This paper generalizes the hidden algebra approach to allow: (P1) operations with multiple hidden arguments, and (P2) defining behavioral equivalence with a subset of operations, in addition to the already present (P3) built-in data types, (P4) nondeterminism, (P5) concurrency, and (P6) non-congruent operations. All important results generalize, but more elegant formulations use the new institution in Section 5. Behavioral satisfaction appeared 1981 in [20], hidden algebra 1989 in [9], multiple hidden arguments 1992 in [1], congruent and behavioral operations in [1, 18], behavioral equivalence defined by a subset of operations in [1], and non-congruent operations in [5]; all this was previously integrated in [21], but this paper gives new examples, institutions, and results relating hidden algebra to information hiding. We assume familiarity with basics of algebraic specification, e.g., [11, 13].

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

Circular coinduction is a technique for behavioral reasoning that extends cobasis coinduction to specifications with circularities. Because behavioral satisfaction is not recursively enumerable, no algorithm can work for every behavioral statement. However, algorithms using circular coinduction can prove every practical behavioral result that we know. This paper proves the correctness of circular coinduction and some consequences.

After a brief review of hidden algebra, we give behavioral specifications for set theory and closure operators, and then use these to give a behavioral specification of an abstract protocol to support distributed cooperative work structured by dependencies in such a way as to form what we call a weak closure operator. We give some correctness proofs for this protocol, and then describe a concrete instance of it, called the tatami protocol, that supports distributed cooperative proving. Finally, we draw some methodological conclusions.

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