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From Total Equational to Partial First Order Logic
, 1998
"... The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to pa ..."
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Cited by 19 (8 self)
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The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to partiality, like (variants of) error algebras and ordersortedness are also discussed, showing their uses and limitations. Moreover, both the total and the partial (positive) conditional fragment are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved. Some more powerful algebraic frameworks are sketched at the end. Equational specifications introduced in last chapter, are a powerful tool to represent the most common data types used in programming languages and their semantics. Indeed, Bergstra and Tucker have shown in a series of papers (see [BT87] for a complete exposition of results) that a data type is semicompu...
Using Limits of Parchments to Systematically Construct Institutions of Partial Algebras
 Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types, volume 1130 of Lecture Notes in Computer Science
, 1996
"... this paper, so we leave them out here. Thus we can apply the idea of combining things via colimits to institutions themselves, with the special point that we have to take limits here instead of colimits. Taking limits in CAT results in categories of "amalgamated objects", i. e. we put sig ..."
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Cited by 15 (5 self)
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this paper, so we leave them out here. Thus we can apply the idea of combining things via colimits to institutions themselves, with the special point that we have to take limits here instead of colimits. Taking limits in CAT results in categories of "amalgamated objects", i. e. we put signatures and models together at the level of single objects. In contrast to this, sentences are combined with colimits in Set (due to the contravariant direction of the sentence component). That is, sets of sentences are combined. To show how this works, we introduce some wellknown institutions and morphisms between them.
Label algebras: a systematic use of terms
 In Bidot and Choppy [7
, 1991
"... We give the main definitions and results of a new framework for algebraic specifications: the framework of label algebras. The main idea underlying our approach is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with ra ..."
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Cited by 6 (1 self)
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We give the main definitions and results of a new framework for algebraic specifications: the framework of label algebras. The main idea underlying our approach is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with range in terms instead of values. Surprisingly, there are several cases where even if two terms have the same value, it is possible that one of them is a suitable instance of a variable in an formula while the other one is not. It is for instance the case for algebraic specifications with exception handling or with observability features. We show that our approach is a useful tool for solving this problem.
Classifications In Algebraic Specifications Of Abstract Data Types
, 1996
"... DATA TYPES Simone Veglioni Programming Research Group University of Oxford Oxford, U.K. email: veglioni@comlab.ox.ac.uk PRGTR796 \Delta Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford OX1 3QD Classifications in Algebraic Specifications of Abstract Data Types Simon ..."
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DATA TYPES Simone Veglioni Programming Research Group University of Oxford Oxford, U.K. email: veglioni@comlab.ox.ac.uk PRGTR796 \Delta Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford OX1 3QD Classifications in Algebraic Specifications of Abstract Data Types Simone Veglioni Programming Research Group University of Oxford Oxford, U.K. email:veglioni@comlab.ox.ac.uk keywords: algebraic specification, sort, strong and weak overloading, manysorted and universal structures. Abstract In this paper we describe the role classifications play in algebraic approaches to specification of Abstract Data Types (ADTs) and show how they influence expressivity and mechanizability. In the last two decades many different logical systems for the algebraic specification of ADTs have been developed, each one pursuing its own principles and goals. Since a careful analysis of these logical systems, taking into account not only their expressivity, but also their mech...
Checking
"... In this paper we introduce a structural and objectoriented model. We present applications of this model to the checking of some illformed classes. We focus on static class diagrams mixing inheritance and composition relations. We consider an approach based on the notion of class usefulness, i.e. f ..."
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In this paper we introduce a structural and objectoriented model. We present applications of this model to the checking of some illformed classes. We focus on static class diagrams mixing inheritance and composition relations. We consider an approach based on the notion of class usefulness, i.e. finitely generated and with at least one defined value. We show that this allows us to eliminate some wrong class designs or wrong schema designs. We present a general process to check this and a static algorithm which applies to the UML language. 1
Algebraic System Specification and Development: Survey and Annotated Bibliography  Second Edition 
, 1997
"... Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.5.4 Special Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.6 Semantics of Programming Languages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.6.1 Semantics of Ada . . . ..."
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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...