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lean2/src/kernel/expr.h
Leonardo de Moura 4a25e7442a feat(kernel/expr): add optional expression caching (aka "partial" hash-consing) 
We do not enforce full hash-consing because we would need to synchronize
the access to the hashtable/cache.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-06-03 15:35:47 -07:00

670 lines
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/*
Copyright (c) 2013-2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include <algorithm>
#include <iostream>
#include <limits>
#include <utility>
#include <tuple>
#include <string>
#include "util/thread.h"
#include "util/lua.h"
#include "util/rc.h"
#include "util/name.h"
#include "util/hash.h"
#include "util/buffer.h"
#include "util/list_fn.h"
#include "util/optional.h"
#include "util/serializer.h"
#include "util/sexpr/format.h"
#include "kernel/level.h"
#include "kernel/extension_context.h"
namespace lean {
// Tags are used by frontends to mark expressions. They are automatically propagated by
// procedures such as update_app, update_binder, etc.
typedef unsigned tag;
constexpr tag nulltag = std::numeric_limits<unsigned>::max();
class expr;
/* =======================================
Expressions
expr ::= Var idx
| Sort level
| Constant name [levels]
| Meta name expr
| Local name expr
| App expr expr
| Lambda name expr expr
| Pi name expr expr
| Let name expr expr expr
| Macro macro
*/
enum class expr_kind { Var, Sort, Constant, Meta, Local, App, Lambda, Pi, Let, Macro };
class expr_cell {
protected:
// The bits of the following field mean:
// 0-1 - term is an arrow (0 - not initialized, 1 - is arrow, 2 - is not arrow)
// Remark: we use atomic_uchar because these flags are computed lazily (i.e., after the expression is created)
atomic_uchar m_flags;
unsigned m_kind:8;
unsigned m_has_mv:1; // term contains metavariables
unsigned m_has_local:1; // term contains local constants
unsigned m_has_param_univ:1; // term constains parametric universe levels
unsigned m_hash; // hash based on the structure of the expression (this is a good hash for structural equality)
unsigned m_hash_alloc; // hash based on 'time' of allocation (this is a good hash for pointer-based equality)
atomic_uint m_tag;
MK_LEAN_RC(); // Declare m_rc counter
void dealloc();
optional<bool> is_arrow() const;
void set_is_arrow(bool flag);
friend bool is_arrow(expr const & e);
static void dec_ref(expr & c, buffer<expr_cell*> & todelete);
public:
expr_cell(expr_kind k, unsigned h, bool has_mv, bool has_local, bool has_param_univ);
expr_kind kind() const { return static_cast<expr_kind>(m_kind); }
unsigned hash() const { return m_hash; }
unsigned hash_alloc() const { return m_hash_alloc; }
bool has_metavar() const { return m_has_mv; }
bool has_local() const { return m_has_local; }
bool has_param_univ() const { return m_has_param_univ; }
void set_tag(tag t);
tag get_tag() const { return m_tag; }
};
class macro_definition;
class binder_info;
/**
\brief Exprs for encoding formulas/expressions, types and proofs.
*/
class expr {
private:
expr_cell * m_ptr;
explicit expr(expr_cell * ptr):m_ptr(ptr) { if (m_ptr) m_ptr->inc_ref(); }
friend class expr_cell;
expr_cell * steal_ptr() { expr_cell * r = m_ptr; m_ptr = nullptr; return r; }
friend class optional<expr>;
public:
/**
\brief The default constructor creates a reference to a "dummy"
expression. The actual "dummy" expression is not relevant, and
no procedure should rely on the kind of expression used.
We have a default constructor because some collections only work
with types that have a default constructor.
