Download e-book for iPad: Semantics of the Probabilistic Typed Lambda Calculus: Markov by Dirk Draheim

By Dirk Draheim

This booklet takes a foundational method of the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, that is the typed lambda calculus with recursion plus probabilistic choice.The ebook starts off with a recapitulation of the fundamental mathematical instruments wanted during the ebook, particularly Markov chains, graph thought and area thought, and likewise explores the subject of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus and, moreover, either a graph and a tree semantics. in response to that, it investigates the termination habit of probabilistic courses. It introduces the notions of termination measure, bounded termination and direction stoppability and investigates their mutual relationships. finally, it defines a denotational semantics of the probabilistic lambda calculus, in line with non-stop capabilities over chance distributions as domains.The paintings ordinarily appeals to researchers in theoretical computing device technology targeting probabilistic programming, randomized algorithms, or programming language theory.

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Semantics of the Probabilistic Typed Lambda Calculus: Markov Chain Semantics, Termination Behavior, and Denotational Semantics by Dirk Draheim


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