Hi, Christopher Howard wrote:
instance Category ...
The Category class is rather restricted: Restriction 1: You cannot choose what the objects of the category are. Instead, the objects are always "all Haskell types". You cannot choose anything at all about the objects. Restriction 2: You cannot freely choose what the morphisms of the category are. Instead, the morphisms are always Haskell values. (To some degree, you can choose *which* values you want to use). These restrictions disallow many categories. For example, the category where the objects are natural numbers and there is a morphism from m to n if m is greater than or equal to n cannot be expressed directly: Natural numbers are not Haskell types; and "is bigger than or equal to" is not a Haskell value. Tillmann