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18
Kripke Logical Relations and PCF
 Information and Computation
, 1995
"... Sieber has described a model of PCF consisting of continuous functions that are invariant under certain (finitary) logical relations, and shown that it is fully abstract for closed terms of up to thirdorder types. We show that one may achieve full abstraction at all types using a form of "Kripke lo ..."
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Sieber has described a model of PCF consisting of continuous functions that are invariant under certain (finitary) logical relations, and shown that it is fully abstract for closed terms of up to thirdorder types. We show that one may achieve full abstraction at all types using a form of "Kripke logical relations" introduced by Jung and Tiuryn to characterize definability. To appear in Information and Computation. (Accepted, October 1994) Supported by NSF grant CCR92110829. 1 Introduction The nature of sequential functional computation has fascinated computer scientists ever since Scott remarked on a curious incompleteness phenomenon when he introduced LCF (Logic for Computable Functions) and its continuous function model in 1969 (Scott, 1993). Scott noted that although the functionals definable by terms in PCFthe term language of LCFadmitted a sequential evaluation strategy, there were functions in the model that seemed to require a parallel evaluation strategy. "Sequen...
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 26 (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
A Relational Account of CallbyValue Sequentiality
 IN: PROC. 12TH SYMP. LOGIC IN COMPUTER SCIENCE
, 1999
"... We construct a model for FPC, a purely functional, sequential, callbyvalue language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract. ..."
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Cited by 13 (2 self)
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We construct a model for FPC, a purely functional, sequential, callbyvalue language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract.
A Characterization Of Lambda Definability In Categorical Models Of Implicit Polymorphism
 Theoretical Computer Science
, 1995
"... . Lambda definability is characterized in categorical models of simply typed lambda calculus with type variables. A categorytheoretic framework known as glueing or sconing is used to extend the JungTiuryn characterization of lambda definability [JuT93], first to ccc models, and then to categor ..."
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. Lambda definability is characterized in categorical models of simply typed lambda calculus with type variables. A categorytheoretic framework known as glueing or sconing is used to extend the JungTiuryn characterization of lambda definability [JuT93], first to ccc models, and then to categorical models of the calculus with type variables. Logical relations are now a wellestablished tool for studying the semantics of various typed lambda calculi. The main lines of research are focused in two areas, the first of which strives for an understanding of Strachey's notion of parametric polymorphism. The main idea is that a parametricly polymorphic function acts independently from the types to which its type variables are instantiated, and that this uniformity may be captured by imposing a relational structure on the types [OHT93, MSd93, MaR91, Wad89, Rey83, Str67]. The other line of research concerns lambda definability and the full abstraction problem for various models of languag...
Mechanizing Logical Relations
 Proc. Mathematical Foundations of Programming Semantics, Lecture Notes in Computer Science 802, SpringerVerlag
, 1994
"... . We give an algorithm for deciding whether there exists a definable element of a finite model of an applied typed lambda calculus that passes certain tests, in the special case when all the constants and test arguments are of order at most one. When there is such an element, the algorithm outputs a ..."
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. We give an algorithm for deciding whether there exists a definable element of a finite model of an applied typed lambda calculus that passes certain tests, in the special case when all the constants and test arguments are of order at most one. When there is such an element, the algorithm outputs a term that passes the tests; otherwise, the algorithm outputs a logical relation that demonstrates the nonexistence of such an element. Several example applications of the C implementation of this algorithm are considered. 1 Introduction Given a model of an applied typed lambda calculus, it is natural to consider the problem of determining whether an element of that model is definable by a term, or, more generally, of determining whether there exists a definable element of the model that passes certain tests. One approach to settling such questions makes use of socalled "logical relations" [Plo80]. Building on recent work on logical relations by Sieber [Sie92], we give an algorithm for dec...
A Fully Abstract Model for Sequential Computation
, 1998
"... In 1977, G. Plotkin pointed out the problem of finding a fully abstract model for the sequential programming language PCF [16], which had been originally developed by D. Scott [19]. This question turned out to be one of the most enduring problems of semantics. A very nice description of the differen ..."
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In 1977, G. Plotkin pointed out the problem of finding a fully abstract model for the sequential programming language PCF [16], which had been originally developed by D. Scott [19]. This question turned out to be one of the most enduring problems of semantics. A very nice description of the different approaches
Logical Relations and Data Abstraction
 Proc. Computer Science Logic, CSL 2000, Fischbachau. Springer LNCS 1862
, 1996
"... We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suita ..."
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We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suitable logical relation. This allows us to introduce new types and operations of any order on those types, and to impose equations between terms of any order. Implementations are required to respect these equations up to a general form of contextual equivalence, and two implementations are equivalent if they produce the same contextual equivalence on terms of the enlarged language. Logical relations are introduced abstractly, soundness is almost automatic, but completeness is more difficult, achieved using a variant of Jung and Tiuryn's logical relations of varying arity. The results are expressed and proved categorically.
Full Abstraction and Universality via Realisability
, 1999
"... ion and Universality via Realisability Michael Marz marz@mathematik.tudarmstadt.de Alexander Rohr y rohr@mathematik.tudarmstadt.de Thomas Streicher streicher@mathematik.tudarmstadt.de Technische Universitat Darmstadt Fachbereich Mathematik Schlogartenstrae 7, D64289 Darmstadt Abstra ..."
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ion and Universality via Realisability Michael Marz marz@mathematik.tudarmstadt.de Alexander Rohr y rohr@mathematik.tudarmstadt.de Thomas Streicher streicher@mathematik.tudarmstadt.de Technische Universitat Darmstadt Fachbereich Mathematik Schlogartenstrae 7, D64289 Darmstadt Abstract We construct fully abstract realisability models of PCF. In particular, we prove a variant of the LongleyPhoa Conjecture by showing that the realisability model over an untyped calculus with arithmetic is fully abstract for PCF. Further we consider the extension of our results to a general sequential functional programming language SFPL giving rise to universal realisability models for SFPL. 1. Introduction Realisability models are known as a flexible tool for organising untyped models of computation into extensional models with a rich type structure where domains appear as sets, see e. g. [5, 8]. For example the Scott model and its effective variant both appear as realisabilit...
A higherorder simulation relation for System F
 Proc. 3rd Intl. Conf. on Foundations of Software Science and Computation Structures. ETAPS 2000
, 2000
"... The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. This pap ..."
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The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. This paper generalises this notion to abstract data types whose signatures contain higherorder and polymorphic functions. At higher order, the tight connection in the logic between the existence of a simulation relation and observational equivalence ostensibly breaks down. We show that an alternative notion of simulation relation is suitable. This also gives a simulation relation in the logic that composes at higher order, thus giving a syntactic logical counterpart to recent advances on the semantic level.