Re: additions

[Steve Vickers <s.j.vickers@cs.bham.ac.uk>]

Dear Mike,

Of course, in functional programming the applications of categories  
go far beyond lambda terms.

(1) At a fairly elementary level, the treatment of list types in  
functional programming languages gives a good lead in to universal  
properties (e.g. list type = free monoid or free (empty, cons)- 
algebra). Things you do with the universal properties are present as  
well known tools in functional programming with lists. The universal  
properties can then be used to motivate the abstract structure of  
categories: they describe data types by their external interfaces  
with the rest of the world rather than by their concrete internal  
structure, and the morphisms play the role of saying what the  
external interactions are. Expositionally, for Mac Lane universal  
properties were an important example where the working mathematician  
had been doing category theory all along without knowing it.

(2) More advanced, Haskell has made important use of monads as a  
programming technique for bringing side-effects, I/O etc into  
functional programming in an elegant way. (The way this came about is  
that it has long been more or less self-evident that categories are  
just what you need for describing the semantics, and the categorical  
experience of the semanticists led to the practical application of  
monads.)

So it could be that the best way forward is to teach them Haskell  
first. (I gave a short introduction to categories at Imperial, in the  
Compujting Department, and I exploited heavily the fact that they had  
all done Miranda, a predecessor of Haskell.)

Regards,

Steve Vickers.

On 22 Dec 2009, at 00:39, Mike Stay wrote:

> On Mon, Dec 21, 2009 at 12:43 AM, Joyal, André  
> <joyal.andre@uqam.ca> wrote:
>> In my message to John Baez, I wrote:
>>
>>> I can distinguish approximatly 6 major currents:
>>
>>> 5) Category theory and computer science
>
> I'm trying to expose my fellow programmers to the joys of category
> theory, but none of them have a math or physics background (or even a
> funcitonal programming background), which is where most of my
> experience with CT has been.
>
> What have been the major applications of category theory to computer
> science that have affected programmers?  Are there new algorithms?
> Are there really nice ways of solving certain problems?  The fact that
> data types with equivalence classes of lambda terms between them form
> a cartesian closed category doesn't seem to inspire them very much.
> -- 
> Mike Stay - metaweta@gmail.com
> http://math.ucr.edu/~mike
> http://reperiendi.wordpress.com


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