Jeffrey,

You didn't explain what you're trying to accomplish, and therefore folks can only address the symptoms.

Here's what I'm seeing:

Suppose you have:

    data A = A | B | C | D | E

You'd like a function that
given A returns E,
given B, returns D

given C, returns er, C

given D, returns B,
given E, returns A.

So you're hoping to write a Rev type class with singleton member
    rev :: Rev a => a -> a

that would do the trick.

Thing is, you can already write a very generic

    rev :: (Enum a, Bounded a) => a -> a

that would do the job.

Why is that sweet?

Because Enum + Bounded are auto-derivable for huge swathes of data types. So you write the rev function (not type class instance!) once, and it'll work for lots of your structures.

The best type class is often no type class. Especially when the compiler isn't smart enough to read your mind. But I'm sure it's flattered you thought so highly of it  ;)

-- Kim-Ee

On Thu, Jan 22, 2015 at 7:23 AM, Jeffrey Brown <jeffbrown.the@gmail.com> wrote:

Dear Haskellers,

The following compiles. (Rev stands for Reversible, and Dirn for Direction.)

    class Rev a where
        rev :: a -> a
   
    data Dirn = Succ | Pred
        deriving (Eq, Show, Ord)

    -- implement Ord
    (<=) Succ Pred = False
    (<=) _ _ = True
   
    -- implement Rev
    instance Rev Dirn where
        rev Succ = Pred
        rev Pred = Succ

But if I try to define the Rev instance the same way the Ord instance is being defined, it does not compile:

    class Rev a where
        rev :: a -> a
   
    data Dirn = Succ | Pred
        deriving (Eq, Show, Ord, Rev)
   
    -- implement Ord, because Dirn is used as a key in a Map
    (<=) Succ Pred = False
    (<=) _ _ = True
   
    -- implement Rev
    rev Succ = Pred
    rev Pred = Succ

What's going on?

Many thanks,
Jeff

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