624 lines
21 KiB
C++
624 lines
21 KiB
C++
/*
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Copyright (c) 2013-2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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Soonho Kong
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*/
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#include <vector>
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#include <sstream>
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#include <string>
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#include <algorithm>
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#include <limits>
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#include "util/list_fn.h"
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#include "util/hash.h"
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#include "util/buffer.h"
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#include "util/object_serializer.h"
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#include "util/lru_cache.h"
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#include "kernel/expr.h"
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#include "kernel/expr_eq_fn.h"
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#include "kernel/free_vars.h"
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#ifndef LEAN_INITIAL_EXPR_CACHE_CAPACITY
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#define LEAN_INITIAL_EXPR_CACHE_CAPACITY 1024*16
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#endif
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namespace lean {
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static expr g_dummy(mk_var(0));
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expr::expr():expr(g_dummy) {}
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unsigned hash_levels(levels const & ls) {
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unsigned r = 23;
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for (auto const & l : ls)
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r = hash(hash(l), r);
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return r;
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}
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MK_THREAD_LOCAL_GET(unsigned, get_hash_alloc_counter, 0)
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expr_cell::expr_cell(expr_kind k, unsigned h, bool has_mv, bool has_local, bool has_param_univ):
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m_flags(0),
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m_kind(static_cast<unsigned>(k)),
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m_has_mv(has_mv),
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m_has_local(has_local),
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m_has_param_univ(has_param_univ),
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m_hash(h),
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m_tag(nulltag),
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m_rc(0) {
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// m_hash_alloc does not need to be a unique identifier.
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// We want diverse hash codes because given expr_cell * c1 and expr_cell * c2,
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// if c1 != c2, then there is high probability c1->m_hash_alloc != c2->m_hash_alloc.
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// Remark: using pointer address as a hash code is not a good idea.
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// - each execution run will behave differently.
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// - the hash is not diverse enough
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m_hash_alloc = get_hash_alloc_counter();
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get_hash_alloc_counter()++;
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}
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void expr_cell::dec_ref(expr & e, buffer<expr_cell*> & todelete) {
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if (e.m_ptr) {
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expr_cell * c = e.steal_ptr();
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lean_assert(!(e.m_ptr));
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if (c->dec_ref_core())
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todelete.push_back(c);
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}
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}
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optional<bool> expr_cell::is_arrow() const {
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// it is stored in bits 0-1
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unsigned r = (m_flags & (1+2));
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if (r == 0) {
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return optional<bool>();
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} else if (r == 1) {
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return optional<bool>(true);
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} else {
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lean_assert(r == 2);
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return optional<bool>(false);
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}
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}
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void expr_cell::set_is_arrow(bool flag) {
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unsigned mask = flag ? 1 : 2;
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m_flags |= mask;
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lean_assert(is_arrow() && *is_arrow() == flag);
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}
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void expr_cell::set_tag(tag t) {
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m_tag = t;
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}
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bool is_meta(expr const & e) {
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return is_metavar(get_app_fn(e));
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}
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// Expr variables
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expr_var::expr_var(unsigned idx):
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expr_cell(expr_kind::Var, idx, false, false, false),
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m_vidx(idx) {
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if (idx == std::numeric_limits<unsigned>::max())
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throw exception("invalid free variable index, de Bruijn index is too big");
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}
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// Expr constants
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expr_const::expr_const(name const & n, levels const & ls):
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expr_cell(expr_kind::Constant, ::lean::hash(n.hash(), hash_levels(ls)), has_meta(ls), false, has_param(ls)),
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m_name(n),
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m_levels(ls) {}
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// Expr metavariables and local variables
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expr_mlocal::expr_mlocal(bool is_meta, name const & n, expr const & t):
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expr_cell(is_meta ? expr_kind::Meta : expr_kind::Local, n.hash(), is_meta || t.has_metavar(), !is_meta || t.has_local(), t.has_param_univ()),
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m_name(n),
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m_type(t) {}
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void expr_mlocal::dealloc(buffer<expr_cell*> & todelete) {
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dec_ref(m_type, todelete);
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delete(this);
