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17
Full Abstraction for PCF
 Information and Computation
, 1996
"... An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable i ..."
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Cited by 195 (15 self)
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An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that it satisfies some remarkable properties, such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an orderextensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntaxindependent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model, and prove a Universality Theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.
Full Abstraction for PCF (Extended Abstract)
 THEORETICAL ASPECTS OF COMPUTER SOFTWARE. INTERNATIONAL SYMPOSIUM TACS'94, NUMBER 789 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1994
"... The Full Abstraction Problem for PCF [23, 20, 7, 11] is one of the longeststanding problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as ..."
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Cited by 66 (11 self)
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The Full Abstraction Problem for PCF [23, 20, 7, 11] is one of the longeststanding problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as to the precise criteria for a solution. The usual formulation is that one wants a "semantic characterization" of the fully abstract model (by which we mean the inequationally fully abstract orderextensional model, which Milner proved to be uniquely specified up to isomorphism by these properties [20]). The problem is to understand what should be meant by a "semantic characterization". Our view is that the essential content of the problem, what makes it important, is that it calls for a semantic characterization of sequential, functional computation at hig...
Game Theoretic Analysis Of CallByValue Computation
, 1997
"... . We present a general semantic universe of callbyvalue computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for callbyvalue PCF, a generic typed programming language with callbyvalue evaluation. The key idea is ..."
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Cited by 59 (20 self)
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. We present a general semantic universe of callbyvalue computation based on elements of game semantics, and validate its appropriateness as a semantic universe by the full abstraction result for callbyvalue PCF, a generic typed programming language with callbyvalue evaluation. The key idea is to consider the distinction between callbyname and callbyvalue as that of the structure of information flow, which determines the basic form of games. In this way the callbyname computation and callbyvalue computation arise as two independent instances of sequential functional computation with distinct algebraic structures. We elucidate the type structures of the universe following the standard categorical framework developed in the context of domain theory. Mutual relationship between the presented category of games and the corresponding callbyname universe is also clarified. 1. Introduction The callbyvalue is a mode of calling procedures widely used in imperative and function...
Fully abstract semantics for observably sequential languages
 Information and Computation
, 1994
"... One of the major challenges in denotational semantics is the construction of a fully abstract semantics for a higherorder sequential programming language. For the past fifteen years, research on this problem has focused on developing a semantics for PCF, an idealized functional programming language ..."
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Cited by 49 (4 self)
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One of the major challenges in denotational semantics is the construction of a fully abstract semantics for a higherorder sequential programming language. For the past fifteen years, research on this problem has focused on developing a semantics for PCF, an idealized functional programming language based on the typed λcalculus. Unlike most practical languages, PCF has no facilities for observing and exploiting the evaluation order of arguments to procedures. Since we believe that these facilities play a crucial role in sequential computation, this paper focuses on a sequential extension of PCF, called SPCF, that includes two classes of control operators: a possibly empty set of error generators and a collection of catch and throw constructs. For each set of error generators, the paper presents a fully abstract semantics for SPCF. If the set of error generators is empty, the semantics interprets all procedures—including catch and throw—as BerryCurien sequential algorithms. If the language contains error generators, procedures denote manifestly sequential functions. The manifestly sequential functions form a Scott domain that is isomorphic to a domain of decision trees, which is the natural
Sequentiality and the πCalculus
, 2001
"... We present a simple type discipline for the πcalculus which precisely captures the notion of sequential functional computation as a specific class of name passing interactive behaviour. The typed calculus allows direct interpretation of both callbyname and callbyvalue sequential functions. T ..."
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Cited by 29 (15 self)
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We present a simple type discipline for the πcalculus which precisely captures the notion of sequential functional computation as a specific class of name passing interactive behaviour. The typed calculus allows direct interpretation of both callbyname and callbyvalue sequential functions. The precision of the representation is demonstrated by way of a fully abstract encoding of PCF.
Correspondence between Operational and Denotational Semantics
 Handbook of Logic in Computer Science
, 1995
"... This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational ..."
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Cited by 23 (0 self)
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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of orderextensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simplytyped lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dIdomains and stable functions Homepa...
Games and full abstraction for PCF: preliminary announcement
, 1993
"... The Full Abstraction Problem for PCF [14, 12, 4, 8] is one of the longeststanding problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as to ..."
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Cited by 5 (0 self)
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The Full Abstraction Problem for PCF [14, 12, 4, 8] is one of the longeststanding problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most difficult; there is much less agreement as to what exactly the problem is, or more particularly as to the precise criteria for a solution. The usual formulation is that one wants a &quot;semantic characterization &quot; of the fully abstract model (by which we mean the inequationally fully abstract orderextensional model, which Milner proved to be uniquely specified up to isomorphism by these properties [12]). The problem is to understand what should be meant by a &quot;semantic characterization&quot;. Our view is that the essential content of the problem, what makes it important, is that it calls for a semantic characterization of sequential, functional computation at higher types. The phrase &quot;sequential functional computation &quot; deserves careful consideration. On the one hand, sequentiality refers to a computational process extended over time, not a mere function; on the other hand, we want to capture just those sequential computations in which the different parts or &quot;modules &quot; interact with each other in a purely functional fashion.
Focusing in Asynchronous Games
"... Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically interested here in relating two such semantics of linear lo ..."
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Cited by 2 (0 self)
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Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically interested here in relating two such semantics of linear logic, of very different flavor, which both take in account concurrent features of the proofs: asynchronous games and concurrent games. Interestingly, we show that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic.
Inductive Definition and Domain Theoretic Properties of Fully Abstract Models for PCF and PCF+
 LOGICAL METHODS IN COMPUTER SCIENCE 3(3:7), 1–50 (2007)
, 2007
"... A construction of fully abstract typed models for PCF and PCF+ (i.e., PCF+ “parallel conditional function”), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent nondeterministic strategies introduced by the author in the sevent ..."
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Cited by 1 (1 self)
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A construction of fully abstract typed models for PCF and PCF+ (i.e., PCF+ “parallel conditional function”), respectively, is presented. It is based on general notions of sequential computational strategies and wittingly consistent nondeterministic strategies introduced by the author in the seventies. Although these notions of strategies are old, the definition of the fully abstract models is new, in that it is given levelbylevel in the finite type hierarchy. To prove full abstraction and nondcpo domain theoretic properties of these models, a theory of computational strategies is developed. This is also an alternative and, in a sense, an analogue to the later game strategy semantics approaches of Abramsky, Jagadeesan, and Malacaria; Hyland and Ong; and Nickau. In both cases of PCF and PCF+ there are definable universal (surjective) functionals from numerical functions to any given type, respectively, which also makes each of these models unique up to isomorphism. Although such models are nonomegacomplete and therefore not continuous in the traditional terminology, they are also proved to be sequentially complete (a weakened form of omegacompleteness), “naturally” continuous (with respect to existing directed “pointwise”, or “natural” lubs) and also “naturally” omegaalgebraic and “naturally” bounded complete—appropriate generalisation of the ordinary notions of domain theory to the case of nondcpos.