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32
A Semantic analysis of control
, 1998
"... This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that ..."
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Cited by 38 (6 self)
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This thesis examines the use of denotational semantics to reason about control flow in sequential, basically functional languages. It extends recent work in game semantics, in which programs are interpreted as strategies for computation by interaction with an environment. Abramsky has suggested that an intensional hierarchy of computational features such as state, and their fully abstract models, can be captured as violations of the constraints on strategies in the basic functional model. Nonlocal control flow is shown to fit into this framework as the violation of strong and weak ‘bracketing ’ conditions, related to linear behaviour. The language µPCF (Parigot’s λµ with constants and recursion) is adopted as a simple basis for highertype, sequential computation with access to the flow of control. A simple operational semantics for both callbyname and callbyvalue evaluation is described. It is shown that dropping the bracketing condition on games models of PCF yields fully abstract models of µPCF.
Computation with classical sequents
 MATHEMATICAL STRUCTURES OF COMPUTER SCIENCE
, 2008
"... X is an untyped continuationstyle formal language with a typed subset which provides a CurryHoward isomorphism for a sequent calculus for implicative classical logic. X can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make X ..."
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Cited by 17 (16 self)
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X is an untyped continuationstyle formal language with a typed subset which provides a CurryHoward isomorphism for a sequent calculus for implicative classical logic. X can also be viewed as a language for describing nets by composition of basic components connected by wires. These features make X an expressive platform on which algebraic objects and many different (applicative) programming paradigms can be mapped. In this paper we will present the syntax and reduction rules for X and in order to demonstrate the expressive power of X, we will show how elaborate calculi can be embedded, like the λcalculus, Bloo and Rose’s calculus of explicit substitutions λx, Parigot’s λµ and Curien and Herbelin’s λµ ˜µ.
Completeness and Partial Soundness Results for Intersection & Union Typing for λµ ˜µ
 Annals of Pure and Applied Logic
"... This paper studies intersection and union type assignment for the calculus λµ ˜µ [17], a proofterm syntax for Gentzen’s classical sequent calculus, with the aim of defining a typebased semantics, via setting up a system that is closed under conversion. We will start by investigating what the minima ..."
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Cited by 8 (7 self)
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This paper studies intersection and union type assignment for the calculus λµ ˜µ [17], a proofterm syntax for Gentzen’s classical sequent calculus, with the aim of defining a typebased semantics, via setting up a system that is closed under conversion. We will start by investigating what the minimal requirements are for a system for λµ ˜µ to be closed under subject expansion; this coincides with System M ∩ ∪ , the notion defined in [19]; however, we show that this system is not closed under subject reduction, so our goal cannot be achieved. We will then show that System M ∩ ∪ is also not closed under subjectexpansion, but can recover from this by presenting System M C as an extension of M ∩ ∪ (by adding typing rules) and showing that it satisfies subject expansion; it still lacks subject reduction. We show how to restrict M ∩ ∪ so that it satisfies subjectreduction as well by limiting the applicability to type assignment rules, but only when limiting reduction to (confluent) callbyname or callbyvalue reduction M ∩ ∪ ; in restricting the system, we sacrifice subject expansion. These results combined show that a sound and complete intersection and union type assignment system cannot be defined for λµ ˜µ with respect to full reduction.
An OutputBased Semantics of Λµ with Explicit Substitution
 in the πcalculus. IFIPTCS’12, LNCS 7604
, 2012
"... We study the Λµcalculus, extended with explicit substitution, and define a compositional outputbased translation into a variant of the πcalculus with pairing. We show that this translation preserves singlestep explicit head reduction with respect to contextual equivalence. We use this result to ..."
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Cited by 6 (6 self)
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We study the Λµcalculus, extended with explicit substitution, and define a compositional outputbased translation into a variant of the πcalculus with pairing. We show that this translation preserves singlestep explicit head reduction with respect to contextual equivalence. We use this result to show operational soundness for head reduction, adequacy, and operational completeness. Using a notion of implicative typecontext assignment for the πcalculus, we also show that assignable types are preserved by the translation. We finish by showing that termination is preserved.
Strong Normalization of Second Order Symmetric Lambdamu Calculus
 Information and Computation
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*X: a diagrammatic calculus with a classical fragrance
"... *X is a diagrammatic calculus. This means that it describes programs by 2dimensional diagrams and computations are reductions of those diagrams. In addition it has a 1dimensional syntax. Type system of *X interprets simply classical logic in a CurryHoward correspondence. Since λcalculus can be ..."
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Cited by 4 (2 self)
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*X is a diagrammatic calculus. This means that it describes programs by 2dimensional diagrams and computations are reductions of those diagrams. In addition it has a 1dimensional syntax. Type system of *X interprets simply classical logic in a CurryHoward correspondence. Since λcalculus can be easily implemented, its untyped version is Turing complete.
Sound and Complete Typing for λµ
"... In this paper we define intersection and union type assignment for Parigot’s calculus λµ. We show that this notion is complete (i.e. closed under subjectexpansion), and show also that it is sound (i.e. closed under subjectreduction). This implies that this notion of intersectionunion type assignme ..."
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In this paper we define intersection and union type assignment for Parigot’s calculus λµ. We show that this notion is complete (i.e. closed under subjectexpansion), and show also that it is sound (i.e. closed under subjectreduction). This implies that this notion of intersectionunion type assignment is suitable to define a semantics.