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Permissive Subsorted Partial Logic in CASL
, 1997
"... . This paper presents a permissive subsorted partial logic used in the CoFI Algebraic Specification Language. In contrast to other ordersorted logics, subsorting is not modeled by set inclusions, but by injective embeddings allowing for more general models in which subtypes can have different data t ..."
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Cited by 13 (8 self)
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. This paper presents a permissive subsorted partial logic used in the CoFI Algebraic Specification Language. In contrast to other ordersorted logics, subsorting is not modeled by set inclusions, but by injective embeddings allowing for more general models in which subtypes can have different data type representations. Furthermore, there are no restrictions like monotonicity, regularity or local filtration on signatures at all. Instead, the use of overloaded functions and predicates in formulae is required to be sufficiently disambiguated, such that all parses have the same semantics. An overload resolution algorithm is sketched. 1 Introduction During the past decades a large number of algebraic specification languages have been developed. The presence of so many similar specification languages with no common framework hinders the dissemination and application of research results in algebraic specification. In particular, it makes it difficult to produce educational material, to reus...
Type class polymorphism in an institutional framework
 IN JOSÉ FIADEIRO, EDITOR, 17TH WADT, LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... Higherorder logic with shallow type class polymorphism is widely used as a specification formalism. Its polymorphic entities (types, operators, axioms) can easily be equipped with a ‘naive ’ semantics defined in terms of collections of instances. However, this semantics has the unpleasant property ..."
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Cited by 12 (7 self)
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Higherorder logic with shallow type class polymorphism is widely used as a specification formalism. Its polymorphic entities (types, operators, axioms) can easily be equipped with a ‘naive ’ semantics defined in terms of collections of instances. However, this semantics has the unpleasant property that while model reduction preserves satisfaction of sentences, model expansion generally does not. In other words, unless further measures are taken, type class polymorphism fails to constitute a proper institution, being only a socalled rps preinstitution; this is unfortunate, as it means that one cannot use institutionindependent or heterogeneous structuring languages, proof calculi, and tools with it. Here, we suggest to remedy this problem by modifying the notion of model to include information also about its potential future extensions. Our construction works at a high level of generality in the sense that it provides, for any preinstitution, an institution in which the original preinstitution can be represented. The semantics of polymorphism used in the specification language HasCasl makes use of this result. In fact, HasCasl’s polymorphism is a special case of a general notion of polymorphism in institutions introduced here, and our construction leads to the right notion of semantic consequence when applied to this generic polymorphism. The appropriateness of the construction for other frameworks that share the same problem depends on methodological questions to be decided case by case. In particular, it turns out that our method is apparently unsuitable for observational logics, while it works well with abstract state machine formalisms such as statebased Casl.
Translating OBJ3 into CASL: the Institution Level
 In Recent Trends in Algebraic Development Techniques, Proc. 13th International Workshop, WADT '98
, 1998
"... We translate OBJ3 to CASL. At the level of basic specifications, we set up several institution representations between the underlying institutions. They correspond to different methodological views of OBJ3. The translations can be the basis for automated tools translating OBJ3 to CASL. ..."
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Cited by 3 (0 self)
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We translate OBJ3 to CASL. At the level of basic specifications, we set up several institution representations between the underlying institutions. They correspond to different methodological views of OBJ3. The translations can be the basis for automated tools translating OBJ3 to CASL.
Limits and Colimits in Some Categories of Institutions
, 1997
"... : This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are ..."
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: This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are given. 1 Introduction We have to live with a multitude of logical systems used in various approaches to software specification and development. The proliferation of logical systems in the area is not just researchers' fancy, but results from the very practical needs to capture various aspects of software systems and to cater for various programming paradigms. Each of them leads to a different notion of a semantic model capturing the semantic essence of the adopted view of software systems. For instance, standard (manysorted) algebras [BL70], [GTW78] provide a satisfactory framework for modelling data types where all operations always yield welldefined results. However, if general recursi...
Subsorting in CASL  CoFI Language Design Study Note
, 1996
"... Contents 1 The semantics of subsorting 1 1.1 Concrete representation of manysorted terms and sentences . . . . . 2 1.2 Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Subsorted sentences . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Models . . . . ..."
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Contents 1 The semantics of subsorting 1 1.1 Concrete representation of manysorted terms and sentences . . . . . 2 1.2 Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Subsorted sentences . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 The language for expressing subsorting 3 2.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Predicative subsorts . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Axioms and Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3.1 CASLterms and atomic sentences . . . . . . . . . . . . . . . 4 2.3.2 Expansion of terms and sentences . . . . . . . . . . . . . . . 5 2.3.3 Equivalent expansions . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Type definition group . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Multiple representa