Cellular automata in Elm
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module Zipper exposing (..)
type alias Zipper a =
{ before : List a
, focus : a
, after : List a
}
{- Basic conversion -}
fromList : a -> List a -> Zipper a
fromList a l = Zipper [] a l
toList : Zipper a -> List a
toList rl = List.reverse rl.before ++ [rl.focus] ++ rl.after
{- Functor like things -}
map : (a -> b) -> Zipper a -> Zipper b
map f rl = Zipper (List.map f rl.before) (f rl.focus) (List.map f rl.after)
edit : (a -> a) -> Zipper a -> Zipper a
edit f rl = Zipper rl.before (rl.focus |> f) rl.after
{- Comonad functions -}
extract : Zipper a -> a
extract rl = rl.focus
duplicate : Zipper a -> Zipper (Zipper a)
duplicate rl = let
lefts = iterate1N (List.length rl.before) shiftRight rl
rights = iterate1N (List.length rl.after) shiftLeft rl
in Zipper lefts rl rights
extend : (Zipper a -> b) -> Zipper a -> Zipper b
extend f w = map f (duplicate w)
(=>>) : Zipper a -> (Zipper a -> b) -> Zipper b
(=>>) = flip extend
{- Domain functions -}
shiftLeft : Zipper a -> Zipper a
shiftLeft rl = case rl.after of
[] -> case List.reverse rl.before of
[] -> Zipper [] rl.focus []
x::xs -> Zipper [rl.focus] x xs
x::xs -> Zipper (rl.focus :: rl.before) x xs
shiftRight : Zipper a -> Zipper a
shiftRight rl = case rl.before of
[] -> case List.reverse rl.after of
[] -> Zipper [] rl.focus []
x::xs -> Zipper xs x [rl.focus]
x::xs -> Zipper xs x (rl.focus :: rl.after)
{- From here we have private functions -}
iterate1N : Int -> (a -> a) -> a -> List a
iterate1N n f a = case n of
0 -> []
m -> f a :: List.map f (iterate1N (m - 1) f a)