On Tuesday 05 August 2003 15:23, Wolfgang Jeltsch wrote:
There probably are ways to achieve this with Haskell's type system. The exact solution depends on what exactly you want.
For just distinguishing between lists of different lengths you could use tuples like (a,a) (list of length 2) (a,a,a) (list of length 3) etc.
What would be the advantage to using standard lists? In both cases I'd need explicit length checks everywhere.
A better solution might be: data EmptyList element = EmptyList data TrueList list element = TrueList element (list element) A list of four Ints for example would be represented by a value of type TrueList (TrueList (TrueList (TrueList EmptyList))) Int.
Isn't that just the Haskell list type by another name?
You could define different types for different natural numbers: data Zero = Zero data Succ number = Succ number and do simple arithmetic with them at the type level: class Sum a b c | (a, b) -> c instance Sum 0 a a instance Sum a b c => Sum (Succ a) b (Succ c)
That looks interesting, I need to look into multiple parameter classes...
At the moment, I cannot think of a way of defining a list type which is parameterized by such natural types. What I mean is having a type List :: * -> * -> * where for our above example of a list of four Ints we would have the type List (Succ (Succ (Succ (Succ Zero)))) Int
That's what I would like...
What I can think of, is an association between our above list types (EmptyList and TrueList) and our natural number types by a multi-parameter class: class HasLength list length | list -> length instance HasLength EmptyList Zero instance HasLength list length => HasLength (TrueList list) (Succ length)
Again those multi-parameter classes... and off I go to the Haskell Web site ;-) Thanks for your comments! Konrad.