*/
expr();
expr(expr const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
expr(expr && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
~expr() { if (m_ptr) m_ptr->dec_ref(); }
friend void swap(expr & a, expr & b) { std::swap(a.m_ptr, b.m_ptr); }
expr & operator=(expr const & s) { LEAN_COPY_REF(s); }
expr & operator=(expr && s) { LEAN_MOVE_REF(s); }
expr_kind kind() const { return m_ptr->kind(); }
unsigned hash() const { return m_ptr ? m_ptr->hash() : 23; }
unsigned hash_alloc() const { return m_ptr ? m_ptr->hash_alloc() : 23; }
bool has_metavar() const { return m_ptr->has_metavar(); }
bool has_local() const { return m_ptr->has_local(); }
bool has_param_univ() const { return m_ptr->has_param_univ(); }
void set_tag(tag t) { m_ptr->set_tag(t); }
tag get_tag() const { return m_ptr->get_tag(); }
expr_cell * raw() const { return m_ptr; }
friend expr mk_var(unsigned idx);
friend expr mk_sort(level const & l);
friend expr mk_constant(name const & n, levels const & ls);
friend expr mk_metavar(name const & n, expr const & t);
friend expr mk_local(name const & n, name const & pp_n, expr const & t);
friend expr mk_app(expr const & f, expr const & a);
friend expr mk_pair(expr const & f, expr const & s, expr const & t);
friend expr mk_proj(bool fst, expr const & p);
friend expr mk_binding(expr_kind k, name const & n, expr const & t, expr const & e, binder_info const & i);
friend expr mk_let(name const & n, expr const & t, expr const & v, expr const & e);
friend expr mk_macro(macro_definition const & m, unsigned num, expr const * args);
friend bool is_eqp(expr const & a, expr const & b) { return a.m_ptr == b.m_ptr; }
// Overloaded operator() can be used to create applications
expr operator()(expr const & a1) const;
expr operator()(expr const & a1, expr const & a2) const;
expr operator()(expr const & a1, expr const & a2, expr const & a3) const;
expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4) const;
expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5) const;
expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5, expr const & a6) const;
expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5, expr const & a6,
expr const & a7) const;
expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5, expr const & a6,
expr const & a7, expr const & a8) const;
};
// =======================================
// Structural equality
/** \brief Binder information is ignored in the following predicate */
bool operator==(expr const & a, expr const & b);
inline bool operator!=(expr const & a, expr const & b) { return !operator==(a, b); }
/** \brief Similar to ==, but it also compares binder information */
bool is_bi_equal(expr const & a, expr const & b);
struct is_bi_equal_proc { bool operator()(expr const & e1, expr const & e2) const { return is_bi_equal(e1, e2); } };
// =======================================
SPECIALIZE_OPTIONAL_FOR_SMART_PTR(expr)
inline optional<expr> none_expr() { return optional<expr>(); }
inline optional<expr> some_expr(expr const & e) { return optional<expr>(e); }
inline optional<expr> some_expr(expr && e) { return optional<expr>(std::forward<expr>(e)); }
inline bool is_eqp(optional<expr> const & a, optional<expr> const & b) {
return static_cast<bool>(a) == static_cast<bool>(b) && (!a || is_eqp(*a, *b));
}
/** \brief Bounded variables. They are encoded using de Bruijn's indices. */
class expr_var : public expr_cell {
unsigned m_vidx; // de Bruijn index
public:
expr_var(unsigned idx);
unsigned get_vidx() const { return m_vidx; }
};
/** \brief (parametric) Constants. */
class expr_const : public expr_cell {
name m_name;
levels m_levels;
public:
expr_const(name const & n, levels const & ls);
name const & get_name() const { return m_name; }
levels const & get_levels() const { return m_levels; }
};
/** \brief Metavariables and local constants */
class expr_mlocal : public expr_cell {
protected:
name m_name;
expr m_type;
friend expr_cell;
void dealloc(buffer<expr_cell*> & todelete);
public:
expr_mlocal(bool is_meta, name const & n, expr const & t);
name const & get_name() const { return m_name; }
expr const & get_type() const { return m_type; }
};
/** \brief expr_mlocal subclass for local constants. */
class expr_local : public expr_mlocal {
// The name used in the binder that generate this local,
// it is only used for pretty printing. This field is ignored
// when comparing expressions.
