
On Randomised Strategies in the λCalculus (Long Version)
In this work we introduce randomised reduction strategies, a notion alre...
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Lambda Calculus and Probabilistic Computation
We introduce two extensions of λcalculus with a probabilistic choice op...
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Probabilistic Rewriting: Relations between Normalization, Termination, and Unique Normal Forms
We investigate how techniques from Rewrite Theory can help us to study c...
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The Bang Calculus and the Two Girard's Translations
We study the two Girard's translations of intuitionistic implication int...
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A note on confluence in typed probabilistic lambda calculi
On the topic of probabilistic rewriting, there are several works studyin...
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Fieldbased Coordination with the Share Operator
Fieldbased coordination has been proposed as a model for coordinating c...
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Lambda Calculus with Explicit Readback
This paper introduces a new term rewriting system that is similar to the...
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Decomposing Probabilistic Lambdacalculi
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.
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