Re: [Haskell-cafe] Positive integers

On Fri, 24 Mar 2006, Malcolm Wallace wrote:

Daniel McAllansmith wrote:

...

Unless I've missed it, there is no typeclass for positive integers in GHC. Is there any particular reason it doesn't exist?

Also, it seems Word would be a far better type in the likes of (!!), length, etc. Is it just tradition that resulted in the use of Int?

There is a good argument that what you really want here is the lazy infinite natural numbers. Think Peano:

data Natural = Zero | Succ Natural

The clear correspondance between lazy lists and the size/index of a lazy list makes this type fairly compelling. It can be jolly useful, particularly with infinite streams, to be able to compute (length xs > n) without forcing the evaluation of the list to more than n places.

Fortunately there are already List functions like genericLength and genericTake, which can handle such a number type. Shouldn't be Peano numbers part of the standard libraries?