name m_pp_name;
friend expr_cell;
void dealloc(buffer<expr_cell*> & todelete);
public:
expr_local(name const & n, name const & pp_name, expr const & t);
name const & get_pp_name() const { return m_pp_name; }
};
/** \brief Composite expressions */
class expr_composite : public expr_cell {
protected:
unsigned m_depth;
unsigned m_free_var_range;
friend unsigned get_depth(expr const & e);
friend unsigned get_free_var_range(expr const & e);
public:
expr_composite(expr_kind k, unsigned h, bool has_mv, bool has_local, bool has_param_univ, unsigned d, unsigned fv_range);
};
/** \brief Applications */
class expr_app : public expr_composite {
expr m_fn;
expr m_arg;
friend expr_cell;
void dealloc(buffer<expr_cell*> & todelete);
public:
expr_app(expr const & fn, expr const & arg);
expr const & get_fn() const { return m_fn; }
expr const & get_arg() const { return m_arg; }
};
/**
\brief Auxiliary annotation for binders (Lambda and Pi). This information
is only used for elaboration.
*/
class binder_info {
unsigned m_implicit:1; //! if true, binder argument is an implicit argument
unsigned m_cast:1; //! if true, binder argument is a target for using cast
unsigned m_contextual:1; //! if true, binder argument is assumed to be part of the context, and may be argument for metavariables.
public:
binder_info(bool implicit = false, bool cast = false, bool contextual = true):
m_implicit(implicit), m_cast(cast), m_contextual(contextual) {}
bool is_implicit() const { return m_implicit; }
bool is_cast() const { return m_cast; }
bool is_contextual() const { return m_contextual; }
};
bool operator==(binder_info const & i1, binder_info const & i2);
inline bool operator!=(binder_info const & i1, binder_info const & i2) { return !(i1 == i2); }
class binder {
friend class expr_binding;
name m_name;
expr m_type;
binder_info m_info;
public:
binder(name const & n, expr const & t, binder_info const & bi = binder_info()):
m_name(n), m_type(t), m_info(bi) {}
name const & get_name() const { return m_name; }
expr const & get_type() const { return m_type; }
binder_info const & get_info() const { return m_info; }
binder update_type(expr const & t) const { return binder(m_name, t, m_info); }
};
/** \brief Lambda and Pi expressions */
class expr_binding : public expr_composite {
binder m_binder;
expr m_body;
friend class expr_cell;
void dealloc(buffer<expr_cell*> & todelete);
public:
expr_binding(expr_kind k, name const & n, expr const & t, expr const & e, binder_info const & i = binder_info());
name const & get_name() const { return m_binder.get_name(); }
expr const & get_domain() const { return m_binder.get_type(); }
expr const & get_body() const { return m_body; }
binder_info const & get_info() const { return m_binder.get_info(); }
binder const & get_binder() const { return m_binder; }
};
/** \brief Let expressions */
class expr_let : public expr_composite {
name m_name;
expr m_type;
expr m_value;
expr m_body;
friend class expr_cell;
void dealloc(buffer<expr_cell*> & todelete);
public:
expr_let(name const & n, expr const & t, expr const & v, expr const & b);
~expr_let();
name const & get_name() const { return m_name; }
expr const & get_type() const { return m_type; }
expr const & get_value() const { return m_value; }
expr const & get_body() const { return m_body; }
};
/** \brief Sort */
class expr_sort : public expr_cell {
level m_level;
public:
expr_sort(level const & l);
~expr_sort();
level const & get_level() const { return m_level; }
};
class formatter;
/** \brief Abstract class for macro_definitions */
class macro_definition_cell {
protected:
void dealloc() { delete this; }
MK_LEAN_RC();
/**
\brief Auxiliary method used for implementing a total order on macro
attachments. It is invoked by operator<, and it is only invoked when
<tt>get_name() == other.get_name()</tt>
*/
virtual bool lt(macro_definition_cell const &) const;
public:
macro_definition_cell():m_rc(0) {}
virtual ~macro_definition_cell() {}
virtual name get_name() const = 0;
virtual expr get_type(expr const & m, expr const * arg_types, extension_context & ctx) const = 0;