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}
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expr_local::expr_local(name const & n, name const & pp_name, expr const & t):
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expr_mlocal(false, n, t),
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m_pp_name(pp_name) {}
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void expr_local::dealloc(buffer<expr_cell*> & todelete) {
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dec_ref(m_type, todelete);
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delete(this);
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}
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// Composite expressions
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expr_composite::expr_composite(expr_kind k, unsigned h, bool has_mv, bool has_local, bool has_param_univ, unsigned d, unsigned fv_range):
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expr_cell(k, h, has_mv, has_local, has_param_univ),
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m_depth(d),
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m_free_var_range(fv_range) {}
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// Expr applications
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expr_app::expr_app(expr const & fn, expr const & arg):
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expr_composite(expr_kind::App, ::lean::hash(fn.hash(), arg.hash()),
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fn.has_metavar() || arg.has_metavar(),
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fn.has_local() || arg.has_local(),
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fn.has_param_univ() || arg.has_param_univ(),
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std::max(get_depth(fn), get_depth(arg)) + 1,
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std::max(get_free_var_range(fn), get_free_var_range(arg))),
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m_fn(fn), m_arg(arg) {
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m_hash = ::lean::hash(m_hash, m_depth);
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}
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void expr_app::dealloc(buffer<expr_cell*> & todelete) {
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dec_ref(m_fn, todelete);
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dec_ref(m_arg, todelete);
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delete(this);
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}
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static unsigned dec(unsigned k) { return k == 0 ? 0 : k - 1; }
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bool operator==(binder_info const & i1, binder_info const & i2) {
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return
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i1.is_implicit() == i2.is_implicit() &&
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i1.is_cast() == i2.is_cast() &&
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i1.is_contextual() == i2.is_contextual() &&
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i1.is_strict_implicit() == i2.is_strict_implicit();
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}
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// Expr binders (Lambda, Pi)
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expr_binding::expr_binding(expr_kind k, name const & n, expr const & t, expr const & b, binder_info const & i):
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expr_composite(k, ::lean::hash(t.hash(), b.hash()),
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t.has_metavar() || b.has_metavar(),
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t.has_local() || b.has_local(),
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t.has_param_univ() || b.has_param_univ(),
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std::max(get_depth(t), get_depth(b)) + 1,
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std::max(get_free_var_range(t), dec(get_free_var_range(b)))),
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m_binder(n, t, i),
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m_body(b) {
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m_hash = ::lean::hash(m_hash, m_depth);
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lean_assert(k == expr_kind::Lambda || k == expr_kind::Pi);
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}
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void expr_binding::dealloc(buffer<expr_cell*> & todelete) {
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dec_ref(m_body, todelete);
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dec_ref(m_binder.m_type, todelete);
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delete(this);
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}
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// Expr Sort
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expr_sort::expr_sort(level const & l):
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expr_cell(expr_kind::Sort, ::lean::hash(l), has_meta(l), false, has_param(l)),
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m_level(l) {
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}
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expr_sort::~expr_sort() {}
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// Macro definition
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bool macro_definition_cell::lt(macro_definition_cell const &) const { return false; }
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bool macro_definition_cell::operator==(macro_definition_cell const & other) const { return typeid(*this) == typeid(other); }
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unsigned macro_definition_cell::trust_level() const { return 0; }
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format macro_definition_cell::pp(formatter const &, options const &) const { return format(get_name()); }
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void macro_definition_cell::display(std::ostream & out) const { out << get_name(); }
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bool macro_definition_cell::is_atomic_pp(bool, bool) const { return true; }
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unsigned macro_definition_cell::hash() const { return get_name().hash(); }
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macro_definition::macro_definition(macro_definition_cell * ptr):m_ptr(ptr) { lean_assert(m_ptr); m_ptr->inc_ref(); }
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macro_definition::macro_definition(macro_definition const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
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macro_definition::macro_definition(macro_definition && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
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macro_definition::~macro_definition() { if (m_ptr) m_ptr->dec_ref(); }
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macro_definition & macro_definition::operator=(macro_definition const & s) { LEAN_COPY_REF(s); }
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macro_definition & macro_definition::operator=(macro_definition && s) { LEAN_MOVE_REF(s); }
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bool macro_definition::operator<(macro_definition const & other) const {
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if (get_name() == other.get_name())
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return m_ptr->lt(*other.m_ptr);
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else
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return get_name() < other.get_name();
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}
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static unsigned max_depth(unsigned num, expr const * args) {
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unsigned r = 0;
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for (unsigned i = 0; i < num; i++) {
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unsigned d = get_depth(args[i]);
