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16
TinkerType: a language for playing with formal systems
, 2003
"... TinkerType is a pragmatic framework for compact and modular description of formal systems (type systems, operational semantics, logics, etc.). A family of related systems is broken down into a set of clauses – individual inference rules – and a set of features controlling the inclusion of clauses in ..."
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Cited by 20 (0 self)
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TinkerType is a pragmatic framework for compact and modular description of formal systems (type systems, operational semantics, logics, etc.). A family of related systems is broken down into a set of clauses – individual inference rules – and a set of features controlling the inclusion of clauses in particular systems. Simple static checks are used to help maintain consistency of the generated systems. We present TinkerType and its implementation and describe its application to two substantial repositories of typed lambdacalculi. The first repository covers a broad range of typing features, including subtyping, polymorphism, type operators and kinding, computational effects, and dependent types. It describes both declarative and algorithmic aspects of the systems, and can be used with our tool, the TinkerType Assembler,to generate calculi either in the form of typeset collections of inference rules or as executable ML typecheckers. The second repository addresses a smaller collection of systems, and provides modularized proofs of basic safety properties.
A Simply Typed Context Calculus with FirstClass Environments
, 2002
"... . We introduce a simply typed calculus " which has both contexts and environments as firstclass values. In ", holes in contexts are represented by ordinary variables of appropriate types and hole filling is represented by the functional application together with a new abstraction mechanism which t ..."
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Cited by 12 (1 self)
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. We introduce a simply typed calculus " which has both contexts and environments as firstclass values. In ", holes in contexts are represented by ordinary variables of appropriate types and hole filling is represented by the functional application together with a new abstraction mechanism which takes care of packing and unpacking of the term which is used to fill in the holes of the context. " is a conservative extension of the simply typed ficalculus, enjoys subject reduction property, is confluent and strongly normalizing. The traditional method of defining substitution does not work for our calculus. So, we also introduce a new method of defining substitution. Although we introduce the new definition of substitution out of necessity, the new definition turns out to be conceptually simpler than the traditional definition of substitution. 1 Introduction Informally speaking, a context (in calculus) is a term with some holes in it. For example, writing [ ] for a hole, y: [ ] is a...
Relationally Staged Computations in Calculi of Mobile Processes
, 2004
"... ... syntax and functorial operational semantics to give a compositional and fully abstract semantics for the πcalculus equipped with open bisimulation. The key novelty in our work is the realisation that the sophistication of open bisimulation requires us to move from the usual semantic domain of p ..."
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Cited by 10 (2 self)
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... syntax and functorial operational semantics to give a compositional and fully abstract semantics for the πcalculus equipped with open bisimulation. The key novelty in our work is the realisation that the sophistication of open bisimulation requires us to move from the usual semantic domain of presheaves over subcategories of Set to presheaves over subcategories of Rel. This extra structure is crucial in controlling the renaming of extruded names and in providing a variety of different dynamic allocation operators to model the different binders of the πcalculus.
General structural operational semantics through categorical logic (Extended Abstract)
, 2008
"... Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rulebased definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formul ..."
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Cited by 7 (6 self)
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Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rulebased definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formulation we recover precise results for particular language idioms by interpreting the logic in particular categories. For instance, results for firstorder calculi, such as CCS, arise from considering the general results in the category of sets. Results for languages involving substitution and name generation, such as the πcalculus, arise from considering the general results in categories of sheaves and group actions. As an extended example, we develop a tyft/tyxtlike rule format for open bisimulation in the πcalculus.
Model checking for nominal calculi
 IN FOSSACS, VOLUME 3441 OF LNCS
, 2005
"... Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we f ..."
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Cited by 6 (2 self)
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Nominal calculi have been shown very effective to formally model a variety of computational phenomena. The models of nominal calculi have often infinite states, thus making model checking a difficult task. In this note we survey some of the approaches for model checking nominal calculi. Then, we focus on HistoryDependent automata, a syntaxfree automatonbased model of mobility. HistoryDependent automata have provided the formal basis to design and implement some existing verification toolkits. We then introduce a novel syntaxfree setting to model the symbolic semantics of a nominal calculus. Our approach relies on the notions of reactive systems and observed borrowed contexts introduced by Leifer and Milner, and further developed by Sassone, Lack and Sobocinski. We argue that the symbolic semantics model based on borrowed contexts can be conveniently applied to web service discovery and binding.
Modules over Monads and Linearity
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 4 (2 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
Confluence of the Coinductive LambdaCalculus
, 2001
"... The coinductive calculus co arises by a coinductive interpretation of the grammar of the standard calculus and contains nonwellfounded terms. An appropriate notion of reduction is analyzed and proven to be conuent by means of a detailed analysis of the usual Tait/MartinL of style developme ..."
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Cited by 3 (2 self)
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The coinductive calculus co arises by a coinductive interpretation of the grammar of the standard calculus and contains nonwellfounded terms. An appropriate notion of reduction is analyzed and proven to be conuent by means of a detailed analysis of the usual Tait/MartinL of style development argument. This yields bounds for the lengths of those joining reduction sequences that are guaranteed to exist by conuence. These bounds also apply to the wellfounded calculus.
External and internal syntax of the λcalculus
 In: Buchberger, Ida, Kutsia (Eds.), Proc. of the AustrianJapanese Workshop on Symbolic Computation in Software Science, SCSS 2008. No. 08–08 in RISCLinz Report Series
"... There is growing interest in the study of the syntactic structure of expressions equipped with a variable binding mechanism. The importance of this study can be justified for various reasons, e.g. educational, scientific and engineering reasons. This study is educationally important since in logic a ..."
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Cited by 2 (1 self)
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There is growing interest in the study of the syntactic structure of expressions equipped with a variable binding mechanism. The importance of this study can be justified for various reasons, e.g. educational, scientific and engineering reasons. This study is educationally important since in logic and computer science, we cannot avoid teaching the
Strong normalization for System F by HOAS on top of FOAS
"... Abstract—We present a point of view concerning HOAS (HigherOrder Abstract Syntax) and an extensive exercise in HOAS along this point of view. The point of view is that HOAS can be soundly and fruitfully regarded as a definitional extension on top of FOAS (FirstOrder Abstract Syntax). As such, HOAS ..."
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Abstract—We present a point of view concerning HOAS (HigherOrder Abstract Syntax) and an extensive exercise in HOAS along this point of view. The point of view is that HOAS can be soundly and fruitfully regarded as a definitional extension on top of FOAS (FirstOrder Abstract Syntax). As such, HOAS is not only an encoding technique, but also a higherorder view of a firstorder reality. A rich collection of concepts and proof principles is developed inside the standard mathematical universe to give technical life to this point of view. The exercise consists of a new proof of Strong Normalization for System F. HOAS makes our proof considerably more direct than previous proofs. The concepts and results presented here have been formalized in the theorem prover Isabelle/HOL.
αConversion Is Easy
"... We present a new and simple account of αconversion suitable for formal reasoning. Our main tool is to define αconversion as a a structural congruence parametrized by a partial bijection on free variables. We show a number of basic properties of substitution. e.g. that substitution is m ..."
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We present a new and simple account of αconversion suitable for formal reasoning. Our main tool is to define αconversion as a a structural congruence parametrized by a partial bijection on free variables. We show a number of basic properties of substitution. e.g. that substitution is monadic which entails all the usual substitution laws. Finally, we relate αequivalence classes to de Bruijn terms.