Overview
- Provides an in-depth discussion of the semantics of the probabilistic typed lambda calculus and its termination behavior
- Self-contained, offering a recapitulation of the basic mathematical tools needed
- Includes an extensive list of further references for researchers
- Includes supplementary material: sn.pub/extras
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 distributionsas domains.
The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.
Authors and Affiliations
About the author
Dirk Draheim is full professor of information society technologies and head of the large-scale systems group at Tallinn University of Technology. From to 1990 to 2006 he worked as an IT project manager, IT consultant and IT author in Berlin. In summer 2006, he was Lecturer at the University of Auckland and from 2006-2008 he was area manager for database systems at the Software Competence Center Hagenberg as well as Adjunct Lecturer in information systems at the Johannes-Kepler-University Linz. From 2008 to 2016 he was head of the data center of the University of Innsbruck and, in parallel, from 2010 to 2016, Adjunct Reader at the Faculty of Information Systems of the University of Mannheim. Dirk is co-author of the Springer book "Form-Oriented Analysis" and author of the Springer book "Business Process Technology", and a member of the ACM.
Bibliographic Information
Book Title: Semantics of the Probabilistic Typed Lambda Calculus
Book Subtitle: Markov Chain Semantics, Termination Behavior, and Denotational Semantics
Authors: Dirk Draheim
DOI: https://doi.org/10.1007/978-3-642-55198-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2017
Hardcover ISBN: 978-3-642-55197-0Published: 10 March 2017
Softcover ISBN: 978-3-662-56872-9Published: 04 May 2018
eBook ISBN: 978-3-642-55198-7Published: 28 February 2017
Edition Number: 1
Number of Pages: VIII, 218
Number of Illustrations: 6 b/w illustrations
Topics: Theory of Computation, Programming Languages, Compilers, Interpreters, Probability and Statistics in Computer Science