RE: [Axiom-developer] Time for another crazy idea...

[Bill Page]

On February 22, 2006 10:07 AM Gaby wrote:
> 
> Bill Page writes:
> 
> | ... From the point of view of applications of category theory
> | in computer science, I think there are several better books for
> | the beginner, e.g.
> | 
> |  Basic Category Theory for Computer Scientists
> |  by Benjamin C. Pierce
> |  http://www.amazon.com/gp/product/0262660717
> 
> I usually recommend Barr and Wells' to students.
> 

http://crm.umontreal.ca/pub/Ventes/desc/PM023.html
http://www.cwru.edu/artsci/math/wells/pub/ctcs.html
http://www.amazon.com/gp/product/0131204866

Certainly! I was a student of Michael Barr at McGill in the 1980's.
But this book is a little hard to get and I think these days it
makes a better "2nd book" on category theory for computer science,
rather than a beginner's book.

Pierce's book can take you are far as cartesian closed categories
and their equivalence to typed lambda calculus and thus relevance
to programming language semantics. Since Axiom implements 'Record'
(products), 'Union' (sums) and 'Mapping' (typed functions with
evaluation), it's characterization in these terms is quite
straight forward.

But the Barr and Wells book ends up at Topos Theory (algebraic
set theory) and I do believe that is where we want to be in a
computer algebra system like Axiom.

Regards,
Bill Page.