diff options
Diffstat (limited to 'Precond.agda')
| -rw-r--r-- | Precond.agda | 34 |
1 files changed, 17 insertions, 17 deletions
diff --git a/Precond.agda b/Precond.agda index afb77d8..cf7c1dc 100644 --- a/Precond.agda +++ b/Precond.agda @@ -25,7 +25,7 @@ open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨ open import Relation.Nullary using (yes ; no) open import Generic using (mapMV ; sequenceV ; sequence-map) -open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; lemma-lookupM-empty ; delete-many ; lemma-tabulate-∘ ; delete ; lemma-lookupM-delete) +open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; lemma-lookupM-empty ; delete-many ; lemma-tabulate-∘ ; delete ; lemma-lookupM-delete ; lemma-lookupM-fromFunc) import CheckInsert open CheckInsert (decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other) import BFF @@ -43,33 +43,33 @@ lemma-maybe-just : {A : Set} → (a : A) → (ma : Maybe A) → maybe′ Maybe.j lemma-maybe-just a (just x) = refl lemma-maybe-just a nothing = refl -lemma-union-delete-fromFunc : {m n : ℕ} {A : Set} {is : Vec (Fin n) m} {h : FinMapMaybe n A} {g : Vec A n} → (toList is) in-domain-of h → ∃ λ v → union h (delete-many is (map just g)) ≡ map just v +lemma-union-delete-fromFunc : {m n : ℕ} {A : Set} {is : Vec (Fin n) m} {h : FinMapMaybe n A} {g : Fin n → A} → (toList is) in-domain-of h → ∃ λ v → union h (delete-many is (fromFunc g)) ≡ map just v lemma-union-delete-fromFunc {is = []} {h = h} {g = g} p = _ , (begin - union h (map just g) + union h (fromFunc g) ≡⟨ lemma-tabulate-∘ (λ f → begin - maybe′ just (lookup f (map just g)) (lookup f h) - ≡⟨ cong (flip (maybe′ just) (lookup f h)) (lemma-lookup-map-just f g) ⟩ - maybe′ just (just (lookup f g)) (lookup f h) - ≡⟨ lemma-maybe-just (lookup f g) (lookup f h) ⟩ - just (maybe′ id (lookup f g) (lookup f h)) ∎) ⟩ - tabulate (λ f → just (maybe′ id (lookup f g) (lookup f h))) - ≡⟨ tabulate-∘ just (λ f → maybe′ id (lookup f g) (lookup f h)) ⟩ - map just (tabulate (λ f → maybe′ id (lookup f g) (lookup f h))) ∎) + maybe′ just (lookup f (fromFunc g)) (lookup f h) + ≡⟨ cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-fromFunc g f) ⟩ + maybe′ just (just (g f)) (lookup f h) + ≡⟨ lemma-maybe-just (g f) (lookup f h) ⟩ + just (maybe′ id (g f) (lookup f h)) ∎) ⟩ + tabulate (λ f → just (maybe′ id (g f) (lookup f h))) + ≡⟨ tabulate-∘ just (λ f → maybe′ id (g f) (lookup f h)) ⟩ + map just (tabulate (λ f → maybe′ id (g f) (lookup f h))) ∎) lemma-union-delete-fromFunc {n = n} {is = i ∷ is} {h = h} {g = g} (Data.List.All._∷_ (x , px) ps) = _ , (begin - union h (delete i (delete-many is (map just g))) + union h (delete i (delete-many is (fromFunc g))) ≡⟨ lemma-tabulate-∘ inner ⟩ - union h (delete-many is (map just g)) + union h (delete-many is (fromFunc g)) ≡⟨ proj₂ (lemma-union-delete-fromFunc ps) ⟩ map just _ ∎) - where inner : (f : Fin n) → maybe′ just (lookupM f (delete i (delete-many is (map just g)))) (lookup f h) ≡ maybe′ just (lookupM f (delete-many is (map just g))) (lookup f h) + where inner : (f : Fin n) → maybe′ just (lookupM f (delete i (delete-many is (fromFunc g)))) (lookup f h) ≡ maybe′ just (lookupM f (delete-many is (fromFunc g))) (lookup f h) inner f with f ≟ i inner .i | yes refl = begin - maybe′ just (lookupM i (delete i (delete-many is (map just g)))) (lookup i h) + maybe′ just (lookupM i (delete i (delete-many is (fromFunc g)))) (lookup i h) ≡⟨ cong (maybe′ just _) px ⟩ just x ≡⟨ cong (maybe′ just _) (sym px) ⟩ - maybe′ just (lookupM i (delete-many is (map just g))) (lookup i h) ∎ - inner f | no f≢i = cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-delete (delete-many is (map just g)) f≢i) + maybe′ just (lookupM i (delete-many is (fromFunc g))) (lookup i h) ∎ + inner f | no f≢i = cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-delete (delete-many is (fromFunc g)) f≢i) assoc-enough : (G : Get) → {m : ℕ} → (s : Vec Carrier m) → (v : Vec Carrier (Get.getlen G m)) → ∃ (λ h → assoc (Get.get G (enumerate s)) v ≡ just h) → ∃ λ u → bff G s v ≡ just u assoc-enough G s v (h , p) = _ , (begin |