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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′