Results 1  10
of
14
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 32 (5 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.
Finitary PCF is not decidable
 Theoretical Computer Science
, 1996
"... The question of the decidability of the observational ordering of finitary PCF was raised [5] to give mathematical content to the full abstraction problem for PCF [9, 14]. We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstra ..."
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Cited by 25 (0 self)
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The question of the decidability of the observational ordering of finitary PCF was raised [5] to give mathematical content to the full abstraction problem for PCF [9, 14]. We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstract model can be. It also gives a slight strengthening of the author’s earlier result on typed λdefinability [6].
DECIDABILITY OF HIGHERORDER MATCHING
"... Abstract. We show that the higherorder matching problem is decidable using a gametheoretic argument. ..."
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Cited by 8 (3 self)
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Abstract. We show that the higherorder matching problem is decidable using a gametheoretic argument.
Unary PCF is decidable
 Theoretical Computer Science
, 1998
"... We show that unary PCF, a very small fragment of Plotkin’s PCF [?], model is effectively presentable. This is in marked contrast to larger fragments, where corresponding results fail [?]. The techniques used are adaptions of those of Padovani [?], who applied them to the minimal model of the simply ..."
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Cited by 8 (2 self)
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We show that unary PCF, a very small fragment of Plotkin’s PCF [?], model is effectively presentable. This is in marked contrast to larger fragments, where corresponding results fail [?]. The techniques used are adaptions of those of Padovani [?], who applied them to the minimal model of the simply typed lambda calculus.
Fully Complete Minimal PER Models for the Simply Typed λcalculus
 CSL'01, LNCS 2142
, 2001
"... We show how to build a fully complete model for the maximal theory of the simply typed λcalculus with k ground constants, k. This is obtained by linear realizability over an affine combinatory algebra of partial involutions from natural numbers into natural numbers. For simplicitly, we give the det ..."
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Cited by 6 (3 self)
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We show how to build a fully complete model for the maximal theory of the simply typed λcalculus with k ground constants, k. This is obtained by linear realizability over an affine combinatory algebra of partial involutions from natural numbers into natural numbers. For simplicitly, we give the details of the construction of a fully complete model for k extended with ground permutations. The fully complete minimal model for k can be obtained by carrying out the previous construction over a suitable subalgebra of partial involutions. The full completeness result is then put to use in order to prove some simple results on the maximal theory.
Games and Sequential Algorithms
, 2001
"... The relationship between HylandOngstyle games and BerryCurien sequential algorithms is investigated, with the object of describing semantic solutions to two problems  to characterise eectively the \minimal models" of the simplytyped calculus and the fully abstract model of PCF with control ..."
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Cited by 4 (0 self)
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The relationship between HylandOngstyle games and BerryCurien sequential algorithms is investigated, with the object of describing semantic solutions to two problems  to characterise eectively the \minimal models" of the simplytyped calculus and the fully abstract model of PCF with control operators  which are shown to be equivalent.
Bistable biorders: a sequential domain theory
 Oura) Physics of Snow and Ice
, 2005
"... Abstract. We give a simple ordertheoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order — the extensional order — and a bistable coherence, which captures equivalence of program behaviour, up to permutation ..."
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Abstract. We give a simple ordertheoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order — the extensional order — and a bistable coherence, which captures equivalence of program behaviour, up to permutation of top (error) and bottom (divergence). We show that monotone and bistable functions (which are required to preserve bistably bounded meets and joins) are strongly sequential, and use this fact to prove universality results for the bistable biorder semantics of the simplytyped lambdacalculus (with atomic constants), and an extension with arithmetic and recursion. We also construct a bistable model of SPCF, a higherorder functional programming language with nonlocal control. We use our universality result for the lambdacalculus to show that the semantics of SPCF is fully abstract. We then establish a direct correspondence between bistable functions and sequential algorithms by showing that sequential data structures give rise to bistable biorders, and that each bistable function between such biorders is computed by a sequential algorithm. 1.
Linear realizability and full completeness for typed lambda calculi
 Annals of Pure and Applied Logic
, 2005
"... We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λcalculi. In particular, we ..."
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We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λcalculi. In particular, we focus on special Linear Combinatory Algebras of partial involutions, and we present PER models over them which are fully complete, inter alia, w.r.t. the following languages and theories: the fragment of System F consisting of MLtypes, the maximal theory on the simply typed λcalculus with finitely many ground constants, and the maximal theory on an infinitary version of this latter calculus. Key words: Typed lambdacalculi, MLpolymorphic types, linear logic, hyperdoctrines, PER models, Geometry of Interaction, (axiomatic) full completeness
An Algorithm for the Minimal Model
, 1997
"... Padovani [3] gave algorithms that (a) calculate a presentation of the minimal model of the simply typed lambda calculus, and (b) decides the equational theory of that model. Loader [2] generalised that work to unary PCF. SchmidtSchau [4] gave much simpler algorithms and proofs (based on strictness ..."
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Padovani [3] gave algorithms that (a) calculate a presentation of the minimal model of the simply typed lambda calculus, and (b) decides the equational theory of that model. Loader [2] generalised that work to unary PCF. SchmidtSchau [4] gave much simpler algorithms and proofs (based on strictness analyses) for unary PCF. Here, we present SchmidtSchau's method restricted to the minimal model. 1 Introduction We consider the simply typed lambda calculus with a single ground type o and two constants ? and ?, both of ground type. We order ? and ? by setting ? 6 ?, ? 66 ?. This is extended to all (closed) terms of ground type by comparing normal forms. There are two natural ways of extending this to higher types. The pointwise, applicative ordering is given by f 6 g if and only if f a 6 g a (8a): Alternative we can extend as a logical relation: f 6 g if and only if f a 6 g b (8 a; b s.t. a 6 b): (In both cases, f and g are two terms of the same function type, a and b range over term...
Bistability and Bisequentiality
"... We give a simple construction of fully abstract extensional models of sequential functional languages such as the calculus with constants and SPCF. Our models are based on biordered sets analogous to bidomains except that the stable order is replaced with a new notion, bistability, which entails ..."
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We give a simple construction of fully abstract extensional models of sequential functional languages such as the calculus with constants and SPCF. Our models are based on biordered sets analogous to bidomains except that the stable order is replaced with a new notion, bistability, which entails that our models are both (MilnerVuillemin) sequential and errorpropagating.