From dd95d0924df51daeac7176d4010a30d34bae2b02 Mon Sep 17 00:00:00 2001 From: Helmut Grohne Date: Fri, 19 Apr 2013 12:08:55 +0200 Subject: move lemma-\notin-lookupM-assoc to Precond This removes imports. --- Precond.agda | 21 ++++++++++++++++----- 1 file changed, 16 insertions(+), 5 deletions(-) (limited to 'Precond.agda') diff --git a/Precond.agda b/Precond.agda index f3df111..f1b5e82 100644 --- a/Precond.agda +++ b/Precond.agda @@ -5,21 +5,21 @@ module Precond (Carrier : Set) (deq : Decidable {A = Carrier} _≡_) where open import Data.Nat using (ℕ) open import Data.Fin using (Fin) open import Data.List using (List ; [] ; _∷_) +open import Data.Maybe using (nothing ; just) open import Data.Vec using (Vec ; [] ; _∷_ ; map ; lookup ; toList) -import Data.List.Any +open import Data.List.Any using (here ; there) open Data.List.Any.Membership-≡ using (_∉_) open import Data.Maybe using (just) open import Data.Product using (∃ ; _,_) open import Function using (flip ; _∘_) -open import Relation.Binary.PropositionalEquality using (refl ; cong) +open import Relation.Binary.PropositionalEquality using (refl ; cong ; inspect ; [_] ; sym) open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) -open import FinMap using (FinMap ; FinMapMaybe ; union ; fromFunc ; empty ; insert) +open import FinMap using (FinMap ; FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; lemma-lookupM-empty) import CheckInsert -open CheckInsert Carrier deq using (checkInsert ; lemma-checkInsert-new) +open CheckInsert Carrier deq using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other) open import BFF using (fmap ; _>>=_) import Bidir -open Bidir Carrier deq using (lemma-∉-lookupM-assoc) open BFF.VecBFF Carrier deq using (get-type ; assoc ; enumerate ; denumerate ; bff) @@ -33,6 +33,17 @@ data All-different {A : Set} : List A → Set where different-[] : All-different [] different-∷ : {x : A} {xs : List A} → x ∉ xs → All-different xs → All-different (x ∷ xs) +lemma-∉-lookupM-assoc : {m n : ℕ} → (i : Fin n) → (is : Vec (Fin n) m) → (xs : Vec Carrier m) → (h : FinMapMaybe n Carrier) → assoc is xs ≡ just h → (i ∉ toList is) → lookupM i h ≡ nothing +lemma-∉-lookupM-assoc i [] [] .empty refl i∉is = lemma-lookupM-empty i +lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h ph i∉is with assoc is' xs' | inspect (assoc is') xs' +lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h () i∉is | nothing | [ ph' ] +lemma-∉-lookupM-assoc i (i' ∷ is') (x' ∷ xs') h ph i∉is | just h' | [ ph' ] = begin + lookupM i h + ≡⟨ sym (lemma-lookupM-checkInsert-other i i' (i∉is ∘ here) x' h' h ph) ⟩ + lookupM i h' + ≡⟨ lemma-∉-lookupM-assoc i is' xs' h' ph' (i∉is ∘ there) ⟩ + nothing ∎ + different-assoc : {m n : ℕ} → (u : Vec (Fin n) m) → (v : Vec Carrier m) → All-different (toList u) → ∃ λ h → assoc u v ≡ just h different-assoc [] [] p = empty , refl different-assoc (u ∷ us) (v ∷ vs) (different-∷ u∉us diff-us) with different-assoc us vs diff-us -- cgit v1.2.3