virtual optional<expr> expand(expr const & m, extension_context & ctx) const = 0;
virtual optional<expr> expand1(expr const & m, extension_context & ctx) const { return expand(m, ctx); }
virtual unsigned trust_level() const;
virtual bool operator==(macro_definition_cell const & other) const;
virtual void display(std::ostream & out) const;
virtual format pp(formatter const & fmt, options const & opts) const;
virtual bool is_atomic_pp(bool unicode, bool coercion) const;
virtual unsigned hash() const;
virtual void write(serializer & s) const = 0;
typedef std::function<expr(deserializer&, unsigned, expr const *)> reader;
};
/** \brief Smart pointer for macro definitions */
class macro_definition {
public:
macro_definition_cell * m_ptr;
public:
explicit macro_definition(macro_definition_cell * ptr);
macro_definition(macro_definition const & s);
macro_definition(macro_definition && s);
~macro_definition();
macro_definition & operator=(macro_definition const & s);
macro_definition & operator=(macro_definition && s);
name get_name() const { return m_ptr->get_name(); }
expr get_type(expr const & m, expr const * arg_types, extension_context & ctx) const { return m_ptr->get_type(m, arg_types, ctx); }
optional<expr> expand(expr const & m, extension_context & ctx) const { return m_ptr->expand(m, ctx); }
optional<expr> expand1(expr const & m, extension_context & ctx) const { return m_ptr->expand1(m, ctx); }
unsigned trust_level() const { return m_ptr->trust_level(); }
bool operator==(macro_definition const & other) const { return m_ptr->operator==(*other.m_ptr); }
bool operator!=(macro_definition const & other) const { return !operator==(other); }
bool operator<(macro_definition const & other) const;
void display(std::ostream & out) const { return m_ptr->display(out); }
format pp(formatter const & fmt, options const & opts) const { return m_ptr->pp(fmt, opts); }
bool is_atomic_pp(bool unicode, bool coercion) const { return m_ptr->is_atomic_pp(unicode, coercion); }
unsigned hash() const { return m_ptr->hash(); }
void write(serializer & s) const { return m_ptr->write(s); }
};
/** \brief Macro attachments */
class expr_macro : public expr_composite {
macro_definition m_definition;
unsigned m_num_args;
expr * m_args;
friend class expr_cell;
friend expr copy(expr const & a);
friend expr update_macro(expr const & e, unsigned num, expr const * args);
void dealloc(buffer<expr_cell*> & todelete);
public:
expr_macro(macro_definition const & v, unsigned num, expr const * args);
~expr_macro();
macro_definition const & get_def() const { return m_definition; }
expr const * get_args() const { return m_args; }
expr const & get_arg(unsigned idx) const { lean_assert(idx < m_num_args); return m_args[idx]; }
unsigned get_num_args() const { return m_num_args; }
};
// =======================================
// Testers
inline bool is_var(expr_cell * e) { return e->kind() == expr_kind::Var; }
inline bool is_constant(expr_cell * e) { return e->kind() == expr_kind::Constant; }
inline bool is_local(expr_cell * e) { return e->kind() == expr_kind::Local; }
inline bool is_metavar(expr_cell * e) { return e->kind() == expr_kind::Meta; }
inline bool is_macro(expr_cell * e) { return e->kind() == expr_kind::Macro; }
inline bool is_app(expr_cell * e) { return e->kind() == expr_kind::App; }
inline bool is_lambda(expr_cell * e) { return e->kind() == expr_kind::Lambda; }
inline bool is_pi(expr_cell * e) { return e->kind() == expr_kind::Pi; }
inline bool is_sort(expr_cell * e) { return e->kind() == expr_kind::Sort; }
inline bool is_let(expr_cell * e) { return e->kind() == expr_kind::Let; }
inline bool is_binding(expr_cell * e) { return is_lambda(e) || is_pi(e); }
inline bool is_mlocal(expr_cell * e) { return is_metavar(e) || is_local(e); }
inline bool is_var(expr const & e) { return e.kind() == expr_kind::Var; }
inline bool is_constant(expr const & e) { return e.kind() == expr_kind::Constant; }
inline bool is_local(expr const & e) { return e.kind() == expr_kind::Local; }
inline bool is_metavar(expr const & e) { return e.kind() == expr_kind::Meta; }
inline bool is_macro(expr const & e) { return e.kind() == expr_kind::Macro; }
