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feat(library/simplifier): contextual simplification for A -> B

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-01-24 22:32:55 -08:00
parent c2381e43f1
commit 7a4eb4b8ed
3 changed files with 108 additions and 9 deletions
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69
src/library/simplifier/simplifier.cpp
View file

@ -100,6 +100,7 @@ unsigned get_simplifier_max_steps(options const & opts) { return opts.get_unsign
static name g_local("local");
static name g_C("C");
static name g_H("H");
static name g_x("x");
static name g_unique = name::mk_internal_unique_name();
@ -108,6 +109,7 @@ class simplifier_fn {
expr m_out; // the result of a simplification step
optional<expr> m_proof; // a proof that the result is equal to the input (when m_proofs_enabled)
bool m_heq_proof; // true if the proof is for heterogeneous equality
result() {}
explicit result(expr const & out, bool heq_proof = false):
m_out(out), m_heq_proof(heq_proof) {}
result(expr const & out, expr const & pr, bool heq_proof = false):
@ -920,22 +922,71 @@ class simplifier_fn {
result simplify_pi(expr const & e) {
lean_assert(is_pi(e));
// TODO(Leo): handle implication, i.e., e is_proposition and is_arrow
if (m_has_heq) {
expr const & d = abst_domain(e);
expr b = abst_body(e);
bool is_prop = is_proposition(e);
bool is_d_prop = is_proposition(d);
bool is_arr = is_arrow(e);
if (is_d_prop && is_arr) {
if (m_contextual) {
// Contextual simplification for A -> B
// Rewrite A to A'
// And rewrite B to B' using A'
result res_d = simplify(d);
ensure_homogeneous(d, res_d);
flet<unsigned> set_depth(m_contextual_depth, m_contextual_depth+1);
expr H_proof = mk_constant(name(g_unique, m_contextual_depth));
result res_b;
{
updt_rule_set update(m_rule_sets[0], res_d.m_out, H_proof);
freset<cache> m_reset_cache(m_cache); // must reset cache for the recursive call because we updated the rule_sets
set_context set(*this, extend(m_ctx, abst_name(e), res_d.m_out));
res_b = simplify(b);
}
ensure_homogeneous(b, res_b);
if (is_eqp(res_d.m_out, d) && is_eqp(res_b.m_out, b))
return rewrite(e, result(e));
expr out = update_pi(e, res_d.m_out, res_b.m_out);
if (!m_proofs_enabled)
return rewrite(e, result(out));
name C_name(g_C, m_contextual_depth); // H_name is a cryptic unique name
expr proof = mk_imp_congr_th(d, lower_free_vars(b, 1, 1),
res_d.m_out, lower_free_vars(res_b.m_out, 1, 1),
get_proof(res_d), mk_lambda(C_name, res_d.m_out, abstract(get_proof(res_b), H_proof)));
return rewrite(e, result(out, proof));
} else {
// Simplify A -> B (when m_contextual == false)
result res_d = simplify(d);
ensure_homogeneous(d, res_d);
set_context set(*this, extend(m_ctx, abst_name(e), res_d.m_out));
result res_b = simplify(b);
ensure_homogeneous(b, res_b);
if (is_eqp(res_d.m_out, d) && is_eqp(res_b.m_out, b))
return rewrite(e, result(e));
expr out = update_pi(e, res_d.m_out, res_b.m_out);
if (!m_proofs_enabled)
return rewrite(e, result(out));
expr proof = mk_imp_congr_th(d, lower_free_vars(b, 1, 1),
res_d.m_out, lower_free_vars(res_b.m_out, 1, 1),
get_proof(res_d), mk_lambda(g_H, res_d.m_out, get_proof(res_b)));
return rewrite(e, result(out, proof));
}
} else if (m_has_heq) {
// TODO(Leo)
return result(e);
} else if (is_proposition(e)) {
set_context set(*this, extend(m_ctx, abst_name(e), abst_domain(e)));
result res_body = simplify(abst_body(e));
} else if (is_prop) {
// Simplify (forall x : A, P x)
set_context set(*this, extend(m_ctx, abst_name(e), d));
result res_body = simplify(b);
lean_assert(!res_body.m_heq_proof);
expr new_body = res_body.m_out;
if (is_eqp(new_body, abst_body(e)))
if (is_eqp(new_body, b))
return rewrite(e, result(e));
expr out = mk_pi(abst_name(e), abst_domain(e), new_body);
expr out = mk_pi(abst_name(e), d, new_body);
if (!m_proofs_enabled || !res_body.m_proof)
return rewrite(e, result(out));
expr pr = mk_allext_th(abst_domain(e),
mk_lambda(e, abst_body(e)),
expr pr = mk_allext_th(d,
mk_lambda(e, b),
mk_lambda(e, abst_body(out)),
mk_lambda(e, *res_body.m_proof));
return rewrite(e, result(out, pr));

36
tests/lean/simp24.lean Normal file
View file

@ -0,0 +1,36 @@
rewrite_set simple
add_rewrite eq_id imp_truel imp_truer Nat::add_zeror : simple
variables a b : Nat
(*
local opts = options({"simplifier", "contextual"}, false)
local t = parse_lean('λ x, a = a → x = a')
local t2, pr = simplify(t, "simple", get_environment(), context(), opts)
print(t2)
print(pr)
get_environment():type_check(pr)
*)
(*
local opts = options({"simplifier", "contextual"}, false)
local t = parse_lean('λ x, x = a → x = x')
local t2, pr = simplify(t, "simple", get_environment(), context(), opts)
print(t2)
print(pr)
get_environment():type_check(pr)
*)
(*
local opts = options({"simplifier", "contextual"}, false)
local t = parse_lean('λ x, x = a + 0 → a = a')
local t2, pr = simplify(t, "simple", get_environment(), context(), opts)
print(t2)
print(pr)
*)
(*
local t = parse_lean('λ x, a + 0 = 1 → x > a')
local t2, pr = simplify(t, "simple")
print(t2)
print(pr)
get_environment():type_check(pr)
*)

12
tests/lean/simp24.lean.expected.out Normal file
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@ -0,0 +1,12 @@
Set: pp::colors
Set: pp::unicode
Assumed: a
Assumed: b
λ x : ℕ, x = a
funext (λ x : ℕ, trans (imp_congr (eq_id a) (λ H : ⊤, refl (x = a))) (imp_truel (x = a)))
λ x : ℕ, ⊤
funext (λ x : ℕ, trans (imp_congr (refl (x = a)) (λ H : x = a, eq_id x)) (imp_truer (x = a)))
λ x : ℕ, ⊤
funext (λ x : ℕ, trans (imp_congr (congr2 (eq x) (Nat::add_zeror a)) (λ H : x = a, eq_id a)) (imp_truer (x = a)))
λ x : ℕ, a = 1 → x > 1
funext (λ x : ℕ, imp_congr (congr1 1 (congr2 eq (Nat::add_zeror a))) (λ C::1 : a = 1, congr2 (Nat::gt x) C::1))