[Haskell-cafe] No Enum for (,), no Enum or Bounded for Either

MarLinn monkleyon at gmail.com
Fri Jun 1 20:21:45 UTC 2018

> Sorry, could you explain further?  I don't understand what the
> implementation of any of those proposed instances is supposed to be.


     {-# LANGUAGE ConstraintKinds #-}

     type BoundedEnum a = (Bounded a, Enum a)

     instance (BoundedEnum b) => Enum (Either a b) where
         fromEnum (Left  _) = 0
         fromEnum (Right x) = 1 + fromEnum x
         toEnum 0           = error "toEnum: zero" -- could also add a Monoid constraint instead
         toEnum n 	   = Right . toEnum $ n-1
     instance (Bounded b) => Bounded (Either a b) where
         minBound = Right minBound
         maxBound = Right maxBound

Rationale: these two implement the use case of working on something from 
a finite selection of elements inside a monad stack.
In other words it's a special case of

     instance (Applicative f, Bounded a) => Bounded (f a) where
         minBound = pure minBound
         maxBound = pure maxBound

Is it a good idea to implement this? Probably not, but it serves as an 

On the other hand, many error types are bounded and enumerable, so why 
not enhance the error handling instead?

     instance (BoundedEnum a, Monoid b) => Enum (Either a b) where -- okay, I cheated by adding the Monoid constraint this time
         fromEnum (Right _) = 0
         fromEnum (Left  e) = 1 + fromEnum e
         toEnum 0           = Right mempty
         toEnum n 	   = Left . toEnum $ n-1
     instance (Bounded a) => Bounded (Either a b) where
         minBound = Left minBound
         maxBound = Left maxBound

Which is better? That depends.

Now for product types:

     instance (Enum a, Monoid b) => Enum (a, b) where
         toEnum   = (,mempty) . toEnum
         fromEnum = fromEnum  . fst
     instance (Enum b, Monoid a) => Enum (a, b) where
         toEnum 	 = (mempty,) . toEnum
         fromEnum = fromEnum  . snd

And to be thorough

     enumAll :: (BoundedEnum a) => [a]
     enumAll = enumFromTo minBound maxBound

Hope it's clearer now what I meant.

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