diff options
Diffstat (limited to 'Precond.agda')
| -rw-r--r-- | Precond.agda | 14 |
1 files changed, 9 insertions, 5 deletions
diff --git a/Precond.agda b/Precond.agda index 2be3f3a..787f010 100644 --- a/Precond.agda +++ b/Precond.agda @@ -6,7 +6,7 @@ open import Data.Nat using (ℕ) open import Data.Fin using (Fin ; zero ; suc) open import Data.Fin.Props using (_≟_) open import Data.List using (List ; [] ; _∷_) -import Level +open import Level using () renaming (zero to ℓ₀) import Category.Monad import Category.Functor open import Data.Maybe using (Maybe ; nothing ; just ; maybe′) @@ -20,7 +20,11 @@ open Data.List.Any.Membership-≡ using (_∉_) open import Data.Maybe using (just) open import Data.Product using (∃ ; _,_ ; proj₂) open import Function using (flip ; _∘_ ; id) -open import Relation.Binary.PropositionalEquality using (refl ; cong ; inspect ; [_] ; sym ; decSetoid) +open import Function.Equality using (_⟶_ ; _⟨$⟩_) +open import Function.Injection using (module Injection) renaming (Injection to _↪_) +open Injection using (to) +open import Relation.Binary using (Setoid) +open import Relation.Binary.PropositionalEquality using (refl ; cong ; inspect ; [_] ; sym ; decSetoid) renaming (setoid to EqSetoid) open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) open import Relation.Nullary using (yes ; no) @@ -31,8 +35,8 @@ open CheckInsert (decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; le import BFF open import Bidir (decSetoid deq) using (_in-domain-of_ ; lemma-assoc-domain ; lemma-just-sequence) import GetTypes -open GetTypes.VecVec using (Get ; module Get) -open BFF.VecBFF (decSetoid deq) using (assoc ; enumerate ; denumerate ; bff) +open GetTypes.PartialVecVec using (Get ; module Get) +open BFF.PartialVecBFF (decSetoid deq) using (assoc ; enumerate ; denumerate ; bff) lemma-lookup-map-just : {n : ℕ} (f : Fin n) {A : Set} (v : Vec A n) → lookup f (map Maybe.just v) ≡ Maybe.just (lookup f v) lemma-lookup-map-just zero (x ∷ xs) = refl @@ -70,7 +74,7 @@ lemma-union-delete-fromFunc {n = n} {is = i ∷ is} {h = h} {g = g} ((x , px) Da maybe′ just (lookupM i (delete-many is (map just g))) (lookup i h) ∎ inner f | no f≢i = cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-delete (delete-many is (map just g)) f≢i) -assoc-enough : (G : Get) → {m : ℕ} → (s : Vec Carrier m) → (v : Vec Carrier (Get.getlen G m)) → ∃ (λ h → assoc (Get.get G (enumerate s)) v ≡ just h) → ∃ λ u → bff G s v ≡ just u +assoc-enough : (G : Get) → {i : Setoid.Carrier (Get.I G)} → (s : Vec Carrier (to (Get.gl₁ G) ⟨$⟩ i)) → (v : Vec Carrier (Get.gl₂ G ⟨$⟩ i)) → ∃ (λ h → assoc (Get.get G (enumerate s)) v ≡ just h) → ∃ λ u → bff G s v ≡ just u assoc-enough G s v (h , p) = let w , pw = lemma-union-delete-fromFunc (lemma-assoc-domain (get s′) v h p) in _ , (begin bff G s v ≡⟨ cong (flip _>>=_ (flip mapMV s′ ∘ flip lookupM) ∘ _<$>_ (flip union g′)) p ⟩ |