# Semantics of the Probabilistic Typed Lambda Calculus

## Markov Chain Semantics, Termination Behavior, and Denotational Semantics

- 4 Citations
- 1 Mentions
- 2.4k Downloads

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- 4 Citations
- 1 Mentions
- 2.4k Downloads

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.

The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.

Markov chains Probabilistic computation Lambda calculus Computability Randomized algorithms Programming language theory Verification by model checking

- DOI https://doi.org/10.1007/978-3-642-55198-7
- Copyright Information Springer-Verlag Berlin Heidelberg 2017
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Computer Science Computer Science (R0)
- Print ISBN 978-3-642-55197-0
- Online ISBN 978-3-642-55198-7
- Buy this book on publisher's site