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Rewriting with a nondeterministic choice operator : From algebra to proofs
[chapter]

1986
*
Lecture Notes in Computer Science
*

result of the computations, even if there exist several different computation paths~ In this paper, we develop

doi:10.1007/3-540-16442-1_27
fatcat:khddvgchxjd6zcfjxk36j4dieq
*a*new formalism introducing*a*bounded nondeterministie*choice**operator*'¢' into*algebraic*... The privileged field of classical*algebra*and term*rewriting*systems is that of strictly deterministic sysi~ems: the confl~tence property is generaly assumed*to*hold, which ensures determinism about the ... Our main idea is*to*introduce*a*special purpose*operator*t, realizing bounded*nondeterministic**choice*. ...##
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Rewriting with a nondeterministic choice operator

1988
*
Theoretical Computer Science
*

In this paper, we introduce

doi:10.1016/0304-3975(86)90005-8
fatcat:vbzjnh7lnvfulni4xwag7g7tu4
*a*bounded*nondeterministic**choice**operator*"u" into*algebraic*specifications and related term-*rewriting*systems. ... Attention is then mainly restricted*to*so-called regular systems, where*nondeterministic**choice*is constraint-free. ... Our main idea is*to*introduce*a*special purpose*operator*"u", which realizes bounded*nondeterministic**choice*by constructing sets of results. ...##
###
Nondeterministic operations on finite relational structures

1998
*
Theoretical Computer Science
*

First,

doi:10.1016/s0304-3975(97)00263-6
fatcat:r22a673slnfk7kf2hzjzcr7rda
*nondeterministic**operations*are considered, i.e.,*operations*which give*a*set of results instead of*a*single one. ... This article builds on*a*tutorial introduction*to*universal*algebra*for language theory (Courcelle, Theoret. Comput. Sci. 163 (1996) l-54) and extends it in two directions. ... Acknowledgements The author likes*to*thank Bruno Courcelle for the initial idea, enlightening discussions and many useful suggestions*to*improve this article. ...##
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Operational and axiomatic semantics of PCF

1990
*
Proceedings of the 1990 ACM conference on LISP and functional programming - LFP '90
*

The system pcf is confluent when combined

doi:10.1145/91556.91677
dblp:conf/lfp/HowardM90
fatcat:vfqoypttzzhynj2uapkngnsr3i
*with*any linear, confluent*algebraic**rewrite*rules. ... PCF, as considered in this paper, is*a*lazy typed lambda calculus*with*functions, pairing, fixed-point*operators*and arbitrary*algebraic*data types. ...*With*the added flexibility of "*nondeterministic**choice*," the steps involved mimic the action of any ordinary interpreter fairly closely. ...##
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Demonic operators and monotype factors

1993
*
Mathematical Structures in Computer Science
*

This paper tackles the problem of constructing

doi:10.1017/s096012950000030x
fatcat:fatpcbqnwbbhfal5okcosqsdku
*a*compact, point-free*proof*of the associativity of demonic composition of binary relations and its distributivity through demonic*choice*. ... The identi cation of such*a*connection is argued*to*be highly conducive*to*the desired compactness of calculation. ... Thanks also*to*the continuing interest and enthusiasm of members of the Eindhoven speculist club. ...##
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Substructural Operational Semantics as Ordered Logic Programming

2009
*
2009 24th Annual IEEE Symposium on Logic In Computer Science
*

We describe

doi:10.1109/lics.2009.8
dblp:conf/lics/PfenningS09
fatcat:4ou76lgejzazleihm2zqh7rzea
*a*substructural logic*with*ordered, linear, and persistent propositions and then endow*a*fragment*with**a*committed*choice*forward-chaining*operational*interpretation. ... The specifications exhibit*a*high degree of uniformity and modularity that allows us*to*analyze the structural properties required for each feature in isolation. ... We would like*to*thank the anonymous reviewers for their comments, Jason Reed for*a*key insight in the*proof*of completeness, and Noam Zeilberger for pointing us*to*Laurent's unpublished note [9] . ...##
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Basic Operational Preorders for Algebraic Effects in General, and for Combined Probability and Nondeterminism in Particular

2018
*
Annual Conference for Computer Science Logic
*

We illustrate these via

doi:10.4230/lipics.csl.2018.29
dblp:conf/csl/LopezS18
fatcat:wins7aui3bgvbkkwwv3hpp4z3e
*a*nontrivial case study: the combination of probabilistic*choice**with*nondeterminism, for which we show that natural instantiations of the three specification methods (*operational*... The "generic*operational*metatheory" of Johann, Simpson and Voigtländer (LiCS 2010) defines contextual equivalence, in the presence of*algebraic*effects, in terms of*a*basic*operational*preorder on ground-type ... Another related completeness result is given in [12] , where inequational axioms for*a*simple process*algebra**with**nondeterministic*and probabilistic*choice*are proved complete*with*respect*to**a*domain-theoretic ...##
###
Delayed choice: an operator for joining Message Sequence Charts
[chapter]

