feat(library/blast/simplifier): conditional rewriting

This commit is contained in:
Daniel Selsam 2015-11-07 12:54:01 -08:00 committed by Leonardo de Moura
parent d4e410162b
commit 6c2c82f47c
10 changed files with 182 additions and 28 deletions

View file

@ -1335,6 +1335,7 @@ static environment simplify_cmd(parser & p) {
}
else {
auto tc = mk_type_checker(p.env(), p.mk_ngen());
expr pf_type = tc->check(r.get_proof(), ls).first;
if (o == 0) p.regular_stream() << r.get_new() << endl;

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@ -97,7 +97,6 @@ class simplifier {
branch m_branch;
name m_rel;
list<expr> m_local_ctx;
simp_rule_sets m_ctx_srss;
/* Logging */
@ -250,7 +249,7 @@ result simplifier::simplify(expr const & e) {
flet<unsigned> inc_depth(m_depth, m_depth+1);
if (m_trace) {
ios().get_diagnostic_channel() << m_depth << "." << m_rel << "." << m_local_ctx << " " << e << "\n";
ios().get_diagnostic_channel() << m_depth << "." << m_rel << ": " << e << "\n";
}
if (m_num_steps > m_max_steps)
@ -335,7 +334,6 @@ result simplifier::simplify_pi(expr const & e) {
result simplifier::simplify_app(expr const & e) {
lean_assert(is_app(e));
// TODO simplify operator as well, in cases (1) and (2)
/* (1) Try user-defined congruences */
result r = try_congrs(e);
@ -419,8 +417,9 @@ result simplifier::rewrite(expr const & e, simp_rule const & sr) {
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() << "[" << sr.get_lhs() << " =?= " << sr.get_rhs() << "] ==> ";
ios().get_diagnostic_channel() << "[" << new_lhs << " =?= " << new_rhs << "]\n";
ios().get_diagnostic_channel()
<< "REW(" << sr.get_id() << ") "
<< "[" << new_lhs << " =?= " << new_rhs << "]\n";
}
/* Traverse metavariables backwards */
@ -429,27 +428,39 @@ result simplifier::rewrite(expr const & e, simp_rule const & sr) {
bool is_instance = sr.is_instance(i);
if (is_instance) {
expr type = tmp_tctx->instantiate_uvars_mvars(tmp_tctx->infer(m));
if (auto v = tmp_tctx->mk_class_instance(type)) {
if (!tmp_tctx->force_assign(m, *v))
expr m_type = tmp_tctx->instantiate_uvars_mvars(tmp_tctx->infer(m));
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";
}
return result(e);
}
} else {
if (m_trace) {
ios().get_diagnostic_channel() << "unable to synthesize instance for: " << m_type << "\n";
}
return result(e);
}
}
if (tmp_tctx->is_mvar_assigned(i)) continue;
// TODO REMOVE DEBUG
expr m_assigned = tmp_tctx->instantiate_uvars_mvars(m);
if (tmp_tctx->is_prop(tmp_tctx->infer(m))) {
// TODO try to prove
return result(e);
