user_sort_family_id; }

    user_sort_plugin * get_user_sort_plugin() const { return static_cast<user_sort_plugin*>(get_plugin(m_user_sort_family_id)); }

    /**
       \brief Debugging support method: set the next expression identifier to be the least value id' s.t.
              - id' >= id
              - id' is not used by any AST in m_table
              - id' is not in the expression m_free_ids

        This method should be only used to create small repros that exposes bugs in Z3.
    */
    void set_next_expr_id(unsigned id);

    bool is_value(expr * e) const;

    bool is_unique_value(expr * e) const;

    bool are_equal(expr * a, expr * b) const;

    bool are_distinct(expr * a, expr * b) const;

    bool contains(ast * a) const { return m_ast_table.contains(a); }

    bool is_rec_fun_def(quantifier* q) const { return q->get_qid() == m_rec_fun; }
    
    symbol const& rec_fun_qid() const { return m_rec_fun; }

    unsigned get_num_asts() const { return m_ast_table.size(); }

    void debug_ref_count() { m_debug_ref_count = true; }

    void inc_ref(ast * n) {
        if (n) {
            n->inc_ref();
        }
    }
    
    void dec_ref(ast* n) {
        if (n) {
            n->dec_ref();
            if (n->get_ref_count() == 0)
                delete_node(n);
        }
    }

    template<typename T>
    void inc_array_ref(unsigned sz, T * const * a) {
        for(unsigned i = 0; i < sz; i++) {
            inc_ref(a[i]);
        }
    }

    template<typename T>
    void dec_array_ref(unsigned sz, T * const * a) {
        for(unsigned i = 0; i < sz; i++) {
            dec_ref(a[i]);
        }
    }

    static unsigned get_node_size(ast const * n);

    size_t get_allocation_size() const {
        return m_alloc.get_allocation_size();
    }

protected:
    ast * register_node_core(ast * n);

    template<typename T>
    T * register_node(T * n) {
        return static_cast<T *>(register_node_core(n));
    }

    void delete_node(ast * n);

    void * allocate_node(unsigned size) {
        return m_alloc.allocate(size);
    }

    void deallocate_node(ast * n, unsigned sz) {
        m_alloc.deallocate(sz, n);
    }

public:
    sort * get_sort(expr const * n) const { return ::get_sort(n); }
    void check_sort(func_decl const * decl, unsigned num_args, expr * const * args) const;
    void check_sorts_core(ast const * n) const;
    bool check_sorts(ast const * n) const;

    bool is_bool(expr const * n) const;
    bool is_bool(sort const * s) const { return s == m_bool_sort; }
    decl_kind get_eq_op(expr const * n) const { return is_bool(n) ? OP_IFF : OP_EQ; }

private:
    sort * mk_sort(symbol const & name, sort_info * info);

public:
    sort * mk_uninterpreted_sort(symbol const & name, unsigned num_parameters, parameter const * parameters);

    sort * mk_uninterpreted_sort(symbol const & name) { return mk_uninterpreted_sort(name, 0, 0); }

    sort * mk_sort(symbol const & name, sort_info const & info) {
        if (info.get_family_id() == null_family_id) {
            return mk_uninterpreted_sort(name);
        }
        else {
            return mk_sort(name, &const_cast<sort_info &>(info));
        }
    }

    sort * mk_sort(family_id fid, decl_kind k, unsigned num_parameters = 0, parameter const * parameters = 0);

    sort * mk_bool_sort() const { return m_bool_sort; }

    sort * mk_proof_sort() const { return m_proof_sort; }

    sort * mk_fresh_sort(char const * prefix = "");

    bool is_uninterp(sort const * s) const { return s->get_family_id() == null_family_id || s->get_family_id() == m_user_sort_family_id; }

    /**
       \brief A sort is "fully" interpreted if it is interpreted,
       and doesn't depend on other uninterpreted sorts.
    */
    bool is_fully_interp(sort const * s) const;

    func_decl * mk_func_decl(family_id fid, decl_kind k, unsigned num_parameters, parameter const * parameters,
                             unsigned arity, sort * const * domain, sort * range = 0);

    func_decl * mk_func_decl(family_id fid, decl_kind k, unsigned num_parameters, parameter const * parameters,
                             unsigned num_args, expr * const * args, sort * range = 0);

    app * mk_app(family_id fid, decl_kind k, unsigned num_parameters = 0, parameter const * parameters = 0,
                 unsigned num_args = 0, expr * const * args = 0, sort * range = 0);

    app * mk_app(family_id fid, decl_kind k, unsigned num_args, expr * const * args);

    app * mk_app(family_id fid, decl_kind k, expr * arg);

    app * mk_app(family_id fid, decl_kind k, expr * arg1, expr * arg2);

    app * mk_app(family_id fid, decl_kind k, expr * arg1, expr * arg2, expr * arg3);

    app * mk_const(family_id fid, decl_kind k) { return mk_app(fid, k, 0, static_cast<expr * const *>(0)); }
private:
    func_decl * mk_func_decl(symbol const & name, unsigned arity, sort * const * domain, sort * range,
                             func_decl_info * info);

    app * mk_app_core(func_decl * decl, expr * arg1, expr * arg2);

