[Haskell-beginners] typeclass woes...how to constain a typeclass to be "closed" under an operation....

[Nicholls, Mark]

> {-# LANGUAGE TypeFamilies, MultiParamTypeClasses, FlexibleContexts,  FlexibleInstances, GADTs #-}

lets say I have a data type

> data S a = S a deriving Show

and a nice simple typeclass

> class Foo a where
>   inc :: a -> S a

make Integer an instance and....

> instance Foo Integer where
>   inc x = S x

brilliant...

now lets say I want my typeclass to enforce that any result of inc is also of a type that is an instance of the typeclass
I'll follow my nose...which causes me a problem that makes me realise I maybe I don't understand whats going on.

> class Bar a where
>   inc' :: (Bar (S a)) => a -> S a

follow it to....

> instance Bar Integer where
>   inc' x = S x

this WORKS!...even though "S Integer" is not an instance of Bar!...maybe I don't understand.

> -- x = inc' (1 :: Integer)

This would go BOOM ...."no instance of (Bar (S Integer))"
...so that makes sense....

How do I force Haskell to check the constraint before I evaluate an expression?

follow my nose?

> -- class (Baz (S a)) => Baz a where
> --  inc'' :: a -> S a

BOOM ...."Cycle in class declaration"....
booo..but I suppose thats understandable....

so

a) is my use of typeclasses correct?...or am I missing something?
b) if so, how do I force the compiler to make sure my typeclass operations is nicely closed (under the typeclass)?


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