inline bool is_app(expr const & e) { return e.kind() == expr_kind::App; }
inline bool is_lambda(expr const & e) { return e.kind() == expr_kind::Lambda; }
inline bool is_pi(expr const & e) { return e.kind() == expr_kind::Pi; }
inline bool is_sort(expr const & e) { return e.kind() == expr_kind::Sort; }
inline bool is_let(expr const & e) { return e.kind() == expr_kind::Let; }
inline bool is_binding(expr const & e) { return is_lambda(e) || is_pi(e); }
inline bool is_mlocal(expr const & e) { return is_metavar(e) || is_local(e); }
bool is_atomic(expr const & e);
bool is_arrow(expr const & t);
/** \brief Return true iff \c e is a metavariable or an application of a metavariable */
bool is_meta(expr const & e);
// =======================================
// =======================================
// Constructors
expr mk_var(unsigned idx);
inline expr Var(unsigned idx) { return mk_var(idx); }
expr mk_constant(name const & n, levels const & ls);
inline expr mk_constant(name const & n) { return mk_constant(n, levels()); }
inline expr Const(name const & n) { return mk_constant(n); }
expr mk_macro(macro_definition const & m, unsigned num = 0, expr const * args = nullptr);
expr mk_metavar(name const & n, expr const & t);
expr mk_local(name const & n, name const & pp_n, expr const & t);
expr mk_app(expr const & f, expr const & a);
expr mk_app(expr const & f, unsigned num_args, expr const * args);
expr mk_app(unsigned num_args, expr const * args);
inline expr mk_app(std::initializer_list<expr> const & l) { return mk_app(l.size(), l.begin()); }
template<typename T> expr mk_app(T const & args) { return mk_app(args.size(), args.data()); }
template<typename T> expr mk_app(expr const & f, T const & args) { return mk_app(f, args.size(), args.data()); }
expr mk_rev_app(expr const & f, unsigned num_args, expr const * args);
expr mk_rev_app(unsigned num_args, expr const * args);
template<typename T> expr mk_rev_app(T const & args) { return mk_rev_app(args.size(), args.data()); }
template<typename T> expr mk_rev_app(expr const & f, T const & args) { return mk_rev_app(f, args.size(), args.data()); }
expr mk_binding(expr_kind k, name const & n, expr const & t, expr const & e, binder_info const & i = binder_info());
inline expr mk_lambda(name const & n, expr const & t, expr const & e, binder_info const & i = binder_info()) {
return mk_binding(expr_kind::Lambda, n, t, e, i);
}
inline expr mk_pi(name const & n, expr const & t, expr const & e, binder_info const & i = binder_info()) {
return mk_binding(expr_kind::Pi, n, t, e, i);
}
expr mk_let(name const & n, expr const & t, expr const & v, expr const & e);
expr mk_sort(level const & l);
/** \brief Return <tt>Pi(x.{sz-1}, domain[sz-1], ..., Pi(x.{0}, domain[0], range)...)</tt> */
expr mk_pi(unsigned sz, expr const * domain, expr const & range);
inline expr mk_pi(buffer<expr> const & domain, expr const & range) { return mk_pi(domain.size(), domain.data(), range); }
expr mk_Bool();
expr mk_Type();
extern expr Type;
extern expr Bool;
bool is_default_var_name(name const & n);
expr mk_arrow(expr const & t, expr const & e);
inline expr operator>>(expr const & t, expr const & e) { return mk_arrow(t, e); }
// Auxiliary
inline expr mk_app(expr const & e1, expr const & e2, expr const & e3) { return mk_app({e1, e2, e3}); }
inline expr mk_app(expr const & e1, expr const & e2, expr const & e3, expr const & e4) { return mk_app({e1, e2, e3, e4}); }
inline expr mk_app(expr const & e1, expr const & e2, expr const & e3, expr const & e4, expr const & e5) {
return mk_app({e1, e2, e3, e4, e5});
}
inline expr expr::operator()(expr const & a1) const { return mk_app({*this, a1}); }
inline expr expr::operator()(expr const & a1, expr const & a2) const { return mk_app({*this, a1, a2}); }
inline expr expr::operator()(expr const & a1, expr const & a2, expr const & a3) const { return mk_app({*this, a1, a2, a3}); }
inline expr expr::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4) const {
return mk_app({*this, a1, a2, a3, a4});
}
inline expr expr::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5) const {
