feat(library/tactic/rewrite_tactic): elaborate rewrite rule using unifier
This commit is contained in:
Leonardo de Moura
parent
49323ab598
commit
09818adf90
1 changed files with 117 additions and 28 deletions
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@ -15,9 +15,13 @@ Author: Leonardo de Moura
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#include "library/util.h"
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#include "library/match.h"
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#include "library/projection.h"
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#include "library/local_context.h"
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#include "library/unifier.h"
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#include "library/util.h"
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#include "library/generic_exception.h"
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#include "library/tactic/rewrite_tactic.h"
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#include "library/tactic/expr_to_tactic.h"
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#include "library/tactic/class_instance_synth.h"
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// #define TRACE_MATCH_PLUGIN
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@ -339,6 +343,7 @@ class rewrite_fn {
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type_checker_ptr m_tc;
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rewrite_match_plugin m_mplugin;
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goal m_g;
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local_context m_ctx;
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substitution m_subst;
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expr m_expr_loc; // auxiliary expression used for error localization
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@ -353,6 +358,13 @@ class rewrite_fn {
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throw_generic_exception(strm, m_expr_loc);
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}
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void update_goal(goal const & g) {
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m_g = g;
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buffer<expr> hyps;
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g.get_hyps(hyps);
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m_ctx = local_context(to_list(hyps));
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}
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expr mk_meta(expr const & type) {
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return m_g.mk_meta(m_ngen.next(), type);
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}
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@ -473,10 +485,87 @@ class rewrite_fn {
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e = none_expr();
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}
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optional<expr> find_target(expr const & e, expr const & pattern) {
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optional<expr> found;
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pair<expr, constraint> mk_class_instance_elaborator(expr const & type) {
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unifier_config cfg;
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cfg.m_conservative = true;
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bool use_local_instances = true;
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bool is_strict = false;
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return ::lean::mk_class_instance_elaborator(m_env, m_ios, m_ctx, m_ngen.next(), optional<name>(),
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m_ps.relax_main_opaque(), use_local_instances, is_strict,
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some_expr(type), m_expr_loc.get_tag(), cfg, nullptr);
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}
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// rule, new_t
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typedef optional<pair<expr, expr>> unify_result;
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unify_result unify_target(expr const & t, expr const & pre_elem) {
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try {
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expr rule = get_rewrite_rule(pre_elem);
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auto rcs = m_elab(m_g, m_ngen.mk_child(), rule, false);
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rule = rcs.first;
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buffer<constraint> cs;
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to_buffer(rcs.second, cs);
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constraint_seq cs_seq;
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expr rule_type = m_tc->whnf(m_tc->infer(rule, cs_seq), cs_seq);
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while (is_pi(rule_type)) {
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expr meta;
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if (binding_info(rule_type).is_inst_implicit()) {
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auto mc = mk_class_instance_elaborator(binding_domain(rule_type));
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meta = mc.first;
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cs_seq += mc.second;
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} else {
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meta = mk_meta(binding_domain(rule_type));
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}
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rule_type = m_tc->whnf(instantiate(binding_body(rule_type), meta), cs_seq);
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rule = mk_app(rule, meta);
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}
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lean_assert(is_eq(rule_type));
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bool symm = get_rewrite_info(pre_elem).symm();
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expr src;
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if (symm)
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src = app_arg(rule_type);
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else
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src = app_arg(app_fn(rule_type));
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if (!m_tc->is_def_eq(t, src, justification(), cs_seq))
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return unify_result();
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cs_seq.linearize(cs);
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unifier_config cfg;
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cfg.m_conservative = false;
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unify_result_seq rseq = unify(m_env, cs.size(), cs.data(), m_ngen.mk_child(), m_subst, cfg);
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if (auto p = rseq.pull()) {
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substitution new_subst = p->first.first;
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constraints new_postponed = p->first.second;
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if (new_postponed)
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return unify_result(); // all constraints must be solved
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rule = new_subst.instantiate_all(rule);
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rule_type = new_subst.instantiate_all(rule_type);
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if (has_expr_metavar_strict(rule) || has_expr_metavar_strict(rule_type))
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return unify_result(); // rule was not completely instantiate.
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m_subst = new_subst;
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expr lhs = app_arg(app_fn(rule_type));
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expr rhs = app_arg(rule_type);
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if (symm) {
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rule = mk_symm(*m_tc, rule);
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return unify_result(rule, lhs);
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} else {
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return unify_result(rule, rhs);
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}
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}
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} catch (exception&) {}
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return unify_result();
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}
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// target, rule, new_target : represents the rewrite rule : target = new_target
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typedef optional<std::tuple<expr, expr, expr>> find_result;
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// Search for \c pattern in \c e. If \c t is a match, then try to unify the type of the rule
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// in the rewrite step \c pre_elem with \c t.
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// When successful, this method returns the target \c t, the fully elaborated rule \c r,
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// and the new value \c new_t (i.e., the expression that will replace \c t).
