http://hdl.handle.net/1880/45289 Thu, 20 Jun 2013 09:34:36 GMT 2013-06-20T09:34:36Z http://hdl.handle.net/1880/45460 Title: ABOUT CHARITY Authors: Fukushima, Tom; Cockett, Robin Abstract: Charity is a categorical programming language based on distributive categories (in the sense of Schanuel and Lawvere) with strong datatypes (in the sense of Hagino). Distributive categories come with a term logic which can express most standard programs; and they are fundamental to computer science because they permit proof by case analysis and, when strong datatypes are introduced, proof by structural induction. Charity is functional and polymorphic in style, and is strongly normalizing. As a categorical programming language it provides a unique marriage of computer science and mathematical thought. The above aspects are particularly important for the production of verified programs as the naturality of morphisms gives us ``theorems for free'', termination proofs are not required, and mathemathical specifications can be used. Mon, 01 Jun 1992 00:00:00 GMT http://hdl.handle.net/1880/45460 1992-06-01T00:00:00Z http://hdl.handle.net/1880/45459 Title: An introduction to partial lambda algebras Authors: Cockett, J. R. B.; Hofstra, P. J. W. Abstract: The purpose of this paper is to give an exposition of the theory of partial combinatory algebras, models of the partial lambda calculus and various related concepts from the point of view of restriction categories. We feel that restriction categories not only simplify and clarify the presentation of the subject matter, but also provide us with precisely the right type of logic to reason about the structures involved. Tue, 31 Oct 2006 00:00:00 GMT http://hdl.handle.net/1880/45459 2006-10-31T00:00:00Z