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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.
Parametrized exceptions
 IN CALCO 05, LNCS 3629
, 2005
"... Following the paradigm of encapsulation of side effects via monads, the Java execution mechanism has been described by the socalled Java monad, encorporating essentially stateful computation and exceptions, which are heavily used in Java control flow. A technical problem that appears in this model ..."
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Cited by 4 (3 self)
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Following the paradigm of encapsulation of side effects via monads, the Java execution mechanism has been described by the socalled Java monad, encorporating essentially stateful computation and exceptions, which are heavily used in Java control flow. A technical problem that appears in this model is the fact that the return exception in Java is parametrized by the return value, so that method calls actually move between slightly different monads, depending on the type of the return value. We provide a treatment of this problem in the general framework of exception monads as introduced in earlier work by some of the authors; this framework includes generic partial and total Hoare calculi for abrupt termination. Moreover, we illustrate this framework by means of a verification of a pattern match algorithm.
The Logic of the Partial λCalculus With Equality
"... We investigate the logical aspects of the partial λcalculus with equality, exploiting an equivalence between partial λtheories and partial cartesian closed categories (pcccs) established here. The partial λcalculus with equality provides a fullblown intuitionistic higher order logic, which in a ..."
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Cited by 3 (1 self)
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We investigate the logical aspects of the partial λcalculus with equality, exploiting an equivalence between partial λtheories and partial cartesian closed categories (pcccs) established here. The partial λcalculus with equality provides a fullblown intuitionistic higher order logic, which in a precise sense turns out to be almost the logic of toposes, the distinctive feature of the latter being unique choice. We give a linguistic proof of the generalization of the fundamental theorem of toposes to pcccs with equality; type theoretically, one thus obtains that the partial λcalculus with equality encompasses a MartinLöfstyle dependent type theory. This work forms part of the semantical foundations for the higher order algebraic specification language HasCasl.
www.elsevier.com/locate/entcs HigherOrder Nets for Mobile Policies 1,5
"... Since the early 80’s the combination of Petri nets and rulebased transformations has been extensively researched to obtain new concepts and results. In this paper we consider rules as tokens leading to the concept of higherorder nets for mobile policies. The rules are used on the one hand for the ..."
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Since the early 80’s the combination of Petri nets and rulebased transformations has been extensively researched to obtain new concepts and results. In this paper we consider rules as tokens leading to the concept of higherorder nets for mobile policies. The rules are used on the one hand for the specification of policy rules and on the other hand for the modification of policy rules, i.e. for the definition of new rules by reusing existing rules. So the higherorder net models distribution and modification of policy rules in a systematic and structured way. We give HasCaslspecifications of rules and (local) transformations in the sense of the doublepushout approach and illustrate our concept by a small system inspired by the case study of a tax refund process [1].
BOOTSTRAPPING TYPES AND COTYPES IN HASCASL
"... We discuss the treatment of initial datatypes and final process types in the widespectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constructions o ..."
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We discuss the treatment of initial datatypes and final process types in the widespectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constructions of types of finite and infinite trees that establish the conservativity of datatype and process type declarations adhering to certain reasonable formats. The latter amounts to modifying known constructions from HOL to avoid unique choice; in categorical terminology, this means that we establish that quasitoposes with an internal natural numbers object support initial algebras and final coalgebras for a range of polynomial functors, thereby partially generalizing corresponding results from topos theory. Moreover, we present similar constructions in categories of internal complete partial orders.
Coalgebraic Modal Logic in COCASL
"... We extend the algebraiccoalgebraic specification language CoCasl by full coalgebraic modal logic based on predicate liftings for functors. This logic is more general than the modal logic previously used in CoCasl and supports the specification of a variety of modal logics, such as graded modal log ..."
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We extend the algebraiccoalgebraic specification language CoCasl by full coalgebraic modal logic based on predicate liftings for functors. This logic is more general than the modal logic previously used in CoCasl and supports the specification of a variety of modal logics, such as graded modal logic, majority logic, and probabilistic modal logic. CoCasl thus becomes a modern modal language that covers a wide range of Kripke and nonKripke semantics of modal logics via the coalgebraic interpretation.
Preface CASL, theCommon Algebraic Specification Language, has been designed by
"... CoFI, the Common Framework Initiative for algebraic specification and development. CASL is an expressive language for specifying requirements and design for conventional software. It is algebraic in the sense that models of CASL specifications are algebras; the axioms can be arbitrary firstorder fo ..."
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CoFI, the Common Framework Initiative for algebraic specification and development. CASL is an expressive language for specifying requirements and design for conventional software. It is algebraic in the sense that models of CASL specifications are algebras; the axioms can be arbitrary firstorder formulas. CASL is a major new algebraic specification language. It has been carefully designed by a large group of experts as a generalpurpose language for practical use in software development – in particular, for specifying both requirements and design. CASL includes carefully selected features from many previous specification languages, as well as some novel features that allow algebraic specifications to be written much more concisely and perspicuously than hitherto. It may ultimately replace most of the previous languages, and provide a common basis for future research and development. CASL has already attracted widespread interest within the algebraic specification community, and is generally regarded as a de facto standard. Various sublanguages of CASL are available – primarily for use in connection with