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find_result find_target(expr const & e, expr const & pattern, expr const & pre_elem) {
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find_result result;
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for_each(e, [&](expr const & t, unsigned) {
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if (found)
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if (result)
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return false; // stop search
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if (closed(t)) {
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lean_assert(std::all_of(m_esubst.begin(), m_esubst.end(), [&](optional<expr> const & e) { return !e; }));
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@ -485,52 +574,52 @@ class rewrite_fn {
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if (assigned)
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reset_subst();
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if (r) {
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found = t;
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return false;
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if (auto p = unify_target(t, pre_elem)) {
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result = std::make_tuple(t, p->first, p->second);
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return false;
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}
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}
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}
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return true;
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});
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return found;
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return result;
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}
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bool process_rewrite_hypothesis(expr const & hyp, expr const & elem, expr const & pattern) {
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bool process_rewrite_hypothesis(expr const & hyp, expr const & elem, expr const & pre_elem, expr const & pattern) {
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// TODO(Leo)
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return false;
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}
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bool process_rewrite_goal(expr const & elem, expr const & pattern) {
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bool process_rewrite_goal(expr const & elem, expr const & pre_elem, expr const & pattern) {
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expr goal_type = m_g.get_type();
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if (auto it = find_target(goal_type, pattern)) {
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regular(m_env, m_ios) << "found: " << *it << "\n";
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if (auto it = find_target(goal_type, pattern, pre_elem)) {
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regular(m_env, m_ios) << "FOUND\n" << std::get<0>(*it) << "\n==\n" << std::get<1>(*it) << "\n==>\n" << std::get<2>(*it) << "\n";
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// TODO(Leo)
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return false;
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} else {
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return false;
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}
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return false;
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}
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bool process_rewrite_single_step(expr const & elem, expr const & pattern) {
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bool process_rewrite_single_step(expr const & elem, expr const & pre_elem, expr const & pattern) {
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check_system("rewrite tactic");
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rewrite_info const & info = get_rewrite_info(elem);
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location const & loc = info.get_location();
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if (loc.is_goal_only())
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return process_rewrite_goal(elem, pattern);
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return process_rewrite_goal(elem, pre_elem, pattern);
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bool progress = false;
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buffer<expr> hyps;
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m_g.get_hyps(hyps);
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for (expr const & h : hyps) {
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if (!loc.includes_hypothesis(local_pp_name(h)))
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continue;
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if (process_rewrite_hypothesis(h, elem, pattern))
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if (process_rewrite_hypothesis(h, elem, pre_elem, pattern))
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progress = true;
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}
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if (loc.includes_goal() && process_rewrite_goal(elem, pattern))
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if (loc.includes_goal() && process_rewrite_goal(elem, pre_elem, pattern))
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progress = true;
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return progress;
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}
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bool process_rewrite_step(expr const & elem) {
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bool process_rewrite_step(expr const & elem, expr const & pre_elem) {
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lean_assert(is_rewrite_step(elem));
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expr pattern = get_pattern(elem);
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regular(m_env, m_ios) << "pattern: " << pattern << "\n";
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@ -538,31 +627,31 @@ class rewrite_fn {
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unsigned num;
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switch (info.get_multiplicity()) {
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case rewrite_info::Once:
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return process_rewrite_single_step(elem, pattern);
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return process_rewrite_single_step(elem, pre_elem, pattern);
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case rewrite_info::AtMostN:
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num = info.num();
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for (unsigned i = 0; i < num; i++) {
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if (!process_rewrite_single_step(elem, pattern))
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if (!process_rewrite_single_step(elem, pre_elem, pattern))
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return true;
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}
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return true;
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case rewrite_info::ExactlyN:
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num = info.num();
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for (unsigned i = 0; i < num; i++) {
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if (!process_rewrite_single_step(elem, pattern))
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if (!process_rewrite_single_step(elem, pre_elem, pattern))
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return false;
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}
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return true;
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case rewrite_info::ZeroOrMore:
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while (true) {
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if (!process_rewrite_single_step(elem, pattern))
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if (!process_rewrite_single_step(elem, pre_elem, pattern))
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return true;
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}
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case rewrite_info::OneOrMore:
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if (!process_rewrite_single_step(elem, pattern))
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if (!process_rewrite_single_step(elem, pre_elem, pattern))
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return false;
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while (true) {
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if (!process_rewrite_single_step(elem, pattern))
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if (!process_rewrite_single_step(elem, pre_elem, pattern))
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return true;
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}
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}
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@ -571,11 +660,11 @@ class rewrite_fn {
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// Process the given rewrite element/step. This method destructively update
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// m_g, m_subst, m_ngen. It returns true if it succeeded and false otherwise.
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bool process_step(expr const & elem) {
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bool process_step(expr const & elem, expr const & pre_elem) {
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if (is_rewrite_unfold_step(elem)) {
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return process_unfold_step(elem);
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} else {
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return process_rewrite_step(elem);
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return process_rewrite_step(elem, pre_elem);
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}
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}
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@ -586,7 +675,7 @@ public:
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m_mplugin(m_ios, *m_tc) {
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goals const & gs = m_ps.get_goals();
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lean_assert(gs);
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m_g = head(gs);
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update_goal(head(gs));
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m_subst = m_ps.get_subst();
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}
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@ -598,7 +687,7 @@ public:
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lean_assert(elems.size() == new_elems.size());
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for (unsigned i = 0; i < new_elems.size(); i++) {
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flet<expr> set1(m_expr_loc, elems[i]);
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if (!process_step(new_elems[i])) {
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if (!process_step(new_elems[i], elems[i])) {
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return proof_state_seq();
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}
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}
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