1106 lines
40 KiB
C++
1106 lines
40 KiB
C++
/*
|
|
Copyright (c) 2015 Daniel Selsam. All rights reserved.
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
Author: Daniel Selsam
|
|
*/
|
|
#include "kernel/abstract.h"
|
|
#include "kernel/expr_maps.h"
|
|
#include "kernel/instantiate.h"
|
|
#include "library/constants.h"
|
|
#include "library/expr_lt.h"
|
|
#include "library/class_instance_resolution.h"
|
|
#include "library/relation_manager.h"
|
|
#include "library/blast/expr.h"
|
|
#include "library/blast/blast_exception.h"
|
|
#include "library/blast/blast.h"
|
|
#include "library/blast/simplifier.h"
|
|
#include "library/simplifier/simp_rule_set.h"
|
|
#include "library/simplifier/ceqv.h"
|
|
#include "library/app_builder.h"
|
|
#include "library/num.h"
|
|
#include "library/norm_num.h"
|
|
#include "util/flet.h"
|
|
#include "util/freset.h"
|
|
#include "util/pair.h"
|
|
#include "util/sexpr/option_declarations.h"
|
|
#include <functional>
|
|
#include <iostream>
|
|
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_MAX_STEPS
|
|
#define LEAN_DEFAULT_SIMPLIFY_MAX_STEPS 1000
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_TOP_DOWN
|
|
#define LEAN_DEFAULT_SIMPLIFY_TOP_DOWN false
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_EXHAUSTIVE
|
|
#define LEAN_DEFAULT_SIMPLIFY_EXHAUSTIVE true
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_MEMOIZE
|
|
#define LEAN_DEFAULT_SIMPLIFY_MEMOIZE true
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_CONTEXTUAL
|
|
#define LEAN_DEFAULT_SIMPLIFY_CONTEXTUAL true
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_EXPAND_MACROS
|
|
#define LEAN_DEFAULT_SIMPLIFY_EXPAND_MACROS false
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_TRACE
|
|
#define LEAN_DEFAULT_SIMPLIFY_TRACE false
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_FUSE
|
|
#define LEAN_DEFAULT_SIMPLIFY_FUSE false
|
|
#endif
|
|
#ifndef LEAN_DEFAULT_SIMPLIFY_NUMERALS
|
|
#define LEAN_DEFAULT_SIMPLIFY_NUMERALS false
|
|
#endif
|
|
|
|
namespace lean {
|
|
namespace blast {
|
|
|
|
using simp::result;
|
|
|
|
/* Names */
|
|
|
|
static name * g_simplify_empty_namespace = nullptr;
|
|
static name * g_simplify_unit_namespace = nullptr;
|
|
static name * g_simplify_ac_namespace = nullptr;
|
|
static name * g_simplify_som_namespace = nullptr;
|
|
static name * g_simplify_numeral_namespace = nullptr;
|
|
|
|
/* Options */
|
|
|
|
static name * g_simplify_max_steps = nullptr;
|
|
static name * g_simplify_top_down = nullptr;
|
|
static name * g_simplify_exhaustive = nullptr;
|
|
static name * g_simplify_memoize = nullptr;
|
|
static name * g_simplify_contextual = nullptr;
|
|
static name * g_simplify_expand_macros = nullptr;
|
|
static name * g_simplify_trace = nullptr;
|
|
static name * g_simplify_fuse = nullptr;
|
|
static name * g_simplify_numerals = nullptr;
|
|
|
|
unsigned get_simplify_max_steps() {
|
|
return ios().get_options().get_unsigned(*g_simplify_max_steps, LEAN_DEFAULT_SIMPLIFY_MAX_STEPS);
|
|
}
|
|
|
|
bool get_simplify_top_down() {
|
|
return ios().get_options().get_bool(*g_simplify_top_down, LEAN_DEFAULT_SIMPLIFY_TOP_DOWN);
|
|
}
|
|
|
|
bool get_simplify_exhaustive() {
|
|
return ios().get_options().get_bool(*g_simplify_exhaustive, LEAN_DEFAULT_SIMPLIFY_EXHAUSTIVE);
|
|
}
|
|
|
|
bool get_simplify_memoize() {
|
|
return ios().get_options().get_bool(*g_simplify_memoize, LEAN_DEFAULT_SIMPLIFY_MEMOIZE);
|
|
}
|
|
|
|
bool get_simplify_contextual() {
|
|
return ios().get_options().get_bool(*g_simplify_contextual, LEAN_DEFAULT_SIMPLIFY_CONTEXTUAL);
|
|
}
|
|
|
|
bool get_simplify_expand_macros() {
|
|
return ios().get_options().get_bool(*g_simplify_expand_macros, LEAN_DEFAULT_SIMPLIFY_EXPAND_MACROS);
|
|
}
|
|
|
|
bool get_simplify_trace() {
|
|
return ios().get_options().get_bool(*g_simplify_trace, LEAN_DEFAULT_SIMPLIFY_TRACE);
|
|
}
|
|
|
|
bool get_simplify_fuse() {
|
|
return ios().get_options().get_bool(*g_simplify_fuse, LEAN_DEFAULT_SIMPLIFY_FUSE);
|
|
}
|
|
|
|
bool get_simplify_numerals() {
|
|
return ios().get_options().get_bool(*g_simplify_numerals, LEAN_DEFAULT_SIMPLIFY_NUMERALS);
|
|
}
|
|
|
|
/* Miscellaneous helpers */
|
|
|
|
static bool is_add_app(expr const & e) {
|
|
return is_const_app(e, get_add_name(), 4);
|
|
}
|
|
|
|
static bool is_mul_app(expr const & e) {
|
|
return is_const_app(e, get_mul_name(), 4);
|
|
}
|
|
|
|
static bool is_neg_app(expr const & e) {
|
|
return is_const_app(e, get_neg_name(), 3);
|
|
}
|
|
|
|
/* Main simplifier class */
|
|
|
|
class simplifier {
|
|
blast_tmp_type_context m_tmp_tctx;
|
|
name m_rel;
|
|
|
|
simp_rule_sets m_srss;
|
|
simp_rule_sets m_ctx_srss;
|
|
|
|
/* Logging */
|
|
unsigned m_num_steps{0};
|
|
unsigned m_depth{0};
|
|
|
|
/* Options */
|
|
unsigned m_max_steps{get_simplify_max_steps()};
|
|
