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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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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.
Continuous Functions and Parallel Algorithms on Concrete Data Structures
 IN MFPS'91, L.N.C.S
, 1991
"... We report progress in two closely related lines of research: the semantic study of sequentiality and parallelism, and the development of a theory of intensional semantics. We generalize Kahn and Plotkin's concrete data structures to obtain a cartesian closed category of generalized concrete data str ..."
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Cited by 12 (2 self)
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We report progress in two closely related lines of research: the semantic study of sequentiality and parallelism, and the development of a theory of intensional semantics. We generalize Kahn and Plotkin's concrete data structures to obtain a cartesian closed category of generalized concrete data structures and continuous functions. The generalized framework continues to support a definition of sequential functions. Using this ccc as an extensional framework, we define an intensional framework  a ccc of generalized concrete data structures and parallel algorithms. This construction is an instance of a more general and more widely applicable categorytheoretic approach to intensional semantics, encapsulating a notion of intensional behavior as a computational comonad, and employing the coKleisli category as an intensional framework. We discuss the relationship between parallel algorithms and continuous functions, and supply some operational intuition for the parallel algorithms. We s...
Programming Metalogics with a Fixpoint Type
, 1992
"... A programming metalogic is a formal system into which programming languages can be translated and given meaning. The translation should both reflect the structure of the language and make it easy to prove properties of programs. This thesis develops certain metalogics using techniques of category th ..."
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Cited by 12 (6 self)
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A programming metalogic is a formal system into which programming languages can be translated and given meaning. The translation should both reflect the structure of the language and make it easy to prove properties of programs. This thesis develops certain metalogics using techniques of category theory and treats recursion in a new way. The notion of a category with fixpoint object is defined. Corresponding to this categorical structure there are type theoretic equational rules which will be present in all of the metalogics considered. These rules define the fixpoint type which will allow the interpretation of recursive declarations. With these core notions FIX categories are defined. These are the categorical equivalent of an equational logic which can be viewed as a very basic programming metalogic. Recursion is treated both syntactically and categorically. The expressive power of the equational logic is increased by embedding it in an intuitionistic predicate calculus, giving rise to the FIX logic. This contains propositions about the evaluation of computations to values and an induction principle which is derived from the definition of a fixpoint object as an initial algebra. The categorical structure which accompanies the FIX logic is defined, called a FIX hyperdoctrine, and certain existence and disjunction properties of FIX are stated. A particular FIX hyperdoctrine is constructed and used in the proof of the same properties. PCFstyle languages are translated into the FIX logic and computational adequacy reaulta are proved. Two languages are studied: Both are similar to PCF except one has call by value recursive function declararations and the other higher order conditionals. ...
Programming Language Semantics
 In CRC Handbook of Computer Science
, 1995
"... interpretation provides the theory that allows a compiler writer to prove the correctness of compilers. Finally, axiomatic semantics is a longstanding fundamental technique for validating the correctness of computer code. Recent emphasis on largescale and safetycritical systems has again placed t ..."
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Cited by 11 (0 self)
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interpretation provides the theory that allows a compiler writer to prove the correctness of compilers. Finally, axiomatic semantics is a longstanding fundamental technique for validating the correctness of computer code. Recent emphasis on largescale and safetycritical systems has again placed the spotlight on this technique. Current research on data type theory [5] suggests that a marriage between the techniques of datatype checking and axiomatic semantics is not far in the future. 4 Research Issues in Semantics The techniques in this chapter have proved highly successful for defining, improving, and implementing traditional, sequential programming languages. But new language paradigms present new challenges to the semantics methods. In the functional programming paradigm, a higherorder functional language can use functions as arguments to other functions. This makes the language's domains more complex than those in Figure 2. Denotational semantics can be used to understand the...
Programming Languages: Design, Analysis, and Semantics
, 2000
"... This thesis contains three parts. The first part presents contributions in the fields of domainspecific language design, runtime system design, and static program analysis, the second part presents contributions in the field of control synthesis, and finally the third part presents contributions in ..."
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Cited by 7 (0 self)
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This thesis contains three parts. The first part presents contributions in the fields of domainspecific language design, runtime system design, and static program analysis, the second part presents contributions in the field of control synthesis, and finally the third part presents contributions in the field of denotational semantics.
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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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 "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 [12]). 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 higher types. The phrase "sequential functional computation " 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 "modules " interact with each other in a purely functional fashion.