return mk_app({*this, a1, a2, a3, a4, a5});
}
inline expr expr::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5,
expr const & a6) const {
return mk_app({*this, a1, a2, a3, a4, a5, a6});
}
inline expr expr::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5,
expr const & a6, expr const & a7) const {
return mk_app({*this, a1, a2, a3, a4, a5, a6, a7});
}
inline expr expr::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5,
expr const & a6, expr const & a7, expr const & a8) const {
return mk_app({*this, a1, a2, a3, a4, a5, a6, a7, a8});
}
/** \brief Return application (...((f x_{n-1}) x_{n-2}) ... x_0) */
expr mk_app_vars(expr const & f, unsigned n);
bool enable_expr_caching(bool f);
/** \brief Helper class for temporarily enabling/disabling expression caching */
struct scoped_expr_caching {
bool m_old;
scoped_expr_caching(bool f) { m_old = enable_expr_caching(f); }
~scoped_expr_caching() { enable_expr_caching(m_old); }
};
// =======================================
// =======================================
// Casting (these functions are only needed for low-level code)
inline expr_var * to_var(expr_cell * e) { lean_assert(is_var(e)); return static_cast<expr_var*>(e); }
inline expr_const * to_constant(expr_cell * e) { lean_assert(is_constant(e)); return static_cast<expr_const*>(e); }
inline expr_app * to_app(expr_cell * e) { lean_assert(is_app(e)); return static_cast<expr_app*>(e); }
inline expr_binding * to_binding(expr_cell * e) { lean_assert(is_binding(e)); return static_cast<expr_binding*>(e); }
inline expr_let * to_let(expr_cell * e) { lean_assert(is_let(e)); return static_cast<expr_let*>(e); }
inline expr_sort * to_sort(expr_cell * e) { lean_assert(is_sort(e)); return static_cast<expr_sort*>(e); }
inline expr_mlocal * to_mlocal(expr_cell * e) { lean_assert(is_mlocal(e)); return static_cast<expr_mlocal*>(e); }
inline expr_local * to_local(expr_cell * e) { lean_assert(is_local(e)); return static_cast<expr_local*>(e); }
inline expr_mlocal * to_metavar(expr_cell * e) { lean_assert(is_metavar(e)); return static_cast<expr_mlocal*>(e); }
inline expr_macro * to_macro(expr_cell * e) { lean_assert(is_macro(e)); return static_cast<expr_macro*>(e); }
inline expr_var * to_var(expr const & e) { return to_var(e.raw()); }
inline expr_const * to_constant(expr const & e) { return to_constant(e.raw()); }
inline expr_app * to_app(expr const & e) { return to_app(e.raw()); }
inline expr_binding * to_binding(expr const & e) { return to_binding(e.raw()); }
inline expr_let * to_let(expr const & e) { return to_let(e.raw()); }
inline expr_sort * to_sort(expr const & e) { return to_sort(e.raw()); }
inline expr_mlocal * to_mlocal(expr const & e) { return to_mlocal(e.raw()); }
inline expr_mlocal * to_metavar(expr const & e) { return to_metavar(e.raw()); }
inline expr_local * to_local(expr const & e) { return to_local(e.raw()); }
inline expr_macro * to_macro(expr const & e) { return to_macro(e.raw()); }
// =======================================
// =======================================
// Accessors
inline unsigned get_rc(expr_cell * e) { return e->get_rc(); }
inline bool is_shared(expr_cell * e) { return get_rc(e) > 1; }
inline unsigned var_idx(expr_cell * e) { return to_var(e)->get_vidx(); }
inline bool is_var(expr_cell * e, unsigned i) { return is_var(e) && var_idx(e) == i; }
inline name const & const_name(expr_cell * e) { return to_constant(e)->get_name(); }
inline levels const & const_levels(expr_cell * e) { return to_constant(e)->get_levels(); }
inline macro_definition const & macro_def(expr_cell * e) { return to_macro(e)->get_def(); }
inline expr const * macro_args(expr_cell * e) { return to_macro(e)->get_args(); }
inline expr const & macro_arg(expr_cell * e, unsigned i) { return to_macro(e)->get_arg(i); }
inline unsigned macro_num_args(expr_cell * e) { return to_macro(e)->get_num_args(); }
inline expr const & app_fn(expr_cell * e) { return to_app(e)->get_fn(); }
inline expr const & app_arg(expr_cell * e) { return to_app(e)->get_arg(); }
inline name const & binding_name(expr_cell * e) { return to_binding(e)->get_name(); }
