From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1333 Path: news.gmane.org!not-for-mail From: Barry Jay Newsgroups: gmane.science.mathematics.categories Subject: functorial lambda calculus Date: Mon, 10 Jan 2000 14:57:41 +1100 (EST) Message-ID: <200001100357.OAA15318__26931.9218270995$1241017757$gmane$org@algae.socs.uts.EDU.AU> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241017756 30767 80.91.229.2 (29 Apr 2009 15:09:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:09:16 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Jan 10 11:10:54 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA16757 for categories-list; Mon, 10 Jan 2000 09:40:29 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:1333 Archived-At: The following report is available from: Comments most welcome. Barry Jay ------------------------------------------------------------------- Functorial Lambda-calculus C. Barry Jay Functorial lambda-calculus represents some type constructors as functors, whose quantification supports new forms of polymorphism. This is exploited by a powerful new generic programming technique, called program extension, whose evaluation does not use explicit types. It can be used to define all the standard second-order combinators, for mapping, folding, etc. so that they apply to arbitrary data types. It can also be used to define generic functions for equality, addition, assignment and shape. In particular, shape evaluation can be used to support static specialisation, and to reduce space usage. This paper introduces the calculus, provides a type inference algorithm, and shows how to augment its expressive power and improve its efficiency by adding more constructions and optimising evaluation.