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if (d > r)
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r = d;
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}
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return r;
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}
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static unsigned get_free_var_range(unsigned num, expr const * args) {
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unsigned r = 0;
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for (unsigned i = 0; i < num; i++) {
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unsigned d = get_free_var_range(args[i]);
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if (d > r)
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r = d;
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}
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return r;
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}
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expr_macro::expr_macro(macro_definition const & m, unsigned num, expr const * args):
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expr_composite(expr_kind::Macro,
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lean::hash(num, [&](unsigned i) { return args[i].hash(); }, m.hash()),
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std::any_of(args, args+num, [](expr const & e) { return e.has_metavar(); }),
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std::any_of(args, args+num, [](expr const & e) { return e.has_local(); }),
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std::any_of(args, args+num, [](expr const & e) { return e.has_param_univ(); }),
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max_depth(num, args) + 1,
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get_free_var_range(num, args)),
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m_definition(m),
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m_num_args(num) {
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m_args = new expr[num];
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for (unsigned i = 0; i < m_num_args; i++)
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m_args[i] = args[i];
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}
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void expr_macro::dealloc(buffer<expr_cell*> & todelete) {
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for (unsigned i = 0; i < m_num_args; i++) dec_ref(m_args[i], todelete);
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delete(this);
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}
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expr_macro::~expr_macro() {
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delete[] m_args;
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}
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// =======================================
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// Constructors
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#ifdef LEAN_CACHE_EXPRS
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typedef lru_cache<expr, expr_hash, is_bi_equal_proc> expr_cache;
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MK_THREAD_LOCAL_GET(bool, get_expr_cache_enabled, true)
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MK_THREAD_LOCAL_GET(expr_cache, get_expr_cache, LEAN_INITIAL_EXPR_CACHE_CAPACITY);
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bool enable_expr_caching(bool f) {
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bool r = get_expr_cache_enabled();
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get_expr_cache_enabled() = f;
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return r;
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}
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inline expr cache(expr const & e) {
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if (get_expr_cache_enabled()) {
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if (auto r = get_expr_cache().insert(e))
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return *r;
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}
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return e;
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}
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#else
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inline expr cache(expr && e) { return e; }
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bool enable_expr_caching(bool) { return true; } // NOLINT
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#endif
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expr mk_var(unsigned idx) { return cache(expr(new expr_var(idx))); }
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expr mk_constant(name const & n, levels const & ls) { return cache(expr(new expr_const(n, ls))); }
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expr mk_macro(macro_definition const & m, unsigned num, expr const * args) { return cache(expr(new expr_macro(m, num, args))); }
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expr mk_metavar(name const & n, expr const & t) { return cache(expr(new expr_mlocal(true, n, t))); }
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expr mk_local(name const & n, name const & pp_n, expr const & t) { return cache(expr(new expr_local(n, pp_n, t))); }
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expr mk_app(expr const & f, expr const & a) { return cache(expr(new expr_app(f, a))); }
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expr mk_binding(expr_kind k, name const & n, expr const & t, expr const & e, binder_info const & i) {
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return cache(expr(new expr_binding(k, n, t, e, i)));
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}
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expr mk_sort(level const & l) { return cache(expr(new expr_sort(l))); }
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// =======================================
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void expr_cell::dealloc() {
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try {
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buffer<expr_cell*> todo;
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todo.push_back(this);
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while (!todo.empty()) {
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expr_cell * it = todo.back();
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todo.pop_back();
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lean_assert(it->get_rc() == 0);
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switch (it->kind()) {
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case expr_kind::Var: delete static_cast<expr_var*>(it); break;
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case expr_kind::Macro: static_cast<expr_macro*>(it)->dealloc(todo); break;
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case expr_kind::Meta: static_cast<expr_mlocal*>(it)->dealloc(todo); break;
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case expr_kind::Local: static_cast<expr_local*>(it)->dealloc(todo); break;
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case expr_kind::Constant: delete static_cast<expr_const*>(it); break;
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case expr_kind::Sort: delete static_cast<expr_sort*>(it); break;
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case expr_kind::App: static_cast<expr_app*>(it)->dealloc(todo); break;
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case expr_kind::Lambda:
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case expr_kind::Pi: static_cast<expr_binding*>(it)->dealloc(todo); break;
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}
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}
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} catch (std::bad_alloc&) {
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// We need this catch, because push_back may fail when expanding the buffer.
