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

Nicholls, Mark nicholls.mark at vimn.com
Wed May 6 13:06:24 UTC 2015

lets try it the other way around

> instance Foo' SNat1 where
>   type Bar' SNat1 = Z1
>   bar' = SZ1

that works!

(my language will be wrong here...but the jist is)

So in some something of kind
"*->*" is substitutable for a parameter of kind "k -> *"
"Nat->*" is substitutable for a parameter of kind "k -> *"
"*->*" is substitutable for a parameter of kind "* -> *"
"Nat->*" is NOT substitutable for a parameter of kind "* -> *"


So why would I ever want to define a type class of kind
(* -> *) -> Constraint
Instead of
(k -> *) -> Constraint


I think I don't completely understand what's going on.

From: Nicholls, Mark
Sent: 06 May 2015 1:02 PM
To: haskell-cafe at haskell.org
Subject: minor confusion over kinds....

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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