## Non-Deterministic Extensions of Untyped λ-calculus (1995)

Venue: | INFO. AND COMP |

Citations: | 6 - 0 self |

### BibTeX

@ARTICLE{de'Liguoro95non-deterministicextensions,

author = {Ugo de'Liguoro and Adolfo Piperno},

title = {Non-Deterministic Extensions of Untyped λ-calculus},

journal = {INFO. AND COMP},

year = {1995},

volume = {122},

pages = {149--177}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 λ-calculus with the absence of the Church-Rosser 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 deterministic-calculus, 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...