Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples demonstrate the surprising power of circular coinductive rewriting. The paper also sketches the underlying hidden algebraic theory and briefly describes BOBJ and some of its algorithms.

We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples.

This paper describes the Tatami project at UCSD, which is developing a system to support distributed cooperative software development over the web, and in particular, the validation of concurrent distributed software. The main components of our current prototype are a proof assistant, a generator for documentation websites, a database, an equational proof engine, and a communication protocol to support distributed cooperative work. We believe behavioral specification and verification are important for software development, and for this purpose we use first order hidden logic with equational atoms. The paper also briefly describes some novel user interface design methods that have been developed and applied in the project

recent advances in web technology, interface design, and specification. Our effort to improve the usability of such systems has led us into algebraic semiotics, while our effort to develop better formal methods for distributed concurrent systems has led us into hidden algebra and fuzzy logic. This paper discusses the Tatami system design, especially its software architecture, and its user interface principles. New work in the latter area includes an extension of algebraic semiotics to dynamic multimedia interfaces, and integrating Gibsonian affordances with algebraic semiotics. 1

Abstract. Using equational logic as a specification language, we investigate the proof theory of behavioral subtyping for object-oriented abstract data types with immutable objects and deterministic methods that can use multiple dispatch. In particular, we investigate a proof technique for correct behavioral subtyping in which each subtype’s specification includes terms that can be used to coerce its objects to objects of each of its supertypes. We show that this technique is sound, using our previous work on the model theory of such abstract data types. We also give an example to show that the technique is not complete, even if the methods do not use multiple dispatch, and even if types specified are term-generated. In preparation for the results on equational subtyping we develop the proof theory of a richer form of equational logic that is suitable for dealing with subtyping and behavioral equivalence. This gives some insight into question of when our proof techniques can be make effectively computable, but in general behavioral consequence is not effectively computable. 1.

In this paper we prove coinduction theorems for nal coalgebras of endofunctors on categories of partial orders and (generalized) metric spaces. These results characterize the order, respectively the metric, on a nal coalgebra as maximum amongst all simulations. As suggested in [15], and motivated by the idea that partial orders and metric spaces are types of enriched category, the notion of simulation is based on the enriched categorical counterpart of relations, called bimodules. In fact, the results above arise as instances of a coinduction theorem, parametric in a quantale applying to nal coalgebras of endofunctors on the category of all (small) all) 50147 and 18636-3 Also, we give a condition under which the operational notion of simulation coincides with the denotational notion of nal semantics. 1 Introduction Coinduction is a principle for reasoning about potentially innite or circular elements of recursive data types, like streams, processes or exact reals [14,5,7]. Typ...

Abstract: We investigate behavioral institutions and refinements in the context of the object oriented paradigm. The novelty of our approach is the application of generalized abstract algebraic logic theory of hidden heterogeneous deductive systems (called hidden k-logics) to the algebraic specification of object oriented programs. This is achieved through the Leibniz congruence relation and its combinatorial properties. We reformulate the notion of hidden k-logic as well as the behavioral logic of a hidden k-logic as institutions. We define refinements as hidden signature morphisms having the extra property of preserving logical consequence. A stricter class of refinements, the ones that preserve behavioral consequence, is studied. We establish sufficient conditions for an ordinary signature morphism to be a behavioral refinement.