This paper gives a short introduction to the algebraic specification language Spectrum. Using simple, well-known examples, the objectives and concepts of Spectrum are explained. The Spectrum language is based on axiomatic specification techniques and is oriented towards functional programs. Spectrum includes the following features: ffl partial functions, definedness logic and fixed point theory ffl higher-order elements and typed -abstraction ffl non-strict functions and infinite objects ffl full first-order predicate logic with induction principles ffl predicative polymorphism with sort classes ffl parameterization and modularization Spectrum is based on the concept of loose semantics.

The signature and logical calculus of the algebraic specification language Spectrum are formalized in the generic language Deva. This language is designed to express formal methods as well as proofs of propositions about the objects of such methods and the relations between them. This work is understood as a first step towards a formalization of the software development methodology induced by specifying software in Spectrum. This work has been funded by the German Ministry of Research and Technology as part of the project KORSO under contract 01 IS 203 C9. I thank Martin Beyer, Maritta Heisel, and Matthias Weber for constructive comments on several drafts of this paper. Florian Kammuller checked the entire formalization and developed the example given in the appendix with the Deva support system. Contents 1 Introduction 3 2 Two Brief Language Descriptions 3 2.1 The Algebraic Specification Language Spectrum : : : : : : : : : : : : : : : : : : 3 2.2 The Generic Language Deva : : : :...

. The Spectrum project concentrates on the process of developing well-structured, precise system specifications. Spectrum is a specification language, with a deduction calculus and a development methodology. An informal presentation of the Spectrum language with many examples illustrating its properties is given in [2, 3]. The purpose of this article is to describe its formal semantics. 1 Introduction The Spectrum specification language is axiomatic and borrows concepts both from algebraic languages (e.g. LARCH [12]) as well as from type theoretic languages (e.g. LCF [4]). An informal presentation with many examples illustrating its properties is given in [2, 3]. We briefly summarize its principal characteristics. Influences from algebra. In Spectrum specifications the influence of algebraic techniques is evident. Every specification consists of a signature and an axioms part. However, in contrast to most algebraic specification languages, the semantics of a specification in Spectrum...

Syntax : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.3 The Translation Rules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2 Lexical Syntax 5 3 The Core Language 7 3.1 In the Small : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 3.1.1 Context Free Syntax : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 3.1.2 Semantic Objects : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 3.1.3 Translation Rules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 3.1.4 The Sort Inference : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 15 3.1.5 Class Inference : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 16 3.1.6 Infix Symbols : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 17 3.2 In the Large : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 17 3.2.1 Context Free Syntax : : :...

Classical approaches to parameterization in axiomatic specification languages require the user to explicitly handle specification instantiation. This often makes specifications less readable and manageable. We therefore present a new parameterization mechanism which allows implicit instantiation. However, since this mechanism is less powerful as the first one we show how to combine them to achieve both elegance and power. We included both mechanisms in the specification language Spectrum.

. The specification language Spectrum [BFG + 93] melts a wide range of concepts into a single language frame: three-valued first-order logic, polymorphism, type classes, higher-order functions, infinite objects. The desire of identifying and relating sub-languages satisfying certain constraints given by syntactical and pragmatic considerations appears. In this paper we consider the constructive oriented algebraic sub-language ACT ONE as an example of a specification sub-language of Spectrum. As a candidate for an implementation language of Spectrum we focus on the functional language Opal. The overall intention is to establish a semantically compatible embedding of ACT ONE and Opal into Spectrum. However, in this paper we will not describe all aspects of this embedding. As a first step of our ongoing work we will relate the underlying logical systems using the concept of institutions, i.e. we will relate the loose semantics of ACT ONE and Opal specifications with the lo...

This paper gives a short introduction to the algebraic specification language Spectrum.

. We propose a new approach to algebraic semantics of functional languages based on higher-order partial algebras and conditional existence equations. After dicussing more generally the relation ships between certain features of functional languages and special algebraic concepts and techniques the paper presents the theoretical basis of our approach. The main result concerns the existence of higher-order partial algebras freely generated by a set of variables and a set of existence equations. This result ensures the existence of free functor semantics in our approach. 1 Introduction We propose in this paper a new pragmatical approach to algebraic semantics of functional languages. The development of this approach was guided by the following heuristic principles: -- The basis should be a well-developed first-order algebraic specification formalism providing initial/free semantics and compositional operations on specifications. -- Higher-order features should be incorporated...

The primary focus of my research is to develop formal methods and tools which support the modeling and automated analysis of complex computational systems, including software systems, embedded systems and biological systems. To manage complexity we used two complementary approaches: statistical analysis and modular reasoning. For the latter we carefully distinguish between architectural hierarchy, behavioral hierarchy and interaction hierarchy. Moreover, we equip the modeling formalisms and their associated semantics with corresponding hierarchy building operators. To support automated analysis we focused on (software) model checking and testing techniques. In this context, we use statistical methods to derive a novel Monte Carlo model checking algorithm, which allows to trade time and space for precision and confidence in the result. We also exploit behavioral and interaction hierarchies to devise more efficient search routines as well as new modular reasoning techniques. To apply our techniques to a large variety of applications we developed modeling formalisms for both discrete and mixed discrete and continuous systems. In particular, for discrete systems we proposed algebraic techniques, stream processing functions and relations, hierarchic reactive

Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.2 Action Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.1 Early Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . . 53 4.7.2 Recent Algebraic Specification Languages . . . . . . . . . . . . . . . . . . . . . . . 55 4.7.3 The Common Framework Initiative. . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5 Methodology 57 5.1 Development Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.1.1 Applica...