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feat(library/tactic/rewrite_tactic): add "reduce_to" step at rewrite tactic

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This commit is contained in:
Leonardo de Moura 2015-02-05 13:59:55 -08:00
parent 116c65bff5
commit ffe0d1186e
2 changed files with 104 additions and 24 deletions
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120
src/library/tactic/rewrite_tactic.cpp
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@ -458,37 +458,47 @@ class rewrite_fn {
return some_expr(r);
}
// Replace goal with definitionally equal one
void replace_goal(expr const & new_type) {
expr M = m_g.mk_meta(m_ngen.next(), new_type);
goal new_g(M, new_type);
expr val = m_g.abstract(M);
m_subst.assign(m_g.get_name(), val);
update_goal(new_g);
}
bool process_reduce_goal(optional<name> const & to_unfold) {
if (auto new_type = reduce(m_g.get_type(), to_unfold)) {
expr M = m_g.mk_meta(m_ngen.next(), *new_type);
goal new_g(M, *new_type);
expr val = m_g.abstract(M);
m_subst.assign(m_g.get_name(), val);
update_goal(new_g);
replace_goal(*new_type);
return true;
} else {
return false;
}
}
// Replace hypothesis type with definitionally equal one
void replace_hypothesis(expr const & hyp, expr const & new_hyp_type) {
expr new_hyp = update_mlocal(hyp, new_hyp_type);
buffer<expr> new_hyps;
m_g.get_hyps(new_hyps);
for (expr & h : new_hyps) {
if (mlocal_name(h) == mlocal_name(hyp)) {
h = new_hyp;
break;
}
}
expr new_type = m_g.get_type();
expr new_mvar = mk_metavar(m_ngen.next(), Pi(new_hyps, new_type));
expr new_meta = mk_app(new_mvar, new_hyps);
goal new_g(new_meta, new_type);
expr val = m_g.abstract(new_meta);
m_subst.assign(m_g.get_name(), val);
update_goal(new_g);
}
bool process_reduce_hypothesis(expr const & hyp, optional<name> const & to_unfold) {
if (auto new_hyp_type = reduce(mlocal_type(hyp), to_unfold)) {
expr new_hyp = update_mlocal(hyp, *new_hyp_type);
buffer<expr> new_hyps;
m_g.get_hyps(new_hyps);
for (expr & h : new_hyps) {
if (mlocal_name(h) == mlocal_name(hyp)) {
h = new_hyp;
break;
}
}
expr new_type = m_g.get_type();
expr new_mvar = mk_metavar(m_ngen.next(), Pi(new_hyps, new_type));
expr new_meta = mk_app(new_mvar, new_hyps);
goal new_g(new_meta, new_type);
expr val = m_g.abstract(new_meta);
m_subst.assign(m_g.get_name(), val);
update_goal(new_g);
replace_hypothesis(hyp, *new_hyp_type);
return true;
} else {
return false;
@ -520,14 +530,76 @@ class rewrite_fn {
return process_reduce_step(optional<name>(info.get_name()), info.get_location());
}
optional<expr> unify_with(expr const & t, expr const & e) {
auto ecs = m_elab(m_g, m_ngen.mk_child(), e, false);
expr new_e = ecs.first;
buffer<constraint> cs;
to_buffer(ecs.second, cs);
constraint_seq cs_seq;
if (!m_tc->is_def_eq(t, new_e, justification(), cs_seq))
return none_expr();
cs_seq.linearize(cs);
unifier_config cfg;
unify_result_seq rseq = unify(m_env, cs.size(), cs.data(), m_ngen.mk_child(), m_subst, cfg);
if (auto p = rseq.pull()) {
substitution new_subst = p->first.first;
constraints new_postponed = p->first.second;
if (new_postponed)
return none_expr(); // all constraints must be solved
new_e = new_subst.instantiate_all(new_e);
if (has_expr_metavar_strict(new_e))
return none_expr(); // new expressions was not completely instantiated
m_subst = new_subst;
return some_expr(new_e);
}
return none_expr();
}
bool process_reduce_to_goal(expr const & e) {
if (auto new_type = unify_with(m_g.get_type(), e)) {
replace_goal(*new_type);
return true;
} else {
return false;
}
}
bool process_reduce_to_hypothesis(expr const & hyp, expr const & e) {
if (auto new_hyp_type = unify_with(mlocal_type(hyp), e)) {
replace_hypothesis(hyp, *new_hyp_type);
return true;
} else {
return false;
}
}
bool process_reduce_to_step(expr const & e, location const & loc) {
if (loc.is_goal_only())
return process_reduce_to_goal(e);
bool progress = false;
buffer<expr> hyps;
m_g.get_hyps(hyps);
for (expr const & h : hyps) {
if (!loc.includes_hypothesis(local_pp_name(h)))
continue;
if (process_reduce_to_hypothesis(h, e))
progress = true;
}
if (loc.includes_goal()) {
if (process_reduce_to_goal(e))
progress = true;
}
return progress;
}
bool process_reduce_step(expr const & elem) {
lean_assert(is_rewrite_reduce_step(elem));
if (macro_num_args(elem) == 0) {
auto info = get_rewrite_reduce_info(elem);
return process_reduce_step(optional<name>(), info.get_location());
} else {
// TODO
return false;
auto info = get_rewrite_reduce_info(elem);
return process_reduce_to_step(macro_arg(elem, 0), info.get_location());
}
}
@ -676,7 +748,7 @@ class rewrite_fn {
rule = new_subst.instantiate_all(rule);
rule_type = new_subst.instantiate_all(rule_type);
if (has_expr_metavar_strict(rule) || has_expr_metavar_strict(rule_type))
return unify_result(); // rule was not completely instantiate.
return unify_result(); // rule was not completely instantiated.
m_subst = new_subst;
expr lhs = app_arg(app_fn(rule_type));
expr rhs = app_arg(rule_type);

8
tests/lean/run/rewrite9.lean Normal file
View file

@ -0,0 +1,8 @@
import data.nat
open nat
constant f : nat → nat
theorem tst1 (x y : nat) (H1 : (λ z, z + 0) x = y) (H2 : x = y + 0) (H3 : x = y * 0) : f x = f y :=
begin
rewrite [▸ x = y at (H1, H2), H2]
end