We consider the problem of proving termination of ordersorted rewrite systems. The dominating method for proving termination of order-sorted systems has been to simply ignore sort information, and use the techniques developed for unsorted rewriting. The problem with this approach is that many order-sorted rewrite systems terminate because of the structure of the set of sorts. In these cases the...

The paper provides an organisation of order-sorted equational logic as an Institution.

We study the problem of pattern matching in order-sorted languages whose evaluation strategy is lazy. We propose an extension of the Puel-Suárez compilation scheme to function definitions via order-sorted patterns. Basically, a list of ordered and possibly ambiguous linear patterns is transformed into a set of disjoint order-sorted constrained terms. This set is in turn transformed according to...

Term rewriting system is a helpful tool for implementing functional programming languages. We focus upon a transformation of term rewriting systems called currying. Currying transforms a term rewriting system with symbols of arbitrary arity into another one, which contains only nullary symbols with a single binary symbol called application. Currying in single-sorted case is explored in [1] but ...

ion mechanism. Many database researchers have used OSFOL to view the Relational Data Model (RDM) ; however, no RDM has been modelled by MSFOL. This paper first gives a formal definition for MSFOL and then its advantages of expressiveness and of abstraction are illustrated. Two reduction algorithms which can transform an MSFOL-based language into\from an OSFOL-based language are given. The seman...

This paper develops a sound and complete transformation-based algorithm for uniication in an extensional order-sorted combinatory logic supporting constant overloading and a higher-order sort concept. Appropriate notions of order-sorted weak equality and extensionality | reeecting order-sorted-equality in the corresponding lambda calculus given by Johann and Kohlhase | are deened, and the typed...

Order-sorted algebras and many sorted algebras exist in a long history with many different implementations and applications. A lot of language specifications have been defined in order-sorted algebra frameworks such as the language specifications in K (an order-sorted algebra framework). The biggest problem in a lot of the order-sorted algebra frameworks is that even if they might allow develop...

Order-sorted type systems supporting inheritance hierarchies and subtype polymorphism are used in theorem proving, AI, and declarative programming. The satisfiability problems for the theories of: (i) order-sorted uninterpreted function symbols, and (ii) of such symbols modulo a subset Δ of associative-commutative ones are reduced to the unsorted versions of such problems at no extra computatio...

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...

Let I be a set, let f be a many sorted set indexed by I, and let p be a finite sequence of elements of I. Observe that f · p is finite sequence-like. Let S be a non empty many sorted signature. A sort symbol of S is an element of S. Let S be a non empty many sorted signature. An operation symbol of S is an element of the operation symbols of S. Let S be a non void non empty many sorted signatur...