bool m_top_down{get_simplify_top_down()};
|
|
bool m_exhaustive{get_simplify_exhaustive()};
|
|
bool m_memoize{get_simplify_memoize()};
|
|
bool m_contextual{get_simplify_contextual()};
|
|
bool m_expand_macros{get_simplify_expand_macros()};
|
|
bool m_trace{get_simplify_trace()};
|
|
bool m_fuse{get_simplify_fuse()};
|
|
bool m_numerals{get_simplify_numerals()};
|
|
|
|
/* Cache */
|
|
struct key {
|
|
name m_rel;
|
|
expr m_e;
|
|
unsigned m_hash;
|
|
|
|
key(name const & rel, expr const & e):
|
|
m_rel(rel), m_e(e), m_hash(hash(rel.hash(), abstract_hash(e))) { }
|
|
};
|
|
|
|
struct key_hash_fn {
|
|
unsigned operator()(key const & k) const { return k.m_hash; }
|
|
};
|
|
|
|
struct key_eq_fn {
|
|
bool operator()(key const & k1, key const & k2) const {
|
|
return k1.m_rel == k2.m_rel && abstract_is_equal(k1.m_e, k2.m_e);
|
|
}
|
|
};
|
|
|
|
typedef std::unordered_map<key, result, key_hash_fn, key_eq_fn> simplify_cache;
|
|
simplify_cache m_cache;
|
|
|
|
optional<result> cache_lookup(expr const & e);
|
|
void cache_save(expr const & e, result const & r);
|
|
|
|
/* Basic helpers */
|
|
bool using_eq() { return m_rel == get_eq_name(); }
|
|
|
|
bool is_dependent_fn(expr const & f) {
|
|
expr f_type = m_tmp_tctx->whnf(m_tmp_tctx->infer(f));
|
|
lean_assert(is_pi(f_type));
|
|
return has_free_vars(binding_body(f_type));
|
|
}
|
|
|
|
simp_rule_sets add_to_srss(simp_rule_sets const & _srss, buffer<expr> & ls) {
|
|
simp_rule_sets srss = _srss;
|
|
for (unsigned i = 0; i < ls.size(); i++) {
|
|
expr & l = ls[i];
|
|
if (m_trace) {
|
|
ios().get_diagnostic_channel() << "Local: " << l << " : " << mlocal_type(l) << "\n";
|
|
}
|
|
tmp_type_context tctx(env(), ios());
|
|
try {
|
|
// TODO(Leo,Daniel): should we allow the user to set the priority of local lemmas
|
|
srss = add(tctx, srss, mlocal_name(l), tctx.infer(l), l, LEAN_SIMP_DEFAULT_PRIORITY);
|
|
} catch (exception e) {
|
|
}
|
|
}
|
|
return srss;
|
|
}
|
|
|
|
expr unfold_reducible_instances(expr const & e);
|
|
expr remove_unnecessary_casts(expr const & e);
|
|
|
|
bool instantiate_emetas(blast_tmp_type_context & tmp_tctx, unsigned num_emeta,
|
|
list<expr> const & emetas, list<bool> const & instances);
|
|
|
|
/* Results */
|
|
result lift_from_eq(expr const & e_old, result const & r_eq);
|
|
result join(result const & r1, result const & r2);
|
|
result funext(result const & r, expr const & l);
|
|
result finalize(result const & r);
|
|
|
|
/* Simplification */
|
|
result simplify(expr const & e, simp_rule_sets const & srss);
|
|
result simplify(expr const & e, bool is_root);
|
|
result simplify_lambda(expr const & e);
|
|
result simplify_pi(expr const & e);
|
|
result simplify_app(expr const & e);
|
|
result simplify_fun(expr const & e);
|
|
optional<result> simplify_numeral(expr const & e);
|
|
|
|
/* Proving */
|
|
optional<expr> prove(expr const & thm);
|
|
optional<expr> prove(expr const & thm, simp_rule_sets const & srss);
|
|
|
|
/* Rewriting */
|
|
result rewrite(expr const & e);
|
|
result rewrite(expr const & e, simp_rule_sets const & srss);
|
|
result rewrite(expr const & e, simp_rule const & sr);
|
|
|
|
/* Congruence */
|
|
result congr_fun_arg(result const & r_f, result const & r_arg);
|
|
result congr(result const & r_f, result const & r_arg);
|
|
result congr_fun(result const & r_f, expr const & arg);
|
|
result congr_arg(expr const & f, result const & r_arg);
|
|
result congr_funs(result const & r_f, buffer<expr> const & args);
|
|
|
|
result try_congrs(expr const & e);
|
|
result try_congr(expr const & e, congr_rule const & cr);
|
|
|
|
template<typename F>
|
|
optional<result> synth_congr(expr const & e, F && simp);
|
|
|
|
/* Fusion */
|
|
result maybe_fuse(expr const & e, bool is_root);
|
|
result fuse(expr const & e);
|
|
expr_pair split_summand(expr const & e, expr const & f_mul, expr const & one);
|
|
|
|
|
|
public:
|
|
simplifier(name const & rel): m_rel(rel) { }
|
|
result operator()(expr const & e, simp_rule_sets const & srss) { return simplify(e, srss); }
|
|
};
|
|
|
|
/* Cache */
|
|
|
|
optional<result> simplifier::cache_lookup(expr const & e) {
|
|
auto it = m_cache.find(key(m_rel, e));
|
|
if (it == m_cache.end()) return optional<result>();
|
|
/* The cache ignores subsingletons, so we may need to
|
|
synthesize a congruence lemma. */
|
|
expr e_old = it->first.m_e;
|
|
result r_old = it->second;
|
|
lean_assert(abstract_is_equal(e, e_old));
|
|
if (e == e_old) return optional<result>(r_old);
|
|
lean_assert(is_app(e_old));
|
|
buffer<expr> new_args, old_args;
|
|
expr const & f_new = get_app_args(e, new_args);
|
|
DEBUG_CODE(expr const & f_old =) get_app_args(e_old, old_args);
|
|
lean_assert(f_new == f_old);
|
|
auto congr_lemma = mk_congr_lemma(f_new, new_args.size());
|
|
if (!congr_lemma) return optional<result>();
