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35
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 255 (16 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.
Games and Full Abstraction for the Lazy lambdacalculus
 In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science
, 1995
"... ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typ ..."
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Cited by 149 (9 self)
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ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typefree functional language based on evaluation to weak head normal form, is given in G, yielding an extensional model in E . This model is shown to be fully abstract with respect to applicative simulation. This is, so far as we know, the first purely semantic construction of a fully abstract model for a reflexivelytyped sequential language. 1 Introduction Full Abstraction is a key concept in programming language semantics [9, 12, 23, 26]. The ingredients are as follows. We are given a language L, with an `observational preorder'  on terms in L such that P  Q means that every observable property of P is also satisfied by Q; and a denotational model MJ\DeltaK. The model M is then said to be f...
Categorical Models for Local Names
 LISP AND SYMBOLIC COMPUTATION
, 1996
"... This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. T ..."
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Cited by 46 (2 self)
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This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. The intent behind this language is to examine one aspect of the imperative character of Standard ML: the use of local state by dynamic creation of references. The nucalculus is equivalent to a certain fragment of ML, omitting side effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higherorder functions can be complex and subtle; it is particularly difficult to characterise the observable behaviour of expressions. Categorical monads, in the style of Moggi, are used to build denotational models for the nucalculus. An intermediate stage is the use of a computational metalanguage, which distinguishes in the type system between values and computations. The general requirements for a categorical model are presented, and two specific examples described in detail. These provide a sound denotational semantics for the nucalculus, and can be used to reason about observable equivalence in the language. In particular a model using logical relations is fully abstract for firstorder expressions.
Operational Semantics and Program Equivalence
 INRIA Sophia Antipolis, 2000. Lectures at the International Summer School On Applied Semantics, APPSEM 2000, Caminha, Minho
, 2000
"... This tutorial paper discusses a particular style of operational semantics that enables one to give a `syntaxdirected' inductive definition of termination which is very useful for reasoning about operational equivalence of programs. We restrict attention to contextual equivalence of express ..."
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Cited by 41 (4 self)
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This tutorial paper discusses a particular style of operational semantics that enables one to give a `syntaxdirected' inductive definition of termination which is very useful for reasoning about operational equivalence of programs. We restrict attention to contextual equivalence of expressions in the ML family of programming languages, concentrating on functions involving local state. A brief tour of structural operational semantics culminates in a structural definition of termination via an abstract machine using `frame stacks'. Applications of this to reasoning about contextual equivalence are given.
Prelogical Relations
, 1999
"... this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results ..."
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Cited by 25 (5 self)
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this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results
Definability and full abstraction
 GDP FESTSCHRIFT
"... Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown sin ..."
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Cited by 24 (1 self)
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Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown since the early nineties. In this note, we review the relation between definability and full abstraction, and we put a few old and recent results of this kind in perspective.
Bistructures, Bidomains and Linear Logic
 in Proc. 21st ICALP
, 1997
"... Bistructures are a generalisation of event structures which allow a representation of spaces of functions at higher types in an orderextensional setting. The partial order of causal dependency is replaced by two orders, one associated with input and the other with output in the behaviour of func ..."
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Cited by 14 (3 self)
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Bistructures are a generalisation of event structures which allow a representation of spaces of functions at higher types in an orderextensional setting. The partial order of causal dependency is replaced by two orders, one associated with input and the other with output in the behaviour of functions. Bistructures form a categorical model of Girard's classical linear logic in which the involution of linear logic is modelled, roughly speaking, by a reversal of the roles of input and output. The comonad of the model has an associated coKleisli category which is closely related to that of Berry's bidomains (both have equivalent nontrivial full subcartesian closed categories).