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fix(library/blast/simplifier): remove unnecessary casts

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This commit is contained in:
Daniel Selsam 2015-11-16 16:00:00 -08:00
parent 550cac6065
commit b9a516783c
14 changed files with 161 additions and 135 deletions
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45
src/library/blast/simplifier.cpp
View file

@ -50,7 +50,7 @@
#define LEAN_DEFAULT_SIMPLIFY_FUSE false
#endif
#ifndef LEAN_DEFAULT_SIMPLIFY_NUMERALS
#define LEAN_DEFAULT_SIMPLIFY_NUMERALS true
#define LEAN_DEFAULT_SIMPLIFY_NUMERALS false
#endif
namespace lean {
@ -198,6 +198,7 @@ class simplifier {
}
expr unfold_reducible_instances(expr const & e);
expr remove_unnecessary_casts(expr const & e);
bool instantiate_emetas(blast_tmp_type_context & tmp_tctx, unsigned num_emeta,
list<expr> const & emetas, list<bool> const & instances);
@ -801,27 +802,59 @@ optional<result> simplifier::synth_congr(expr const & e, F && simp) {
expr proof = congr_lemma->get_proof();
expr type = congr_lemma->get_type();
unsigned i = 0;
bool simplified = false;
bool has_proof = false;
bool has_cast = false;
buffer<expr> locals;
for_each(congr_lemma->get_arg_kinds(), [&](congr_arg_kind const & ckind) {
proof = mk_app(proof, args[i]);
type = instantiate(binding_body(type), args[i]);
if (ckind == congr_arg_kind::Eq) {
result r_arg = simp(args[i]);
if (r_arg.has_proof()) simplified = true;
if (r_arg.has_proof()) has_proof = true;
r_arg = finalize(r_arg);
proof = mk_app(proof, r_arg.get_new(), r_arg.get_proof());
type = instantiate(binding_body(type), r_arg.get_new());
type = instantiate(binding_body(type), r_arg.get_proof());
} else if (ckind == congr_arg_kind::Cast) {
has_cast = true;
}
i++;
});
lean_assert(is_eq(type));
buffer<expr> type_args;
get_app_args(type, type_args);
expr & new_e = type_args[2];
if (simplified) return optional<result>(result(new_e, proof));
else return optional<result>(result(new_e));
expr e_new = remove_unnecessary_casts(type_args[2]);
if (has_proof) return optional<result>(result(e_new, proof));
else return optional<result>(result(e_new));
}
expr simplifier::remove_unnecessary_casts(expr const & e) {
buffer<expr> args;
expr f = get_app_args(e, args);
fun_info f_info = get_fun_info(f, args.size());
int i = -1;
for_each(f_info.get_params_info(), [&](param_info const & p_info) {
i++;
if (p_info.is_subsingleton()) {
while (is_constant(get_app_fn(args[i]))) {
buffer<expr> cast_args;
expr f_cast = get_app_args(args[i], cast_args);
name n_f = const_name(f_cast);
if (n_f == get_eq_rec_name() || n_f == get_eq_drec_name() || n_f == get_eq_nrec_name()) {
lean_assert(cast_args.size() == 6);
expr major_premise = cast_args[5];
expr f_major_premise = get_app_fn(major_premise);
if (is_constant(f_major_premise) && const_name(f_major_premise) == get_eq_refl_name())
args[i] = cast_args[3];
else
return;
} else {
return;
}
}
}
});
return mk_app(f, args);
}
/* Fusion */

13
tests/lean/simplifier10.lean
View file

@ -4,15 +4,14 @@ 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))
namespace tst
attribute px true_iff [simp]
attribute wxz [simp]
attribute vzy [simp]
attribute H [simp]
end tst
#simplify iff tst 0 P x
#simplify iff tst 0 W x z
#simplify iff tst 0 V z y
#simplify iff tst 0 Q z y x
#simplify iff tst 0 V z y ↔ Q z y x
#simplify iff env 0 P x
#simplify iff env 0 W x z
#simplify iff env 0 V z y
#simplify iff env 0 Q z y x
#simplify iff env 0 V z y ↔ Q z y x