|
|
expr proof = congr_lemma->get_proof();
|
|
expr type = congr_lemma->get_type();
|
|
|
|
unsigned i = 0;
|
|
for_each(congr_lemma->get_arg_kinds(), [&](congr_arg_kind const & ckind) {
|
|
if (ckind != congr_arg_kind::Cast) {
|
|
lean_assert(new_args[i] == old_args[i]);
|
|
}
|
|
proof = mk_app(proof, new_args[i]);
|
|
type = instantiate(binding_body(type), new_args[i]);
|
|
expr rfl;
|
|
switch (ckind) {
|
|
case congr_arg_kind::Fixed:
|
|
break;
|
|
case congr_arg_kind::Eq:
|
|
rfl = get_app_builder().mk_eq_refl(old_args[i]);
|
|
proof = mk_app(proof, old_args[i], rfl);
|
|
type = instantiate(binding_body(type), old_args[i]);
|
|
type = instantiate(binding_body(type), rfl);
|
|
break;
|
|
case congr_arg_kind::Cast:
|
|
proof = mk_app(proof, old_args[i]);
|
|
type = instantiate(binding_body(type), old_args[i]);
|
|
break;
|
|
}
|
|
i++;
|
|
});
|
|
|
|
lean_assert(is_eq(type));
|
|
result r_congr = result(e_old, proof);
|
|
return optional<result>(join(r_congr, r_old));
|
|
}
|
|
|
|
void simplifier::cache_save(expr const & e, result const & r) {
|
|
m_cache.insert(mk_pair(key(m_rel, e), r));
|
|
}
|
|
|
|
/* Results */
|
|
|
|
result simplifier::lift_from_eq(expr const & e_old, result const & r_eq) {
|
|
if (!r_eq.has_proof()) return r_eq;
|
|
lean_assert(r_eq.has_proof());
|
|
/* r_eq.get_proof() : e_old = r_eq.get_new() */
|
|
/* goal : e_old <m_rel> r_eq.get_new() */
|
|
expr l = m_tmp_tctx->mk_tmp_local(m_tmp_tctx->infer(e_old));
|
|
expr motive_local = get_app_builder().mk_app(m_rel, e_old, l);
|
|
/* motive = fun y, e_old <m_rel> y */
|
|
expr motive = Fun(l, motive_local);
|
|
/* Rxx = x <m_rel> x */
|
|
expr Rxx = get_app_builder().mk_refl(m_rel, e_old);
|
|
expr pf = get_app_builder().mk_eq_rec(motive, Rxx, r_eq.get_proof());
|
|
return result(r_eq.get_new(), pf);
|
|
}
|
|
|
|
result simplifier::join(result const & r1, result const & r2) {
|
|
/* Assumes that both results are with respect to the same relation */
|
|
if (!r1.has_proof()) {
|
|
return r2;
|
|
} else if (!r2.has_proof()) {
|
|
lean_assert(r1.has_proof());
|
|
return result(r2.get_new(), r1.get_proof());
|
|
} else {
|
|
/* If they both have proofs, we need to glue them together with transitivity. */
|
|
lean_assert(r1.has_proof() && r2.has_proof());
|
|
expr trans = get_app_builder().mk_trans(m_rel, r1.get_proof(), r2.get_proof());
|
|
return result(r2.get_new(), trans);
|
|
}
|
|
}
|
|
|
|
result simplifier::funext(result const & r, expr const & l) {
|
|
// theorem funext {f₁ f₂ : Πx : A, B x} : (∀x, f₁ x = f₂ x) → f₁ = f₂ :=
|
|
expr e = Fun(l, r.get_new());
|
|
if (!r.has_proof()) return result(e);
|
|
expr pf = get_app_builder().mk_app(get_funext_name(), Fun(l, r.get_proof()));
|
|
return result(e, pf);
|
|
}
|
|
|
|
result simplifier::finalize(result const & r) {
|
|
if (r.has_proof()) return r;
|
|
expr pf = get_app_builder().mk_refl(m_rel, r.get_new());
|
|
return result(r.get_new(), pf);
|
|
}
|
|
|
|
/* Simplification */
|
|
|
|
result simplifier::simplify(expr const & e, simp_rule_sets const & srss) {
|
|
flet<simp_rule_sets> set_srss(m_srss, srss);
|
|
freset<simplify_cache> reset(m_cache);
|
|
return simplify(e, true);
|
|
}
|
|
|
|
result simplifier::simplify(expr const & e, bool is_root) {
|
|
m_num_steps++;
|
|
flet<unsigned> inc_depth(m_depth, m_depth+1);
|
|
|
|
if (m_trace) {
|
|
ios().get_diagnostic_channel() << m_depth << "." << m_rel << ": " << e << "\n";
|
|
}
|
|
|
|
if (m_num_steps > m_max_steps)
|
|
throw blast_exception("simplifier failed, maximum number of steps exceeded", e);
|
|
|
|
if (m_memoize) {
|
|
if (auto it = cache_lookup(e)) return *it;
|
|
}
|
|
|
|
if (m_numerals && using_eq()) {
|
|
if (auto r = simplify_numeral(e)) {
|
|
return *r;
|
|
}
|
|
}
|
|
|
|
result r(e);
|
|
|
|
if (m_top_down) r = join(r, rewrite(whnf(r.get_new())));
|
|
|
|
r.update(whnf(r.get_new()));
|
|
|
|
switch (r.get_new().kind()) {
|
|
case expr_kind::Local:
|
|
case expr_kind::Meta:
|
|
case expr_kind::Sort:
|
|
case expr_kind::Constant:
|
|
// no-op
|
|
break;
|
|
case expr_kind::Var:
|
|
lean_unreachable();
|
|
case expr_kind::Macro:
|
|
if (m_expand_macros) {
|
|
if (auto m = m_tmp_tctx->expand_macro(e)) r = join(r, simplify(whnf(*m), is_root));
|
|
}
|
|
break;
|
|
case expr_kind::Lambda:
|
|
if (using_eq()) r = join(r, simplify_lambda(r.get_new()));
|
|
break;
|
|
case expr_kind::Pi:
|
|
r = join(r, simplify_pi(r.get_new()));
|
|
break;
|
|
case expr_kind::App:
|
|
r = join(r, simplify_app(r.get_new()));
|
|
break;
|
|
}
|
|
|
|
if (!m_top_down) r = join(r, rewrite(whnf(r.get_new())));
|
|
|
|
if (r.get_new() == e && !using_eq()) {
|
|
result r_eq;
|
|
{
|
|
flet<name> use_eq(m_rel, get_eq_name());
|
|
r_eq = simplify(r.get_new(), is_root);
|
|
}
|
|
r = join(r, lift_from_eq(r.get_new(), r_eq));
|
|
}
|
