Abstract Data Types (ADTs) can be specified by the Classified Model (CM) specification language—a first-order Horn language with equality and sort “classification” assertions. Sort assertions generalize the traditional syntactic signatures of ADT specifications, resulting in all of the specification capability of traditional equational specifications, but with the improved expressibility of the...

We show that a suitable abstraction of the notion of term-algebra, called compositum, can be used to capture in a precise mathematical way the intuition that the category of algebras of most (order-sorted) equational theories is completely characterised by their term-model. We also use the relationship between composita and order-sorted equa-tional theories to show that every order-sorted compo...

SUMMARY In this paper, we extend the Gnaedig's re-sults[2][3] on termination of order-sorted rewriting. Gnaedig required a condition for order-sorted signatures, called minimality, for the termination proof. We get rid of this restriction by introducing a transformation from a TRS with an arbitrary order-sorted signature to another TRS with a minimal signature, and proving that this transformat...

We develop an order-sorted higher-order calculus suitable for automatic theorem proving applications by extending the extensional simply typed lambda calculus with a higher-order ordered sort concept and constant overloading. Huet's well-known techniques for unifying simply typed lambda terms are generalized to arrive at a complete transformation-based uniication algorithm for this sorted calcu...

Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In this setting, Order-Sorted First-Order Logic provides a powerful framework to represent declarative programs. It also provides a target logic to obtain models f...

We introduce the notions of sequentiality and strong sequentiality in order-sorted rewriting systems, both closely related to the subsort order and to the form of declarations of the signature. We deene free sequentiality for the class of orthogonal systems with constructors, a notion which does not impose conditions over the signature. We provide an eeective decision procedure for free sequent...

We propose three different notions of completeness for term rewrite specifications supporting order-sorted signatures, deduction modulo axioms, and context-sensitive rewriting relative to a replacement map μ. Our three notions are: (1) an appropriate definition of μ-sufficient completeness with respect to a set of constructor symbols; (2) a definition of μ-canonical completeness under which μ-c...

Our main goal is automating termination proofs for programs in rewriting-based languages with features such as: (i) expressive type structures, (ii) conditional rules, (iii) matching modulo axioms, and (iv) contextsensitive rewriting. Specifically, we present a new operational termination method for membership equational programs with features (i)-(iv) that can be applied to programs in members...