diff options
| -rw-r--r-- | Bidir.agda | 12 | ||||
| -rw-r--r-- | CheckInsert.agda | 10 |
2 files changed, 11 insertions, 11 deletions
@@ -16,7 +16,7 @@ open import Function using (id ; _∘_ ; flip) open import Relation.Nullary using (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 @@ -66,8 +66,8 @@ lemma-∉-lookupM-assoc eq i [] [] h ph i∉is = begin ≡⟨ lemma-lookupM-empty i ⟩ nothing ∎ lemma-∉-lookupM-assoc eq i (i' ∷ is') (x' ∷ xs') h ph i∉is with assoc eq is' xs' | inspect (assoc eq is') xs' -lemma-∉-lookupM-assoc eq i (i' ∷ is') (x' ∷ xs') h () i∉is | nothing | Reveal_is_.[_] ph' -lemma-∉-lookupM-assoc eq i (i' ∷ is') (x' ∷ xs') h ph i∉is | just h' | Reveal_is_.[_] ph' = apply-checkInsertProof eq i' x' h' record { +lemma-∉-lookupM-assoc eq i (i' ∷ is') (x' ∷ xs') h () i∉is | nothing | [ ph' ] +lemma-∉-lookupM-assoc eq i (i' ∷ is') (x' ∷ xs') h ph i∉is | just h' | [ ph' ] = apply-checkInsertProof eq i' x' h' record { same = λ lookupM-i'-h'≡just-x' → begin lookupM i h ≡⟨ cong (lookupM i) (lemma-from-just (trans (sym ph) (lemma-checkInsert-same eq i' x' h' lookupM-i'-h'≡just-x'))) ⟩ @@ -91,8 +91,8 @@ _in-domain-of_ is h = All (λ i → ∃ λ x → lookupM i h ≡ just x) is lemma-assoc-domain : {m n : â„•} {A : Set} → (eq : EqInst A) → (is : Vec (Fin n) m) → (xs : Vec A m) → (h : FinMapMaybe n A) → assoc eq is xs ≡ just h → (toList is) in-domain-of h lemma-assoc-domain eq [] [] h ph = Data.List.All.[] lemma-assoc-domain eq (i' ∷ is') (x' ∷ xs') h ph with assoc eq is' xs' | inspect (assoc eq is') xs' -lemma-assoc-domain eq (i' ∷ is') (x' ∷ xs') h () | nothing | ph' -lemma-assoc-domain eq (i' ∷ is') (x' ∷ xs') h ph | just h' | Reveal_is_.[_] ph' = apply-checkInsertProof eq i' x' h' record { +lemma-assoc-domain eq (i' ∷ is') (x' ∷ xs') h () | nothing | [ ph' ] +lemma-assoc-domain eq (i' ∷ is') (x' ∷ xs') h ph | just h' | [ ph' ] = apply-checkInsertProof eq i' x' h' record { same = λ lookupM-i'-h'≡just-x' → Data.List.All._∷_ (x' , (trans (cong (lookupM i') (lemma-from-just (trans (sym ph) (lemma-checkInsert-same eq i' x' h' lookupM-i'-h'≡just-x')))) lookupM-i'-h'≡just-x')) (lemma-assoc-domain eq is' xs' h (trans ph' (trans (sym (lemma-checkInsert-same eq i' x' h' lookupM-i'-h'≡just-x')) ph))) @@ -132,7 +132,7 @@ lemma-2 : {Ï„ : Set} {m n : â„•} → (eq : EqInst Ï„) → (is : Vec (Fin n) m) â lemma-2 eq [] [] h p = refl lemma-2 eq (i ∷ is) (x ∷ xs) h p with assoc eq is xs | inspect (assoc eq is) xs lemma-2 eq (i ∷ is) (x ∷ xs) h () | nothing | _ -lemma-2 eq (i ∷ is) (x ∷ xs) h p | just h' | Reveal_is_.[_] ir = begin +lemma-2 eq (i ∷ is) (x ∷ xs) h p | just h' | [ ir ] = begin map (flip lookupM h) (i ∷ is) ≡⟨ refl ⟩ lookupM i h ∷ map (flip lookupM h) is 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 : â„•} (eq : EqInst A) (i : Fin n) (x : A) apply-checkInsertProof : {A P : Set} {n : â„•} → (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 : â„•} → (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 {Ï„} eq f i is = apply-checkInsertProof eq i (f i) (r lemma-lookupM-checkInsert : {A : Set} {n : â„•} → (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) ⟩ |