|
|
|
if (m_exhaustive && r.has_proof()) r = join(r, simplify(r.get_new(), is_root));
|
|
|
|
if (m_memoize) cache_save(e, r);
|
|
|
|
if (m_fuse && using_eq()) r = join(r, maybe_fuse(r.get_new(), is_root));
|
|
|
|
return r;
|
|
}
|
|
|
|
result simplifier::simplify_lambda(expr const & e) {
|
|
lean_assert(is_lambda(e));
|
|
expr t = e;
|
|
|
|
buffer<expr> ls;
|
|
while (is_lambda(t)) {
|
|
expr d = instantiate_rev(binding_domain(t), ls.size(), ls.data());
|
|
expr l = m_tmp_tctx->mk_tmp_local(d, binding_info(t));
|
|
ls.push_back(l);
|
|
t = instantiate(binding_body(t), l);
|
|
}
|
|
|
|
result r = simplify(t, false);
|
|
for (int i = ls.size() - 1; i >= 0; --i) r = funext(r, ls[i]);
|
|
return r;
|
|
}
|
|
|
|
result simplifier::simplify_pi(expr const & e) {
|
|
lean_assert(is_pi(e));
|
|
return try_congrs(e);
|
|
}
|
|
|
|
expr simplifier::unfold_reducible_instances(expr const & e) {
|
|
buffer<expr> args;
|
|
expr f = get_app_args(e, args);
|
|
fun_info f_info = get_fun_info(f, args.size());
|
|
int i = -1;
|
|
for_each(f_info.get_params_info(), [&](param_info const & p_info) {
|
|
i++;
|
|
if (p_info.is_inst_implicit() && !p_info.is_subsingleton()) {
|
|
args[i] = blast::normalize(args[i]);
|
|
}
|
|
});
|
|
return mk_app(f, args);
|
|
}
|
|
|
|
result simplifier::simplify_app(expr const & _e) {
|
|
lean_assert(is_app(_e));
|
|
expr e = unfold_reducible_instances(_e);
|
|
|
|
/* (1) Try user-defined congruences */
|
|
result r_user = try_congrs(e);
|
|
if (r_user.has_proof()) {
|
|
if (using_eq()) return join(r_user, simplify_fun(r_user.get_new()));
|
|
else return r_user;
|
|
}
|
|
|
|
/* (2) Synthesize congruence lemma */
|
|
if (using_eq()) {
|
|
optional<result> r_args = synth_congr(e, [&](expr const & e) {
|
|
return simplify(e, false);
|
|
});
|
|
if (r_args) return join(*r_args, simplify_fun(r_args->get_new()));
|
|
}
|
|
|
|
/* (3) Fall back on generic binary congruence */
|
|
if (using_eq()) {
|
|
expr const & f = app_fn(e);
|
|
expr const & arg = app_arg(e);
|
|
|
|
// TODO(dhs): it is not clear if this recursive call should be considered
|
|
// a root or not, though does not matter since if + were being applied,
|
|
// we would have synthesized a congruence rule in step (2).
|
|
result r_f = simplify(f, false);
|
|
|
|
if (is_dependent_fn(f)) {
|
|
if (r_f.has_proof()) return congr_fun(r_f, arg);
|
|
else return mk_app(r_f.get_new(), arg);
|
|
} else {
|
|
result r_arg = simplify(arg, false);
|
|
return congr_fun_arg(r_f, r_arg);
|
|
}
|
|
}
|
|
return result(e);
|
|
}
|
|
|
|
result simplifier::simplify_fun(expr const & e) {
|
|
lean_assert(is_app(e));
|
|
buffer<expr> args;
|
|
expr const & f = get_app_args(e, args);
|
|
result r_f = simplify(f, true);
|
|
return congr_funs(r_f, args);
|
|
}
|
|
|
|
optional<result> simplifier::simplify_numeral(expr const & e) {
|
|
if (is_num(e)) { return optional<result>(result(e)); }
|
|
|
|
try {
|
|
expr_pair r = mk_norm_num(*m_tmp_tctx, e);
|
|
return optional<result>(result(r.first, r.second));
|
|
} catch (exception e) {
|
|
return optional<result>();
|
|
}
|
|
}
|
|
|
|
/* Proving */
|
|
|
|
optional<expr> simplifier::prove(expr const & thm) {
|
|
flet<name> set_name(m_rel, get_iff_name());
|
|
result r_cond = simplify(thm, true);
|
|
if (is_constant(r_cond.get_new()) && const_name(r_cond.get_new()) == get_true_name()) {
|
|
expr pf = get_app_builder().mk_app(get_iff_elim_right_name(),
|
|
finalize(r_cond).get_proof(),
|
|
mk_constant(get_true_intro_name()));
|
|
return some_expr(pf);
|
|
}
|
|
return none_expr();
|
|
}
|
|
|
|
optional<expr> simplifier::prove(expr const & thm, simp_rule_sets const & srss) {
|
|
flet<name> set_name(m_rel, get_iff_name());
|
|
result r_cond = simplify(thm, srss);
|
|
if (is_constant(r_cond.get_new()) && const_name(r_cond.get_new()) == get_true_name()) {
|
|
expr pf = get_app_builder().mk_app(get_iff_elim_right_name(),
|
|
finalize(r_cond).get_proof(),
|
|
mk_constant(get_true_intro_name()));
|
|
return some_expr(pf);
|
|
}
|
|
return none_expr();
|
|
}
|
|
|
|
/* Rewriting */
|
|
|
|
result simplifier::rewrite(expr const & e) {
|
|
result r(e);
|
|
while (true) {
|
|
result r_ctx = rewrite(r.get_new(), m_ctx_srss);
|
|
result r_new = rewrite(r_ctx.get_new(), m_srss);
|
|
if (!r_ctx.has_proof() && !r_new.has_proof()) break;
|
|
r = join(join(r, r_ctx), r_new);
|
|
}
|
|
return r;
|
|
}
|
|
|
|
result simplifier::rewrite(expr const & e, simp_rule_sets const & srss) {
|
|
result r(e);
|
|
|
|
simp_rule_set const * sr = srss.find(m_rel);
|
|
if (!sr) return r;
|
|
|
|
list<simp_rule> const * srs = sr->find_simp(e);
|
|
if (!srs) return r;
|
|
|
|
for_each(*srs, [&](simp_rule const & sr) {
|
|
result r_new = rewrite(r.get_new(), sr);
|
|
if (!r_new.has_proof()) return;
|
|
r = join(r, r_new);
|
|
});
|
|
return r;
|
