[Haskell-cafe] minor confusion over kinds....

6 May 2015

      And what "*" means as opposed to other things e.g. an explicit name "Nat" or a kind variable "k"
...
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE ExplicitForAll #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
what I want is a typeclass with instances of type level Naturals

here's the class, the parameter is of kind (* -> *) i.e. a is some sort of wrapper that maps from types to values
...
class Foo (a :: * -> *) where
  type Bar a
  bar :: a (Bar a)
lets ignore DataKinds define Zero and Succ as distinct types

uninhabited...but of kind "*" and "k -> *"
...
data Z1
data S1 nat
SNat1 :: * -> *
...
data SNat1 a where
  SZ1 :: SNat1 Z1
  SS1 :: SNat1 a -> SNat1 (S1 a)
off we go...
...
instance Foo SNat1 where
  type Bar SNat1 = Z1
  bar = SZ1
now lets do it the datakind route
...
data Nat where
  Z :: Nat
  S :: Nat -> Nat
ahhh...SNat is of kind "Nat -> *"
...
data SNat a where
  SZ :: SNat 'Z
  SS :: SNat a -> SNat ('S a)
so I cant make it an instance of the same type class

"The first argument of 'Foo' should have kind '* -> *',
      but 'SNat' has kind 'Nat -> *'
    In the instance declaration for 'Foo SNat'"
...
--instance Foo SNat where
--  type Bar SNat = 'Z
--  bar = SZ
unless I redefine my class (which seems a bit silly)
...
class Foo' (a :: k -> *) where
  type Bar' a :: k
  bar' :: a (Bar' a)
now it works.
...
instance Foo' SNat where
  type Bar' SNat = 'Z
  bar' = SZ
clearly named kinds (?) are somehow distinct from unnames ones?
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[Haskell-cafe] minor confusion over kinds....

Nicholls, Mark