3 open import Data.Nat using (ℕ)
4 open import Data.Fin using (Fin)
5 open import Data.Maybe using (Maybe ; just ; nothing ; maybe′)
6 open import Data.List using (List ; [] ; _∷_ ; map ; length)
7 open import Data.Vec using (Vec ; toList ; fromList ; tabulate ; allFin) renaming (lookup to lookupV ; map to mapV ; [] to []V ; _∷_ to _∷V_)
8 open import Function using (id ; _∘_ ; flip)
11 open import CheckInsert
13 _>>=_ : {A B : Set} → Maybe A → (A → Maybe B) → Maybe B
14 _>>=_ = flip (flip maybe′ nothing)
16 fmap : {A B : Set} → (A → B) → Maybe A → Maybe B
17 fmap f = maybe′ (λ a → just (f a)) nothing
21 assoc : {A : Set} {n : ℕ} → EqInst A → List (Fin n) → List A → Maybe (FinMapMaybe n A)
22 assoc _ [] [] = just empty
23 assoc eq (i ∷ is) (b ∷ bs) = (assoc eq is bs) >>= (checkInsert eq i b)
26 enumerate : {A : Set} → (l : List A) → List (Fin (length l))
27 enumerate l = toList (tabulate id)
29 denumerate : {A : Set} (l : List A) → Fin (length l) → A
30 denumerate l = flip lookupV (fromList l)
32 bff : ({A : Set} → List A → List A) → ({B : Set} → EqInst B → List B → List B → Maybe (List B))
33 bff get eq s v = let s′ = enumerate s
34 g = fromFunc (denumerate s)
35 h = assoc eq (get s′) v
36 h′ = fmap (flip union g) h
37 in fmap (flip map s′ ∘ flip lookup) h′
40 assoc : {A : Set} {m n : ℕ} → EqInst A → Vec (Fin m) n → Vec A n → Maybe (FinMapMaybe m A)
41 assoc _ []V []V = just empty
42 assoc eq (i ∷V is) (b ∷V bs) = (assoc eq is bs) >>= (checkInsert eq i b)
44 enumerate : {A : Set} {n : ℕ} → Vec A n → Vec (Fin n) n
45 enumerate _ = tabulate id
47 denumerate : {A : Set} {n : ℕ} → Vec A n → Fin n → A
48 denumerate = flip lookupV
50 bff : {getlen : ℕ → ℕ} → ({A : Set} {n : ℕ} → Vec A (getlen n) → Vec A n) → ({m : ℕ} {B : Set} → EqInst B → Vec B (getlen m) → Vec B m → Maybe (Vec B (getlen m)))
51 bff get eq s v = let s′ = enumerate s
52 g = fromFunc (denumerate s)
53 h = assoc eq (get s′) v
54 h′ = fmap (flip union g) h
55 in fmap (flip mapV s′ ∘ (flip lookup)) h′