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// In this case, we avoid the crash, and "accept" the memory leak.
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}
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}
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// Auxiliary constructors
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expr mk_app(expr const & f, unsigned num_args, expr const * args) {
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expr r = f;
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for (unsigned i = 0; i < num_args; i++)
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r = mk_app(r, args[i]);
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return r;
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}
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expr mk_app(unsigned num_args, expr const * args) {
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lean_assert(num_args >= 2);
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return mk_app(mk_app(args[0], args[1]), num_args - 2, args+2);
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}
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expr mk_rev_app(expr const & f, unsigned num_args, expr const * args) {
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expr r = f;
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unsigned i = num_args;
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while (i > 0) {
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--i;
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r = mk_app(r, args[i]);
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}
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return r;
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}
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expr mk_rev_app(unsigned num_args, expr const * args) {
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lean_assert(num_args >= 2);
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return mk_rev_app(mk_app(args[num_args-1], args[num_args-2]), num_args-2, args);
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}
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expr mk_app_vars(expr const & f, unsigned n) {
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expr r = f;
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while (n > 0) {
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--n;
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r = mk_app(r, Var(n));
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}
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return r;
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}
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expr const & get_app_args(expr const & e, buffer<expr> & args) {
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unsigned sz = args.size();
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expr const * it = &e;
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while (is_app(*it)) {
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args.push_back(app_arg(*it));
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it = &(app_fn(*it));
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}
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std::reverse(args.begin() + sz, args.end());
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return *it;
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}
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void flat_app(expr const & e, buffer<expr> & args) {
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unsigned i = args.size();
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args.push_back(expr());
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expr const & f = get_app_args(e, args);
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args[i] = f;
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}
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expr const & get_app_rev_args(expr const & e, buffer<expr> & args) {
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expr const * it = &e;
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while (is_app(*it)) {
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args.push_back(app_arg(*it));
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it = &(app_fn(*it));
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}
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return *it;
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}
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expr const & get_app_fn(expr const & e) {
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expr const * it = &e;
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while (is_app(*it)) {
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it = &(app_fn(*it));
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}
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return *it;
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}
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unsigned get_app_num_args(expr const & e) {
