On 8/8/12 9:41 PM, Jay Sulzberger wrote:
Haskell's type classes look to me to be a provision for declaring a signature in the sense of the above article.
Just to clarify this in the context of my previous post, type classes define signatures in two significantly different ways. (1) The first way is as you suggest: the methods of a type class specify a signature, and for convenience we give that signature a name (i.e., the type class' name). However, this is a signature for the term level of Haskell (i.e., a signature in the Term sort not discussed previously; elements of Type classify elements of Term, just as elements of Kind classify elements of Type). (2) The second way is that, at the type level, the collection of type class names together form a signature. Namely they form the signature comprising the majority of the Context sort. Both senses are important for understanding the role of type classes in Haskell, but I believe that some of Patrick Browne's confusion is due to trying to conflate these into a single notion. Just as terms and types should not be confused, neither should methods and type classes. In both cases, each is defined in terms of the other, however they live in separate universes. This is true even in languages which allow terms to occur in type expressions and allow types to occur in term expressions. Terms denote values and computations (even if abstractly); whereas, types denote collections of expressions (proper types denote collections of term expressions; kinds denote collections of type expressions;...). -- Live well, ~wren