[Haskell-cafe] 3 level hierarchy of Haskell objects
Ertugrul Söylemez
es at ertes.de
Wed Aug 8 20:40:24 CEST 2012
Patrick Browne <patrick.browne at dit.ie> wrote:
> > > If we include super-classes would the following be an appropriate
> > > mathematical representation?
> >
> > What is a superclass? What are the semantics?
>
> I assume that like a normal class a super-class *defines* a set
> operations for types, but it is not *a set* of types. A sub-class can
> use the signature and default methods of its super-class. I have no
> particular super-class in mind.
So you basically just mean
class (Functor f) => Applicative f
where Functor is a superclass of Applicative? There is really nothing
special about that. Notice that type classes are a language feature
that is translated to a core language, which is essentially an extended
System F_omega. See below.
> Rather I am trying to make sense of how these Haskell objects are
> mathematically related.
They are mainly related by logic, in particular type theory. You may be
interested in System F_omega [1].
[1]: http://en.wikipedia.org/wiki/System_F#System_F.CF.89
Greets,
Ertugrul
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