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Filter Models for ConjunctiveDisjunctive λcalculi
, 1996
"... The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction i ..."
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Cited by 11 (6 self)
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The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction is introduced, extending fireduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially defined constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually reflecting the disjunctive and conjunctive behaviour of the operators, and we build a filter model. The theory of this model is compared both with a Morrisstyle operational semantics and with a semantics based on a notion of capabilities.
A Filter Model for Concurrent λCalculus
 SIAM J. COMPUT
, 1998
"... Type free lazy λcalculus is enriched with angelic parallelism and demonic nondeterminism. Callbyname and callbyvalue abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union ty ..."
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Cited by 7 (2 self)
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Type free lazy λcalculus is enriched with angelic parallelism and demonic nondeterminism. Callbyname and callbyvalue abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union types and we prove that the induced logical semantics is fully abstract.
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 ..."
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Cited by 1 (1 self)
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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 ...
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"... Lambda calculus is well established as the formal model of functional programming. Nondeterminism is an interesting conceptual issue, often considered in processcalculi. It is interesting to mix lambdacalculus and nondeterminism, firstly because programmers use functional programming but also co ..."
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Lambda calculus is well established as the formal model of functional programming. Nondeterminism is an interesting conceptual issue, often considered in processcalculi. It is interesting to mix lambdacalculus and nondeterminism, firstly because programmers use functional programming but also concurrent methods, networks and multiusers systems, secondly as a step towards more complex languages as for example those providing patternmatching features. That is why we add to an already known language a piece of uncertainty. Thus we are able to study nondeterminism by using the tools for lambdacalculus, all its background and the same rigor. In order to remain as general as possible, the considered language will be the untyped lambdacalculus endowed with a simple choice operation between terms. We call it the nondeterministic lambdacalculus. Our motivation is to have a comprehensive study of a basic language with nondeterminism, its syntax and its operational and denotational semantics, following and extending the work of de’Liguoro and Piperno [1]. As in [1], we choose a natural and simple nondeterministic lambda calculus, where terms are defined as follows: