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module BFF where
open import Data.Nat using (ℕ)
open import Data.Fin using (Fin)
open import Data.Maybe using (Maybe ; just ; nothing ; maybe′)
open import Data.List using (List ; [] ; _∷_ ; map ; length)
open import Data.Vec using (Vec ; toList ; fromList ; tabulate) renaming (lookup to lookupVec)
open import Function using (id ; _∘_ ; flip)
open import FinMap
open import CheckInsert
_>>=_ : {A B : Set} → Maybe A → (A → Maybe B) → Maybe B
_>>=_ = flip (flip maybe′ nothing)
fmap : {A B : Set} → (A → B) → Maybe A → Maybe B
fmap f = maybe′ (λ a → just (f a)) nothing
module ListBFF where
assoc : {A : Set} {n : ℕ} → EqInst A → List (Fin n) → List A → Maybe (FinMapMaybe n A)
assoc _ [] [] = just empty
assoc eq (i ∷ is) (b ∷ bs) = (assoc eq is bs) >>= (checkInsert eq i b)
assoc _ _ _ = nothing
enumerate : {A : Set} → (l : List A) → List (Fin (length l))
enumerate l = toList (tabulate id)
denumerate : {A : Set} (l : List A) → Fin (length l) → A
denumerate l = flip lookupVec (fromList l)
bff : ({A : Set} → List A → List A) → ({B : Set} → EqInst B → List B → List B → Maybe (List B))
bff get eq s v = let s′ = enumerate s
g = fromFunc (denumerate s)
h = assoc eq (get s′) v
h′ = fmap (flip union g) h
in fmap (flip map s′ ∘ flip lookup) h′
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