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module Bidir where
open import Data.Bool hiding (_≟_)
open import Data.Nat
open import Data.Fin
open import Data.Maybe
open import Data.List hiding (replicate)
open import Data.Vec hiding (map ; zip) renaming (lookup to lookupVec)
open import Data.Product hiding (zip ; map)
open import Function
open import Relation.Nullary
open import Relation.Binary.Core
module FinMap where
FinMap : ℕ → Set → Set
FinMap n A = Vec (Maybe A) n
lookup : {A : Set} {n : ℕ} → Fin n → FinMap n A → Maybe A
lookup = lookupVec
notMember : {A : Set} → {n : ℕ} → Fin n → FinMap n A → Bool
notMember n = not ∘ maybeToBool ∘ lookup n
insert : {A : Set} {n : ℕ} → Fin n → A → FinMap n A → FinMap n A
insert f a m = m [ f ]≔ (just a)
empty : {A : Set} {n : ℕ} → FinMap n A
empty = replicate nothing
fromAscList : {A : Set} {n : ℕ} → List (Fin n × A) → FinMap n A
fromAscList [] = empty
fromAscList ((f , a) ∷ xs) = insert f a (fromAscList xs)
union : {A : Set} {n : ℕ} → FinMap n A → FinMap n A → FinMap n A
union m1 m2 = tabulate (λ f → maybe′ just (lookup f m2) (lookup f m1))
open FinMap
checkInsert : {A : Set} {n : ℕ} → ((x y : A) → Dec (x ≡ y)) → Fin n → A → FinMap n A → Maybe (FinMap n A)
checkInsert eq i b m with lookup i m
checkInsert eq i b m | just c with eq b c
checkInsert eq i b m | just .b | yes refl = just m
checkInsert eq i b m | just c | no ¬p = nothing
checkInsert eq i b m | nothing = just (insert i b m)
assoc : {A : Set} {n : ℕ} → ((x y : A) → Dec (x ≡ y)) → List (Fin n) → List A → Maybe (FinMap n A)
assoc _ [] [] = just empty
assoc eq (i ∷ is) (b ∷ bs) = maybe′ (checkInsert eq i b) nothing (assoc eq is bs)
assoc _ _ _ = nothing
generate : {A : Set} {n : ℕ} → (Fin n → A) → List (Fin n) → FinMap n A
generate f [] = empty
generate f (n ∷ ns) = insert n (f n) (generate f ns)
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)
lemma-1 eq f [] = refl
lemma-1 eq f (i ∷ is′) = {!!}
idrange : (n : ℕ) → List (Fin n)
idrange n = toList (tabulate id)
bff : ({A : Set} → List A → List A) → ({B : Set} → ((x y : B) → Dec (x ≡ y)) → List B → List B → Maybe (List B))
bff get eq s v = let s′ = idrange (length s)
g = fromAscList (zip s′ s)
h = assoc eq (get s′) v
h′ = maybe′ (λ jh → just (union jh g)) nothing h
in maybe′ (λ jh′ → just (map {!!} s′)) nothing h′
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