d4b08fcf96
Unification constraints of the form
ctx |- ?m[inst:i v] == T
and
ctx |- (?m a1 ... an) == T
are delayed by elaborator because the produce case-splits.
On the other hand, the step that puts terms is head-normal form is eagerly applied.
This is a bad idea for constraints like the two above. The elaborator will put T in head normal form
before executing process_meta_app and process_meta_inst. This is just wasted work, and creates
fully unfolded terms for solvers and provers.
The new test demonstrates the problem. In this test, we mark several terms as non-opaque.
Without this commit, the produced goal is a huge term.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
95 lines
4.6 KiB
Text
95 lines
4.6 KiB
Text
-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
|
||
-- Released under Apache 2.0 license as described in the file LICENSE.
|
||
-- Author: Leonardo de Moura
|
||
import macros
|
||
import pair
|
||
import subtype
|
||
import optional
|
||
using subtype
|
||
using optional
|
||
-- We are encoding the (sum A B) as a subtype of (optional A) # (optional B), where
|
||
-- (proj1 n = none) ≠ (proj2 n = none)
|
||
definition sum_pred (A B : (Type U)) := λ p : (optional A) # (optional B), (proj1 p = none) ≠ (proj2 p = none)
|
||
definition sum (A B : (Type U)) := subtype ((optional A) # (optional B)) (sum_pred A B)
|
||
|
||
namespace sum
|
||
theorem inl_pred {A : (Type U)} (a : A) (B : (Type U)) : sum_pred A B (pair (some a) none)
|
||
:= not_intro
|
||
(assume N : (some a = none) = (none = (@none B)),
|
||
have eq : some a = none,
|
||
from (symm N) ◂ (refl (@none B)),
|
||
show false,
|
||
from absurd eq (distinct a))
|
||
|
||
theorem inr_pred (A : (Type U)) {B : (Type U)} (b : B) : sum_pred A B (pair none (some b))
|
||
:= not_intro
|
||
(assume N : (none = (@none A)) = (some b = none),
|
||
have eq : some b = none,
|
||
from N ◂ (refl (@none A)),
|
||
show false,
|
||
from absurd eq (distinct b))
|
||
|
||
theorem inhabl {A : (Type U)} (H : inhabited A) (B : (Type U)) : inhabited (sum A B)
|
||
:= inhabited_elim H (take w : A,
|
||
subtype_inhabited (exists_intro (pair (some w) none) (inl_pred w B)))
|
||
|
||
theorem inhabr (A : (Type U)) {B : (Type U)} (H : inhabited B) : inhabited (sum A B)
|
||
:= inhabited_elim H (take w : B,
|
||
subtype_inhabited (exists_intro (pair none (some w)) (inr_pred A w)))
|
||
|
||
definition inl {A : (Type U)} (a : A) (B : (Type U)) : sum A B
|
||
:= abst (pair (some a) none) (inhabl (inhabited_intro a) B)
|
||
|
||
definition inr (A : (Type U)) {B : (Type U)} (b : B) : sum A B
|
||
:= abst (pair none (some b)) (inhabr A (inhabited_intro b))
|
||
|
||
theorem inl_inj {A B : (Type U)} {a1 a2 : A} : inl a1 B = inl a2 B → a1 = a2
|
||
:= assume Heq : inl a1 B = inl a2 B,
|
||
have eq1 : inl a1 B = abst (pair (some a1) none) (inhabl (inhabited_intro a1) B),
|
||
from refl (inl a1 B),
|
||
have eq2 : inl a2 B = abst (pair (some a2) none) (inhabl (inhabited_intro a1) B),
|
||
from subst (refl (inl a2 B)) (proof_irrel (inhabl (inhabited_intro a2) B) (inhabl (inhabited_intro a1) B)),
|
||
have rep_eq : (pair (some a1) none) = (pair (some a2) none),
|
||
from abst_inj (inhabl (inhabited_intro a1) B) (inl_pred a1 B) (inl_pred a2 B) (trans (trans (symm eq1) Heq) eq2),
|
||
show a1 = a2,
|
||
from optional::injectivity
|
||
(calc some a1 = proj1 (pair (some a1) (@none B)) : refl (some a1)
|
||
... = proj1 (pair (some a2) (@none B)) : pair_inj1 rep_eq
|
||
... = some a2 : refl (some a2))
|
||
|
||
theorem inr_inj {A B : (Type U)} {b1 b2 : B} : inr A b1 = inr A b2 → b1 = b2
|
||
:= assume Heq : inr A b1 = inr A b2,
|
||
have eq1 : inr A b1 = abst (pair none (some b1)) (inhabr A (inhabited_intro b1)),
|
||
from refl (inr A b1),
|
||
have eq2 : inr A b2 = abst (pair none (some b2)) (inhabr A (inhabited_intro b1)),
|
||
from subst (refl (inr A b2)) (proof_irrel (inhabr A (inhabited_intro b2)) (inhabr A (inhabited_intro b1))),
|
||
have rep_eq : (pair none (some b1)) = (pair none (some b2)),
|
||
from abst_inj (inhabr A (inhabited_intro b1)) (inr_pred A b1) (inr_pred A b2) (trans (trans (symm eq1) Heq) eq2),
|
||
show b1 = b2,
|
||
from optional::injectivity
|
||
(calc some b1 = proj2 (pair (@none A) (some b1)) : refl (some b1)
|
||
... = proj2 (pair (@none A) (some b2)) : pair_inj2 rep_eq
|
||
... = some b2 : refl (some b2))
|
||
|
||
theorem distinct {A B : (Type U)} (a : A) (b : B) : inl a B ≠ inr A b
|
||
:= assume N : inl a B = inr A b,
|
||
have eq1 : inl a B = abst (pair (some a) none) (inhabl (inhabited_intro a) B),
|
||
from refl (inl a B),
|
||
have eq2 : inr A b = abst (pair none (some b)) (inhabl (inhabited_intro a) B),
|
||
from subst (refl (inr A b)) (proof_irrel (inhabr A (inhabited_intro b)) (inhabl (inhabited_intro a) B)),
|
||
have rep_eq : (pair (some a) none) = (pair none (some b)),
|
||
from abst_inj (inhabl (inhabited_intro a) B) (inl_pred a B) (inr_pred A b) (trans (trans (symm eq1) N) eq2),
|
||
show false,
|
||
from absurd (pair_inj1 rep_eq) (optional::distinct a)
|
||
|
||
set_opaque optional false
|
||
set_opaque subtype false
|
||
set_opaque optional::some false
|
||
set_opaque optional::none false
|
||
set_opaque subtype::rep false
|
||
set_opaque subtype::abst false
|
||
set_opaque optional_pred false
|
||
|
||
theorem dichotomy {A B : (Type U)} (n : sum A B) : (∃ a, n = inl a B) ∨ (∃ b, n = inr A b)
|
||
:= let pred : (proj1 (rep n) = none) ≠ (proj2 (rep n) = none) := P_rep n
|
||
in _
|