[Haskell-cafe] Mild confusion around type family

Nicholls, Mark nicholls.mark at vimn.com
Fri Jun 19 14:14:57 UTC 2015

Ah ok...my mistake...

Lets do closed (below)....same problem.

Its not partial.....so how do we make it a type error?...."1 - 2" is not defined on the natural numbers (I'll have a go with datakinds....)

> {-# LANGUAGE DataKinds #-}
> {-# LANGUAGE ExplicitForAll #-}
> {-# LANGUAGE FlexibleContexts #-}
> {-# LANGUAGE FlexibleInstances #-}
> {-# LANGUAGE GADTs #-}
> {-# LANGUAGE MultiParamTypeClasses #-}
> {-# LANGUAGE PolyKinds #-}
> {-# LANGUAGE StandaloneDeriving #-}
> {-# LANGUAGE TypeFamilies #-}
> {-# LANGUAGE TypeOperators #-}
> {-# LANGUAGE UndecidableInstances #-}
> {-# LANGUAGE ScopedTypeVariables #-}

lets do something simple

> data Z
> data S n

> type family Sub a b where
> -- a - 0 == a
>   Sub a Z = a
> -- (a + 1) - (b + 1) == a - b
>   Sub (S a) (S b) = Sub a b

> oneMinusOne :: Z
> oneMinusOne = undefined :: Sub (S Z) (S Z)

I want this to be a type error!...

> oneMinusTwo :: Sub Z (S Z)
> oneMinusTwo = undefined :: Sub (S Z) (S (S Z))

>-----Original Message-----
>From: Haskell-Cafe [mailto:haskell-cafe-bounces at haskell.org] On Behalf Of
>Adam Gundry
>Sent: 19 June 2015 2:20 PM
>To: haskell-cafe at haskell.org
>Subject: Re: [Haskell-cafe] Mild confusion around type family
>On 18/06/15 17:19, Nicholls, Mark wrote:
>>> data Z
>>> data S n
>>> type family Sub a b
>>> type instance Sub a Z = a
>>> type instance Sub (S a) (S b) = Sub a b
>> I want this to be a type error!...but the above type family appears to
>> not be partial...this IS defined...."Sub Z (S Z)" is a type! (I thought it
>> wasn't)
>>> oneMinusTwo :: Sub Z (S Z)
>>> oneMinusTwo = undefined :: Sub (S Z) (S (S Z))
>This is a slightly subtle point about type families. The type family application
>`Sub Z (S Z)` does not reduce, but neither is it an error.
>In this case, because Sub is an open type family, there is nothing to stop
>someone subsequently defining something like
>    type instance Sub Z (S b) = Z
>in another module.
>Type families are functional relations, not functions in the FP sense.
>See also the discussion here, about the corresponding situation for a closed
>type family: https://ghc.haskell.org/trac/ghc/ticket/9636
>Hope this helps,
>Adam Gundry, Haskell Consultant
>Well-Typed LLP, http://www.well-typed.com/
>Haskell-Cafe mailing list
>Haskell-Cafe at haskell.org

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