A Computer Algebra System based on Order-sorted Algebra

Order Sorted Quotient Algebra

Let R be a non empty poset. One can verify that there exists an order sorted set of R which is binary relation yielding. Let R be a non empty poset, let A, B be many sorted sets indexed by the carrier of R, and let I1 be a many sorted relation between A and B. We say that I1 is os-compatible if and only if the condition (Def. 1) is satisfied. (Def. 1) Let s1, s2 be elements of the carrier of R....

Free Order Sorted Universal Algebra

In this paper S is an order sorted signature. Let S be an order sorted signature and let U0 be an order sorted algebra of S. A subset of U0 is called an order sorted generator set of U0 if: (Def. 1) For every OSSubset O of U0 such that O = OSCl it holds the sorts of OSGenO = the sorts of U0. The following proposition is true (1) Let S be an order sorted signature, U0 be a strict non-empty order...

Order Sorted Computer Algebra and Coercions Submitted By

Computer algebra systems are large collections of routines for solving mathematical problems algorithmically e ciently and above all symbolically The more advanced and rigorous computer algebra systems for example Axiom use the concept of strong types based on order sorted algebra and category theory to ensure that operations are only applied to expressions when they make sense In cases where A...

A Framework for Order-Sorted Algebra

Order-sorted algebra is a generalization of many-sorted algebra obtained by having a partially ordered set of sorts rather than merely a set. It has numerous applications in computer science. There are several variants of order sorted algebra, and some relationships between these are known. However there seems to be no single conceptual framework within which all the connections between the var...

An Oxford Survey of Order Sorted Algebra