    app * mk_app_core(func_decl * decl, unsigned num_args, expr * const * args);

public:
    func_decl * mk_func_decl(symbol const & name, unsigned arity, sort * const * domain, sort * range) {
        return mk_func_decl(name, arity, domain, range, static_cast<func_decl_info *>(0));
    }

    func_decl * mk_func_decl(symbol const & name, unsigned arity, sort * const * domain, sort * range,
                             func_decl_info const & info) {
        if (info.is_null()) {
            return mk_func_decl(name, arity, domain, range, static_cast<func_decl_info *>(0));
        }
        else {
            return mk_func_decl(name, arity, domain, range, & const_cast<func_decl_info&>(info));
        }
    }

    func_decl * mk_func_decl(unsigned arity, sort * const * domain, func_decl_info const & info) {
        return mk_func_decl(info.get_family_id(), info.get_decl_kind(), info.get_num_parameters(), info.get_parameters(),
                            arity, domain);
    }

    func_decl * mk_const_decl(symbol const & name, sort * s) {
        return mk_func_decl(name, static_cast<unsigned>(0), 0, s);
    }

    func_decl * mk_const_decl(symbol const & name, sort * s, func_decl_info const & info) {
        return mk_func_decl(name, static_cast<unsigned>(0), 0, s, info);
    }

    func_decl * mk_func_decl(symbol const & name, sort * domain, sort * range, func_decl_info const & info) {
        return mk_func_decl(name, 1, &domain, range, info);
    }

    func_decl * mk_func_decl(symbol const & name, sort * domain, sort * range) {
        return mk_func_decl(name, 1, &domain, range);
    }

    func_decl * mk_func_decl(symbol const & name, sort * domain1, sort * domain2, sort * range, func_decl_info const & info) {
        sort * d[2] = { domain1, domain2 };
        return mk_func_decl(name, 2, d, range, info);
    }

    func_decl * mk_func_decl(symbol const & name, sort * domain1, sort * domain2, sort * range) {
        sort * d[2] = { domain1, domain2 };
        return mk_func_decl(name, 2, d, range);
    }

    func_decl * mk_func_decl(symbol const & name, unsigned arity, sort * const * domain, sort * range,
                             bool assoc, bool comm = false, bool inj = false);

    func_decl * mk_func_decl(symbol const & name, sort * domain1, sort * domain2, sort * range, bool assoc, bool comm = false) {
        sort * d[2] = { domain1, domain2 };
        return mk_func_decl(name, 2, d, range, assoc, comm, false);
    }

    app * mk_app(func_decl * decl, unsigned num_args, expr * const * args);

    app * mk_app(func_decl * decl, expr * const * args) {
        return mk_app(decl, decl->get_arity(), args);
    }

    app * mk_app(func_decl * decl, expr * arg) {
        SASSERT(decl->get_arity() == 1);
        return mk_app(decl, 1, &arg);
    }

    app * mk_app(func_decl * decl, expr * arg1, expr * arg2) {
        SASSERT(decl->get_arity() == 2);
        expr * args[2] = { arg1, arg2 };
        return mk_app(decl, 2, args);
    }

    app * mk_app(func_decl * decl, expr * arg1, expr * arg2, expr * arg3) {
        SASSERT(decl->get_arity() == 3);
        expr * args[3] = { arg1, arg2, arg3 };
        return mk_app(decl, 3, args);
    }

    app * mk_const(func_decl * decl) {
        SASSERT(decl->get_arity() == 0);
        return mk_app(decl, static_cast<unsigned>(0), static_cast<expr**>(0));
    }

    app * mk_const(symbol const & name, sort * s) {
        return mk_const(mk_const_decl(name, s));
    }

    func_decl * mk_fresh_func_decl(symbol const & prefix, symbol const & suffix, unsigned arity,
                                   sort * const * domain, sort * range);

    func_decl * mk_fresh_func_decl(unsigned arity, sort * const * domain, sort * range) { return mk_fresh_func_decl(symbol::null, symbol::null, arity, domain, range); }

    func_decl * mk_fresh_func_decl(char const * prefix, char const * suffix, unsigned arity,
                                   sort * const * domain, sort * range) {
        return mk_fresh_func_decl(symbol(prefix), symbol(suffix), arity, domain, range);
    }

    func_decl * mk_fresh_func_decl(char const * prefix, unsigned arity, sort * const * domain, sort * range) {
        return mk_fresh_func_decl(symbol(prefix), symbol::null, arity, domain, range);
    }

    app * mk_fresh_const(char const * prefix, sort * s) { return mk_const(mk_fresh_func_decl(prefix, 0, 0, s)); }

    symbol mk_fresh_var_name(char const * prefix = 0);

    var * mk_var(unsigned idx, sort * ty);

    app * mk_label(bool pos, unsigned num_names, symbol const * names, expr * n);

    app * mk_label(bool pos, symbol const & name, expr * n);

    bool is_label(expr const * n, bool & pos, buffer<symbol> & names) const;

    bool is_label(expr const * n, bool & pos, buffer<symbol> & names, expr*& l) const {
        return is_label(n, pos, names)?(l = to_app(n)->get_arg(0), true):false;
    }

    bool is_label(expr const * n) const { return is_app_of(n, m_label_family_id, OP_LABEL); }

