Date: Thu, 7 Nov 1996 08:30:51 -0400 (AST)
Subject: Category for higher-order functions

Date: Thu, 7 Nov 96 8:29:30 MET
From: Scott Thibault <Scott.Thibault@irisa.fr>

Hi,
  I've been looking at some applications of category theory in the area of
computer science, where people have defined a category whose objects are
types and arrows are functions.  I've tried to extended this idea to
functions that return functions, A->(A->B), but can't seem to find the right
way to do it.  Has this been done before or is there an obvious representation
for this?

--Scott


Date: Fri, 8 Nov 1996 11:38:24 -0400 (AST)
Subject: Re: Category for higher-order functions
Date: 07 Nov 96 10:48:36 EST
From: Robert McGrail <103004.2770@CompuServe.COM>

Scott,
        I believe that you are looking for Cartesian Closed categories.  In such
categories the types (A->B) are also objects and a "natural" curry operation on
arrows exists.  Good references include Gunter's Semantics of Programming
Languages and Lambek and Scott's Introduction to Higher Order Categorical Logic.
Also you may want to peek at Ben Pierce's book on Category Theory for Computer
Scientists.

Bob McGrail