3 open import Data.Bool hiding (_≟_)
7 open import Data.List hiding (replicate)
8 open import Data.Vec hiding (map ; zip) renaming (lookup to lookupVec)
9 open import Data.Product hiding (zip ; map)
11 open import Relation.Nullary
12 open import Relation.Binary.Core
16 FinMapMaybe : ℕ → Set → Set
17 FinMapMaybe n A = Vec (Maybe A) n
19 lookupM : {A : Set} {n : ℕ} → Fin n → FinMapMaybe n A → Maybe A
22 insert : {A : Set} {n : ℕ} → Fin n → A → FinMapMaybe n A → FinMapMaybe n A
23 insert f a m = m [ f ]≔ (just a)
25 empty : {A : Set} {n : ℕ} → FinMapMaybe n A
26 empty = replicate nothing
28 FinMap : ℕ → Set → Set
31 lookup : {A : Set} {n : ℕ} → Fin n → FinMap n A → A
34 fromFunc : {A : Set} {n : ℕ} → (Fin n → A) → FinMap n A
37 union : {A : Set} {n : ℕ} → FinMapMaybe n A → FinMap n A → FinMap n A
38 union m1 m2 = tabulate (λ f → maybe′ id (lookup f m2) (lookupM f m1))
42 checkInsert : {A : Set} {n : ℕ} → ((x y : A) → Dec (x ≡ y)) → Fin n → A → FinMapMaybe n A → Maybe (FinMapMaybe n A)
43 checkInsert eq i b m with lookupM i m
44 checkInsert eq i b m | just c with eq b c
45 checkInsert eq i b m | just .b | yes refl = just m
46 checkInsert eq i b m | just c | no ¬p = nothing
47 checkInsert eq i b m | nothing = just (insert i b m)
49 assoc : {A : Set} {n : ℕ} → ((x y : A) → Dec (x ≡ y)) → List (Fin n) → List A → Maybe (FinMapMaybe n A)
50 assoc _ [] [] = just empty
51 assoc eq (i ∷ is) (b ∷ bs) = maybe′ (checkInsert eq i b) nothing (assoc eq is bs)
54 generate : {A : Set} {n : ℕ} → (Fin n → A) → List (Fin n) → FinMapMaybe n A
56 generate f (n ∷ ns) = insert n (f n) (generate f ns)
58 lemma-1 : {τ : Set} {n : ℕ} → (eq : (x y : τ) → Dec (x ≡ y)) → (f : Fin n → τ) → (is : List (Fin n)) → assoc eq is (map f is) ≡ just (generate f is)
59 lemma-1 eq f [] = refl
60 lemma-1 eq f (i ∷ is′) = {!!}
62 idrange : (n : ℕ) → List (Fin n)
63 idrange n = toList (tabulate id)
65 bff : ({A : Set} → List A → List A) → ({B : Set} → ((x y : B) → Dec (x ≡ y)) → List B → List B → Maybe (List B))
66 bff get eq s v = let s′ = idrange (length s)
67 g = fromFunc (λ f → lookupVec f (fromList s))
68 h = assoc eq (get s′) v
69 h′ = maybe′ (λ jh → just (union jh g)) nothing h
70 in maybe′ (λ jh′ → just (map (flip lookup jh′) s′)) nothing h′