556 lines
20 KiB
C++
556 lines
20 KiB
C++
/*
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Copyright (c) 2015 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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*/
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#include <string>
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#include "util/sstream.h"
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#include "kernel/instantiate.h"
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#include "kernel/find_fn.h"
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#include "kernel/error_msgs.h"
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#include "library/scoped_ext.h"
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#include "library/expr_pair.h"
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#include "library/relation_manager.h"
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#include "library/simplifier/ceqv.h"
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#include "library/simplifier/simp_rule_set.h"
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namespace lean {
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simp_rule_core::simp_rule_core(name const & id, levels const & univ_metas, list<expr> const & metas,
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expr const & lhs, expr const & rhs, expr const & proof):
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m_id(id), m_univ_metas(univ_metas), m_metas(metas), m_lhs(lhs), m_rhs(rhs), m_proof(proof) {}
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simp_rule::simp_rule(name const & id, levels const & univ_metas, list<expr> const & metas,
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expr const & lhs, expr const & rhs, expr const & proof, bool is_perm):
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simp_rule_core(id, univ_metas, metas, lhs, rhs, proof),
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m_is_permutation(is_perm) {}
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bool operator==(simp_rule const & r1, simp_rule const & r2) {
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return r1.m_lhs == r2.m_lhs && r1.m_rhs == r2.m_rhs;
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}
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format simp_rule::pp(formatter const & fmt) const {
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format r;
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r += format("#") + format(length(m_metas));
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if (m_is_permutation)
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r += space() + format("perm");
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format r1 = comma() + space() + fmt(m_lhs);
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r1 += space() + format("↦") + pp_indent_expr(fmt, m_rhs);
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r += group(r1);
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return r;
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}
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congr_rule::congr_rule(name const & id, levels const & univ_metas, list<expr> const & metas,
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expr const & lhs, expr const & rhs, expr const & proof, list<expr> const & congr_hyps):
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simp_rule_core(id, univ_metas, metas, lhs, rhs, proof),
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m_congr_hyps(congr_hyps) {}
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bool operator==(congr_rule const & r1, congr_rule const & r2) {
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return r1.m_lhs == r2.m_lhs && r1.m_rhs == r2.m_rhs && r1.m_congr_hyps == r2.m_congr_hyps;
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}
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format congr_rule::pp(formatter const & fmt) const {
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format r;
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r += format("#") + format(length(m_metas));
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format r1;
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for (expr const & h : m_congr_hyps) {
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r1 += space() + paren(fmt(mlocal_type(h)));
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}
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r += group(r1);
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r += space() + format(":") + space();
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format r2 = paren(fmt(m_lhs));
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r2 += space() + format("↦") + space() + paren(fmt(m_rhs));
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r += group(r2);
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return r;
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}
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simp_rule_set::simp_rule_set(name const & eqv):
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m_eqv(eqv) {}
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void simp_rule_set::insert(simp_rule const & r) {
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m_simp_set.insert(r.get_lhs(), r);
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}
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void simp_rule_set::erase(simp_rule const & r) {
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m_simp_set.erase(r.get_lhs(), r);
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}
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void simp_rule_set::insert(congr_rule const & r) {
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m_congr_set.insert(r.get_lhs(), r);
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}
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void simp_rule_set::erase(congr_rule const & r) {
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m_congr_set.erase(r.get_lhs(), r);
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}
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list<simp_rule> const * simp_rule_set::find_simp(head_index const & h) const {
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return m_simp_set.find(h);
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}
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void simp_rule_set::for_each_simp(std::function<void(simp_rule const &)> const & fn) const {
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m_simp_set.for_each_entry([&](head_index const &, simp_rule const & r) { fn(r); });
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}
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list<congr_rule> const * simp_rule_set::find_congr(head_index const & h) const {
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return m_congr_set.find(h);
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}
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void simp_rule_set::for_each_congr(std::function<void(congr_rule const &)> const & fn) const {
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m_congr_set.for_each_entry([&](head_index const &, congr_rule const & r) { fn(r); });
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}
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void simp_rule_set::erase_simp(name_set const & ids) {
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// This method is not very smart and doesn't use any indexing or caching.
