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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.
Discrimination by Parallel Observers: the Algorithm
 LICS '97 , IEEE Comp. Soc
, 1998
"... The main result of the paper is a constructive proof of the following equivalence: two pure terms are observationally equivalent in the lazy concurrent calculus iff they have the same L'evyLongo trees. An algorithm which allows to build a context discriminating any two pure terms with differe ..."
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Cited by 6 (3 self)
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The main result of the paper is a constructive proof of the following equivalence: two pure terms are observationally equivalent in the lazy concurrent calculus iff they have the same L'evyLongo trees. An algorithm which allows to build a context discriminating any two pure terms with different L'evyLongo trees is described. It follows that contextual equivalence coincides with behavioural equivalence (bisimulation) as considered by Sangiorgi. Another consequence is that the discriminating power of concurrent lambda contexts is the same as that of BoudolLaneve's contexts with multiplicities. 3 1 Introduction The aim of this paper is to improve our understanding of what is the "meaning" of a term in the lazy calculus. To explain our result let us begin with the following few observations borrowed from the paper [2] of Abramsky and Ong. In the ordinary calculus, the most natural understanding of evaluation to a "value" is reduction to a normal form. It is however wellk...
The Discriminating Power of Multiplicities in the λCalculus
, 1996
"... The λcalculus with multiplicities is a refinement of the lazy λcalculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over ..."
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Cited by 2 (0 self)
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The λcalculus with multiplicities is a refinement of the lazy λcalculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual λterms. We prove in particular that the observational equivalence induced by contexts with multiplicities coincides with the equality of LévyLongo trees associated with λterms. This is a consequence of the characterization we give of the corresponding observational precongruence, as an intensional preorder involving etaexpansion, namely Ong's lazy PlotkinScottEngeler preorder.
The Discriminating Power of Multiplicities in the LambdaCalculus
, 1996
"... The calculus with multiplicities is a refinement of the lazy calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over th ..."
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Cited by 1 (0 self)
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The calculus with multiplicities is a refinement of the lazy calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual terms. We prove in particular that the observational equivalence induced by contexts with multiplicities coincides with the equality of L'evyLongo trees associated with terms. This is a consequence of the characterization we give of the corresponding observational precongruence, as an intensional preorder involving jexpansion, namely Ong's lazy PlotkinScottEngeler preorder. 1 Introduction The calculus with multiplicities was introduced in [5] for the purpose of studying the relationship between the calculus and Milner's ßcalculus [13]. It is a "resource conscious" refinement of the calculus, based on the following observation: in an application MN the argument N is infini...
Structures for Lazy Semantics
 In Programming Concepts and Methods, PROCOMET'98. Chapman
, 1997
"... The paper explores different approaches for modeling the lazy calculus, which is a paradigmatic language for studying the operational behaviour of programming languages, like Haskell, using a callbyname and lazy evaluation mechanism. Two models for lazy calculus in the coherence spaces setting a ..."
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Cited by 1 (0 self)
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The paper explores different approaches for modeling the lazy calculus, which is a paradigmatic language for studying the operational behaviour of programming languages, like Haskell, using a callbyname and lazy evaluation mechanism. Two models for lazy calculus in the coherence spaces setting are built. They give a new insight in the behaviour of the language since their local structures are different from the one of all existing models in the literature. In order to compare different models, a class of models for lazy calculus is defined, namely, the lazy regular models class. All the models adequate for the lazy calculus studied in the literature belong to this class. Moreover, all the lazy regular model share important properties, like the approximation property, which is a key tool for studying their local structure. 1