Assuming you mean things like the 'Extend' type family, and 'extend' function, this illustrates one of the doubts I have. In particular, if I have a type family:

data TypeA = TypeA

type family TF where
TF Bool = TypeA

then I can write a corresponding function with signature Bool -> TF Bool (since there is only one case for the type family). But suppose I extend TF:

data TypeB = TypeB

type family TF where
TF Bool = TypeA
TF Char = TypeB

Now, I want to write a function "transformTF :: a -> TF a", but 'a' should really just be restricted to those cases for which 'TF a' is defined. I can obviously do this with fundeps or ATPs (and a class constraint), but then I'm moving in the type-class direction, and, as far as I can tell, no longer benefit from having type families at all. I guess I could also explicitly pass dictionaries, but that seems even worse.

I guess that's my basic question: can one write a function that, for a type family of arbitrary structure (possibly recursive or mutually recusrive, multiple cases) "implements" (i.e., has the corresponding signatures of) that type family?

On Tue, Dec 30, 2014 at 6:47 PM, Atze van der Ploeg <atzeus@gmail.com> wrote:

Hi Julian,

Check out my package ctrex. https://www.haskell.org/haskellwiki/CTRex

Cheers,

Atze

On Dec 30, 2014 6:20 PM, "Julian Arni" <jkarni@gmail.com> wrote:
Hi all,

I've been playing around with what might be described as type-directed
functions. One example is a list-like structure of phantom-typed values

{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE PolyKinds #-}

import GHC.TypeLits

infixr 6 :::
data a ::: b = a ::: b
deriving (Show, Eq)

data Tag b = Tag String
deriving (Show, Eq)

ex1 :: Tag 5 ::: Tag 3 ::: Tag 7
ex1 = Tag "Alice" ::: Tag "Bob" ::: Tag "Carol"

And then sorting 'ex1' based on the Nats, such that

sort ex1 :: Tag 3 ::: Tag 5 ::: Tag 7
sort ex1 = Tag "Bob" ::: Tag "Alice" ::: Tag "Carol"

Notice how it's the types, not the values, that determine the result, but
that the value-level also changes.

I know how to do this using classes, but it's a little excruciating - it's
like programming in a verbose and very restricted Prolog. With type families
it's much easier to get the result *type* (pattern matching is simple,
recursive calls are natural, and it all looks a lot more like Haskell), but
I haven't yet seen a way of effectively using type families to direct
the value-level component of the calculation.

Are there any examples of how this might be done? Or are there other
alternatives to using type-classes that I am missing? Or, alternatively, are
there libraries to reduce the boilerplate of this type-class code?

Thanks,
Julian

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