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| author | Helmut Grohne <helmut@subdivi.de> | 2012-09-26 15:35:32 +0200 |
|---|---|---|
| committer | Helmut Grohne <helmut@subdivi.de> | 2012-09-26 15:35:32 +0200 |
| commit | c1d4b4bd8d8c785a4745cb8be5d2b6094bd38def (patch) | |
| tree | fee40f7c1de57058f81995733deb414ae4380b07 /CheckInsert.agda | |
| parent | 01273a8a6109d9e45c9c24b6049c63f8321de403 (diff) | |
| download | bidiragda-c1d4b4bd8d8c785a4745cb8be5d2b6094bd38def.tar.gz | |
import [_] instead of Reveal_is_
This makes things a little shorter and more readable.
Diffstat (limited to 'CheckInsert.agda')
| -rw-r--r-- | CheckInsert.agda | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/CheckInsert.agda b/CheckInsert.agda index 408a5b2..c482423 100644 --- a/CheckInsert.agda +++ b/CheckInsert.agda @@ -8,7 +8,7 @@ open import Data.List using (List ; [] ; _∷_) open import Relation.Nullary using (Dec ; yes ; no ; ¬_) open import Relation.Nullary.Negation using (contradiction) open import Relation.Binary.Core using (_≡_ ; refl) -open import Relation.Binary.PropositionalEquality using (cong ; sym ; inspect ; Reveal_is_ ; trans) +open import Relation.Binary.PropositionalEquality using (cong ; sym ; inspect ; [_] ; trans) open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) open import FinMap @@ -32,9 +32,9 @@ record checkInsertProof {A : Set} {n : ℕ} (eq : EqInst A) (i : Fin n) (x : A) apply-checkInsertProof : {A P : Set} {n : ℕ} → (eq : EqInst A) → (i : Fin n) → (x : A) → (m : FinMapMaybe n A) → checkInsertProof eq i x m P → P apply-checkInsertProof eq i x m rp with lookupM i m | inspect (lookupM i) m apply-checkInsertProof eq i x m rp | just x' | il with eq x x' -apply-checkInsertProof eq i x m rp | just .x | Reveal_is_.[_] il | yes refl = checkInsertProof.same rp il -apply-checkInsertProof eq i x m rp | just x' | Reveal_is_.[_] il | no x≢x' = checkInsertProof.wrong rp x' x≢x' il -apply-checkInsertProof eq i x m rp | nothing | Reveal_is_.[_] il = checkInsertProof.new rp il +apply-checkInsertProof eq i x m rp | just .x | [ il ] | yes refl = checkInsertProof.same rp il +apply-checkInsertProof eq i x m rp | just x' | [ il ] | no x≢x' = checkInsertProof.wrong rp x' x≢x' il +apply-checkInsertProof eq i x m rp | nothing | [ il ] = checkInsertProof.new rp il lemma-checkInsert-same : {A : Set} {n : ℕ} → (eq : EqInst A) → (i : Fin n) → (x : A) → (m : FinMapMaybe n A) → lookupM i m ≡ just x → checkInsert eq i x m ≡ just m lemma-checkInsert-same eq i x m p with lookupM i m @@ -75,7 +75,7 @@ lemma-checkInsert-restrict {τ} eq f i is = apply-checkInsertProof eq i (f i) (r lemma-lookupM-checkInsert : {A : Set} {n : ℕ} → (eq : EqInst A) → (i j : Fin n) → (x y : A) → (h h' : FinMapMaybe n A) → lookupM i h ≡ just x → checkInsert eq j y h ≡ just h' → lookupM i h' ≡ just x lemma-lookupM-checkInsert eq i j x y h h' pl ph' with lookupM j h | inspect (lookupM j) h lemma-lookupM-checkInsert eq i j x y h .(insert j y h) pl refl | nothing | pl' with i ≟ j -lemma-lookupM-checkInsert eq i .i x y h .(insert i y h) pl refl | nothing | Reveal_is_.[_] pl' | yes refl = lemma-just≢nothing (begin just x ≡⟨ sym pl ⟩ lookupM i h ≡⟨ pl' ⟩ (nothing ∎)) +lemma-lookupM-checkInsert eq i .i x y h .(insert i y h) pl refl | nothing | [ pl' ] | yes refl = lemma-just≢nothing (begin just x ≡⟨ sym pl ⟩ lookupM i h ≡⟨ pl' ⟩ (nothing ∎)) lemma-lookupM-checkInsert eq i j x y h .(insert j y h) pl refl | nothing | pl' | no ¬p = begin lookupM i (insert j y h) ≡⟨ sym (lemma-lookupM-insert-other i j y h ¬p) ⟩ |