28
tests/lean/simplifier11.lean
View file

@ -6,28 +6,28 @@ 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)
attribute dec_b [instance]
attribute dec_c [instance]
attribute h_c [simp]
attribute h_t [simp]
attribute h_e [simp]
attribute dec_c [instance]
attribute h_c [simp]
attribute h_t [simp]
attribute h_e [simp]
attribute if_congr [congr]
#simplify eq if_congr 0 (ite b x y)
#simplify eq env 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)
attribute dec_b [instance]
attribute h_c [simp]
attribute h_t [simp]
attribute h_e [simp]
attribute dec_b [instance]
attribute h_c [simp]
attribute h_t [simp]
attribute h_e [simp]
attribute if_ctx_simp_congr [congr]
-- TODO(Daniel): lean_unreachable
#simplify eq if_ctx_simp_congr 0 (ite b x y)
#simplify eq env 0 (ite b x y)
end if_ctx_simp_congr
@ -43,7 +43,7 @@ constants {b c x y u v : Prop} (dec_b : decidable b) (dec_c : decidable c)
attribute if_congr_prop [congr]
#simplify iff if_congr_prop 0 (ite b x y)
#simplify iff env 0 (ite b x y)
end if_congr_prop
namespace if_ctx_simp_congr_prop
@ -56,7 +56,7 @@ constants (b c x y u v : Prop) (dec_b : decidable b)
attribute h_e [simp]
attribute if_ctx_simp_congr_prop [congr]
#simplify iff if_ctx_simp_congr_prop 0 (ite b x y)
#simplify iff env 0 (ite b x y)
end if_ctx_simp_congr_prop
@ -70,5 +70,5 @@ constants (b c x y u v : Prop) (dec_b : decidable b)
attribute h_e [simp]
attribute if_simp_congr_prop [congr]
#simplify iff if_simp_congr_prop 0 (ite b x y)
#simplify iff env 0 (ite b x y)
end if_simp_congr_prop

7
tests/lean/simplifier13.lean
View file

@ -3,8 +3,7 @@ constants (T : Type.{l}) (f : T → T → T) (g : T → T)
constants (P : T → Prop) (Q : Prop) (Hfg : ∀ (x : T), f x x = g x)
constants (c : Π (x y z : T), P x → P y → P z → Q)
constants (x y z : T) (px : P (f x x)) (py : P (f y y)) (pz : P (g z))
namespace tst
attribute Hfg [simp]
end tst
-- TODO(Daniel): extra step? Similar to simplifier1.hlean
#simplify eq tst 0 c (f x x) (f y y) (g z) px py pz
#simplify eq env 0 c (f x x) (f y y) (g z) px py pz

2
tests/lean/simplifier13.lean.expected.out
View file

@ -1 +1 @@
c (g x) (g y) (g z) (eq.rec px (Hfg x)) (eq.rec py (Hfg y)) (eq.rec pz (eq.refl (g z)))
c (g x) (g y) (g z) (eq.rec px (Hfg x)) (eq.rec py (Hfg y)) pz

11
tests/lean/simplifier3.lean
View file

@ -7,13 +7,12 @@ constant T : Type.{l}
constants (x y z : T → T) (f g h : (T → T) → (T → T)) (a b c : T)
constants (Hfxgy : f x = g y) (Hgyhz : g y = h z) (Hab : a = b) (Hbc : b = c)
namespace tst
attribute Hfxgy [simp]
attribute Hgyhz [simp]
attribute Hab [simp]
attribute Hbc [simp]
end tst
#simplify eq tst 2 (f x a)
#simplify eq env 2 (f x a)
end test_congr
@ -23,9 +22,9 @@ universes l1 l2
constants (T : Type.{l1}) (U : T → Type.{l2})
constants (f g : Π (x:T), U x) (x y : T)
constants (Hfg : f = g) (Hxy : x = y)
namespace tst
attribute Hfg [simp]
attribute Hxy [simp]
end tst
#simplify eq tst 2 (f x)
#simplify eq env 2 (f x)
end test_congr_fun