1995
*
IFIP Advances in Information and Communication Technology
*

We study the extension of

doi:10.1007/978-0-387-34878-0_27
fatcat:zywngba5znhshmowzvbt3fvray
*a*simple process*algebra**with*the delayed*choice**operator*. ... It di ers*from*the normal non-deterministic*choice*in that the moment of*choice*is delayed until all alternatives can be distinguished by their rst action. ... However, we do not want*to*remove*nondeterministic**choices*which are internal*to*x or y. This is expressed in the de nition of the delayed*choice**operator*in Table 3 . ...##
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Probabilistic operational semantics for the lambda calculus

2012
*
RAIRO - Theoretical Informatics and Applications
*

Plotkin's CPS translation is extended

doi:10.1051/ita/2012012
fatcat:dz2orum5lrctvj2siqgsy2mw2i
*to*accommodate the*choice**operator*and shown correct*with*respect*to*the*operational*semantics. ... Probabilistic*operational*semantics for*a**nondeterministic*extension of pure λ-calculus is studied. In this semantics,*a*term evaluates*to**a*(finite or infinite) distribution of values. ... Λ ⊕ is nothing more than the usual, untyped, λ-calculus*with*an additional binary*operator*⊕ which represents binary,*nondeterministic**choice*: M ⊕N*rewrites**to*either M or N . ...##
###
Probabilistic Operational Semantics for the Lambda Calculus
[article]

2011
*
arXiv
*
pre-print

Plotkin's CPS translation is extended

arXiv:1104.0195v2
fatcat:jw7iqqhmtjba7bjskrheuefzum
*to*accommodate the*choice**operator*and shown correct*with*respect*to*the*operational*semantics. ... Probabilistic*operational*semantics for*a**nondeterministic*extension of pure lambda calculus is studied. In this semantics,*a*term evaluates*to**a*(finite or infinite) distribution of values. ... Λ ⊕ is nothing more than the usual, untyped, λ-calculus*with*an additional binary*operator*⊕ which serves*to*represent binary,*nondeterministic**choice*: M ⊕ N*rewrites**to*either M or N . ...##
###
Structural Operational Semantics for Weighted Transition Systems
[chapter]

2009
*
Lecture Notes in Computer Science
*

Weighted transition systems are defined, parametrized by

doi:10.1007/978-3-642-04164-8_7
fatcat:dq65lpqzerfnzl7br7cdmzormy
*a*commutative monoid of weights. These systems are further understood as coalgebras for functors of*a*specific form. ...*A*general rule format for the SOS specification of weighted systems is obtained via the coalgebraic approach of Turi and Plotkin. ... For example,*a*unary prefixing*operator*and*a*binary*nondeterministic**choice**operator*,*with*syntax given by: P ::= nil | (*a*, w).P | P + P (*a*∈*A*, w ∈ R + ) can be defined by rules: (*a*, w).x*a*,w x x*a*,u ...##
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Structural operational semantics for stochastic and weighted transition systems

2013
*
Information and Computation
*

We introduce weighted GSOS,

doi:10.1016/j.ic.2013.04.001
fatcat:lkx2b6dsvnaddcaksqbfoztqci
*a*general syntactic framework*to*specify wellbehaved transition systems where transitions are equipped*with*weights coming*from**a*commutative monoid. ... Through examples we provide weighted-GSOS definitions for common stochastic*operators*in the literature. ... For example,*a*unary prefixing*operator*and*a*binary*nondeterministic**choice**operator*,*with*syntax given by: P ::= nil | (*a*, w).P | P + P (*a*∈*A*, w ∈ R + ) can be defined by rules: (*a*, w).x*a*,w x x*a*,u ...##
###
An operational semantics for timed RAISE
[chapter]

1999
*
Lecture Notes in Computer Science
*

Some

doi:10.1007/3-540-48118-4_4
fatcat:k4pv6u7rlvehzo32qw6gv7vagu
*proof*rules for TRSL are listed, and their soundness corresponding*to*our*operational*model is also explained. ... We then have*to*find*a*theoretical foundation for TRSL. In this paper, an*operational*semantics of TRSL is first introduced. Then we define*a*pre-order and test equivalence relation for TRSL. ... Acknowledgements The authors thank Zhou Chaochen for his advice and guidance while doing this research work, Anne Haxthausen for her ideas and comments on Timed RAISE, and He Jifeng for his comments on*a*...##
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Nondeterministic algebraic specifications and nonconfluent term rewriting

1992
*
The Journal of Logic Programming
*

D

doi:10.1016/0743-1066(92)90026-y
fatcat:l5rvzgbizzfyhjd5dyljx6hlmq
*Algebraic*specifications are generalized*to*the case of*nondeterministic**operations*by admitting models*with*set-valued functions (multialgebras). ...*A*calculus for*nondeterministic*specifications is given which is similar*to*term*rewriting*but which employs an additional determinacy predicate. ... D*Algebraic*specifications are generalized*to*the case of*nondeterministic**operations*by admitting models*with*set-valued functions (multialgebras). ...##
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Syntax and Semantics for Operations with Scopes

2018
*
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18
*

selects

doi:10.1145/3209108.3209166
dblp:conf/lics/PirogSWJ18
fatcat:ugfepo5cijdk5fent4av4srnra
*a*single solution*from**a**nondeterministic*computation. ...*with*so-called scoped*operations*. ... Acknowledgments The authors would like*to*thank Marcelo Fiore for enlightening discussions, and the anonymous reviewers for their constructive comments regarding presentation. ...
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