expr m_type = tmp_tctx->instantiate_uvars_mvars(tmp_tctx->infer(m));
if (tmp_tctx->is_prop(m_type)) {
flet<name> set_name(m_rel,get_iff_name());
result r_cond = simplify(m_type);
if (is_constant(r_cond.get_new()) && const_name(r_cond.get_new()) == get_true_name()) {
auto pf = m_app_builder.mk_app(name("iff","elim_right"),finalize(r_cond).get_proof(),mk_constant(get_true_intro_name()));
lean_assert(pf);
bool success = tmp_tctx->is_def_eq(m,*pf);
lean_assert(success);
continue;
}
}
if (m_trace) {
ios().get_diagnostic_channel() << "failed to assign: " << m << "\n";
ios().get_diagnostic_channel() << "failed to assign: " << m << " : " << m_type << "\n";
}
/* We fail if there is a meta variable that we still cannot assign */
@ -459,17 +470,23 @@ result simplifier::rewrite(expr const & e, simp_rule const & sr) {
for (unsigned i = 0; i < sr.get_num_umeta(); i++) {
if (!tmp_tctx->is_uvar_assigned(i)) return result(e);
}
expr e_s = tmp_tctx->instantiate_uvars_mvars(sr.get_rhs());
if (sr.is_perm() && !is_lt(e_s,e,false)) 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(result(e_s,pf));
return result(result(new_rhs,pf));
}
/* Congruence */
result simplifier::congr(result const & r_f, result const & r_arg) {
lean_assert(!r_f.is_none() && !r_arg.is_none());
// theorem congr {A B : Type} {f₁ f₂ : A → B} {a₁ a₂ : A} (H₁ : f₁ = f₂) (H₂ : a₁ = a₂) : f₁ a₁ = f₂ a₂
@ -546,11 +563,11 @@ result simplifier::try_congr(expr const & e, congr_rule const & cr) {
for_each(congr_hyps,[&](expr const & m) {
if (failed) return;
buffer<expr> ls;
expr m_type = tmp_tctx->infer(m);
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(e));
expr l = tmp_tctx->mk_tmp_local(d,binding_info(m_type));
ls.push_back(l);
m_type = instantiate(binding_body(m_type),l);
}
@ -563,10 +580,7 @@ result simplifier::try_congr(expr const & e, congr_rule const & cr) {
flet<simplify_caches> set_simplify_caches(m_simplify_caches,fresh_caches);
flet<name> set_name(m_rel,const_name(h_rel));
buffer<expr> ls_instantiated;
for (unsigned i = 0; i < ls.size(); i++) ls_instantiated.push_back(tmp_tctx->instantiate_uvars_mvars(ls[i]));
flet<simp_rule_sets> set_ctx_srss(m_ctx_srss,add_to_srss(m_ctx_srss,ls_instantiated));
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);
result r_congr_hyp = simplify(h_lhs);
@ -579,8 +593,7 @@ result simplifier::try_congr(expr const & e, congr_rule const & cr) {
simplified = true;
}
hyp = Fun(ls_instantiated,hyp);
if (!tmp_tctx->is_def_eq(m,hyp)) failed = true;
if (!tmp_tctx->is_def_eq(m,Fun(ls,hyp))) failed = true;
}
});