inline expr const & binding_domain(expr_cell * e) { return to_binding(e)->get_domain(); }
inline expr const & binding_body(expr_cell * e) { return to_binding(e)->get_body(); }
inline binder_info const & binding_info(expr_cell * e) { return to_binding(e)->get_info(); }
inline binder const & binding_binder(expr_cell * e) { return to_binding(e)->get_binder(); }
inline level const & sort_level(expr_cell * e) { return to_sort(e)->get_level(); }
inline name const & let_name(expr_cell * e) { return to_let(e)->get_name(); }
inline expr const & let_value(expr_cell * e) { return to_let(e)->get_value(); }
inline expr const & let_type(expr_cell * e) { return to_let(e)->get_type(); }
inline expr const & let_body(expr_cell * e) { return to_let(e)->get_body(); }
inline name const & mlocal_name(expr_cell * e) { return to_mlocal(e)->get_name(); }
inline expr const & mlocal_type(expr_cell * e) { return to_mlocal(e)->get_type(); }
inline unsigned get_rc(expr const & e) { return e.raw()->get_rc(); }
inline bool is_shared(expr const & e) { return get_rc(e) > 1; }
inline unsigned var_idx(expr const & e) { return to_var(e)->get_vidx(); }
inline bool is_var(expr const & e, unsigned i) { return is_var(e) && var_idx(e) == i; }
inline name const & const_name(expr const & e) { return to_constant(e)->get_name(); }
inline levels const & const_levels(expr const & e) { return to_constant(e)->get_levels(); }
inline macro_definition const & macro_def(expr const & e) { return to_macro(e)->get_def(); }
inline expr const * macro_args(expr const & e) { return to_macro(e)->get_args(); }
inline expr const & macro_arg(expr const & e, unsigned i) { return to_macro(e)->get_arg(i); }
inline unsigned macro_num_args(expr const & e) { return to_macro(e)->get_num_args(); }
inline expr const & app_fn(expr const & e) { return to_app(e)->get_fn(); }
inline expr const & app_arg(expr const & e) { return to_app(e)->get_arg(); }
inline name const & binding_name(expr const & e) { return to_binding(e)->get_name(); }
inline expr const & binding_domain(expr const & e) { return to_binding(e)->get_domain(); }
inline expr const & binding_body(expr const & e) { return to_binding(e)->get_body(); }
inline binder_info const & binding_info(expr const & e) { return to_binding(e)->get_info(); }
inline binder const & binding_binder(expr const & e) { return to_binding(e)->get_binder(); }
inline level const & sort_level(expr const & e) { return to_sort(e)->get_level(); }
inline name const & let_name(expr const & e) { return to_let(e)->get_name(); }
inline expr const & let_value(expr const & e) { return to_let(e)->get_value(); }
inline expr const & let_type(expr const & e) { return to_let(e)->get_type(); }
inline expr const & let_body(expr const & e) { return to_let(e)->get_body(); }
inline name const & mlocal_name(expr const & e) { return to_mlocal(e)->get_name(); }
inline expr const & mlocal_type(expr const & e) { return to_mlocal(e)->get_type(); }
inline name const & local_pp_name(expr const & e) { return to_local(e)->get_pp_name(); }
inline bool is_constant(expr const & e, name const & n) { return is_constant(e) && const_name(e) == n; }
inline bool has_metavar(expr const & e) { return e.has_metavar(); }
inline bool has_local(expr const & e) { return e.has_local(); }
inline bool has_param_univ(expr const & e) { return e.has_param_univ(); }
unsigned get_depth(expr const & e);
/**
\brief Return \c R s.t. the de Bruijn index of all free variables
occurring in \c e is in the interval <tt>[0, R)</tt>.
*/
unsigned get_free_var_range(expr const & e);
/** \brief Return true iff the given expression has free variables. */
inline bool has_free_vars(expr const & e) { return get_free_var_range(e) > 0; }
/** \brief Return true iff the given expression does not have free variables. */
inline bool closed(expr const & e) { return !has_free_vars(e); }
/** \brief Return true iff \c e contains a free variable >= low. */
inline bool has_free_var_ge(expr const & e, unsigned low) { return get_free_var_range(e) > low; }
/**
\brief Given \c e of the form <tt>(...(f a1) ... an)</tt>, store a1 ... an in args.