    bool is_label(expr const * n, expr*& l) const {
        return is_label(n)?(l = to_app(n)->get_arg(0), true):false;
    }

    bool is_label(expr const * n, bool& pos) const {
        if (is_app_of(n, m_label_family_id, OP_LABEL)) {
            pos  = to_app(n)->get_decl()->get_parameter(0).get_int() != 0;
            return true;
        }
        else {
            return false;
        }
    }

    app * mk_label_lit(unsigned num_names, symbol const * names);

    app * mk_label_lit(symbol const & name);

    bool is_label_lit(expr const * n, buffer<symbol> & names) const;

    bool is_label_lit(expr const * n) const { return is_app_of(n, m_label_family_id, OP_LABEL_LIT); }

    family_id get_label_family_id() const { return m_label_family_id; }

    app * mk_pattern(unsigned num_exprs, app * const * exprs);

    app * mk_pattern(app * expr) { return mk_pattern(1, &expr); }

    bool is_pattern(expr const * n) const;

    bool is_pattern(expr const *n, ptr_vector<expr> &args);

public:

    quantifier * mk_quantifier(bool forall, unsigned num_decls, sort * const * decl_sorts, symbol const * decl_names, expr * body,
                               int weight = 0, symbol const & qid = symbol::null, symbol const & skid = symbol::null,
                               unsigned num_patterns = 0, expr * const * patterns = 0,
                               unsigned num_no_patterns = 0, expr * const * no_patterns = 0);

    quantifier * mk_forall(unsigned num_decls, sort * const * decl_sorts, symbol const * decl_names, expr * body,
                           int weight = 0, symbol const & qid = symbol::null, symbol const & skid = symbol::null,
                           unsigned num_patterns = 0, expr * const * patterns = 0,
                           unsigned num_no_patterns = 0, expr * const * no_patterns = 0) {
        return mk_quantifier(true, num_decls, decl_sorts, decl_names, body, weight, qid, skid, num_patterns, patterns,
                             num_no_patterns, no_patterns);
    }

    quantifier * mk_exists(unsigned num_decls, sort * const * decl_sorts, symbol const * decl_names, expr * body,
                           int weight = 0, symbol const & qid = symbol::null, symbol const & skid = symbol::null,
                           unsigned num_patterns = 0, expr * const * patterns = 0,
                           unsigned num_no_patterns = 0, expr * const * no_patterns = 0) {
        return mk_quantifier(false, num_decls, decl_sorts, decl_names, body, weight, qid, skid, num_patterns, patterns,
                             num_no_patterns, no_patterns);
    }

    quantifier * update_quantifier(quantifier * q, unsigned new_num_patterns, expr * const * new_patterns, expr * new_body);

    quantifier * update_quantifier(quantifier * q, unsigned new_num_patterns, expr * const * new_patterns, unsigned new_num_no_patterns, expr * const * new_no_patterns, expr * new_body);

    quantifier * update_quantifier(quantifier * q, expr * new_body);

    quantifier * update_quantifier_weight(quantifier * q, int new_weight);

    quantifier * update_quantifier(quantifier * q, bool new_is_forall, expr * new_body);

    quantifier * update_quantifier(quantifier * q, bool new_is_forall, unsigned new_num_patterns, expr * const * new_patterns, expr * new_body);

// -----------------------------------
//
// expr_array
//
// -----------------------------------
public:
    void mk(expr_array & r) { m_expr_array_manager.mk(r); }
    void del(expr_array & r) { m_expr_array_manager.del(r); }
    void copy(expr_array const & s, expr_array & r) { m_expr_array_manager.copy(s, r); }
    unsigned size(expr_array const & r) const { return m_expr_array_manager.size(r); }
    bool empty(expr_array const & r) const { return m_expr_array_manager.empty(r); }
    expr * get(expr_array const & r, unsigned i) const { return m_expr_array_manager.get(r, i); }
    void set(expr_array & r, unsigned i, expr * v) { m_expr_array_manager.set(r, i, v); }
    void set(expr_array const & s, unsigned i, expr * v, expr_array & r) { m_expr_array_manager.set(s, i, v, r); }
    void push_back(expr_array & r, expr * v) { m_expr_array_manager.push_back(r, v); }
    void push_back(expr_array const & s, expr * v, expr_array & r) { m_expr_array_manager.push_back(s, v, r); }
    void pop_back(expr_array & r) { m_expr_array_manager.pop_back(r); }
    void pop_back(expr_array const & s, expr_array & r) { m_expr_array_manager.pop_back(s, r); }
    void unshare(expr_array & r) { m_expr_array_manager.unshare(r); }
    void unfold(expr_array & r) { m_expr_array_manager.unfold(r); }
    void reroot(expr_array & r) { m_expr_array_manager.reroot(r); }