18
tests/lean/simplifier4.lean
View file

@ -8,12 +8,12 @@ constants (R : T → T → Prop)
constants (R_refl : ∀ x, R x x) (R_sym : ∀ x y, R x y → R y x) (R_trans : ∀ x y z, R x y → R y z → R x z)
constants (Hfxgy : R (f x) (g y)) (Hgyhz : R (g y) (h z))
namespace tst attribute R_refl [refl] end tst
namespace tst attribute R_sym [symm] end tst
#simplify R tst 2 (f x) -- f x
namespace tst attribute R_trans [trans] end tst
#simplify R tst 2 (f x) -- f x
namespace tst attribute Hfxgy [simp] end tst
#simplify R tst 2 (f x) -- f x
namespace tst attribute Hgyhz [simp] end tst
#simplify R tst 2 (f x) -- f x
attribute R_refl [refl]
attribute R_sym [symm]
#simplify R env 2 (f x) -- f x
attribute R_trans [trans]
#simplify R env 2 (f x) -- f x
attribute Hfxgy [simp]
#simplify R env 2 (f x) -- f x
attribute Hgyhz [simp]
#simplify R env 2 (f x) -- f x

4
tests/lean/simplifier4.lean.expected.out
View file

@ -1,4 +1,4 @@
<refl>
<refl>
(refl): f x
(refl): f x
R (f x) (g y)
R (f x) (h z)

26
tests/lean/simplifier5.lean
View file

@ -1,16 +1,16 @@
/- Basic rewriting with iff with congr_iff -/
import logic.connectives
open nat
namespace tst
attribute iff_self true_iff_false self_lt_succ_iff_true zero_lt_succ_iff_true zero_le_iff_true succ_le_self_iff_false succ_le_self_iff_false lt_self_iff_false [simp]
end tst
#simplify iff tst 2 (@le nat nat_has_le 0 0) -- true
#simplify iff tst 2 (@le nat nat_has_le 0 1) -- true
#simplify iff tst 2 (@le nat nat_has_le 0 2) -- true
#simplify iff tst 2 (@lt nat nat_has_lt 0 0) -- false
#simplify iff tst 2 (@lt nat nat_has_lt 0 (succ 0)) -- true
#simplify iff tst 2 (@lt nat nat_has_lt 1 (succ 1)) -- true
#simplify iff tst 2 (@lt nat nat_has_lt 0 (succ (succ 0))) -- true
#simplify iff tst 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 0) -- true
#simplify iff tst 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 1) -- true
#simplify iff tst 2 (@le nat nat_has_le 0 0 ↔ @lt nat nat_has_lt 0 0) -- false
attribute not_true [simp]
#simplify iff env 2 (@le nat nat_has_le 0 0) -- true
#simplify iff env 2 (@le nat nat_has_le 0 1) -- true
#simplify iff env 2 (@le nat nat_has_le 0 2) -- true
#simplify iff env 2 (@lt nat nat_has_lt 0 0) -- false
#simplify iff env 2 (@lt nat nat_has_lt 0 (succ 0)) -- true
#simplify iff env 2 (@lt nat nat_has_lt 1 (succ 1)) -- true
#simplify iff env 2 (@lt nat nat_has_lt 0 (succ (succ 0))) -- true
#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 0) -- true
#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @le nat nat_has_le 0 1) -- true
#simplify iff env 2 (@le nat nat_has_le 0 0 ↔ @lt nat nat_has_lt 0 0) -- false

15
tests/lean/simplifier6.lean
View file

@ -3,29 +3,28 @@ import logic.connectives logic.quantifiers
namespace pi_congr1
constants (p1 q1 p2 q2 p3 q3 : Prop) (H1 : p1 ↔ q1) (H2 : p2 ↔ q2) (H3 : p3 ↔ q3)
namespace tst
attribute congr_forall [congr]
attribute congr_imp [congr]
attribute H1 [simp]
attribute H2 [simp]
attribute H3 [simp]
end tst
#simplify iff tst 1 p1 -- Broken?
#simplify iff tst 1 p1 → p2
#simplify iff tst 1 p1 → p2 → p3
#simplify iff env 1 p1 -- Broken?
#simplify iff env 1 p1 → p2
#simplify iff env 1 p1 → p2 → p3
end pi_congr1
namespace pi_congr2
universe l
constants (T : Type.{l}) (P Q : T → Prop) (H : ∀ (x : T), P x ↔ Q x)
namespace tst
attribute congr_forall [congr]
attribute H [simp]
end tst
constant (x : T)
#simplify iff tst 1 (∀ (x : T), P x)
#simplify iff env 1 (∀ (x : T), P x)
end pi_congr2