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@ -100,7 +100,7 @@ class to_ceqvs_fn {
}
if (is_standard(m_env) && is_prop(e)) {
expr new_e = mk_iff(e, mk_true());
expr new_H = mk_app(mk_constant(get_iff_true_intro_name()), arg1, H);
expr new_H = mk_app(mk_constant(get_iff_true_intro_name()), e, H);
return mk_singleton(new_e, new_H);
} else {
return list<expr_pair>();

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@ -0,0 +1,19 @@
import logic.connectives logic.quantifiers
universe l
constants (T : Type.{l}) (x y z : T) (P : T → Prop) (Q : T → T → T → Prop) (R W V : T → T → Prop)
constants (px : P x) (wxz : W x z) (vzy : V z y)
constants (H : ∀ (x y z : T), P x → W x z → V z y → (Q z y x ↔ R x y))
attribute px [simp]
attribute wxz [simp]
attribute vzy [simp]
attribute H [simp]
#simplify iff 0 P x
#simplify iff 0 W x z
#simplify iff 0 V z y
#simplify iff 0 Q z y x
#simplify iff 0 V z y ↔ Q z y x

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@ -0,0 +1,5 @@
true
true
true
R x y
R x y

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@ -0,0 +1,74 @@
-- Conditional congruence
import logic.connectives logic.quantifiers
namespace if_congr
constants {A : Type} {b c : Prop} (dec_b : decidable b) (dec_c : decidable c)
{x y u v : A} (h_c : b ↔ c) (h_t : x = u) (h_e : y = v)
local attribute dec_b [instance]
local attribute dec_c [instance]
local attribute h_c [simp]
local attribute h_t [simp]
local attribute h_e [simp]
attribute if_congr [congr]
#simplify eq 0 (ite b x y)
end if_congr
namespace if_ctx_simp_congr
constants {A : Type} {b c : Prop} (dec_b : decidable b)
{x y u v : A} (h_c : b ↔ c) (h_t : c → x = u) (h_e : ¬c → y = v)
local attribute dec_b [instance]
local attribute h_c [simp]
local attribute h_t [simp]
local attribute h_e [simp]
attribute if_ctx_simp_congr [congr]
#simplify eq 0 (ite b x y)
end if_ctx_simp_congr
namespace if_congr_prop
constants {b c x y u v : Prop} (dec_b : decidable b) (dec_c : decidable c)
(h_c : b ↔ c) (h_t : c → (x ↔ u)) (h_e : ¬c → (y ↔ v))
local attribute dec_b [instance]
local attribute dec_c [instance]
local attribute h_c [simp]
local attribute h_t [simp]
local attribute h_e [simp]
attribute if_congr_prop [congr]
#simplify iff 0 (ite b x y)
end if_congr_prop
namespace if_ctx_simp_congr_prop
constants (b c x y u v : Prop) (dec_b : decidable b)
(h_c : b ↔ c) (h_t : c → (x ↔ u)) (h_e : ¬ c → (y ↔ v))
local attribute dec_b [instance]
local attribute h_c [simp]
local attribute h_t [simp]
local attribute h_e [simp]
attribute if_ctx_simp_congr_prop [congr]
#simplify iff 0 (ite b x y)
end if_ctx_simp_congr_prop
namespace if_simp_congr_prop
constants (b c x y u v : Prop) (dec_b : decidable b)
(h_c : b ↔ c) (h_t : x ↔ u) (h_e : y ↔ v)
local attribute dec_b [instance]
local attribute h_c [simp]
local attribute h_t [simp]
local attribute h_e [simp]
attribute if_simp_congr_prop [congr]
#simplify iff 0 (ite b x y)
end if_simp_congr_prop

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@ -0,0 +1,5 @@
ite c u v
ite c u v
ite c u v
ite c u v
ite c u v

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@ -0,0 +1,23 @@
import algebra.ring
open algebra
set_option simplify.max_steps 1000
universe l
constants (T : Type.{l}) (s : algebra.comm_ring T)
constants (x1 x2 x3 x4 : T) (f g : T → T)
attribute s [instance]
attribute add.comm [simp]
attribute add.assoc [simp]
attribute left_distrib [simp]
attribute right_distrib [simp]
attribute mul.comm [simp]
attribute mul.assoc [simp]
theorem add.o2 [simp] {A : Type} [s : add_comm_semigroup A] (a b c : A) :
a + (b + c) = b + (a + c) := sorry
#simplify eq 0 x2 + (g x1 + (f x3 * 3 * (x2 + g x1 * 7) * x2)) + 5 * (x4 + f x1)

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@ -0,0 +1 @@
x2 + (g x1 + (x4 * 5 + (f x1 * 5 + (x2 * (f x3 * (x2 * 3)) + x2 * (f x3 * (3 * (g x1 * 7)))))))

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@ -0,0 +1,13 @@
x = y → y = y
T → x = y → y = y
∀ (x_1 : T), x = x_1 → x_1 = y
∀ (x_1 : T), x_1 = x → x = x
T → T → x = y → y = y
T → T → x = y → P y
(∀ (x : T), P x ↔ Q x) → Q x
Prop → (∀ (x : T), P x ↔ Q x) → Prop → Q x
∀ (x_1 : Prop), (∀ (x : T), P x ↔ Q x) → x_1 Q x
(∀ (x : T), P x ↔ Q x) → Q x
(∀ (x : T), P x ↔ Q x) → Q x
∀ (x : T), T → (∀ (x : T), P x ↔ Q x) → Q x
∀ (x x_1 : T), x = x_1 → (∀ (w : T), P w ↔ Q w) → Q x_1