[Haskell-cafe] typeclass to select a list element

[Paolino]

Hello everyone,

I'm still trying to resolve my problem. I try to restate it in a simpler
way.
Is it possible to write extract and update functions for L ?

import Data.Nat

data family X (n::Nat) :: *

data L (n::Nat) where
    Q :: L (Succ n) -> X n -> L n
    E :: L n

extract :: L Zero -> X n
extract = undefined

update :: L Zero -> (X n -> X n) -> L Zero
update = undefined

Thanks for hints and help

paolino



2013/10/7 Paolino <paolo.veronelli at gmail.com>

> Hello, I'm trying to use a type class to select an element from a list.
> I would like to have a String "CC" as a value for l10'.
>
>
> {-# LANGUAGE MultiParamTypeClasses, GADTs,FlexibleInstances,  DataKinds
> ,TypeFamilies, KindSignatures, FlexibleContexts, OverlappingInstances,
> StandaloneDeriving, UndecidableInstances #-}
>
>
>
> import Data.Nat
> import Data.Monoid
>
> data family X (n::Nat) :: *
>
> data L (n::Nat) where
>     Q :: (Monoid (X n), Show (X n)) => L (Succ n) -> X n -> L n
>     E :: Monoid (X n) => L n
>
> deriving instance Show (L n)
> data instance X n = String String
>
> instance Monoid (X n) where
>     String x `mappend` String y = String $ x `mappend` y
>     mempty = String ""
> deriving instance Show (X n)
>
> class Compose n n' where
>     compose :: L n  -> L n  -> X n'
>
> instance Compose n n where
>     compose (Q _ x) (Q _ y) = x `mappend` y
>     compose _ _ = mempty
>
> instance Compose n n' where
>     compose (Q x _) (Q y _) = compose x y
>     compose _ _ = mempty
>
> l0 :: L Zero
> l0 = Q (Q E $ String "C") $ String "A"
>
> l0' :: L Zero
> l0' = Q (Q E $ String "C") $ String "B"
>
>
> l10' :: X (Succ Zero)
> l10' = compose l0 l0'
>
> l00' :: X Zero
> l00' = compose l0 l0'
> {-
>
> *Main> l00'
> String "AB"
> *Main> l10'
> String ""
>
> -}
>
> Thanks for help.
>
> paolino
>
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