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expr const * it = &e;
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unsigned n = 0;
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while (is_app(*it)) {
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it = &(app_fn(*it));
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n++;
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}
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return n;
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}
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static name const & get_default_var_name() {
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static name r("a");
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return r;
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}
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static name const & g_default_var_name = get_default_var_name(); // force it to be initialized
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bool is_default_var_name(name const & n) { return n == get_default_var_name(); }
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expr mk_arrow(expr const & t, expr const & e) { return mk_pi(get_default_var_name(), t, e); }
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expr mk_pi(unsigned sz, expr const * domain, expr const & range) {
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expr r = range;
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unsigned i = sz;
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while (i > 0) {
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--i;
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r = mk_pi(name(g_default_var_name, i), domain[i], r);
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}
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return r;
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}
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expr mk_Bool() {
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static optional<expr> Bool;
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if (!Bool) Bool = mk_sort(mk_level_zero());
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return *Bool;
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}
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expr mk_Type() {
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static optional<expr> Type;
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if (!Type) Type = mk_sort(mk_level_one());
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return *Type;
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}
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expr Bool = mk_Bool();
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expr Type = mk_Type();
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unsigned get_depth(expr const & e) {
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switch (e.kind()) {
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case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
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case expr_kind::Meta: case expr_kind::Local:
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return 1;
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case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Macro:
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case expr_kind::App:
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return static_cast<expr_composite*>(e.raw())->m_depth;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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unsigned get_free_var_range(expr const & e) {
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switch (e.kind()) {
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case expr_kind::Var:
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return var_idx(e) + 1;
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case expr_kind::Constant: case expr_kind::Sort:
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return 0;
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case expr_kind::Meta: case expr_kind::Local:
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return get_free_var_range(mlocal_type(e));
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case expr_kind::Lambda: case expr_kind::Pi:
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case expr_kind::App:
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case expr_kind::Macro:
|
|
return static_cast<expr_composite*>(e.raw())->m_free_var_range;
|
|
}
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
}
|
|
|
|
bool operator==(expr const & a, expr const & b) { return expr_eq_fn()(a, b); }
|
|
bool is_bi_equal(expr const & a, expr const & b) { return expr_eq_fn(true)(a, b); }
|
|
|
|
expr copy_tag(expr const & e, expr && new_e) {
|
|
tag t = e.get_tag();
|
|
if (t != nulltag)
|
|
new_e.set_tag(t);
|
|
return new_e;
|
|
}
|
|
|
|
expr update_app(expr const & e, expr const & new_fn, expr const & new_arg) {
|
|
if (!is_eqp(app_fn(e), new_fn) || !is_eqp(app_arg(e), new_arg))
|
|
return copy_tag(e, mk_app(new_fn, new_arg));
|
|
else
|
|
return e;
|
|
}
|
|
|
|
