[Haskell-cafe] Mild confusion around type family

18 Jun 2015

      Below is a very simple almost canonical natural number model.

I'm slightly confused by how type families work

Wikipedia says....

"Type families are a feature of some type systemshttps://en.wikipedia.org/wiki/Type_system that allow PARTIAL functions between types to be defined by pattern matchinghttps://en.wikipedia.org/wiki/Pattern_matching"

So...
...
{-# 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
...
-- a - 0 == a
type instance Sub a Z = a
-- (a + 1) - (b + 1) == a - b
type instance 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!...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))
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[Haskell-cafe] Mild confusion around type family

Nicholls, Mark