If \c e is not an application, then nothing is stored in args.
It returns the f.
*/
expr const & get_app_args(expr const & e, buffer<expr> & args);
/**
\brief Similar to \c get_app_args, but arguments are stored in reverse order in \c args.
If e is of the form <tt>(...(f a1) ... an)</tt>, then the procedure stores [an, ..., a1] in \c args.
*/
expr const & get_app_rev_args(expr const & e, buffer<expr> & args);
/** \brief Given \c e of the form <tt>(...(f a_1) ... a_n)</tt>, return \c f. If \c e is not an application, then return \c e. */
expr const & get_app_fn(expr const & e);
/** \brief Given \c e of the form <tt>(...(f a_1) ... a_n)</tt>, return \c n. If \c e is not an application, then return 0. */
unsigned get_app_num_args(expr const & e);
/** \brief Return the name of constant, local, metavar */
inline name const & named_expr_name(expr const & e) { return is_constant(e) ? const_name(e) : mlocal_name(e); }
// =======================================
// =======================================
// Expression+Offset
typedef std::pair<expr, unsigned> expr_offset;
typedef std::pair<expr_cell*, unsigned> expr_cell_offset;
// =======================================
// =======================================
// Auxiliary functionals
/** \brief Functional object for hashing kernel expressions. */
struct expr_hash { unsigned operator()(expr const & e) const { return e.hash(); } };
/**
\brief Functional object for hashing (based on allocation time) kernel expressions.
This hash is compatible with pointer equality.
\warning This hash is incompatible with structural equality (i.e., std::equal_to<expr>)
*/
struct expr_hash_alloc { unsigned operator()(expr const & e) const { return e.hash_alloc(); } };
/** \brief Functional object for testing pointer equality between kernel expressions. */
struct expr_eqp { bool operator()(expr const & e1, expr const & e2) const { return is_eqp(e1, e2); } };
/** \brief Functional object for hashing kernel expression cells. */
struct expr_cell_hash { unsigned operator()(expr_cell * e) const { return e->hash_alloc(); } };
/** \brief Functional object for testing pointer equality between kernel cell expressions. */
struct expr_cell_eqp { bool operator()(expr_cell * e1, expr_cell * e2) const { return e1 == e2; } };
/** \brief Functional object for hashing a pair (n, k) where n is a kernel expressions, and k is an offset. */
struct expr_offset_hash { unsigned operator()(expr_offset const & p) const { return hash(p.first.hash_alloc(), p.second); } };
/** \brief Functional object for comparing pairs (expression, offset). */
struct expr_offset_eqp { unsigned operator()(expr_offset const & p1, expr_offset const & p2) const { return is_eqp(p1.first, p2.first) && p1.second == p2.second; } };
/** \brief Functional object for hashing a pair (n, k) where n is a kernel cell expressions, and k is an offset. */
struct expr_cell_offset_hash { unsigned operator()(expr_cell_offset const & p) const { return hash(p.first->hash_alloc(), p.second); } };
/** \brief Functional object for comparing pairs (expression cell, offset). */
struct expr_cell_offset_eqp { unsigned operator()(expr_cell_offset const & p1, expr_cell_offset const & p2) const { return p1 == p2; } };
// =======================================
// =======================================
// Update
expr update_app(expr const & e, expr const & new_fn, expr const & new_arg);
expr update_rev_app(expr const & e, unsigned num, expr const * new_args);
template<typename C> expr update_rev_app(expr const & e, C const & c) { return update_rev_app(e, c.size(), c.data()); }
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body);
expr update_let(expr const & e, expr const & new_type, expr const & new_val, expr const & new_body);
expr update_mlocal(expr const & e, expr const & new_type);
expr update_sort(expr const & e, level const & new_level);
expr update_constant(expr const & e, levels const & new_levels);
expr update_macro(expr const & e, unsigned num, expr const * args);
// =======================================
std::ostream & operator<<(std::ostream & out, expr const & e);
}
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