// -----------------------------------
//
// expr_dependency
//
// -----------------------------------
public:
    expr_dependency * mk_empty_dependencies() { return m_expr_dependency_manager.mk_empty(); }
    expr_dependency * mk_leaf(expr * t);
    expr_dependency * mk_join(unsigned n, expr * const * ts);
    expr_dependency * mk_join(expr_dependency * d1, expr_dependency * d2) { return m_expr_dependency_manager.mk_join(d1, d2); }
    void inc_ref(expr_dependency * d) { if (d) m_expr_dependency_manager.inc_ref(d); }
    void dec_ref(expr_dependency * d) { if (d) m_expr_dependency_manager.dec_ref(d); }
    void linearize(expr_dependency * d, ptr_vector<expr> & ts);
    bool contains(expr_dependency * d, expr * t) { return m_expr_dependency_manager.contains(d, t); }

// -----------------------------------
//
// expr_dependency_array
//
// -----------------------------------
public:
    void mk(expr_dependency_array & r) { m_expr_dependency_array_manager.mk(r); }
    void del(expr_dependency_array & r) { m_expr_dependency_array_manager.del(r); }
    void copy(expr_dependency_array const & s, expr_dependency_array & r) { m_expr_dependency_array_manager.copy(s, r); }
    unsigned size(expr_dependency_array const & r) const { return m_expr_dependency_array_manager.size(r); }
    bool empty(expr_dependency_array const & r) const { return m_expr_dependency_array_manager.empty(r); }
    expr_dependency * get(expr_dependency_array const & r, unsigned i) const { return m_expr_dependency_array_manager.get(r, i); }
    void set(expr_dependency_array & r, unsigned i, expr_dependency * v) { m_expr_dependency_array_manager.set(r, i, v); }
    void set(expr_dependency_array const & s, unsigned i, expr_dependency * v, expr_dependency_array & r) {
        m_expr_dependency_array_manager.set(s, i, v, r);
    }
    void push_back(expr_dependency_array & r, expr_dependency * v) { m_expr_dependency_array_manager.push_back(r, v); }
    void push_back(expr_dependency_array const & s, expr_dependency * v, expr_dependency_array & r) {
        m_expr_dependency_array_manager.push_back(s, v, r);
    }
    void pop_back(expr_dependency_array & r) { m_expr_dependency_array_manager.pop_back(r); }
    void pop_back(expr_dependency_array const & s, expr_dependency_array & r) { m_expr_dependency_array_manager.pop_back(s, r); }
    void unshare(expr_dependency_array & r) { m_expr_dependency_array_manager.unshare(r); }
    void unfold(expr_dependency_array & r) { m_expr_dependency_array_manager.unfold(r); }
    void reroot(expr_dependency_array & r) { m_expr_dependency_array_manager.reroot(r); }

// -----------------------------------
//
// Builtin operators
//
// -----------------------------------

public:

    bool is_or(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_OR); }
    bool is_implies(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_IMPLIES); }
    bool is_and(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_AND); }
    bool is_not(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_NOT); }
    bool is_eq(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_EQ); }
    bool is_oeq(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_OEQ); }
    bool is_distinct(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_DISTINCT); }
    bool is_iff(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_IFF); }
    bool is_xor(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_XOR); }
    bool is_ite(expr const * n) const { return is_app_of(n, m_basic_family_id, OP_ITE); }
    bool is_term_ite(expr const * n) const { return is_ite(n) && !is_bool(n); }
    bool is_true(expr const * n) const { return n == m_true; }
    bool is_false(expr const * n) const { return n == m_false; }
    bool is_complement_core(expr const * n1, expr const * n2) const {
        return (is_true(n1) && is_false(n2)) || (is_not(n1) && to_app(n1)->get_arg(0) == n2);
    }
    bool is_complement(expr const * n1, expr const * n2) const { return is_complement_core(n1, n2) || is_complement_core(n2, n1); }

    bool is_or(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_OR); }
    bool is_implies(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_IMPLIES); }
    bool is_and(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_AND); }
    bool is_not(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_NOT); }
    bool is_eq(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_EQ); }
    bool is_iff(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_IFF); }
    bool is_xor(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_XOR); }
    bool is_ite(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_ITE); }
    bool is_term_ite(func_decl const * d) const { return is_ite(d) && !is_bool(d->get_range()); }
    bool is_distinct(func_decl const * d) const { return is_decl_of(d, m_basic_family_id, OP_DISTINCT); }

public:

    MATCH_UNARY(is_not);
    MATCH_BINARY(is_eq);
    MATCH_BINARY(is_iff);
    MATCH_BINARY(is_implies);
    MATCH_BINARY(is_and);
    MATCH_BINARY(is_or);
    MATCH_BINARY(is_xor);
    MATCH_TERNARY(is_and);
    MATCH_TERNARY(is_or);

    bool is_ite(expr const* n, expr*& t1, expr*& t2, expr*& t3) const {
        if (is_ite(n)) {
            t1 = to_app(n)->get_arg(0);
            t2 = to_app(n)->get_arg(1);
            t3 = to_app(n)->get_arg(2);
            return true;
        }
        return false;
    }

