โ Scribed by Dirk Draheim (auth.)
No coin nor oath required. For personal study only.
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.
Front Matter....Pages I-VIII
Introduction....Pages 1-16
Preliminary Mathematics....Pages 17-64
Syntax and Operational Semantics....Pages 65-92
Termination Behavior....Pages 93-133
Denotational Semantics....Pages 135-191
Back Matter....Pages 193-218
Theory of Computation;Programming Languages, Compilers, Interpreters;Probability and Statistics in Computer Science
๐ SIMILAR VOLUMES
MS-CIS-89-16, LOGIC & COMPUTATION 04
The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general