|
}
|
|
|
|
result simplifier::rewrite(expr const & e, simp_rule const & sr) {
|
|
blast_tmp_type_context tmp_tctx(sr.get_num_umeta(), sr.get_num_emeta());
|
|
|
|
if (!tmp_tctx->is_def_eq(e, sr.get_lhs())) return result(e);
|
|
|
|
if (m_trace) {
|
|
expr new_lhs = tmp_tctx->instantiate_uvars_mvars(sr.get_lhs());
|
|
expr new_rhs = tmp_tctx->instantiate_uvars_mvars(sr.get_rhs());
|
|
ios().get_diagnostic_channel()
|
|
<< "REW(" << sr.get_id() << ") "
|
|
<< "[" << new_lhs << " =?= " << new_rhs << "]\n";
|
|
}
|
|
|
|
if (!instantiate_emetas(tmp_tctx, sr.get_num_emeta(), sr.get_emetas(), sr.get_instances())) return result(e);
|
|
|
|
for (unsigned i = 0; i < sr.get_num_umeta(); i++) {
|
|
if (!tmp_tctx->is_uvar_assigned(i)) return result(e);
|
|
}
|
|
|
|
expr new_lhs = tmp_tctx->instantiate_uvars_mvars(sr.get_lhs());
|
|
expr new_rhs = tmp_tctx->instantiate_uvars_mvars(sr.get_rhs());
|
|
|
|
if (sr.is_perm()) {
|
|
if (!is_lt(new_rhs, new_lhs, false))
|
|
return result(e);
|
|
}
|
|
|
|
expr pf = tmp_tctx->instantiate_uvars_mvars(sr.get_proof());
|
|
return result(new_rhs, pf);
|
|
}
|
|
|
|
/* Congruence */
|
|
|
|
result simplifier::congr_fun_arg(result const & r_f, result const & r_arg) {
|
|
if (!r_f.has_proof() && !r_arg.has_proof()) return result(mk_app(r_f.get_new(), r_arg.get_new()));
|
|
else if (!r_f.has_proof()) return congr_arg(r_f.get_new(), r_arg);
|
|
else if (!r_arg.has_proof()) return congr_fun(r_f, r_arg.get_new());
|
|
else return congr(r_f, r_arg);
|
|
}
|
|
|
|
result simplifier::congr(result const & r_f, result const & r_arg) {
|
|
lean_assert(r_f.has_proof() && r_arg.has_proof());
|
|
// theorem congr {A B : Type} {f₁ f₂ : A → B} {a₁ a₂ : A} (H₁ : f₁ = f₂) (H₂ : a₁ = a₂) : f₁ a₁ = f₂ a₂
|
|
expr e = mk_app(r_f.get_new(), r_arg.get_new());
|
|
expr pf = get_app_builder().mk_congr(r_f.get_proof(), r_arg.get_proof());
|
|
return result(e, pf);
|
|
}
|
|
|
|
result simplifier::congr_fun(result const & r_f, expr const & arg) {
|
|
lean_assert(r_f.has_proof());
|
|
// theorem congr_fun {A : Type} {B : A → Type} {f g : Π x, B x} (H : f = g) (a : A) : f a = g a
|
|
expr e = mk_app(r_f.get_new(), arg);
|
|
expr pf = get_app_builder().mk_congr_fun(r_f.get_proof(), arg);
|
|
return result(e, pf);
|
|
}
|
|
|
|
result simplifier::congr_arg(expr const & f, result const & r_arg) {
|
|
lean_assert(r_arg.has_proof());
|
|
// theorem congr_arg {A B : Type} {a₁ a₂ : A} (f : A → B) : a₁ = a₂ → f a₁ = f a₂
|
|
expr e = mk_app(f, r_arg.get_new());
|
|
expr pf = get_app_builder().mk_congr_arg(f, r_arg.get_proof());
|
|
return result(e, pf);
|
|
}
|
|
|
|
/* Note: handles reflexivity */
|
|
result simplifier::congr_funs(result const & r_f, buffer<expr> const & args) {
|
|
// congr_fun : ∀ {A : Type} {B : A → Type} {f g : Π (x : A), B x}, f = g → (∀ (a : A), f a = g a)
|
|
expr e = r_f.get_new();
|
|
for (unsigned i = 0; i < args.size(); ++i) {
|
|
e = mk_app(e, args[i]);
|
|
}
|
|
if (!r_f.has_proof()) return result(e);
|
|
expr pf = r_f.get_proof();
|
|
for (unsigned i = 0; i < args.size(); ++i) {
|
|
pf = get_app_builder().mk_app(get_congr_fun_name(), pf, args[i]);
|
|
}
|
|
return result(e, pf);
|
|
}
|
|
|
|
result simplifier::try_congrs(expr const & e) {
|
|
simp_rule_set const * sr = get_simp_rule_sets(env()).find(m_rel);
|
|
if (!sr) return result(e);
|
|
|
|
list<congr_rule> const * crs = sr->find_congr(e);
|
|
if (!crs) return result(e);
|
|
|
|
result r(e);
|
|
for_each(*crs, [&](congr_rule const & cr) {
|
|
if (r.has_proof()) return;
|
|
r = try_congr(e, cr);
|
|
});
|
|
return r;
|
|
}
|
|
|
|
result simplifier::try_congr(expr const & e, congr_rule const & cr) {
|
|
blast_tmp_type_context tmp_tctx(cr.get_num_umeta(), cr.get_num_emeta());
|
|
|
|
if (!tmp_tctx->is_def_eq(e, cr.get_lhs())) return result(e);
|
|
|
|
if (m_trace) {
|
|
expr new_lhs = tmp_tctx->instantiate_uvars_mvars(cr.get_lhs());
|
|
expr new_rhs = tmp_tctx->instantiate_uvars_mvars(cr.get_rhs());
|
|
ios().get_diagnostic_channel()
|
|
<< "CONGR(" << cr.get_id() << ") "
|
|
<< "[" << new_lhs << " =?= " << new_rhs << "]\n";
|
|
}
|
|
|
|
/* First, iterate over the congruence hypotheses */
|
|
bool failed = false;
|
|
bool simplified = false;
|
|
list<expr> const & congr_hyps = cr.get_congr_hyps();
|
|
for_each(congr_hyps, [&](expr const & m) {
|
|
if (failed) return;
|
|
buffer<expr> ls;
|
|
expr m_type = tmp_tctx->instantiate_uvars_mvars(tmp_tctx->infer(m));
|
|
|
|
while (is_pi(m_type)) {
|
|
expr d = instantiate_rev(binding_domain(m_type), ls.size(), ls.data());
|
|
expr l = tmp_tctx->mk_tmp_local(d, binding_info(m_type));
|
|
lean_assert(!has_metavar(l));
|
|
ls.push_back(l);
|
|
m_type = instantiate(binding_body(m_type), l);
|
|
}
|
|
|
|
expr h_rel, h_lhs, h_rhs;
|
|
lean_verify(is_simp_relation(env(), m_type, h_rel, h_lhs, h_rhs) && is_constant(h_rel));
