Results 11 
19 of
19
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 ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
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...
Full Abstractness for a Functional/Concurrent Language With HigherOrder ValuePassing
, 1998
"... We study an applied typed callbyvalue calculus which in addition to the usual types for higherorder functions contains an extra type called proc, for processes. The constructors for terms of this type are similar to those found in standard process calculi such as CCS. We first give an operationa ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
We study an applied typed callbyvalue calculus which in addition to the usual types for higherorder functions contains an extra type called proc, for processes. The constructors for terms of this type are similar to those found in standard process calculi such as CCS. We first give an operational semantics for this language in terms of a labelled transition system which is then used to give a behavioural preorder based on contexts: the expression N dominates M if in every appropriate context if M can produce a boolean value then so can N. Based on standard domain constructors we define a model, a prime algebraic lattice, which is fully abstract with respect to this behaviour preorder.
NonDeterministic Extensions of Untyped λcalculus
 INFO. AND COMP
, 1995
"... The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in presence of functional application and abstraction. We identify non determinism in the setting of λcalculus with the absence of the ChurchRosser property plus the inconsistency of the equational theory obtained by the symmetric closure of the reduction relation. We argue in favour of a distinction between non determinism and parallelism, due to the conjunctive nature of the former in contrast to the disjunctive character of the latter. This is the basis of our analysis of the operational and denotational semantics of non deterministiccalculus, which is the classical calculus plus a choice operator, and of our election of bounded indeterminacy as the semantical counterpart of conjunctive non determinism. This leads to operational semantics based on...
A Convex Powerdomain over Lattices: its Logic and λCalculus
, 1997
"... . To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive f ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive from the algebras of P the logic of D 1 , that is the axiomatic description of its compact elements. We then define a calculus and a type assignment system using the logic of D 1 as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D 1 , is fully abstract with respect to the observational preorder of the calculus. Keywords: calculus, Nondeterminism, Full Abstraction, Powerdomain Construction, Intersection Type Disciplines. 1. Introduction One of the main issues in the design of programming languages is the achievement of a good compromise between the multiplicity of control structures and data types and the unicity of the mathematica...
Principal Typing for Parallel and nonDeterministic lambdacalculus
, 1997
"... Parallelism and nondeterminism are fundamental concepts in the process algebra theory. Combining them with calculus can enlighten the theory of higherorder process algebras. In recent papers an analysis of a calculus containing parallel and nondeterministic operators was carried on by means of ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Parallelism and nondeterminism are fundamental concepts in the process algebra theory. Combining them with calculus can enlighten the theory of higherorder process algebras. In recent papers an analysis of a calculus containing parallel and nondeterministic operators was carried on by means of a type assignment system with intersection and union types. The present paper answers the problem of determining principal types for this system. For correspondence contact Franco Barbanera Dipartimento di Informatica, Universit'a di Torino Corso Svizzera 185, 10149 Torino Italy email: barba@di.unito.it tel: +39 11 7429111 Fax: +39 11 751603 1 Principal Typing for Parallel and nonDeterministic calculus Abstract Parallelism and nondeterminism are fundamental concepts in the process algebra theory. Combining them with calculus can enlighten the theory of higherorder process algebras. In recent papers an analysis of a calculus containing parallel and nondeterministic operators ...
Types for Trees
 In PROCOMET'98 (Shelter Island
, 1998
"... We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating terms (Bohm trees, LevyLongo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by th ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating terms (Bohm 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. Keywords Bohm trees, approximants, intersection types. 1 INTRODUCTION A theory of functions like the calculus, which provides a foundation for the functional programming paradigm in computer science, can be seen essentially as a theory of "programs". This point of view leads naturally to the intuitive idea that the meaning of a term (program) is represented by the amount of "meaningful information " we can extract from the term by "running it". The formalization of "the information"...
Distributed Processes and Location Failures (Extended Abstract)
"... ) James Riely and Matthew Hennessy Abstract Site failure is an essential aspect of distributed systems; nonetheless its effect on programming language semantics remains poorly understood. To model such systems, we define a process calculus in which processes are run at distributed locations. The ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
) James Riely and Matthew Hennessy Abstract Site failure is an essential aspect of distributed systems; nonetheless its effect on programming language semantics remains poorly understood. To model such systems, we define a process calculus in which processes are run at distributed locations. The language provides operators to kill locations, to test the status (dead or alive) of locations, and to spawn processes at remote locations. Using a variation of bisimulation, we provide alternative characterizations of strong and weak barbed congruence for this language, based on an operational semantics that uses configurations to record the status of locations. We then derive a second, symbolic characterization in which configurations are replaced by logical formulae. In the strong case the formulae come from a standard propositional logic, while in the weak case a temporal logic with past time modalities is required. The symbolic characterization establishes that, in principle, barbed con...
Types for Trees
"... We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating terms (Bohm trees, L'evyLongo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by t ..."
Abstract
 Add to MetaCart
We introduce a type assignment system which is parametric with respect to five families of trees obtained by evaluating terms (Bohm trees, L'evyLongo 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. Key words: Bohm trees, approximants, intersection types. 1 Introduction A theory of functions like the calculus, which provides a foundation for the functional programming paradigm in computer science, can be seen essentially as a theory of "programs". This point of view leads naturally to the intuitive idea that the meaning of a term (program) is represented by the amount of "meaningful information" we can extract from the term by "running it". The formalization of "the information"...