[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


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