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// So, it may be a bottleneck in the future
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buffer<simp_rule> to_delete;
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for_each_simp([&](simp_rule const & r) {
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if (ids.contains(r.get_id())) {
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to_delete.push_back(r);
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}
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});
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for (simp_rule const & r : to_delete) {
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erase(r);
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}
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}
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void simp_rule_set::erase_simp(buffer<name> const & ids) {
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erase_simp(to_name_set(ids));
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}
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template<typename R>
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void simp_rule_sets::insert_core(name const & eqv, R const & r) {
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simp_rule_set s(eqv);
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if (auto const * curr = m_sets.find(eqv)) {
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s = *curr;
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}
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s.insert(r);
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m_sets.insert(eqv, s);
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}
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template<typename R>
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void simp_rule_sets::erase_core(name const & eqv, R const & r) {
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if (auto const * curr = m_sets.find(eqv)) {
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simp_rule_set s = *curr;
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s.erase(r);
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if (s.empty())
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m_sets.erase(eqv);
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else
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m_sets.insert(eqv, s);
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}
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}
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void simp_rule_sets::insert(name const & eqv, simp_rule const & r) {
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return insert_core(eqv, r);
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}
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void simp_rule_sets::erase(name const & eqv, simp_rule const & r) {
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return erase_core(eqv, r);
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}
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void simp_rule_sets::insert(name const & eqv, congr_rule const & r) {
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return insert_core(eqv, r);
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}
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void simp_rule_sets::erase(name const & eqv, congr_rule const & r) {
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return erase_core(eqv, r);
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}
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void simp_rule_sets::get_relations(buffer<name> & rs) const {
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m_sets.for_each([&](name const & r, simp_rule_set const &) {
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rs.push_back(r);
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});
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}
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void simp_rule_sets::erase_simp(name_set const & ids) {
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name_map<simp_rule_set> new_sets;
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m_sets.for_each([&](name const & n, simp_rule_set const & s) {
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simp_rule_set new_s = s;
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new_s.erase_simp(ids);
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new_sets.insert(n, new_s);
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});
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m_sets = new_sets;
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}
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void simp_rule_sets::erase_simp(buffer<name> const & ids) {
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erase_simp(to_name_set(ids));
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}
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simp_rule_set const * simp_rule_sets::find(name const & eqv) const {
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return m_sets.find(eqv);
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}
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list<simp_rule> const * simp_rule_sets::find_simp(name const & eqv, head_index const & h) const {
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if (auto const * s = m_sets.find(eqv))
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return s->find_simp(h);
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return nullptr;
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}
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list<congr_rule> const * simp_rule_sets::find_congr(name const & eqv, head_index const & h) const {
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if (auto const * s = m_sets.find(eqv))
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return s->find_congr(h);
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return nullptr;
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}
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void simp_rule_sets::for_each_simp(std::function<void(name const &, simp_rule const &)> const & fn) const {
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m_sets.for_each([&](name const & eqv, simp_rule_set const & s) {
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s.for_each_simp([&](simp_rule const & r) {
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fn(eqv, r);
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});
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});
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}
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void simp_rule_sets::for_each_congr(std::function<void(name const &, congr_rule const &)> const & fn) const {
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m_sets.for_each([&](name const & eqv, simp_rule_set const & s) {
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s.for_each_congr([&](congr_rule const & r) {
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fn(eqv, r);
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});
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});
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}
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format simp_rule_sets::pp(formatter const & fmt, format const & header, bool simp, bool congr) const {
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format r;
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if (simp) {
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name prev_eqv;
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for_each_simp([&](name const & eqv, simp_rule const & rw) {
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if (prev_eqv != eqv) {
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r += format("simplification rules for ") + format(eqv);
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r += header;
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r += line();
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prev_eqv = eqv;
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}
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r += rw.pp(fmt) + line();
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});
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}
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if (congr) {
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name prev_eqv;