|
|
{
|
|
flet<name> set_name(m_rel, const_name(h_rel));
|
|
flet<simp_rule_sets> set_ctx_srss(m_ctx_srss, add_to_srss(m_ctx_srss, ls));
|
|
|
|
h_lhs = tmp_tctx->instantiate_uvars_mvars(h_lhs);
|
|
lean_assert(!has_metavar(h_lhs));
|
|
|
|
result r_congr_hyp = simplify(h_lhs, m_srss);
|
|
if (r_congr_hyp.has_proof()) simplified = true;
|
|
r_congr_hyp = finalize(r_congr_hyp);
|
|
expr hyp = finalize(r_congr_hyp).get_proof();
|
|
|
|
if (!tmp_tctx->is_def_eq(m, Fun(ls, hyp))) failed = true;
|
|
}
|
|
});
|
|
|
|
if (failed || !simplified) return result(e);
|
|
|
|
if (!instantiate_emetas(tmp_tctx, cr.get_num_emeta(), cr.get_emetas(), cr.get_instances())) return result(e);
|
|
|
|
for (unsigned i = 0; i < cr.get_num_umeta(); i++) {
|
|
if (!tmp_tctx->is_uvar_assigned(i)) return result(e);
|
|
}
|
|
|
|
expr e_s = tmp_tctx->instantiate_uvars_mvars(cr.get_rhs());
|
|
expr pf = tmp_tctx->instantiate_uvars_mvars(cr.get_proof());
|
|
return result(e_s, pf);
|
|
}
|
|
|
|
bool simplifier::instantiate_emetas(blast_tmp_type_context & tmp_tctx, unsigned num_emeta, list<expr> const & emetas,
|
|
list<bool> const & instances) {
|
|
bool failed = false;
|
|
unsigned i = num_emeta;
|
|
for_each2(emetas, instances, [&](expr const & m, bool const & is_instance) {
|
|
i--;
|
|
if (failed) return;
|
|
expr m_type = tmp_tctx->instantiate_uvars_mvars(tmp_tctx->infer(m));
|
|
lean_assert(!has_metavar(m_type));
|
|
|
|
if (is_instance) {
|
|
if (auto v = tmp_tctx->mk_class_instance(m_type)) {
|
|
if (!tmp_tctx->force_assign(m, *v)) {
|
|
if (m_trace) {
|
|
ios().get_diagnostic_channel() << "unable to assign instance for: " << m_type << "\n";
|
|
}
|
|
failed = true;
|
|
return;
|
|
}
|
|
} else {
|
|
if (m_trace) {
|
|
ios().get_diagnostic_channel() << "unable to synthesize instance for: " << m_type << "\n";
|
|
}
|
|
failed = true;
|
|
return;
|
|
}
|
|
}
|
|
|
|
if (tmp_tctx->is_mvar_assigned(i)) return;
|
|
|
|
if (tmp_tctx->is_prop(m_type)) {
|
|
if (auto pf = prove(m_type)) {
|
|
lean_verify(tmp_tctx->is_def_eq(m, *pf));
|
|
return;
|
|
}
|
|
}
|
|
|
|
if (m_trace) {
|
|
ios().get_diagnostic_channel() << "failed to assign: " << m << " : " << m_type << "\n";
|
|
}
|
|
|
|
failed = true;
|
|
return;
|
|
});
|
|
|
|
return !failed;
|
|
}
|
|
|
|
template<typename F>
|
|
optional<result> simplifier::synth_congr(expr const & e, F && simp) {
|
|
static_assert(std::is_same<typename std::result_of<F(expr const & e)>::type, result>::value,
|
|
"synth_congr: simp must take expressions to results");
|
|
lean_assert(is_app(e));
|
|
buffer<expr> args;
|
|
expr f = get_app_args(e, args);
|
|
auto congr_lemma = mk_congr_lemma_for_simp(f, args.size());
|
|
if (!congr_lemma) return optional<result>();
|
|
expr proof = congr_lemma->get_proof();
|
|
expr type = congr_lemma->get_type();
|
|
unsigned i = 0;
|
|
bool has_proof = false;
|
|
bool has_cast = false;
|
|
buffer<expr> locals;
|
|
for_each(congr_lemma->get_arg_kinds(), [&](congr_arg_kind const & ckind) {
|
|
proof = mk_app(proof, args[i]);
|
|
type = instantiate(binding_body(type), args[i]);
|
|
if (ckind == congr_arg_kind::Eq) {
|
|
result r_arg = simp(args[i]);
|
|
if (r_arg.has_proof()) has_proof = true;
|
|
r_arg = finalize(r_arg);
|
|
proof = mk_app(proof, r_arg.get_new(), r_arg.get_proof());
|
|
type = instantiate(binding_body(type), r_arg.get_new());
|
|
type = instantiate(binding_body(type), r_arg.get_proof());
|
|
} else if (ckind == congr_arg_kind::Cast) {
|
|
has_cast = true;
|
|
}
|
|
i++;
|
|
});
|
|
lean_assert(is_eq(type));
|
|
buffer<expr> type_args;
|
|
get_app_args(type, type_args);
|
|
expr e_new = remove_unnecessary_casts(type_args[2]);
|
|
if (has_proof) return optional<result>(result(e_new, proof));
|
|
else return optional<result>(result(e_new));
|
|
}
|
|
|
|
expr simplifier::remove_unnecessary_casts(expr const & e) {
|
|
buffer<expr> args;
|
|
expr f = get_app_args(e, args);
|
|
fun_info f_info = get_fun_info(f, args.size());
|
|
int i = -1;
|
|
for_each(f_info.get_params_info(), [&](param_info const & p_info) {
|
|
i++;
|
|
if (p_info.is_subsingleton()) {
|
|
while (is_constant(get_app_fn(args[i]))) {
|
|
buffer<expr> cast_args;
|
|
expr f_cast = get_app_args(args[i], cast_args);
|
|
name n_f = const_name(f_cast);
|
|
if (n_f == get_eq_rec_name() || n_f == get_eq_drec_name() || n_f == get_eq_nrec_name()) {
|
|
lean_assert(cast_args.size() == 6);
|
|
expr major_premise = cast_args[5];
|
|
expr f_major_premise = get_app_fn(major_premise);
|
|
if (is_constant(f_major_premise) && const_name(f_major_premise) == get_eq_refl_name())
|
|
args[i] = cast_args[3];
|
|
else
|
|
return;
|
|
} else {
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
});
|
|
return mk_app(f, args);
|
|
}
|
|
|
|
/* Fusion */
|
|
|
|
