1 option
Semantics of the Probabilistic Typed Lambda Calculus : Markov Chain Semantics, Termination Behavior, and Denotational Semantics / by Dirk Draheim.
- Format:
- Book
- Author/Creator:
- Draheim, Dirk, author.
- Series:
- Computer Science (Springer-11645)
- Language:
- English
- Subjects (All):
- Computers.
- Programming languages (Electronic computers).
- Mathematical statistics.
- Theory of Computation.
- Programming Languages, Compilers, Interpreters.
- Probability and Statistics in Computer Science.
- Local Subjects:
- Theory of Computation.
- Programming Languages, Compilers, Interpreters.
- Probability and Statistics in Computer Science.
- Physical Description:
- 1 online resource (VIII, 218 pages) : 6 illustrations
- Edition:
- First edition 2017.
- Contained In:
- Springer eBooks
- Place of Publication:
- Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2017.
- System Details:
- text file PDF
- Summary:
- 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.
- Contents:
- Part I: The Probabilistic Lambda-Calculus and its Semantics
- Introduction
- Syntax and Operational Semantics
- The Working Probabilistic Lambda Calculus
- Properties of the Markov Chain Semantics
- Denotational Semantics
- Semantical Correspondences
- Categorical Treatment
- Probabilism and Non-Determinism
- Part II: Natural Probabilistic Reasoning
- On Natural Two-Tier Semantics for Propositional Logics
- Natural Semantics of Propositions
- Finite Discrete Stochastics Reconsidered
- Lambda-Calculus Definitions
- Markov Chains
- Basic Logic Language and Semantics Definitions
- References
- Index.
- Other Format:
- Printed edition:
- ISBN:
- 978-3-642-55198-7
- 9783642551987
- Access Restriction:
- Restricted for use by site license.
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.