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Specification Structures and PropositionsasTypes for Concurrency
 Logics for Concurrency: Structure vs. AutomataProceedings of the VIIIth Banff Higher Order Workshop, volume 1043 of Lecture Notes in Computer Science
, 1995
"... Many different notions of "property of interest" and methods of verifying such properties arise naturally in programming. A general framework of "Specification Structures" is presented for combining different notions and methods in a coherent fashion. This is then applied to c ..."
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Many different notions of "property of interest" and methods of verifying such properties arise naturally in programming. A general framework of "Specification Structures" is presented for combining different notions and methods in a coherent fashion. This is then applied to concurrency in the setting of Interaction Categories.
A Structural Approach to Reversible Computation
 Theoretical Computer Science
, 2001
"... Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of lowlevel machine models. By contrast, we develop ..."
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Cited by 19 (3 self)
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Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of lowlevel machine models. By contrast, we develop a more structural approach. We show how highlevel functional programs can be mapped compositionally (i.e. in a syntaxdirected fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logicâ€”but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis. 1
Stratified coherent spaces: a denotational semantics for Light Linear Logic (Extended Abstract)
 Theoretical Computer Science
, 2000
"... We introduce a stratified version of the coherent spaces model where an object is given by a sequence of coherent spaces. The intuition behind it is that each level gives a di#erent degree of precision on the computation, an appearance. A morphism is required to satisfy a coherence condition at each ..."
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Cited by 19 (7 self)
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We introduce a stratified version of the coherent spaces model where an object is given by a sequence of coherent spaces. The intuition behind it is that each level gives a di#erent degree of precision on the computation, an appearance. A morphism is required to satisfy a coherence condition at each level and this setting gives a model of Elementary Linear Logic. We then introduce a measure function on the web meant to describe the di#erence between the number of output and input requests in the computation. The locally bounded morphisms defined thanks to this measure give a subcategory which is a model of Light Linear Logic. 1
Games for Recursive Types
 Theory and Formal Methods of Computing 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods. Imperial
, 1994
"... We present results concerning the solution of recursive domain equations in the category G of games, which is a modified version of the category presented in [AJM94]. New constructions corresponding to lifting and separated sum for games are presented, and are used to generate games for two simple r ..."
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We present results concerning the solution of recursive domain equations in the category G of games, which is a modified version of the category presented in [AJM94]. New constructions corresponding to lifting and separated sum for games are presented, and are used to generate games for two simple recursive types: the vertical and lazy natural numbers. Recently, the "game semantics" paradigm has been used to model the multiplicative fragment of linear logic [AJ94], and to provide a solution to the full abstraction problem for PCF [AJM94, HO94], where the intensional structure of the games model captures both the sequential and functional nature of the language. In the light of these results, it is natural to ask whether recursive types can be handled in this setting. Here we show that they can: for a wide class of functors \Phi, including all of the usual type constructors, the equation D ' \Phi(D) has a (canonical) solution. In fact we solve this equation up to identity, and the solut...
A New Approach to Control Flow Analysis
 Lecture
, 1998
"... We develop a control flow analysis algorithm for PCF based on game semantics. The analysis is closely related to Shivers' 0CFA analysis and the algorithm is shown to be cubic. The game semantics basis for the algorithm means that it can be naturally extended to handle strict languages and lang ..."
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We develop a control flow analysis algorithm for PCF based on game semantics. The analysis is closely related to Shivers' 0CFA analysis and the algorithm is shown to be cubic. The game semantics basis for the algorithm means that it can be naturally extended to handle strict languages and languages with imperative features. These extensions are discussed in the paper. We sketch the correctness proof for the algorithm. We also illustrate an algorithm for computing klimited CFA.
Axiomatic Domain Theory
 in Categories of Partial Maps. Distinguished Dissertations in Computer Science
, 1996
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Timeless Games
 Computer Science Logic: 11th International Workshop Proceedings, volume 1414 of Lecture Notes in Computer Science. EACSL
, 1998
"... . Two models of classical linear logic are set up. First our recent version of AJM games model which will be our source model. Then the target model, polarized pointed relations, a variant of the plain relational model which is constructed in two steps: first the model of pointed relations, then the ..."
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Cited by 14 (1 self)
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. Two models of classical linear logic are set up. First our recent version of AJM games model which will be our source model. Then the target model, polarized pointed relations, a variant of the plain relational model which is constructed in two steps: first the model of pointed relations, then the additional polarization structure which yields a proper duality. Then the natural timeforgetting map is shown to generate a lax functor from the source to the target. Finally a further refinement of the target model using bipolarities is sketched, giving a closer link with the games model for the interpretation of syntax. Thus a bridge is constructed that goes from a dynamic model to a static model of evaluation. 1 Introduction The basic mathematical reflex was to model types, programs, evaluation with sets, functions, composition. As years went by, denotational semantics pictured the syntactic triple with increasingly sophisticated tools: lattices, posets, concrete data structures, coher...
Logical Full Abstraction and PCF
 Tbilisi Symposium on Language, Logic and Computation. SiLLI/CSLI
, 1996
"... ion and PCF John Longley Gordon Plotkin March 15, 1996 Abstract We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with "parallel" operations. The main result is that, for standard interpret ..."
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ion and PCF John Longley Gordon Plotkin March 15, 1996 Abstract We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with "parallel" operations. The main result is that, for standard interpretations, logical full abstraction is equivalent to equational full abstraction together with universality; the proof involves constructing enumeration operators. We also consider restrictions on logical complexity and on the level of types. 1 Introduction The study of denotational semantics seeks to provide mathematical descriptions of programming languages by giving denotations of programs in terms of previously understood mathematical structures. For example, if P is a program that takes an input and produces an output, we might take its denotation to be a function from a set of inputvalues to a set of outputvalues. The most widelyknown approach to denotational semantics is that of traditiona...
Game Semantics and Subtyping
 In Proceedings of the fifteenth annual IEEE symposium on Logic in Computer Science
, 1999
"... While Game Semantics has been remarkably successful at modelling, often in a fully abstract manner, a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of ..."
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While Game Semantics has been remarkably successful at modelling, often in a fully abstract manner, a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of the calculus leads to a notion of subtyping for game semantics. We construct an interpretation of a simple calculus with subtyping and show how the range of the interpretation of types is a complete lattice thus yielding an interpretation of bounded quantification.
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.