public:
    app * mk_eq(expr * lhs, expr * rhs) { return mk_app(m_basic_family_id, get_eq_op(lhs), lhs, rhs); }
    app * mk_iff(expr * lhs, expr * rhs) { return mk_app(m_basic_family_id, OP_IFF, lhs, rhs); }
    app * mk_oeq(expr * lhs, expr * rhs) { return mk_app(m_basic_family_id, OP_OEQ, lhs, rhs); }
    app * mk_xor(expr * lhs, expr * rhs) { return mk_app(m_basic_family_id, OP_XOR, lhs, rhs); }
    app * mk_ite(expr * c, expr * t, expr * e) { return mk_app(m_basic_family_id, OP_ITE, c, t, e); }
    app * mk_xor(unsigned num_args, expr * const * args) { return mk_app(m_basic_family_id, OP_XOR, num_args, args); }
    app * mk_or(unsigned num_args, expr * const * args) { return mk_app(m_basic_family_id, OP_OR, num_args, args); }
    app * mk_and(unsigned num_args, expr * const * args) { return mk_app(m_basic_family_id, OP_AND, num_args, args); }
    app * mk_or(expr * arg1, expr * arg2) { return mk_app(m_basic_family_id, OP_OR, arg1, arg2); }
    app * mk_and(expr * arg1, expr * arg2) { return mk_app(m_basic_family_id, OP_AND, arg1, arg2); }
    app * mk_or(expr * arg1, expr * arg2, expr * arg3) { return mk_app(m_basic_family_id, OP_OR, arg1, arg2, arg3); }
    app * mk_and(expr * arg1, expr * arg2, expr * arg3) { return mk_app(m_basic_family_id, OP_AND, arg1, arg2, arg3); }
    app * mk_implies(expr * arg1, expr * arg2) { return mk_app(m_basic_family_id, OP_IMPLIES, arg1, arg2); }
    app * mk_not(expr * n) { return mk_app(m_basic_family_id, OP_NOT, n); }
    app * mk_distinct(unsigned num_args, expr * const * args);
    app * mk_distinct_expanded(unsigned num_args, expr * const * args);
    app * mk_true() const { return m_true; }
    app * mk_false() const { return m_false; }
    app * mk_bool_val(bool b) { return b?m_true:m_false; }
    app * mk_interp(expr * arg) { return mk_app(m_basic_family_id, OP_INTERP, arg); }


    func_decl* mk_and_decl() {
        sort* domain[2] = { m_bool_sort, m_bool_sort };
        return mk_func_decl(m_basic_family_id, OP_AND, 0, 0, 2, domain);
    }
    func_decl* mk_not_decl() { return mk_func_decl(m_basic_family_id, OP_NOT, 0, 0, 1, &m_bool_sort); }
    func_decl* mk_or_decl() {
        sort* domain[2] = { m_bool_sort, m_bool_sort };
        return mk_func_decl(m_basic_family_id, OP_OR, 0, 0, 2, domain);
    }

// -----------------------------------
//
// Values
//
// -----------------------------------

protected:
    some_value_proc * m_some_value_proc;
public:
    app * mk_model_value(unsigned idx, sort * s);
    bool is_model_value(expr const * n) const { return is_app_of(n, m_model_value_family_id, OP_MODEL_VALUE); }
    bool is_model_value(func_decl const * d) const { return is_decl_of(d, m_model_value_family_id, OP_MODEL_VALUE); }

    expr * get_some_value(sort * s, some_value_proc * p);
    expr * get_some_value(sort * s);

// -----------------------------------
//
// Proof generation
//
// -----------------------------------

protected:
    proof * mk_proof(family_id fid, decl_kind k, unsigned num_args, expr * const * args);
    proof * mk_proof(family_id fid, decl_kind k, expr * arg);
    proof * mk_proof(family_id fid, decl_kind k, expr * arg1, expr * arg2);
    proof * mk_proof(family_id fid, decl_kind k, expr * arg1, expr * arg2, expr * arg3);

public:
    bool proofs_enabled() const { return m_proof_mode != PGM_DISABLED; }
    bool proofs_disabled() const { return m_proof_mode == PGM_DISABLED; }
    bool coarse_grain_proofs() const { return m_proof_mode == PGM_COARSE; }
    bool fine_grain_proofs() const { return m_proof_mode == PGM_FINE; }
    proof_gen_mode proof_mode() const { return m_proof_mode; }
    void toggle_proof_mode(proof_gen_mode m) { m_proof_mode = m; } // APIs for creating proof objects return [undef]

    proof * mk_undef_proof() const { return m_undef_proof; }

    bool is_proof(expr const * n) const { return is_app(n) && to_app(n)->get_decl()->get_range() == m_proof_sort; }

    proof* mk_hyper_resolve(unsigned num_premises, proof* const* premises, expr* concl,
                            svector<std::pair<unsigned, unsigned> > const& positions,
                            vector<ref_vector<expr, ast_manager> > const& substs);