result simplifier::maybe_fuse(expr const & e, bool is_root) {
|
|
if (!is_app(e)) return result(e);
|
|
if (is_root && is_add_app(e)) return fuse(e);
|
|
if (!is_root && is_add_app(e)) return result(e);
|
|
lean_assert(!is_add_app(e));
|
|
/* At this point we know we are an application of something other than + */
|
|
optional<result> r = synth_congr(e, [&](expr const & arg) {
|
|
if (is_add_app(arg)) return fuse(arg);
|
|
else return result(arg);
|
|
});
|
|
if (r) return *r;
|
|
else return result(e);
|
|
}
|
|
|
|
result simplifier::fuse(expr const & e) {
|
|
lean_assert(is_add_app(e));
|
|
// ios().get_diagnostic_channel() << "FUSE: " << e << "\n\n";
|
|
flet<bool> no_recursive_fusion(m_fuse, false);
|
|
|
|
/* Note: we assume all negations are on the outside of the summands */
|
|
|
|
/* Example
|
|
1. Input (e): n1 * x1 * n2 * x2 + x3 + - (x1 * x2 * n3) + (- x3) + x4
|
|
2. Split summands: (n1 * n2) * (x1 * x2) + 1 * x3 + (- n3) * (x1 * x2) + (- 1) * x3 + 1 * x4
|
|
3. Group by variable (e_grp): ((n1 * n2) * (x1 * x2) + (- n3) * (x1 * x2)) + (1 * x3 + (-1) * x3) + x4
|
|
4. Introduce locals (e_grp_ls): ((n1 * n2) * l1 + (- n3) * l1) + (1 * l2 + (-1) * l2) + l3
|
|
5. Fuse (e_fused_ls): (n1 * n2 + (- n3)) * l1 + (1 + (- 1)) * l2 + 1 * l3
|
|
6. Simplify coefficients (e_simp_ls): (n1 * n2 + (- n3)) * l1 + l3
|
|
7. Instantiate locals (e_simp): (n1 * n2 + (- n3)) * (x1 * x2) + x4
|
|
|
|
Proofs
|
|
1. Prove (1) == (3) using simplify with [ac]
|
|
2. Prove (4) == (5) using simplify with [som]
|
|
3. Prove (5) == (6) using simplify with [numeral]
|
|
4. Prove (4) == (6) by transitivity of proofs (2) and (3)
|
|
5. Prove (3) == (7) by instantiating proof (4)
|
|
6. Prove (1) == (7) by transitivity of proofs (1) and (5)
|
|
*/
|
|
|
|
/* Construct useful expressions */
|
|
buffer<expr> args;
|
|
get_app_args(e, args);
|
|
expr T = args[0];
|
|
expr f_add, f_mul, zero, one;
|
|
try {
|
|
f_add = get_app_builder().mk_partial_add(T);
|
|
f_mul = get_app_builder().mk_partial_mul(T);
|
|
zero = get_app_builder().mk_zero(T);
|
|
one = get_app_builder().mk_one(T);
|
|
expr left_distrib = get_app_builder().mk_partial_left_distrib(T);
|
|
} catch (app_builder_exception & ex) {
|
|
ios().get_diagnostic_channel() << "Cannot synthesize necessary instances\n";
|
|
return result(e);
|
|
}
|
|
|
|
/* (1 ==> 2) Split each summand into (a) numerals and (b) variables */
|
|
buffer<expr> numerals;
|
|
buffer<expr> variables;
|
|
expr s = e;
|
|
while (is_add_app(s)) {
|
|
buffer<expr> args;
|
|
expr f = get_app_args(s, args);
|
|
auto n_v = split_summand(args[2], f_mul, one);
|
|
numerals.push_back(n_v.first);
|
|
variables.push_back(n_v.second);
|
|
s = args[3];
|
|
}
|
|
auto n_v = split_summand(s, f_mul, one);
|
|
numerals.push_back(n_v.first);
|
|
variables.push_back(n_v.second);
|
|
lean_assert(numerals.size() == variables.size());
|
|
|
|
/* (2 ==> 3, 4, 5) Group the summands by variable */
|
|
expr_bi_struct_map<list<expr> > variable_to_numerals;
|
|
for (unsigned i = 0; i < numerals.size(); i++) {
|
|
auto it = variable_to_numerals.find(variables[i]);
|
|
if (it != variable_to_numerals.end()) it->second = cons(numerals[i], it->second);
|
|
else variable_to_numerals.insert({variables[i], list<expr>(numerals[i])});
|
|
}
|
|
|
|
expr e_grp = zero;
|
|
expr e_grp_ls = zero;
|
|
expr e_fused_ls = zero;
|
|
|
|
buffer<expr> locals;
|
|
variables.clear();
|
|
for (auto v_ns : variable_to_numerals) {
|
|
expr local;
|
|
if (!is_one(v_ns.first)) {
|
|
local = m_tmp_tctx->mk_tmp_local(T);
|
|
locals.push_back(local);
|
|
variables.push_back(v_ns.first);
|
|
} else {
|
|
local = v_ns.first;
|
|
}
|
|
|
|
expr term = zero;
|
|
expr term_ls = zero;
|
|
expr term_fused_ls = zero;
|
|
for_each(v_ns.second, [&](expr const & n) {
|
|
term = mk_app(f_add, mk_app(f_mul, v_ns.first, n), term);
|
|
term_ls = mk_app(f_add, mk_app(f_mul, local, n), term_ls);
|
|
term_fused_ls = mk_app(f_add, n, term_fused_ls);
|
|
});
|
|
e_grp = mk_app(f_add, term, e_grp);
|
|
e_grp_ls = mk_app(f_add, term_ls, e_grp_ls);
|
|
e_fused_ls = mk_app(f_add, mk_app(f_mul, term_fused_ls, local), e_fused_ls);
|
|
}
|
|
|
|
/* Prove (1) == (3) using simplify with [ac] */
|
|
flet<bool> no_simplify_numerals(m_numerals, false);
|
|
auto pf_1_3 = prove(get_app_builder().mk_eq(e, e_grp),
|
|
get_simp_rule_sets(env(), ios(), *g_simplify_ac_namespace));
|
|
if (!pf_1_3) {
|
|
diagnostic(env(), ios()) << e << "\n\n =?=\n\n" << e_grp << "\n";
|
|
throw blast_exception("Failed to prove (1) == (3) during fusion", e);
|
|
}
|
|
|
|
/* Prove (4) == (5) using simplify with [som] */
|
|
auto pf_4_5 = prove(get_app_builder().mk_eq(e_grp_ls, e_fused_ls),
|
|
get_simp_rule_sets(env(), ios(), *g_simplify_som_namespace));
|
|
if (!pf_4_5) {
|
|
diagnostic(env(), ios()) << e_grp_ls << "\n\n =?=\n\n" << e_fused_ls << "\n";
