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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Semantics of the Probabilistic Typed Lambda Calculus: Markov Chain Semantics, Termination Behavior, and Denotational Semantics

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

Draheim, Dirk

Hardcover

FictionGeneral ComputersProgramming

ISBN10: 3642551971
ISBN13: 9783642551970
Publisher: Springer
Published: Mar 10 2017
Pages: 218
Weight: 1.10
Height: 0.56 Width: 6.14 Depth: 9.21
Language: English

This book takes a foundational approach to the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, which is the typed lambda calculus with recursion plus probabilistic choice.

The book starts with a recapitulation of the basic mathematical tools needed throughout the book, in particular Markov chains, graph theory and domain theory, and also explores the topic of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus and, furthermore, both a graph and a tree semantics. Based on that, it investigates the termination behavior of probabilistic programs. It introduces the notions of termination degree, bounded termination and path stoppability and investigates their mutual relationships. Lastly, it defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains.

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