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for_each_congr([&](name const & eqv, congr_rule const & cr) {
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if (prev_eqv != eqv) {
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r += format("congruencec rules for ") + format(eqv) + line();
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prev_eqv = eqv;
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}
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r += cr.pp(fmt) + line();
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});
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}
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return r;
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}
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format simp_rule_sets::pp_simp(formatter const & fmt, format const & header) const {
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return pp(fmt, header, true, false);
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}
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format simp_rule_sets::pp_simp(formatter const & fmt) const {
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return pp(fmt, format(), true, false);
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}
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format simp_rule_sets::pp_congr(formatter const & fmt) const {
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return pp(fmt, format(), false, true);
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}
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format simp_rule_sets::pp(formatter const & fmt) const {
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return pp(fmt, format(), true, true);
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}
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static name * g_prefix = nullptr;
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simp_rule_sets add_core(type_checker & tc, simp_rule_sets const & s,
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name const & id, levels const & univ_metas, expr const & e, expr const & h) {
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list<expr_pair> ceqvs = to_ceqvs(tc, e, h);
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environment const & env = tc.env();
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simp_rule_sets new_s = s;
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for (expr_pair const & p : ceqvs) {
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expr new_e = p.first;
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expr new_h = p.second;
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bool is_perm = is_permutation_ceqv(env, new_e);
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buffer<expr> metas;
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unsigned idx = 0;
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while (is_pi(new_e)) {
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expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(new_e));
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idx++;
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metas.push_back(mvar);
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new_e = instantiate(binding_body(new_e), mvar);
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}
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expr rel, lhs, rhs;
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if (is_simp_relation(env, new_e, rel, lhs, rhs) && is_constant(rel)) {
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new_s.insert(const_name(rel), simp_rule(id, univ_metas, to_list(metas), lhs, rhs, new_h, is_perm));
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}
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}
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return new_s;
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}
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simp_rule_sets add(type_checker & tc, simp_rule_sets const & s, name const & id, expr const & e, expr const & h) {
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return add_core(tc, s, id, list<level>(), e, h);
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}
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simp_rule_sets join(simp_rule_sets const & s1, simp_rule_sets const & s2) {
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simp_rule_sets new_s1 = s1;
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s2.for_each_simp([&](name const & eqv, simp_rule const & r) {
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new_s1.insert(eqv, r);
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});
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return new_s1;
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}
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static name * g_class_name = nullptr;
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static std::string * g_key = nullptr;
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static simp_rule_sets add_core(type_checker & tc, simp_rule_sets const & s, name const & cname) {
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declaration const & d = tc.env().get(cname);
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buffer<level> us;
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unsigned num_univs = d.get_num_univ_params();
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for (unsigned i = 0; i < num_univs; i++) {
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us.push_back(mk_meta_univ(name(*g_prefix, i)));
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}
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levels ls = to_list(us);
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expr e = instantiate_type_univ_params(d, ls);
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expr h = mk_constant(cname, ls);
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return add_core(tc, s, cname, ls, e, h);
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}
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// Return true iff lhs is of the form (B (x : ?m1), ?m2) or (B (x : ?m1), ?m2 x),
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// where B is lambda or Pi
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static bool is_valid_congr_rule_binding_lhs(expr const & lhs, name_set & found_mvars) {
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lean_assert(is_binding(lhs));
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expr const & d = binding_domain(lhs);
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expr const & b = binding_body(lhs);
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if (!is_metavar(d))
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return false;
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if (is_metavar(b) && b != d) {
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found_mvars.insert(mlocal_name(b));
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found_mvars.insert(mlocal_name(d));
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return true;
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}
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if (is_app(b) && is_metavar(app_fn(b)) && is_var(app_arg(b), 0) && app_fn(b) != d) {
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found_mvars.insert(mlocal_name(app_fn(b)));
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found_mvars.insert(mlocal_name(d));
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return true;
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}
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return false;
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}
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// Return true iff all metavariables in e are in found_mvars
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static bool only_found_mvars(expr const & e, name_set const & found_mvars) {
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return !find(e, [&](expr const & m, unsigned) {
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return is_metavar(m) && !found_mvars.contains(mlocal_name(m));
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});
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}
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// Check whether rhs is of the form (mvar l_1 ... l_n) where mvar is a metavariable,
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// and l_i's are local constants, and mvar does not occur in found_mvars.