    bool is_undef_proof(expr const * e) const { return e == m_undef_proof; }
    bool is_asserted(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_ASSERTED); }
    bool is_hypothesis (expr const *e) const {return is_app_of (e, m_basic_family_id, PR_HYPOTHESIS);}
    bool is_goal(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_GOAL); }
    bool is_modus_ponens(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_MODUS_PONENS); }
    bool is_reflexivity(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_REFLEXIVITY); }
    bool is_symmetry(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_SYMMETRY); }
    bool is_transitivity(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_TRANSITIVITY); }
    bool is_monotonicity(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_MONOTONICITY); }
    bool is_quant_intro(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_QUANT_INTRO); }
    bool is_quant_inst(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_QUANT_INST); }
    bool is_distributivity(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_DISTRIBUTIVITY); }
    bool is_and_elim(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_AND_ELIM); }
    bool is_not_or_elim(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_NOT_OR_ELIM); }
    bool is_rewrite(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_REWRITE); }
    bool is_rewrite_star(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_REWRITE_STAR); }
    bool is_unit_resolution(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_UNIT_RESOLUTION); }
    bool is_lemma(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_LEMMA); }
    bool is_quant_inst(expr const* e, expr*& not_q_or_i, ptr_vector<expr>& binding) const;
    bool is_rewrite(expr const* e, expr*& r1, expr*& r2) const;
    bool is_hyper_resolve(proof* p) const { return is_app_of(p, m_basic_family_id, PR_HYPER_RESOLVE); }
    bool is_hyper_resolve(proof* p,
                          ref_vector<proof, ast_manager>& premises,
                          obj_ref<expr, ast_manager>& conclusion,
                          svector<std::pair<unsigned, unsigned> > & positions,
                          vector<ref_vector<expr, ast_manager> >& substs);


    bool is_def_intro(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_DEF_INTRO); }
    bool is_apply_def(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_APPLY_DEF); }
    bool is_skolemize(expr const * e) const { return is_app_of(e, m_basic_family_id, PR_SKOLEMIZE); }

    MATCH_UNARY(is_asserted);
    MATCH_UNARY(is_hypothesis);
    MATCH_UNARY(is_lemma);

    bool has_fact(proof const * p) const {
        SASSERT(is_proof(p));
        unsigned n = p->get_num_args();
        return n > 0 && get_sort(p->get_arg(n - 1)) != m_proof_sort;
    }
    expr * get_fact(proof const * p) const { SASSERT(is_proof(p)); SASSERT(has_fact(p)); return p->get_arg(p->get_num_args() - 1); }
    unsigned get_num_parents(proof const * p) const {
        SASSERT(is_proof(p));
        unsigned n = p->get_num_args();
        return !has_fact(p) ? n : n - 1;
    }
    proof * get_parent(proof const * p, unsigned idx) const { SASSERT(is_proof(p)); return to_app(p->get_arg(idx)); }
    proof * mk_true_proof();
    proof * mk_asserted(expr * f);
    proof * mk_goal(expr * f);
    proof * mk_modus_ponens(proof * p1, proof * p2);
    proof * mk_reflexivity(expr * e);
    proof * mk_oeq_reflexivity(expr * e);
    proof * mk_symmetry(proof * p);
    proof * mk_transitivity(proof * p1, proof * p2);
    proof * mk_transitivity(proof * p1, proof * p2, proof * p3);
    proof * mk_transitivity(proof * p1, proof * p2, proof * p3, proof * p4);
    proof * mk_transitivity(unsigned num_proofs, proof * const * proofs);
    proof * mk_transitivity(unsigned num_proofs, proof * const * proofs, expr * n1, expr * n2);
    proof * mk_monotonicity(func_decl * R, app * f1, app * f2, unsigned num_proofs, proof * const * proofs);
    proof * mk_congruence(app * f1, app * f2, unsigned num_proofs, proof * const * proofs);
    proof * mk_oeq_congruence(app * f1, app * f2, unsigned num_proofs, proof * const * proofs);
    proof * mk_commutativity(app * f);
    proof * mk_iff_true(proof * pr);
    proof * mk_iff_false(proof * pr);
    proof * mk_quant_intro(quantifier * q1, quantifier * q2, proof * p);
    proof * mk_oeq_quant_intro(quantifier * q1, quantifier * q2, proof * p);
    proof * mk_distributivity(expr * s, expr * r);
    proof * mk_rewrite(expr * s, expr * t);
    proof * mk_oeq_rewrite(expr * s, expr * t);
    proof * mk_rewrite_star(expr * s, expr * t, unsigned num_proofs, proof * const * proofs);
    proof * mk_pull_quant(expr * e, quantifier * q);
    proof * mk_pull_quant_star(expr * e, quantifier * q);
    proof * mk_push_quant(quantifier * q, expr * e);
    proof * mk_elim_unused_vars(quantifier * q, expr * r);
    proof * mk_der(quantifier * q, expr * r);
    proof * mk_quant_inst(expr * not_q_or_i, unsigned num_bind, expr* const* binding);

    proof * mk_def_axiom(expr * ax);
    proof * mk_unit_resolution(unsigned num_proofs, proof * const * proofs);
    proof * mk_unit_resolution(unsigned num_proofs, proof * const * proofs, expr * new_fact);
    proof * mk_hypothesis(expr * h);
    proof * mk_lemma(proof * p, expr * lemma);

    proof * mk_def_intro(expr * new_def);
    proof * mk_apply_defs(expr * n, expr * def, unsigned num_proofs, proof * const * proofs);
    proof * mk_apply_def(expr * n, expr * def, proof * p) { return mk_apply_defs(n, def, 1, &p); }
    proof * mk_iff_oeq(proof * parent);

