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Nondeterministic Games and Program Analysis: An application to security (Extended Abstract)
 Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE
"... Pasquale Malacaria and Chris Hankin Dept. of Computing Imperial College LONDON SW7 2BZ pm5,clh@doc.ic.ac.uk Abstract We present a unifying framework for using game semantics as a basis for program analysis. Also, we present a case study of the techniques. The unifying framework presents games ..."
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Cited by 21 (4 self)
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Pasquale Malacaria and Chris Hankin Dept. of Computing Imperial College LONDON SW7 2BZ pm5,clh@doc.ic.ac.uk Abstract We present a unifying framework for using game semantics as a basis for program analysis. Also, we present a case study of the techniques. The unifying framework presents gamesbased program analysis as an abstract interpretation of an appropriate games category in the category of nondeterministic games. The case study concerns an application to security.
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 18 (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 Logic—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
Axiomatic Domain Theory
 in Categories of Partial Maps. Distinguished Dissertation Series
, 1995
"... The denotational semantics approach to the semantics of programming languages interprets the language constructions by assigning elements of mathematical structures to them. The structures form socalled categories of domains and the study of their closure properties is the subject of domain theory ..."
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Cited by 16 (2 self)
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The denotational semantics approach to the semantics of programming languages interprets the language constructions by assigning elements of mathematical structures to them. The structures form socalled categories of domains and the study of their closure properties is the subject of domain theory [Sco70, Sco82, Plo83, GS90, AJ94]. Typically, categories of domains consist of suitably complete partially ordered sets together with continuous maps. But, what is a category of domains? The main aim of axiomatic domain theory is to answer this question by axiomatising the structure needed on a mathematical universe so that it can be considered a category of domains. Criteria required from categories of domains can be of the most varied sort. For example, we could ask them to * have a rich collection of type constructors: sums, products, exponentials, powerdomains, dependent types, polymorphic types, etc; * have fixedpoint operators for programs and type constructors; * have only computable maps [Sco76, Smy77, Mul81, McC84, Ros86, Pho90, Lon95]; * have a Stone dual providing a logic of observable properties [Abr87, Vic89, Zha91]. An additional aim of the axiomatic approach is to relate these mathematical criteria with computational criteria. As we indicate below an axiomatic treatment of various of the above aspects is now available but much research remains to be done.
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 languages ..."
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Cited by 16 (3 self)
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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.
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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Cited by 16 (4 self)
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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...
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 15 (5 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
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...
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.
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 interpretations, lo ..."
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Cited by 13 (5 self)
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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...
Sequential algorithms and strongly stable functions
 in the Linear Summer School, Azores
, 2003
"... ..."