This paper presents a rule-based algorithm for performing order-sorted E-unification using an unsorted E-unification decision procedure under assumptions about E that are commonly satisfied in practice. We have implemented this algorithm in Maude for use with the Maude-NRL protocol analyzer and have used CiME for unsorted E-unification for E any set of AC and ACU axioms. In many examples of int...

ML-style polymorphism can be generalized from a single-sorted algebra of types to an order-sorted one by adding a partially ordered layer of “sorts” on top of the types. Type inference proceeds as in the Hindley/Milner system, except that order-sorted unification of types is used. The resulting system has been implemented in Isabelle to permit type variables to range over user-definable subsets...

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 feature (OSF) terms provide an adequate representation for objects as flexible records. They are sorted, attributed, possibly nested, structures, ordered thanks to a subsort ordering. Sort definitions offer the functionality of classes imposing structural constraints on objects. These constraints involve variable sorting and equations among feature paths, including self-reference. ...

We prove cocompleteness of the category of CASL signatures , of monotone signatures, of strongly regular signatures and of strongly locally ltered signatures. This shows that using these signature categories is compatible with a pushout or colimit based module system.