Re: [Haskell-cafe] Mild confusion around type family

19 Jun 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@haskell.org] On Behalf Of
Adam Gundry
Sent: 19 June 2015 2:20 PM
To: haskell-cafe@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
--
Adam Gundry, Haskell Consultant
Well-Typed LLP, http://www.well-typed.com/
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