Richard Eisenberg eir at cis.upenn.edu
Fri May 29 18:23:58 UTC 2015

```There is a Fix datatype:

> data Fix f = Fix (f (Fix f))

The problem is that it isn't promotable, because only datatypes whose parameters are all of kind * are promotable. Wait until 7.12, though, and that should promote. :)

Richard

On May 29, 2015, at 12:19 PM, "Nicholls, Mark" <nicholls.mark at vimn.com> wrote:

> My actual use case is a bit more complex than just a repeating [Integer, Integer, Integer, Integer, Integer,…]
>
> And in fact the recursion is not even repeated segments of a list…hmmm….or is it?.....not sure….lets say it isnt…for the moment.
>
> At the moment it feels more like a recursive Tree type... a nice unrecursive one would be
>
> mytree :: MyTree ‘Branch ‘[ ‘Leaf Integer, ‘Branch ‘[ ‘Leaf String, ‘Leaf Bool ] ]
> mytree = ….
>
> Obviously we can construct recursive trees with recursive functions…that leads to recursive types…and BOOOM
>
> I’m not sure I understand your example though….or if it helps in the above example….its all “a”s…I need a’s and b’s.
>
> I know OF “fix”….and how we can use it to stratify (?) recursive structures….so…the question is whether we can “Fix” the above somehow.
>
> There is I believe a “Fix” type….which makes my head hurt even more.
>
>
> From: Richard Eisenberg [mailto:eir at cis.upenn.edu]
> Sent: 29 May 2015 5:01 PM
> To: Nicholls, Mark
> Subject: Re: [Haskell-cafe] recursive datakinds
>
> GHC stubbornly refuses to allow infinite types, although I don't know of a good theoretical reason why. (From a practical standpoint, with infinite types, GHC would be very likely to hang, though that could be avoided with enough engineering, I think.) Your best bet here is, in my view, not to use promoted [] to index your list type, but instead something like
>
> > data List a = Cons a (List a) | Tail [a]
>
> where the Tail constructor marks a (possibly-empty) infinitely-repeating tail of a list. Instead of the infinite (repeat Integer) list, you would just have Tail [Integer], which is much better behaved. I haven't tried to build an indexed list from such a beast, though...
>
> Richard
>
> On May 29, 2015, at 11:47 AM, "Nicholls, Mark" <nicholls.mark at vimn.com> wrote:
>
>
> Hello,
>
> If I were trying to do something like creating types like….
>
>
> > {-# LANGUAGE DataKinds #-}
> > {-# LANGUAGE ExplicitForAll #-}
> > {-# LANGUAGE FlexibleContexts #-}
> > {-# LANGUAGE FlexibleInstances #-}
> > {-# LANGUAGE GADTs #-}
> > {-# LANGUAGE MultiParamTypeClasses #-}
> > {-# LANGUAGE PolyKinds #-}
> > {-# LANGUAGE StandaloneDeriving #-}
> > {-# LANGUAGE TypeFamilies #-}
> > {-# LANGUAGE TypeOperators #-}
> > {-# LANGUAGE UndecidableInstances #-}
> > {-# LANGUAGE ScopedTypeVariables #-}
>
> > data MyList a where
> >   MyEnd :: MyList '[]
> >   MyCons :: a -> MyList b -> MyList (a ': b)
>
> > mysimplelist :: MyList '[Integer]
> > mysimplelist = MyCons 1 (MyEnd)
>
>
> > myrecursivelist = MyCons 1 myrecursivelist
>
> Cafe2.lhs:23:30:
>     Occurs check: cannot construct the infinite type: b ~ a : b
>     Expected type: MyList b
>       Actual type: MyList (a : b)
>     Relevant bindings include
>       myrecursivelist :: MyList (a : b) (bound at Cafe2.lhs:23:3)
>     In the second argument of ‘MyCons’, namely ‘myrecursivelist’
>     In the expression: MyCons 1 myrecursivelist
>
> can I “fix” this somehow?
>
> I obviously want the type of myrecursivelist to be
> MyList  ‘[Integer, Integer, Integer, Integer, Integer, Integer, Integer, Integer,…..]
>
> Something like a completely nonsensical…
>
> MyList  (Fix (Integer ‘: ))
>
> P.S.
>
> Yes, I barely understand “fix” as a function, let alone a data type.
>
>
>
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