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Abstract
A notion of probabilistic lambdacalculus usually comes with a prescribed reduction strategy, typically callbyname or callbyvalue, as the calculus is nonconfluent and these strategies yield different results. This is a break with one of the main advantages of lambdacalculus: confluence, which means results are independent from the choice of strategy. We present a probabilistic lambdacalculus where the probabilistic operator is decomposed into two syntactic constructs: a generator, which represents a probabilistic event; and a consumer, which acts on the term depending on a given event. The resulting calculus, the Probabilistic Event LambdaCalculus, is confluent, and interprets the callbyname and callbyvalue strategies through different interpretations of the probabilistic operator into our generator and consumer constructs. We present two notions of reduction, one via finegrained local rewrite steps, and one by generation and consumption of probabilistic events. Simple types for the calculus are essentially standard, and they convey strong normalization. We demonstrate how we can encode callbyname and callbyvalue probabilistic evaluation.
Original language  English 

Title of host publication  Foundations of Software Science and Computation Structures 
Subtitle of host publication  23rd International Conference, FOSSACS 2020 Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020 Dublin, Ireland, April 25–30, 2020, Proceedings 
Editors  GoubaultLarrecq Jean, Barbara König 
Place of Publication  Cham 
Publisher  Springer 
Pages  136156 
Number of pages  21 
Volume  12077 
ISBN (Electronic)  9783030452315 
ISBN (Print)  9783030452308 
DOIs  
Publication status  Published  17 Apr 2020 
Event  23rd International Conference on Foundations of Software Science and Computation Structures  Dublin, Ireland Duration: 25 Apr 2020 → … https://etaps.org/2020/fossacs 
Publication series
Name  Lecture Notes in Computer Science 

Publisher  Springer 
Volume  12077 
ISSN (Print)  03029743 
ISSN (Electronic)  16113349 
Conference
Conference  23rd International Conference on Foundations of Software Science and Computation Structures 

Abbreviated title  FoSSaCS 2020 
Country/Territory  Ireland 
City  Dublin 
Period  25/04/20 → … 
Internet address 
ASJC Scopus subject areas
 Theoretical Computer Science
 Computer Science(all)
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 1 Finished

Typed LambdaCalculi with Sharing and Unsharing
Engineering and Physical Sciences Research Council
1/01/19 → 30/07/22
Project: Research council
Profiles

Willem Heijltjes
 Department of Computer Science  Senior Lecturer
 Mathematical Foundations of Computation
Person: Research & Teaching