8
tests/lean/simplifier7.lean
View file

@ -4,13 +4,13 @@ import logic.connectives
constants (P1 Q1 P2 Q2 P3 Q3 : Prop) (H1 : P1 ↔ Q1) (H2 : P2 ↔ Q2) (H3 : P3 ↔ Q3)
constants (f g : Prop → Prop → Prop)
constants (Hf : and = f) (Hg : f = g)
namespace tst
attribute H1 [simp]
attribute H2 [simp]
attribute H3 [simp]
attribute Hf [simp]
attribute Hg [simp]
end tst
#simplify iff tst 2 (and P1 (and P2 P3))
#simplify iff tst 2 (and P1 (iff P2 P3))
#simplify iff env 2 (and P1 (and P2 P3))
#simplify iff env 2 (and P1 (iff P2 P3))

5
tests/lean/simplifier8.lean
View file

@ -6,10 +6,9 @@ constants (f_comm : ∀ x y, f x y = f y x)
(f_l : ∀ x y z, f (f x y) z = f x (f y z))
(f_r : ∀ x y z, f x (f y z) = f y (f x z))
namespace tst
attribute f_comm [simp]
attribute f_l [simp]
attribute f_r [simp]
end tst
#simplify eq tst 0 (f (f x2 x4) (f x5 (f x3 (f x1 x6))))
#simplify eq env 0 (f (f x2 x4) (f x5 (f x3 (f x1 x6))))

30
tests/lean/simplifier9.lean
View file

@ -1,30 +1,28 @@
-- Rewriting with (tmp)-local hypotheses
import logic.quantifiers
namespace tst
attribute congr_forall [congr]
attribute congr_imp [congr]
end tst
universe l
constants (T : Type.{l}) (P Q : T → Prop)
set_option simplify.max_steps 50000
constants (x y : T)
-- TODO(Daniel): the following is looping...
#simplify iff tst 0 x = y → x = y
#simplify iff tst 0 T → x = y → x = y
#simplify iff tst 0 ∀ z : T, x = z → x = y
#simplify iff tst 0 ∀ z : T, z = x → x = z
#simplify iff tst 0 ∀ (z w : T), x = y → x = y
#simplify iff tst 0 ∀ (z w : T), x = y → P x
#simplify iff tst 0 ∀ (H : ∀ x, P x ↔ Q x), P x
#simplify iff tst 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x) (q : Prop), P x
#simplify iff env 0 x = y → x = y
#simplify iff env 0 T → x = y → x = y
#simplify iff env 0 ∀ z : T, x = z → x = y
#simplify iff env 0 ∀ z : T, z = x → x = z
#simplify iff env 0 ∀ (z w : T), x = y → x = y
#simplify iff env 0 ∀ (z w : T), x = y → P x
#simplify iff tst 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x), p ∨ P x
#simplify iff tst 0 (∀ (x : T), P x ↔ Q x) → P x
#simplify iff tst 0 (∀ (x : T), P x ↔ Q x) → P x
#simplify iff tst 0 ∀ (x y : T), (∀ (x : T), P x ↔ Q x) → P x
#simplify iff env 0 ∀ (H : ∀ x, P x ↔ Q x), P x
#simplify iff env 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x) (q : Prop), P x
#simplify iff tst 0 ∀ (x z : T), x = z → (∀ (w : T), P w ↔ Q w) → P x
#simplify iff env 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x), p ∨ P x
#simplify iff env 0 (∀ (x : T), P x ↔ Q x) → P x
#simplify iff env 0 (∀ (x : T), P x ↔ Q x) → P x
#simplify iff env 0 ∀ (x y : T), (∀ (x : T), P x ↔ Q x) → P x
#simplify iff env 0 ∀ (x z : T), x = z → (∀ (w : T), P w ↔ Q w) → P x