On the Approximation of Denotational MuSemantics
 Applied Categorical Structures
, 1998
"... A signature \Sigma gives rise to a language L \Sigma (Var) by extending \Sigma with variables x 2 Var and binding constructs ¯x and x, corresponding to least and greatest fixed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone \Sigmaalgebras. ..."
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Cited by 4 (3 self)
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A signature \Sigma gives rise to a language L \Sigma (Var) by extending \Sigma with variables x 2 Var and binding constructs ¯x and x, corresponding to least and greatest fixed points respectively. The natural denotational models for such languages are bicomplete dcpos as monotone \Sigmaalgebras. We prove that several approximating denotational semantics have the usual compositional semantics as their limit. These results provide techniques for relating syntactic and semantic concepts such as in full abstraction or completeness proofs. In the presence of an involutive antitone map on a bicomplete dcpo D we may translate the language L \Sigma (Var) into one with least fixed points only such that meanings are preserved. This allows an approximative semantics where least and greatest fixed points are simultaneously approximated by `unwindings' in the syntax, provided that the limit semantics is substitutive. We discuss the principal difficulties of simultaneous unwindings in the absenc...
Dialogue Games and Innocent Strategies: An Approach to (Intensional) Full Abstraction for PCF
, 1993
"... ion for PCF Preliminary Announcement Martin Hyland and Luke Ong 26th July 1993 This note is (intended to be) released in conjunction with a preliminary announcement of Abramsky, Jagadeesan and Malacaria entitled Games and Full Abstraction of PCF. Like Abramsky et al. (but independently), we have ..."
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ion for PCF Preliminary Announcement Martin Hyland and Luke Ong 26th July 1993 This note is (intended to be) released in conjunction with a preliminary announcement of Abramsky, Jagadeesan and Malacaria entitled Games and Full Abstraction of PCF. Like Abramsky et al. (but independently), we have found an intensionally fully abstract model for pcf [Plo77]. Our model is a Cartesian closed category of Scott domains all of whose compact elements are definable in pcf. Using Stoughton's Theorem [Sto88], the model can be extensionally collapsed by means of a continuous homomorphism to the least fixpoint, orderextensional, fully abstract model which is shown to be unique by Milner [Mil77]. It is unclear at this stage how our model relates to that of Abramsky et al. Our model of computation is based on a kind of game in which each play consists of a dialogue of questions and answers between two players. This approach is very concrete and in nature goes back to Kleene [Kle78] and Gandy in o...
Relating Semantic Models for the Object Calculus
 In Proceedings of Express 97 Workshop, volume 7 of Electronic Notes in Theoretical Computer Science. Elsevier Science B.V
, 1997
"... Abadi and Cardelli have investigated several versions of the &calculus, a calculus for describing central features of objectoriented programs, with particular emphasis on various type systems. In this paper we study the properties of a denotational semantics due to Abadi and Cardelli vis`avis th ..."
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Abadi and Cardelli have investigated several versions of the &calculus, a calculus for describing central features of objectoriented programs, with particular emphasis on various type systems. In this paper we study the properties of a denotational semantics due to Abadi and Cardelli vis`avis the notion of observational congruence for the calculus Ob 1!:¯ . In particular, we prove that the denotational semantics based on partial equivalence relations is correct with respect to observational congruence. By means of a counterexample, we argue that the denotational model is not fully abstract with respect to observational congruence. In fact, the model is able to distinguish objects that have the same behaviour in every Ob 1!:¯ context. 1 Introduction In [AC96] Abadi and Cardelli present and investigate several versions of the &calculus, a calculus for describing central features of objectoriented programs, with particular emphasis on various type systems. These object calculi ...
Parallel PCF has a Unique Extensional Model
 In Proc. 6th IEEE Annual Symp. Logic in Computer Science
, 1991
"... We show that the continuous function model is the unique extensional (but not necessarily pointwise ordered) model of the variant of the applied typed lambda calculus PCF that includes the "parallel or" operation. 1 Introduction Several extensional models of the applied typed lambda calculus PCF ar ..."
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We show that the continuous function model is the unique extensional (but not necessarily pointwise ordered) model of the variant of the applied typed lambda calculus PCF that includes the "parallel or" operation. 1 Introduction Several extensional models of the applied typed lambda calculus PCF are known to exist, including: (i) The continuous function model, which is orderextensional (pointwise ordered) but not equationally fully abstract [Plo]. (A model is equationally fully abstract when terms are identified in the model exactly when they are operationally equivalent.) (ii) The stable function model, which is neither orderextensional nor equationally fully abstract [Ber][BCL]. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and orderextensional [Mil][Sto2]. (A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defin...