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// If it is return true and update found_mvars
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static bool is_valid_congr_hyp_rhs(expr const & rhs, name_set & found_mvars) {
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buffer<expr> rhs_args;
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expr const & rhs_fn = get_app_args(rhs, rhs_args);
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if (!is_metavar(rhs_fn) || found_mvars.contains(mlocal_name(rhs_fn)))
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return false;
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for (expr const & arg : rhs_args)
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if (!is_local(arg))
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return false;
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found_mvars.insert(mlocal_name(rhs_fn));
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return true;
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}
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void add_congr_core(environment const & env, simp_rule_sets & s, name const & n) {
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declaration const & d = env.get(n);
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type_checker tc(env);
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buffer<level> us;
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unsigned num_univs = d.get_num_univ_params();
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for (unsigned i = 0; i < num_univs; i++) {
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us.push_back(mk_meta_univ(name(*g_prefix, i)));
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}
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levels ls = to_list(us);
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expr pr = mk_constant(n, ls);
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expr e = instantiate_type_univ_params(d, ls);
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buffer<bool> explicit_args;
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buffer<expr> metas;
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unsigned idx = 0;
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while (is_pi(e)) {
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expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(e));
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idx++;
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explicit_args.push_back(is_explicit(binding_info(e)));
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metas.push_back(mvar);
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e = instantiate(binding_body(e), mvar);
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pr = mk_app(pr, mvar);
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}
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expr rel, lhs, rhs;
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if (!is_simp_relation(env, e, rel, lhs, rhs) || !is_constant(rel)) {
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throw exception(sstream() << "invalid congruence rule, '" << n
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<< "' resulting type is not of the form t ~ s, where '~' is a transitive and reflexive relation");
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}
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name_set found_mvars;
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buffer<expr> lhs_args, rhs_args;
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expr const & lhs_fn = get_app_args(lhs, lhs_args);
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expr const & rhs_fn = get_app_args(rhs, rhs_args);
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if (is_constant(lhs_fn)) {
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if (!is_constant(rhs_fn) || const_name(lhs_fn) != const_name(rhs_fn) || lhs_args.size() != rhs_args.size()) {
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throw exception(sstream() << "invalid congruence rule, '" << n
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<< "' resulting type is not of the form (" << const_name(lhs_fn) << " ...) "
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<< "~ (" << const_name(lhs_fn) << " ...), where ~ is '" << const_name(rel) << "'");
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}
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for (expr const & lhs_arg : lhs_args) {
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if (is_sort(lhs_arg))
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continue;
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if (!is_metavar(lhs_arg) || found_mvars.contains(mlocal_name(lhs_arg))) {
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throw exception(sstream() << "invalid congruence rule, '" << n
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<< "' the left-hand-side of the congruence resulting type must be of the form ("
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<< const_name(lhs_fn) << " x_1 ... x_n), where each x_i is a distinct variable or a sort");
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}
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found_mvars.insert(mlocal_name(lhs_arg));
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}
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} else if (is_binding(lhs)) {
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if (lhs.kind() != rhs.kind()) {
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throw exception(sstream() << "invalid congruence rule, '" << n
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<< "' kinds of the left-hand-side and right-hand-side of "
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<< "the congruence resulting type do not match");
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}
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if (!is_valid_congr_rule_binding_lhs(lhs, found_mvars)) {
