2008/7/4 phy51km4n
There is a exercise using datatype "Either" I'm a bit confused about...
The following datatypes are given:
data Either a b = Left a | Right b
data Tuple a b c d = One a | Two a b | Three a b c | Four a b c d
Now the exercise:
"Based on our definition of Tuple, write a function which takes a Tuple and returns either the value (if it's a one-tuple), a Haskell-pair (i.e., ('a',5)) if it's a two-tuple, a Haskell-triple if it's a three-tuple or a Haskell-quadruple if it's a four-tuple. You will need to use the Either type to represent this."
Why does that not work? :
fromTuple (One a) = a fromTuple (Two a b) = (a, b) fromTuple (Three a b c) = (a, b, c) fromTuple (Four a b c d) = (a, b, c, d)
The first line tells: fromTuple :: Tuple a b c d -> a The second line tells: fromTuple :: Tuple a b c d -> (a, b) The third line tells: fromTuple :: Tuple a b c d -> (a, b, c) The fourth line tells: fromTuple :: Tuple a b c d -> (a, b, c, d) There is no way you can unify the return types of these four lines (Well, the compiler must have told you something similar). That was the obvious part.
Why is this correct? :
fromTuple (One a ) = Left (Left a) fromTuple (Two a b ) = Left (Right (a,b)) fromTuple (Three a b c ) = Right (Left (a,b,c)) fromTuple (Four a b c d) = Right (Right (a,b,c,d))
Why does this combination of Rights and Lefts work and how does it work??
OK, first, let's simplify things a bit: data Stuple a b = Sone a | Stwo (a, b) fromStuple :: Stuple a b -> Either a (a, b) fromStuple (Sone a) = Left a fromStuple (Stwo (a, b)) = Right (a, b) According to the definition of Either, I can perfectly retrun different types for left and right. (That was the whole point of the Either type.) In your more complicated case, you can see you are using four combination of Left and Rights. The type of your function is (tell me if your compiler says otherwise): Tuple a b c d -> Either (Either a (a, b)) (Either (a, b, c) (a, b, c, d)) Ouch. Either is parametrized by two types: the one used in Left, and the one used in Right. If your are using Either types as left an right, it is possible to parametrize each of them by two types totalazing four types. Let me rewrite the return type above so you can read its tree structure more easily: Either (Either a (a, b)) (Either (a, b, c) (a, b, c, d)) Here, this should be obvious: while an Either type can hold two types, this nested one can hold four types. Hope this helps. Loup