84
tests/lean/simplifier_norm_num.lean
View file

@ -8,51 +8,51 @@ universe l
constants (A : Type.{l}) (A_comm_ring : comm_ring A)
attribute A_comm_ring [instance]
#simplify eq 0 (0:A) + 1
#simplify eq 0 (1:A) + 0
#simplify eq 0 (1:A) + 1
#simplify eq 0 (0:A) + 2
#simplify eq 0 (1:A) + 2
#simplify eq 0 (2:A) + 1
#simplify eq 0 (3:A) + 1
#simplify eq 0 (2:A) + 2
#simplify eq 0 (4:A) + 1
#simplify eq 0 (3:A) + 2
#simplify eq 0 (2:A) + 3
#simplify eq 0 (0:A) + 6
#simplify eq 0 (3:A) + 3
#simplify eq 0 (4:A) + 2
#simplify eq 0 (5:A) + 1
#simplify eq 0 (4:A) + 3
#simplify eq 0 (1:A) + 6
#simplify eq 0 (6:A) + 1
#simplify eq 0 (5:A) + 28
#simplify eq 0 (0 : A) + (2 + 3) + 7
#simplify eq 0 (70 : A) + (33 + 2)
#simplify eq env 0 (0:A) + 1
#simplify eq env 0 (1:A) + 0
#simplify eq env 0 (1:A) + 1
#simplify eq env 0 (0:A) + 2
#simplify eq env 0 (1:A) + 2
#simplify eq env 0 (2:A) + 1
#simplify eq env 0 (3:A) + 1
#simplify eq env 0 (2:A) + 2
#simplify eq env 0 (4:A) + 1
#simplify eq env 0 (3:A) + 2
#simplify eq env 0 (2:A) + 3
#simplify eq env 0 (0:A) + 6
#simplify eq env 0 (3:A) + 3
#simplify eq env 0 (4:A) + 2
#simplify eq env 0 (5:A) + 1
#simplify eq env 0 (4:A) + 3
#simplify eq env 0 (1:A) + 6
#simplify eq env 0 (6:A) + 1
#simplify eq env 0 (5:A) + 28
#simplify eq env 0 (0 : A) + (2 + 3) + 7
#simplify eq env 0 (70 : A) + (33 + 2)
#simplify eq 0 (23000000000 : A) + 22000000000
#simplify eq env 0 (23000000000 : A) + 22000000000
#simplify eq 0 (0 : A) * 0
#simplify eq 0 (0 : A) * 1
#simplify eq 0 (0 : A) * 2
#simplify eq 0 (2 : A) * 0
#simplify eq 0 (1 : A) * 0
#simplify eq 0 (1 : A) * 1
#simplify eq 0 (2 : A) * 1
#simplify eq 0 (1 : A) * 2
#simplify eq 0 (2 : A) * 2
#simplify eq 0 (3 : A) * 2
#simplify eq 0 (2 : A) * 3
#simplify eq 0 (4 : A) * 1
#simplify eq 0 (1 : A) * 4
#simplify eq 0 (3 : A) * 3
#simplify eq 0 (3 : A) * 4
#simplify eq 0 (4 : A) * 4
#simplify eq 0 (11 : A) * 2
#simplify eq 0 (15 : A) * 6
#simplify eq 0 (123456 : A) * 123456
#simplify eq env 0 (0 : A) * 0
#simplify eq env 0 (0 : A) * 1
#simplify eq env 0 (0 : A) * 2
#simplify eq env 0 (2 : A) * 0
#simplify eq env 0 (1 : A) * 0
#simplify eq env 0 (1 : A) * 1
#simplify eq env 0 (2 : A) * 1
#simplify eq env 0 (1 : A) * 2
#simplify eq env 0 (2 : A) * 2
#simplify eq env 0 (3 : A) * 2
#simplify eq env 0 (2 : A) * 3
#simplify eq env 0 (4 : A) * 1
#simplify eq env 0 (1 : A) * 4
#simplify eq env 0 (3 : A) * 3
#simplify eq env 0 (3 : A) * 4
#simplify eq env 0 (4 : A) * 4
#simplify eq env 0 (11 : A) * 2
#simplify eq env 0 (15 : A) * 6
#simplify eq env 0 (123456 : A) * 123456
#simplify eq 0 (0 + 45343453:A) * (53653343 + 1) * (53453 + 2) + (0 + 1 + 2 + 2200000000034733)
#simplify eq env 0 (0 + 45343453:A) * (53653343 + 1) * (53453 + 2) + (0 + 1 + 2 + 2200000000034733)
-- The following test is too slow
-- #simplify eq 0 (23000000000343434534345316:A) * (53653343563534534 + 5367536453653573573453) * 53453756475777536 + 2200000000034733531531531534536