Creating functions over Enumerations

Question

I just started learning Haskell. I think I've got the basics down, but I want to make sure I'm actually forcing myself to think functionally too.

data Dir = Right | Left | Front | Back | Up | Down deriving (Show, Eq, Enum)
inv Right = Left
inv Front = Back
inv Up = Down

Anyway, the jist of what I'm trying to do is to create a function to map between each "Dir" and its opposite/inv. I know I could easily continue this for another 3 lines, but I can't help but wonder if there's a better way. I tried adding:

inv a = b where inv b = a

but apparently you can't do that. So my question is: Is there either a way to generate the rest of the inverses or an altogether better way to create this function?

Thanks much.

Answer 1

If the pairing between Up and Down and so on is an important feature then maybe this knowledge should be reflected in the type.

data Axis = UpDown | LeftRight | FrontBack
data Sign = Positive | Negative
data Dir = Dir Axis Sign

inv is now easy.

Answer 2

Do you have a closed-form solution over the indices that corresponds to this function? If so, yes, you can use the Enum deriving to simplify things. For example,

import Prelude hiding (Either(..))

data Dir = Right
         | Front
         | Up

         | Left
         | Back
         | Down
     deriving (Show, Eq, Ord, Enum)

inv :: Dir -> Dir
inv x = toEnum ((3 + fromEnum x) `mod` 6)

Note, this relies on the ordering of the constructors!

*Main> inv Left
Right
*Main> inv Right
Left
*Main> inv Back
Front
*Main> inv Up
Down

This is very C-like, exploits the ordering of constructors, and is un-Haskelly. A compromise is to use more types, to define a mapping between the constructors and their mirrors, avoiding the use of arithmetic.

import Prelude hiding (Either(..))

data Dir = A NormalDir
         | B MirrorDir
     deriving Show

data NormalDir = Right | Front | Up
     deriving (Show, Eq, Ord, Enum)

data MirrorDir = Left  | Back  | Down     
     deriving (Show, Eq, Ord, Enum)

inv :: Dir -> Dir
inv (A n) = B (toEnum (fromEnum n))
inv (B n) = A (toEnum (fromEnum n))

E.g.

*Main> inv (A Right)
B Left
*Main> inv (B Down)
A Up

So at least we didn't have to do arithmetic. And the types distinguish the mirror cases. However, this is very un-Haskelly. It is absolute fine to enumerate the cases! Others will have to read your code at some point...

Answer 3

pairs = ps ++ map swap ps where
   ps = [(Right, Left), (Front, Back), (Up, Down)]
   swap (a, b) = (b, a)

inv a = fromJust $ lookup a pairs    

[Edit]

Or how about this?

inv a = head $ delete a $ head $ dropWhile (a `notElem`)
        [[Right,Left],[Front,Back],[Up,Down]]

Answer 4

It is good to know, that Enumeration starts with zero.

Mnemonic: fmap fromEnum [False,True] == [0,1]

---

import Data.Bits(xor)

-- Enum:       0   1          2   3       4   5
data Dir = Right | Left | Front | Back | Up | Down
           deriving (Read,Show,Eq,Ord,Enum,Bounded)

inv :: Dir -> Dir
inv = toEnum . xor 1 . fromEnum