How to make a type class instance of another type class

Question

I'm making a Boolean data, that accepts others types as boolean values, just for fun. I have created the data Boolean, for representing the actual Boolean value, and I have made a class named Booleanizable, that represents values that can be turned into Boolean data. The problem is the following: I want to make a single instance statement for every type that belongs to Num class, instead of making a statement for each type. How do I do that? Just to make it clearer, the code:

module Boolean(
    Boolean,
    true,
    false,
    Booleanizable
) where



data Boolean = Boolean Int

false = Boolean 0
true = Boolean 1

instance Show Boolean where
    show (Boolean 0) = "false"
    show (Boolean 1) = "true"

instance Eq Boolean where
    (Boolean 0) == (Boolean 0) = True
    (Boolean 0) == (Boolean 1) = False
    (Boolean 1) == (Boolean 1) = True
    (Boolean 1) == (Boolean 0) = False



class Booleanizable a where
    toBoolean :: (Booleanizable a) => a -> Boolean

instance Booleanizable Boolean where
    toBoolean (Boolean x) = Boolean x

instance Booleanizable Bool where
    toBoolean True = Boolean 1
    toBoolean False = Boolean 0

And what I'm trying to do:

instance (Num a) => Booleanizable a where
    toBoolean 0 = Boolean 0
    toBoolean _ = Boolean 1

This is the error that appears:

Boolean.hs:37:21:
    Illegal instance declaration for ‘Booleanizable a’
      (All instance types must be of the form (T a1 ... an)
       where a1 ... an are *distinct type variables*,
       and each type variable appears at most once in the instance head.
       Use FlexibleInstances if you want to disable this.)
    In the instance declaration for ‘Booleanizable a’

Please show in the question what went wrong in your attempt. (In this case, I was able to correctly guess the error you got, but in other questions it might be trickier to do that.) — duplode, Jan 27 '17 at 15:33
If the problem is simply the error `Constraint is no smaller than the instance head`, here is a good explanation and solution (use a newtype) - http://stackoverflow.com/a/7198951/348716 — Anupam Jain, Jan 27 '17 at 15:55
updated the question. It's not that error. Sorry taking so long @duplode — bzim, Jan 27 '17 at 16:26
No worries. If you turn on the `FlexibleInstances` extension as the error message suggests, you will get the "Constraint is no smaller [...]" error the other question discusses. — duplode, Jan 27 '17 at 16:39

score 2 · Answer 1 · answered Jan 28 '17 at 16:41

I did three things to make your example working:

1.) At the beginning, I added two Language extensions:

{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}

2.) I removed the self reference to Booleanizable a in the definition of the class Booleanizable:

Instead of

class Booleanizable a where
    toBoolean :: (Booleanizable a) => a -> Boolean

use

class Booleanizable a where
    toBoolean :: a -> Boolean

3.) I added an additional constraint Eq a to your last instance definition:

instance (Num a, Eq a) => Booleanizable a where
    toBoolean 0 = Boolean 0
    toBoolean _ = Boolean 1

How to make a type class instance of another type class

1 Answers1