diff options
Diffstat (limited to 'FinMap.agda')
| -rw-r--r-- | FinMap.agda | 8 |
1 files changed, 2 insertions, 6 deletions
diff --git a/FinMap.agda b/FinMap.agda index b069162..459ec7e 100644 --- a/FinMap.agda +++ b/FinMap.agda @@ -6,7 +6,7 @@ open import Data.Maybe using (Maybe ; just ; nothing ; maybe′) open import Data.Fin using (Fin ; zero ; suc) open import Data.Fin.Properties using (_≟_) open import Data.Vec using (Vec ; [] ; _∷_ ; _[_]≔_ ; replicate ; tabulate ; foldr ; zip ; toList) renaming (lookup to lookupVec ; map to mapV) -open import Data.Vec.Properties using (lookup∘update ; lookup∘update′ ; lookup-replicate ; tabulate-cong) +open import Data.Vec.Properties using (lookup∘update ; lookup∘update′ ; lookup-replicate ; tabulate-cong ; lookup∘tabulate) open import Data.Product using (_×_ ; _,_) open import Data.List.All as All using (All) import Data.List.All.Properties as AllP @@ -109,10 +109,6 @@ lemma-lookupM-restrict-∉ i f (j ∷ js) i∉jjs = P.trans (lookup∘update′ (All.head i∉jjs) (restrict f js) (just (f j))) (lemma-lookupM-restrict-∉ i f js (All.tail i∉jjs)) -lemma-lookupM-fromFunc : {n : ℕ} {A : Set} → (f : Fin n → A) → flip lookupM (fromFunc f) ≗ Maybe.just ∘ f -lemma-lookupM-fromFunc f zero = P.refl -lemma-lookupM-fromFunc f (suc i) = lemma-lookupM-fromFunc (f ∘ suc) i - lemma-lookupM-delete : {n : ℕ} {A : Set} {i j : Fin n} → (f : FinMapMaybe n A) → i ≢ j → lookupM i (delete j f) ≡ lookupM i f lemma-lookupM-delete {i = zero} {j = zero} (_ ∷ _) p = contradiction P.refl p lemma-lookupM-delete {i = zero} {j = suc j} (_ ∷ _) p = P.refl @@ -138,7 +134,7 @@ lemma-disjoint-union {n} f t = tabulate-cong inner maybe′ just (lookupM x (delete-many t (fromFunc f))) (lookupM x (restrict f t)) ≡⟨ P.cong₂ (maybe′ just) (lemma-lookupM-delete-many (fromFunc f) x t x∉t) (lemma-lookupM-restrict-∉ x f t x∉t) ⟩ maybe′ just (lookupM x (fromFunc f)) nothing - ≡⟨ lemma-lookupM-fromFunc f x ⟩ + ≡⟨ P.cong (flip (maybe′ just) nothing) (lookup∘tabulate (just ∘ f) x) ⟩ just (f x) ∎ lemma-exchange-maps : {n m : ℕ} → {A : Set} → {h h′ : FinMapMaybe n A} → {P : Fin n → Set} → (∀ j → P j → lookupM j h ≡ lookupM j h′) → {is : Vec (Fin n) m} → All P (toList is) → mapV (flip lookupM h) is ≡ mapV (flip lookupM h′) is |