|
|
throw blast_exception("Failed to prove (4) == (5) during fusion", e);
|
|
}
|
|
|
|
/* Prove (5) == (6) using simplify with [numeral] */
|
|
flet<bool> simplify_numerals(m_numerals, true);
|
|
result r_simp_ls = simplify(e_fused_ls, get_simp_rule_sets(env(), ios(), *g_simplify_ac_namespace));
|
|
|
|
/* Prove (4) == (6) by transitivity of proofs (2) and (3) */
|
|
expr pf_4_6;
|
|
if (!r_simp_ls.has_proof()) pf_4_6 = *pf_4_5;
|
|
else pf_4_6 = get_app_builder().mk_eq_trans(*pf_4_5, r_simp_ls.get_proof());
|
|
|
|
/* Prove (3) == (7) by instantiating proof (4) */
|
|
expr pf_3_7 = mk_app(Fun(locals, pf_4_6), variables);
|
|
|
|
/* Prove (1) == (7) by transitivity of proofs (1) and (5) */
|
|
expr pf_1_7 = get_app_builder().mk_eq_trans(*pf_1_3, pf_3_7);
|
|
|
|
return result(mk_app(Fun(locals, r_simp_ls.get_new()), variables), pf_1_7);
|
|
}
|
|
|
|
expr_pair simplifier::split_summand(expr const & e, expr const & f_mul, expr const & one) {
|
|
/* [e] is a possibly negated, possibly null product, where some of the multiplicands are numerals
|
|
and the rest are treated as variables. This method does the following conversion:
|
|
- (x1 * n1 * x2 * n3) ==> (-1 * n1 * n3) * (x1 * x2) */
|
|
expr s = e;
|
|
expr numeral = one;
|
|
expr variable = one;
|
|
if (is_neg_app(s)) {
|
|
buffer<expr> args;
|
|
get_app_args(s, args);
|
|
numeral = get_app_builder().mk_app(get_neg_name(), one);
|
|
s = args[2];
|
|
}
|
|
while (is_mul_app(s)) {
|
|
buffer<expr> args;
|
|
get_app_args(s, args);
|
|
expr const & multiplicand = args[2];
|
|
if (is_num(multiplicand)) {
|
|
numeral = mk_app(f_mul, multiplicand, numeral);
|
|
} else {
|
|
if (variable == one) variable = multiplicand;
|
|
else variable = mk_app(f_mul, multiplicand, variable);
|
|
}
|
|
s = args[3];
|
|
}
|
|
if (is_num(s)) {
|
|
numeral = mk_app(f_mul, s, numeral);
|
|
} else {
|
|
if (variable == one) variable = s;
|
|
else variable = mk_app(f_mul, s, variable);
|
|
}
|
|
return mk_pair(numeral, variable);
|
|
}
|
|
|
|
/* Setup and teardown */
|
|
|
|
void initialize_simplifier() {
|
|
g_simplify_empty_namespace = new name{"simplifier", "empty"};
|
|
g_simplify_unit_namespace = new name{"simplifier", "unit"};
|
|
g_simplify_ac_namespace = new name{"simplifier", "ac"};
|
|
g_simplify_som_namespace = new name{"simplifier", "som"};
|
|
g_simplify_numeral_namespace = new name{"simplifier", "numeral"};
|
|
|
|
g_simplify_max_steps = new name{"simplify", "max_steps"};
|
|
g_simplify_top_down = new name{"simplify", "top_down"};
|
|
g_simplify_exhaustive = new name{"simplify", "exhaustive"};
|
|
g_simplify_memoize = new name{"simplify", "memoize"};
|
|
g_simplify_contextual = new name{"simplify", "contextual"};
|
|
g_simplify_expand_macros = new name{"simplify", "expand_macros"};
|
|
g_simplify_trace = new name{"simplify", "trace"};
|
|
g_simplify_fuse = new name{"simplify", "fuse"};
|
|
g_simplify_numerals = new name{"simplify", "numerals"};
|
|
|
|
register_unsigned_option(*g_simplify_max_steps, LEAN_DEFAULT_SIMPLIFY_MAX_STEPS,
|
|
"(simplify) max allowed steps in simplification");
|
|
register_bool_option(*g_simplify_top_down, LEAN_DEFAULT_SIMPLIFY_TOP_DOWN,
|
|
"(simplify) use top-down rewriting instead of bottom-up");
|
|
register_bool_option(*g_simplify_exhaustive, LEAN_DEFAULT_SIMPLIFY_EXHAUSTIVE,
|
|
"(simplify) rewrite exhaustively");
|
|
register_bool_option(*g_simplify_memoize, LEAN_DEFAULT_SIMPLIFY_MEMOIZE,
|
|
"(simplify) memoize simplifications");
|
|
register_bool_option(*g_simplify_contextual, LEAN_DEFAULT_SIMPLIFY_CONTEXTUAL,
|
|
"(simplify) use contextual simplification");
|
|
register_bool_option(*g_simplify_expand_macros, LEAN_DEFAULT_SIMPLIFY_EXPAND_MACROS,
|
|
"(simplify) expand macros");
|
|
register_bool_option(*g_simplify_trace, LEAN_DEFAULT_SIMPLIFY_TRACE,
|
|
"(simplify) trace");
|
|
register_bool_option(*g_simplify_fuse, LEAN_DEFAULT_SIMPLIFY_FUSE,
|
|
"(simplify) fuse addition in distrib structures");
|
|
register_bool_option(*g_simplify_numerals, LEAN_DEFAULT_SIMPLIFY_NUMERALS,
|
|
"(simplify) simplify (+, *, -, /) over numerals");
|
|
}
|
|
|
|
void finalize_simplifier() {
|
|
delete g_simplify_numerals;
|
|
delete g_simplify_fuse;
|
|
delete g_simplify_trace;
|
|
delete g_simplify_expand_macros;
|
|
delete g_simplify_contextual;
|
|
delete g_simplify_memoize;
|
|
delete g_simplify_exhaustive;
|
|
delete g_simplify_top_down;
|
|
delete g_simplify_max_steps;
|
|
|
|
delete g_simplify_numeral_namespace;
|
|
delete g_simplify_som_namespace;
|
|
delete g_simplify_ac_namespace;
|
|
delete g_simplify_unit_namespace;
|
|
delete g_simplify_empty_namespace;
|
|
}
|
|
|
|
/* Entry point */
|
|
result simplify(name const & rel, expr const & e, simp_rule_sets const & srss) {
|
|
return simplifier(rel)(e, srss);
|
|
}
|
|
|
|
}}
|