[Haskell-cafe] 3 level hierarchy of Haskell objects

[wren ng thornton]

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