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Domain Theory in Logical Form
 Annals of Pure and Applied Logic
, 1991
"... The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and system ..."
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Cited by 231 (10 self)
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The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:
Operational Properties of Lily, a Polymorphic Linear Lambda Calculus with Recursion
"... Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally callbyvalue operators of linear lambda calculus can be given a ..."
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Cited by 35 (1 self)
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Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally callbyvalue operators of linear lambda calculus can be given a callbyname semantics without affecting termination at exponential types and hence without affecting ground contextual equivalence. This result is used to prove properties of a logical relation that provides a new extensional characterisation of ground contextual equivalence and relational parametricity properties of polymorphic types.
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
Eager normal form bisimulation
 In Proc. 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... Abstract. Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize LévyLongo tree equivalence and Boehm tree equivalence. It has been adapted to a range of untyped, higherorder calculi, but types have presented a difficulty. In this paper, we prese ..."
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Cited by 14 (4 self)
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Abstract. Normal form bisimulation is a powerful theory of program equivalence, originally developed to characterize LévyLongo tree equivalence and Boehm tree equivalence. It has been adapted to a range of untyped, higherorder calculi, but types have presented a difficulty. In this paper, we present an account of normal form bisimulation for types, including recursive types. We develop our theory for a continuationpassing style calculus, JumpWithArgument (JWA), where normal form bisimilarity takes a very simple form. We give a novel congruence proof, based on insights from game semantics. A notable feature is the seamless treatment of etaexpansion. We demonstrate the normal form bisimulation proof principle by using it to establish a syntactic minimal invariance result and the uniqueness of the fixed point operator at each type.
SOS formats and metatheory: 20 years after
, 2007
"... In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical ..."
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Cited by 12 (5 self)
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In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical
CallByPushValue: Decomposing CallByValue And CallByName
"... We present the callbypushvalue (CBPV) calculus, which decomposes the typed callbyvalue (CBV) and typed callbyname (CBN) paradigms into finegrain primitives. On the operational side, we give bigstep semantics and a stack machine for CBPV, which leads to a straightforward push/pop reading of ..."
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Cited by 8 (3 self)
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We present the callbypushvalue (CBPV) calculus, which decomposes the typed callbyvalue (CBV) and typed callbyname (CBN) paradigms into finegrain primitives. On the operational side, we give bigstep semantics and a stack machine for CBPV, which leads to a straightforward push/pop reading of CBPV programs. On the denotational side, we model CBPV using cpos and, more generally, using algebras for a strong monad. For storage, we present an O’Hearnstyle “behaviour semantics” that does not use a monad. We present the translations from CBN and CBV to CBPV. All these translations straightforwardly preserve denotational semantics. We also study their operational properties: simulation and full abstraction. We give an equational theory for CBPV, and show it equivalent to a categorical semantics using monads and algebras. We use this theory to formally compare CBPV to Filinski’s variant of the monadic metalanguage, as well as to Marz’s language SFPL, both of which have essentially the same type structure as CBPV. We also discuss less formally the differences between the CBPV and monadic frameworks.
Programming Research Group
"... This thesis is a detailed examination of the application of game semantics to constructing denotational models of the pure untyped λcalculus. Game semantics is a fairly recent technique, using a formal setting for interaction to model sequential programming languages in an accurate way. syntaxinde ..."
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This thesis is a detailed examination of the application of game semantics to constructing denotational models of the pure untyped λcalculus. Game semantics is a fairly recent technique, using a formal setting for interaction to model sequential programming languages in an accurate way. syntaxindependent model of PCF; the only difference is that in our setting the distinction between “question ” and “answer ” moves is removed. Many of the standard results for PCF games carry through into this setting. Cartesian closed categories of arenas and innocent strategies are constructed, leading to ληalgebras D and DREC. By a method of approximation, these are shown to be sensible models (i.e. all unsolvable terms are equated) but they contain many undefinable elements and are not λmodels. By introducing a new “economical ” representation of innocent strategies we are able to prove a precise syntactic connexion between a term and its denotation. This
Characterizing Recursive Programs Up To Bisimilarity
"... A recursive program is determined, up to bisimilarity, by the operation of the recursion body on arbitrary processes, of which it is a fixpoint. The traditional proof of this fact uses Howe’s method, but that does not tell us how the fixpoint is obtained. In this paper, we show that the fixpoint may ..."
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A recursive program is determined, up to bisimilarity, by the operation of the recursion body on arbitrary processes, of which it is a fixpoint. The traditional proof of this fact uses Howe’s method, but that does not tell us how the fixpoint is obtained. In this paper, we show that the fixpoint may be obtained by a least fixpoint procedure iterated through the hierarchy of countable ordinals, using Groote and Vaandrager’s notion of nested simulation. 1