William Lee Irwin III
literal "5" gets mapped to (fromPositiveInteger 5) literal "-9" gets mapped to (fromNonZeroInteger -9)
On Fri, Feb 16, 2001 at 05:42:17PM +0000, Marcin 'Qrczak' Kowalczyk wrote:
Note that when a discussed generic Prelude replacement framework is done, and ghc's rules are changed to expand -9 to negate (fromInteger 9) instead of fromInteger (-9), then you don't need uglification of the fromInteger function to be able to define types with only nonnegative numeric values. Just define your negate in an appropriate class, different from the fromInteger's class.
Good point, the canonical injection from the positive integers into the various supersets (with structure) thereof handles it nicely. I foresee: fromPositiveInteger :: ContainsPositiveIntegers t => PositiveInteger -> t instance ContainsPositiveIntegers Integer where ... instance AdditiveGroup Integer where ... negate :: AdditiveGroup t => t -> t {- this seems natural, but see below -} fromPositiveInteger 5 :: ContainsPositiveIntegers t => t negate $ fromPositiveInteger 5 :: (AdditiveGroup t, ContainsPositiveIntegers t) => t which is not exactly what I want (and could probably use some aesthetic tweaking); I had in mind that negative integers would somehow imply a ContainsNonZeroIntegers or ContainsAllIntegers instance or the like. The solution actually imposes a rather natural instance (though one which could cause overlaps): instance (AdditiveGroup t, ContainsPositiveIntegers t) => ContainsAllIntegers t where ... I suppose one big wrinkle comes in when I try to discuss negation in the multiplicative monoid of nonzero integers. That question already exists without the Prelude's altered handling of negative literals. negate . fromInteger $ n just brings it immediately to the surface. 0 and 1 will still take some work, but I don't expect help with them. Thanks for the simplification! Cheers, Bill