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throw exception(sstream() << "invalid congruence rule, '" << n
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<< "' left-hand-side of the congruence resulting type must "
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<< "be of the form (fun/Pi (x : A), B x)");
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}
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} else {
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throw exception(sstream() << "invalid congruence rule, '" << n
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<< "' left-hand-side is not an application nor a binding");
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}
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buffer<expr> congr_hyps;
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lean_assert(metas.size() == explicit_args.size());
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for (unsigned i = 0; i < metas.size(); i++) {
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expr const & mvar = metas[i];
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if (explicit_args[i] && !found_mvars.contains(mlocal_name(mvar))) {
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buffer<expr> locals;
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expr type = mlocal_type(mvar);
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while (is_pi(type)) {
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expr local = mk_local(tc.mk_fresh_name(), binding_domain(type));
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locals.push_back(local);
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type = instantiate(binding_body(type), local);
|
|
}
|
|
expr h_rel, h_lhs, h_rhs;
|
|
if (!is_simp_relation(env, type, h_rel, h_lhs, h_rhs) || !is_constant(h_rel))
|
|
continue;
|
|
unsigned j = 0;
|
|
for (expr const & local : locals) {
|
|
j++;
|
|
if (!only_found_mvars(mlocal_type(local), found_mvars)) {
|
|
throw exception(sstream() << "invalid congruence rule, '" << n
|
|
<< "' argument #" << j << " of parameter #" << (i+1) << " contains "
|
|
<< "unresolved parameters");
|
|
}
|
|
}
|
|
if (!only_found_mvars(h_lhs, found_mvars)) {
|
|
throw exception(sstream() << "invalid congruence rule, '" << n
|
|
<< "' argument #" << (i+1) << " is not a valid hypothesis, the left-hand-side contains "
|
|
<< "unresolved parameters");
|
|
}
|
|
if (!is_valid_congr_hyp_rhs(h_rhs, found_mvars)) {
|
|
throw exception(sstream() << "invalid congruence rule, '" << n
|
|
<< "' argument #" << (i+1) << " is not a valid hypothesis, the right-hand-side must be "
|
|
<< "of the form (m l_1 ... l_n) where m is parameter that was not "
|
|
<< "'assigned/resolved' yet and l_i's are locals");
|
|
}
|
|
found_mvars.insert(mlocal_name(mvar));
|
|
congr_hyps.push_back(mvar);
|
|
}
|
|
}
|
|
congr_rule rule(n, ls, to_list(metas), lhs, rhs, pr, to_list(congr_hyps));
|
|
s.insert(const_name(rel), rule);
|
|
}
|
|
|
|
struct rrs_state {
|
|
simp_rule_sets m_sets;
|
|
name_set m_simp_names;
|
|
name_set m_congr_names;
|
|
|
|
void add_simp(environment const & env, name const & cname) {
|
|
type_checker tc(env);
|
|
m_sets = add_core(tc, m_sets, cname);
|
|
m_simp_names.insert(cname);
|
|
}
|
|
|
|
void add_congr(environment const & env, name const & n) {
|
|
add_congr_core(env, m_sets, n);
|
|
m_congr_names.insert(n);
|
|
}
|
|
};
|
|
|
|
struct rrs_config {
|
|
typedef pair<bool, name> entry;
|
|
typedef rrs_state state;
|
|
static void add_entry(environment const & env, io_state const &, state & s, entry const & e) {
|
|
if (e.first)
|
|
s.add_simp(env, e.second);
|
|
else
|
|
s.add_congr(env, e.second);
|
|
}
|
|
static name const & get_class_name() {
|
|
return *g_class_name;
|
|
}
|
|
static std::string const & get_serialization_key() {
|
|
return *g_key;
|
|
}
|
|
static void write_entry(serializer & s, entry const & e) {
|
|
s << e.first << e.second;
|
|
}
|
|
static entry read_entry(deserializer & d) {
|
|
entry e; d >> e.first >> e.second; return e;
|
|
}
|
|
static optional<unsigned> get_fingerprint(entry const & e) {
|
|
return some(hash(e.first ? 17 : 31, e.second.hash()));
|
|
}
|
|
};
|
|
|
|
template class scoped_ext<rrs_config>;
|
|
typedef scoped_ext<rrs_config> rrs_ext;
|
|
|
|
environment add_simp_rule(environment const & env, name const & n, bool persistent) {
|
|
return rrs_ext::add_entry(env, get_dummy_ios(), mk_pair(true, n), persistent);
|
|
}
|
|
|
|
environment add_congr_rule(environment const & env, name const & n, bool persistent) {
|
|
return rrs_ext::add_entry(env, get_dummy_ios(), mk_pair(false, n), persistent);
|
|
}
|
|
|
|
bool is_simp_rule(environment const & env, name const & n) {
|
|
return rrs_ext::get_state(env).m_simp_names.contains(n);
|
|
}
|
|
|
|
bool is_congr_rule(environment const & env, name const & n) {
|
|
return rrs_ext::get_state(env).m_congr_names.contains(n);
|
|
}
|
|
|
|
simp_rule_sets get_simp_rule_sets(environment const & env) {
|
|
return rrs_ext::get_state(env).m_sets;
|
|
}
|
|
|
|
simp_rule_sets get_simp_rule_sets(environment const & env, name const & ns) {
|
|
simp_rule_sets set;
|
|
list<pair<bool, name>> const * cnames = rrs_ext::get_entries(env, ns);
|
|
if (cnames) {
|
|
type_checker tc(env);
|
|
for (pair<bool, name> const & p : *cnames) {
|
|
set = add_core(tc, set, p.second);
|
|
}
|
|
}
|
|
return set;
|
|
}
|
|
|
|
io_state_stream const & operator<<(io_state_stream const & out, simp_rule_sets const & s) {
|
|
options const & opts = out.get_options();
|
|
out.get_stream() << mk_pair(s.pp(out.get_formatter()), opts);
|
|
return out;
|
|
}
|
|
|
|
void initialize_simp_rule_set() {
|
|
g_prefix = new name(name::mk_internal_unique_name());
|
|
g_class_name = new name("rrs");
|
|
g_key = new std::string("rrs");
|
|
rrs_ext::initialize();
|
|
}
|
|
|
|
void finalize_simp_rule_set() {
|
|
rrs_ext::finalize();
|
|
delete g_key;
|
|
delete g_class_name;
|
|
delete g_prefix;
|
|
}
|
|
}
|