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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...
Infinitary Lambda Calculus and Discrimination of Berarducci Trees
, 2001
"... Introduction In this paper we will prove equivalent an operational and a denotational semantics for lambda calculus with the rule. Both semantics are based on the 1 This paper was made possible thanks to the hospitality ETL oered in March 1999 to both Mariangiola Dezani and Paula Severi. 2 Part ..."
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Cited by 2 (2 self)
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Introduction In this paper we will prove equivalent an operational and a denotational semantics for lambda calculus with the rule. Both semantics are based on the 1 This paper was made possible thanks to the hospitality ETL oered in March 1999 to both Mariangiola Dezani and Paula Severi. 2 Partly supported by MURST COFIN'99 TOSCA Project and CNRGNSAGA. 3 Part of this paper was completed when the third author was employed by ETL in Tsukuba, Japan. He acknowledges the excellent research conditions oered by ETL. set of rootactive terms, which is the smallest set of computational meaningless terms that can consistently be equated. The operational semantics that we are interested in is observational equivalence with respect to rootactive behavior. The denotational semantics is the model of the Berarducci trees (Berarducci, 1996), which are a more detailed variant of Bohm trees: the main dierence being th
Böhm's Theorem for Berarducci Trees
, 2000
"... We propose an extension of lambda calculus which internally discriminates two lambda terms if and only if they have dierent Berarducci trees. 1 Introduction The Lambda Calculus is a theory of functions that serves as a foundation for the functional programming paradigm. Lambda terms in this view ar ..."
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Cited by 1 (0 self)
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We propose an extension of lambda calculus which internally discriminates two lambda terms if and only if they have dierent Berarducci trees. 1 Introduction The Lambda Calculus is a theory of functions that serves as a foundation for the functional programming paradigm. Lambda terms in this view are idealized programs. There are essentially two ways of characterizing the meaning of lambda terms. The rst one is to run the program and to study the output. The second one is to observe the eect of the program when used as a subprogram in other programs. With respect to the rst approach, traditionally the output of a lambda term was described by its Bohm tree. But also LevyLongo trees and more recently Berarducci trees have been used. In this paper we will focus on Berarducci trees. These trees provide the possible output of a lambda term in greatest detail. The idea behind all these dierent concepts of tree is stable information, that we can recover by reducing the terms. This is ...
Intersection Types, λmodels, and Böhm Trees
"... This paper is an introduction to intersection type disciplines, with the aim of illustrating their theoretical relevance in the foundations of λcalculus. We start by describing the wellknown results showing the deep connection between intersection type systems and normalization properties, i.e. ..."
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This paper is an introduction to intersection type disciplines, with the aim of illustrating their theoretical relevance in the foundations of λcalculus. We start by describing the wellknown results showing the deep connection between intersection type systems and normalization properties, i.e., their power of naturally characterizing solvable, normalizing, and strongly normalizing pure λterms. We then explain the importance of intersection types for the semantics of λcalculus, through the construction of filter models and the representation of algebraic lattices. We end with an original result that shows how intersection types also allow to naturally characterize tree representations of unfoldings of λterms (Böhm trees).
Intersection Types for λTrees
, 1999
"... We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating λterms (Böhm trees, LevyLongo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by ..."
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We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating λterms (Böhm trees, LevyLongo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by the corresponding tree representation of terms. More precisely, for each family of trees, two terms have the same tree if and only if they get assigned the same types in the corresponding type assignment system.