expr update_rev_app(expr const & e, unsigned num, expr const * new_args) {
|
|
expr const * it = &e;
|
|
for (unsigned i = 0; i < num - 1; i++) {
|
|
if (!is_app(*it) || !is_eqp(app_arg(*it), new_args[i]))
|
|
return copy_tag(e, mk_rev_app(num, new_args));
|
|
it = &app_fn(*it);
|
|
}
|
|
if (!is_eqp(*it, new_args[num - 1]))
|
|
return copy_tag(e, mk_rev_app(num, new_args));
|
|
return e;
|
|
}
|
|
|
|
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body) {
|
|
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body))
|
|
return copy_tag(e, mk_binding(e.kind(), binding_name(e), new_domain, new_body, binding_info(e)));
|
|
else
|
|
return e;
|
|
}
|
|
|
|
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body, binder_info const & bi) {
|
|
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body) || bi != binding_info(e))
|
|
return copy_tag(e, mk_binding(e.kind(), binding_name(e), new_domain, new_body, bi));
|
|
else
|
|
return e;
|
|
}
|
|
|
|
expr update_mlocal(expr const & e, expr const & new_type) {
|
|
if (is_eqp(mlocal_type(e), new_type))
|
|
return e;
|
|
else if (is_metavar(e))
|
|
return copy_tag(e, mk_metavar(mlocal_name(e), new_type));
|
|
else
|
|
return copy_tag(e, mk_local(mlocal_name(e), local_pp_name(e), new_type));
|
|
}
|
|
|
|
expr update_sort(expr const & e, level const & new_level) {
|
|
if (!is_eqp(sort_level(e), new_level))
|
|
return copy_tag(e, mk_sort(new_level));
|
|
else
|
|
return e;
|
|
}
|
|
|
|
expr update_constant(expr const & e, levels const & new_levels) {
|
|
if (!is_eqp(const_levels(e), new_levels))
|
|
return copy_tag(e, mk_constant(const_name(e), new_levels));
|
|
else
|
|
return e;
|
|
}
|
|
|
|
expr update_macro(expr const & e, unsigned num, expr const * args) {
|
|
if (num == macro_num_args(e)) {
|
|
unsigned i = 0;
|
|
for (i = 0; i < num; i++) {
|
|
if (!is_eqp(macro_arg(e, i), args[i]))
|
|
break;
|
|
}
|
|
if (i == num)
|
|
return e;
|
|
}
|
|
return copy_tag(e, mk_macro(to_macro(e)->m_definition, num, args));
|
|
}
|
|
|
|
bool is_atomic(expr const & e) {
|
|
switch (e.kind()) {
|
|
case expr_kind::Constant: case expr_kind::Sort:
|
|
case expr_kind::Var:
|
|
return true;
|
|
case expr_kind::Macro:
|
|
return to_macro(e)->get_num_args() == 0;
|
|
case expr_kind::App: case expr_kind::Meta:
|
|
case expr_kind::Local: case expr_kind::Lambda:
|
|
case expr_kind::Pi:
|
|
return false;
|
|
}
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
}
|
|
|
|
bool is_arrow(expr const & t) {
|
|
optional<bool> r = t.raw()->is_arrow();
|
|
if (r) {
|
|
return *r;
|
|
} else {
|
|
bool res = is_pi(t) && !has_free_var(binding_body(t), 0);
|
|
t.raw()->set_is_arrow(res);
|
|
return res;
|
|
}
|
|
}
|
|
|
|
static name g_let("let");
|
|
std::string const & get_let_macro_opcode() {
|
|
static std::string g_let_macro_opcode("let");
|
|
return g_let_macro_opcode;
|
|
}
|
|
|
|
/**
|
|
\brief We use a macro to mark expressions that denote "let"-expressions.
|
|
This marks have no real semantic meaning, but are used by Lean's pretty printer.
|
|
*/
|
|
class let_macro_definition_cell : public macro_definition_cell {
|
|
static void check_macro(expr const & m) {
|
|
if (!is_macro(m) || macro_num_args(m) != 1)
|
|
throw exception("invalid 'let' macro");
|
|
}
|
|
public:
|
|
virtual name get_name() const { return g_let; }
|
|
virtual expr get_type(expr const & m, expr const * arg_types, extension_context &) const {
|
|
check_macro(m);
|
|
return arg_types[0];
|
|
}
|
|
virtual optional<expr> expand(expr const & m, extension_context &) const {
|
|
check_macro(m);
|
|
return some_expr(macro_arg(m, 0));
|
|
}
|
|
virtual void write(serializer & s) const { s.write_string(get_let_macro_opcode()); }
|
|
};
|
|
|
|
static macro_definition g_let_macro_definition(new let_macro_definition_cell());
|
|
expr mk_let_macro(expr const & e) { return mk_macro(g_let_macro_definition, 1, &e); }
|
|
bool is_let_macro(expr const & e) { return is_macro(e) && macro_def(e) == g_let_macro_definition; }
|
|
expr let_macro_arg(expr const & e) { lean_assert(is_let_macro(e)); return macro_arg(e, 0); }
|
|
|
|
static bool has_free_var_in_domain(expr const & b, unsigned vidx) {
|
|
if (is_pi(b)) {
|
|
return has_free_var(binding_domain(b), vidx) || has_free_var_in_domain(binding_body(b), vidx+1);
|
|
} else {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
expr infer_implicit(expr const & t, unsigned num_params, bool strict) {
|
|
if (num_params == 0) {
|
|
return t;
|
|
} else if (is_pi(t)) {
|
|
expr new_body = infer_implicit(binding_body(t), num_params-1, strict);
|
|
if (binding_info(t).is_implicit() || binding_info(t).is_strict_implicit()) {
|
|
// argument is already marked as implicit
|
|
return update_binding(t, binding_domain(t), new_body);
|
|
} else if ((strict && has_free_var_in_domain(new_body, 0)) ||
|
|
(!strict && has_free_var(new_body, 0))) {
|
|
return update_binding(t, binding_domain(t), new_body, mk_implicit_binder_info());
|
|
} else {
|
|
return update_binding(t, binding_domain(t), new_body);
|
|
}
|
|
} else {
|
|
return t;
|
|
}
|
|
}
|
|
|
|
expr infer_implicit(expr const & t, bool strict) {
|
|
return infer_implicit(t, std::numeric_limits<unsigned>::max(), strict);
|
|
}
|
|
}
|