Initial Semantics of Specifications

Ehrig, Hartmut; Mahr, Bernd

doi:10.1007/978-3-642-69962-7_4

Cited by 36 publications

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“…Whereas genericity by structure is an outcome of the work on abstract datatypes [90], genericity by property follows from the enrichment of that work to include equational constraints, leading to algebraic specifications [28,29], as realised in languages such as Larch [55] and Casl [20,8].…”

Section: Genericity By Propertymentioning

confidence: 99%

Datatype-Generic Programming

Gibbons

2007

Datatype-Generic Programming

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Abstract. Generic programming aims to increase the flexibility of programming languages, by expanding the possibilities for parametrization -ideally, without also expanding the possibilities for uncaught errors. The term means different things to different people: parametric polymorphism, data abstraction, meta-programming, and so on. We use it to mean polytypism, that is, parametrization by the shape of data structures rather than their contents. To avoid confusion with other uses, we have coined the qualified term datatype-generic programming for this purpose. In these lecture notes, we expand on the definition of datatype-generic programming, and present some examples of datatypegeneric programs. We also explore the connection with design patterns in object-oriented programming; in particular, we argue that certain design patterns are just higher-order datatype-generic programs.

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Section: Genericity By Propertymentioning

confidence: 99%

Datatype-Generic Programming

Gibbons

2007

Datatype-Generic Programming

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“…Previous research has viewed composite specifications as colimits; the approaches have varied, however, in the choice of a category with appropriate colimits. For example, the pioneering work by Burstall and Goguen on expressing the structuring of specifications by constructing the colimits of diagrams, in [2,3], was continued in the algebraic approach to specification [5,4,10] and also in proof-theoretic approaches [7,11]. All these research methods depended on the different specification logics that were used, because they constructed colimits over some cocomplete category of specifications.…”

Section: Composite Specifications As Presheavesmentioning

confidence: 99%

A Language for Configuring Multi-level Specifications

Hill

Vickers

2004

Algebraic Methodology and Software Technology

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Abstract. This paper shows how systems can be built from their component parts with specified sharing. Its principle contribution is a modular language for configuring systems. A configuration is a description in the new language of how a system is constructed hierarchically from specifications of its component parts. Category theory has been used to represent the composition of specifications that share a component part by constructing colimits of diagrams. We reformulated this application of category theory to view both configured specifications and their diagrams as algebraic presentations of presheaves. The framework of presheaves leads naturally to a configuration language that expresses structuring from instances of specifications, and also incorporates a new notion of instance reduction to extract the component instances from a particular configuration. The language now expresses the hierarchical structuring of multi-level configured specifications. The syntax is simple because it is independent of any specification language; structuring a diagram to represent a configuration is simple because there is no need to calculate a colimit; and combining specifications is simple because structuring is by configuration morphisms with no need to flatten either specifications or their diagrams to calculate colimits.

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“…In their ftmctional testing approach, Frankl et al use algebraic specifications [17][18][19] of abstract data types (ADTs) to specify classes in target programs. A series of operations on an ADT is known as a term (or called a "word" in Frankl et al).…”

Section: A Summary Of Frankl's Functional Testing Approachmentioning

confidence: 99%

“…Bubble sort is chosen because it is familiar to most readers. [17,18]. A tenn can be transfonned into another using the axioms of the specification as progressive left-to-rigirt rewriting rules.…”

Section: An Axiom-based Strategy For Selecting Equivalent Test Casesmentioning

confidence: 99%

An Axiom-Based Test Case Selection Strategy for Object-Oriented Programs

Tse

Chan

Chen

1995

Software Quality and Productivity

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Because of the growing importance of object-oriented programming, a munber of testing approaches have been proposed. Frankl et: aI. propose the application of the functional approach, using algebraic specifications for the gEneration of test cases and the validation of methods. Given a specification, Frankl et: aI. propose that equivalent terms should give observably equivalent objects, and offer gEneral heuristics on the selection of equivalent terms for testing. Their guidelines, however, are only supported by limited empirical results, do not have a theoretical basis, and provide no guarantee of effectiveness.In this paper, we define the concept of a fundamental pair as a pair of equivalent terms which are formed by replacing all the variables on both sides of an axiom by normal forms. We prove that an implementation is consistent with respect to all equivalent terms if and only if it is consistent with respect to all fundamental pairs. In other words, the testing coverage of fundamental pairs is identical to that of all equivalent tenns, and hence we need only concentrate on the testing of fundamental pairs. Our strate&Y is mathematically based, simple, and much more efficient. Furthermore, it lD1derscores the usefulness of axiom-based specifications.

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Initial Semantics of Specifications

Cited by 36 publications

References 0 publications

Datatype-Generic Programming

Datatype-Generic Programming

A Language for Configuring Multi-level Specifications

An Axiom-Based Test Case Selection Strategy for Object-Oriented Programs

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