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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 ..."
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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 Semantics for Static Type Inference in a Nondeterministic Language
, 1994
"... Plotkin used the models of reduction in order to obtain a semantic characterization of static type inference in the pure calculus. Here we apply these models to the study of a nondeterministic language, obtaining results analogous to Plotkin's. 1 Introduction The models of reduction are a gen ..."
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Plotkin used the models of reduction in order to obtain a semantic characterization of static type inference in the pure calculus. Here we apply these models to the study of a nondeterministic language, obtaining results analogous to Plotkin's. 1 Introduction The models of reduction are a generalization of the usual syntactic models for the pure calculus (see [Plo92] and the references therein). If a term M reduces to a term N then its interpretation in a model of reduction is "smaller than" or equal to the interpretation of N (and not necessarily equal as in models). Plotkin obtained a series of soundness and completeness results for static type inference with respect to models of reduction. With type inference in mind, it seems natural that M and N be interpreted differently, since it may be possible to infer a type for N but not for M . The study of nondeterministic languages gives rise to an alternative motivation for considering models of reduction. In nondeterministic lang...