    proof * mk_nnf_pos(expr * s, expr * t, unsigned num_proofs, proof * const * proofs);
    proof * mk_nnf_neg(expr * s, expr * t, unsigned num_proofs, proof * const * proofs);
    proof * mk_nnf_star(expr * s, expr * t, unsigned num_proofs, proof * const * proofs);
    proof * mk_skolemization(expr * q, expr * e);
    proof * mk_cnf_star(expr * s, expr * t, unsigned num_proofs, proof * const * proofs);

    proof * mk_and_elim(proof * p, unsigned i);
    proof * mk_not_or_elim(proof * p, unsigned i);

    proof * mk_th_lemma(family_id tid,
                        expr * fact, unsigned num_proofs, proof * const * proofs,
                        unsigned num_params = 0, parameter const* params = 0);

protected:
    bool check_nnf_proof_parents(unsigned num_proofs, proof * const * proofs) const;

private:
    void dec_ref(ptr_buffer<ast> & worklist, ast * n) {
        n->dec_ref();
        if (n->get_ref_count() == 0) {
            worklist.push_back(n);
        }
    }

    template<typename T>
    void dec_array_ref(ptr_buffer<ast> & worklist, unsigned sz, T * const * a) {
        for(unsigned i = 0; i < sz; i++) {
            dec_ref(worklist, a[i]);
        }
    }
};

typedef ast_manager::expr_array expr_array;
typedef ast_manager::expr_dependency expr_dependency;
typedef ast_manager::expr_dependency_array expr_dependency_array;
typedef obj_ref<expr_dependency, ast_manager> expr_dependency_ref;
typedef ref_vector<expr_dependency, ast_manager> expr_dependency_ref_vector;
typedef ref_buffer<expr_dependency, ast_manager> expr_dependency_ref_buffer;

// -----------------------------------
//
// More Auxiliary Functions
//
// -----------------------------------

inline bool is_predicate(ast_manager const & m, func_decl const * d) {
    return m.is_bool(d->get_range());
}

struct ast_lt_proc {
    bool operator()(ast const * n1, ast const * n2) const {
        return n1->get_id() < n2->get_id();
    }
};

// -----------------------------------
//
// ast_ref (smart pointer)
//
// -----------------------------------

typedef obj_ref<ast, ast_manager>        ast_ref;
typedef obj_ref<expr, ast_manager>       expr_ref;
typedef obj_ref<sort, ast_manager>       sort_ref;
typedef obj_ref<func_decl, ast_manager>  func_decl_ref;
typedef obj_ref<quantifier, ast_manager> quantifier_ref;
typedef obj_ref<app, ast_manager>        app_ref;
typedef obj_ref<var,ast_manager>         var_ref;
typedef app_ref proof_ref;

// -----------------------------------
//
// ast_vector (smart pointer vector)
//
// -----------------------------------

typedef ref_vector<ast, ast_manager>       ast_ref_vector;
typedef ref_vector<decl, ast_manager>      decl_ref_vector;
typedef ref_vector<sort, ast_manager>      sort_ref_vector;
typedef ref_vector<func_decl, ast_manager> func_decl_ref_vector;
typedef ref_vector<expr, ast_manager>      expr_ref_vector;
typedef ref_vector<app, ast_manager>       app_ref_vector;
typedef ref_vector<var, ast_manager>       var_ref_vector;
typedef ref_vector<quantifier, ast_manager> quantifier_ref_vector;
typedef app_ref_vector                     proof_ref_vector;

// -----------------------------------
//
// ast_buffer
//
// -----------------------------------

typedef ref_buffer<ast, ast_manager>  ast_ref_buffer;
typedef ref_buffer<expr, ast_manager> expr_ref_buffer;
typedef ref_buffer<sort, ast_manager> sort_ref_buffer;
typedef ref_buffer<app, ast_manager>  app_ref_buffer;
typedef app_ref_buffer                proof_ref_buffer;

// -----------------------------------
//
// expr_mark
//
// -----------------------------------

typedef obj_mark<expr> expr_mark;

class expr_sparse_mark {
    obj_hashtable<expr> m_marked;
public:
    expr_sparse_mark() {}
    bool is_marked(expr * n) const { return m_marked.contains(n); }
    void mark(expr * n) { m_marked.insert(n); }
    void mark(expr * n, bool flag) { if (flag) m_marked.insert(n); else m_marked.erase(n); }
    void reset() { m_marked.reset(); }
};

template<unsigned IDX>
class ast_fast_mark {
    ptr_buffer<ast> m_to_unmark;
public:
    ast_fast_mark() {}
    ~ast_fast_mark() {
        reset();
    }
    bool is_marked(ast * n) { return IDX == 1 ? AST_IS_MARKED1(n, this) : AST_IS_MARKED2(n, this); }
    void reset_mark(ast * n) {
        if (IDX == 1) {
            AST_RESET_MARK1(n, this);
        }
        else {
            AST_RESET_MARK2(n, this);
        }
    }
    void mark(ast * n) {
        if (IDX == 1) {
            if (AST_IS_MARKED1(n, this))
                return;
            AST_MARK1(n, true, this);
        }
        else {
            if (AST_IS_MARKED2(n, this))
                return;
            AST_MARK2(n, true, this);
        }
        m_to_unmark.push_back(n);
    }

    void reset() {
        ptr_buffer<ast>::iterator it  = m_to_unmark.begin();
        ptr_buffer<ast>::iterator end = m_to_unmark.end();
        for (; it != end; ++it) {
            reset_mark(*it);
        }
        m_to_unmark.reset();
    }

    void mark(ast * n, bool flag) { if (flag) mark(n); else reset_mark(n); }

    unsigned get_level() {
        return m_to_unmark.size();
    }

    void set_level(unsigned new_size) {
        SASSERT(new_size <= m_to_unmark.size());
        while (new_size < m_to_unmark.size()) {
            reset_mark(m_to_unmark.back());
            m_to_unmark.pop_back();
        }
    }
};

typedef ast_fast_mark<1> ast_fast_mark1;
typedef ast_fast_mark<2> ast_fast_mark2;
typedef ast_fast_mark1   expr_fast_mark1;
typedef ast_fast_mark2   expr_fast_mark2;

/**
   Similar to ast_fast_mark, but increases reference counter.
*/
template<unsigned IDX>
class ast_ref_fast_mark {
    ast_ref_buffer m_to_unmark;
public:
    ast_ref_fast_mark(ast_manager & m):m_to_unmark(m) {}
    ~ast_ref_fast_mark() {
        reset();
    }
    bool is_marked(ast * n) { return IDX == 1 ? AST_IS_MARKED1(n, this) : AST_IS_MARKED2(n, this); }

    // It will not decrease the reference counter
    void reset_mark(ast * n) {
        if (IDX == 1) {
            AST_RESET_MARK1(n, this);
        }
        else {
            AST_RESET_MARK2(n, this);
        }
    }

    void mark(ast * n) {
        if (IDX == 1) {
            if (AST_IS_MARKED1(n, this))
                return;
            AST_MARK1(n, true, this);
        }
        else {
            if (AST_IS_MARKED2(n, this))
                return;
            AST_MARK2(n, true, this);
        }
        m_to_unmark.push_back(n);
    }

    void reset() {
        ast * const * it  = m_to_unmark.c_ptr();
        ast * const * end = it + m_to_unmark.size();
        for (; it != end; ++it) {
            reset_mark(*it);
        }
        m_to_unmark.reset();
    }

    void mark(ast * n, bool flag) { if (flag) mark(n); else reset_mark(n); }
};

typedef ast_ref_fast_mark<1> ast_ref_fast_mark1;
typedef ast_ref_fast_mark<2> ast_ref_fast_mark2;
typedef ast_ref_fast_mark1   expr_ref_fast_mark1;
typedef ast_ref_fast_mark2   expr_ref_fast_mark2;

// -----------------------------------
//
// ast_mark
//
// -----------------------------------

/**
   \brief A mapping from AST to Boolean

   \warning This map does not cleanup the entry associated with a node N,
   when N is deleted.
*/
class ast_mark {
    struct decl2uint { unsigned operator()(decl const & d) const { return d.get_decl_id(); } };
    obj_mark<expr>                        m_expr_marks;
    obj_mark<decl, bit_vector, decl2uint> m_decl_marks;
public:
    virtual ~ast_mark() {}
    bool is_marked(ast * n) const;
    virtual void mark(ast * n, bool flag);
    virtual void reset();
};

// -----------------------------------
//
// scoped_mark
//
// -----------------------------------

/**
   \brief Class for scoped-based marking of asts.
   This class is safe with respect to life-times of asts.
*/
class scoped_mark : public ast_mark {
    ast_ref_vector  m_stack;
    unsigned_vector m_lim;
public:
    scoped_mark(ast_manager& m): m_stack(m) {}
    virtual ~scoped_mark() {}
    virtual void mark(ast * n, bool flag);
    virtual void reset();
    void mark(ast * n);
    void push_scope();
    void pop_scope();
    void pop_scope(unsigned num_scopes);
};

// -------------------------------------
//
// inc_ref & dec_ref functors
//
// -------------------------------------

template<typename AST>
class dec_ref_proc {
    ast_manager & m_manager;
public:
    dec_ref_proc(ast_manager & m):m_manager(m) {}
    void operator()(AST * n) { m_manager.dec_ref(n); }
};


template<typename AST>
class inc_ref_proc {
    ast_manager & m_manager;
public:
    inc_ref_proc(ast_manager & m):m_manager(m) {}
    void operator()(AST * n) { m_manager.inc_ref(n); }
};

class justified_expr {
    ast_manager& m;
    expr*        m_fml;
    proof*       m_proof;
 public:
 justified_expr(ast_manager& m, expr* fml, proof* p):
    m(m),
    m_fml(fml),
    m_proof(p) {
        m.inc_ref(fml);
        m.inc_ref(p);
    }

    justified_expr& operator=(justified_expr& other) {
        SASSERT(&m == &other.m);
        if (this != &other) {
            m.dec_ref(m_fml);
            m.dec_ref(m_proof);
            m_fml = other.get_fml();
            m_proof = other.get_proof();
            m.inc_ref(m_fml);
            m.inc_ref(m_proof);
        }
        return *this;
    }
    
    ~justified_expr() {
        m.dec_ref(m_fml);
        m.dec_ref(m_proof);
    }
    
    expr* get_fml() const { return m_fml; }
    proof* get_proof() const { return m_proof; }        
};


#endif /* AST_H_ */