[Haskell-cafe] I seem to constantly abuse TypeFamilies; what do i really want?

[jberryman]

On Friday, March 14, 2014 5:19:40 PM UTC-4, Eric Walkingshaw wrote:
>
> I'm not sure if this answers your questions, but I think this particular 
> problem has a cleaner solution with GADTs:
>
>     {-# LANGUAGE GADTs #-}
>     
>     data Cmd s t where
>       Push :: a             -> Cmd s         (a,s)
>       F1   :: (a -> b)      -> Cmd (a,s)     (b,s)
>       F2   :: (a -> b -> c) -> Cmd (a,(b,s)) (c,s)
>     
>     data Prog s t where
>       (:.) :: Cmd s t -> Prog t u -> Prog s u
>       End  :: Prog s s
>     
>     infixr 5 :.
>     
>     cmd :: Cmd s t -> s -> t
>     cmd (Push a) s         = (a, s)
>     cmd (F1 f)   (a,s)     = (f a, s)
>     cmd (F2 f)   (a,(b,s)) = (f a b, s)
>     
>     prog :: Prog s t -> s -> t
>     prog (c :. p) s = prog p (cmd c s)
>     prog End      s = s
>     
>     run :: Prog () t -> t
>     run p = prog p ()
>
> Then from GHCi:
>     
>     > run (Push 3 :. Push 4 :. F2 (+) :. F1 show :. End)
>     ("7",())
>
> Maybe you really want GADTs? :)
>
> -Eric
>

That's a great point, thanks. I'll have to remember to interrogate myself 
on that next time I find myself reaching for this pattern. I wonder if your 
version can be made to work for functions of any arity?

But in most (maybe not all) cases I really don't want to be defining new 
types.

Thanks,
Brandon
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