Semantics of the Probabilistic Typed Lambda Calculus

Markov Chain Semantics, Termination Behavior, and Denotational Semantics

  • Dirk┬áDraheim

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Dirk Draheim
    Pages 1-16
  3. Dirk Draheim
    Pages 17-64
  4. Dirk Draheim
    Pages 65-92
  5. Dirk Draheim
    Pages 93-133
  6. Dirk Draheim
    Pages 135-191
  7. Back Matter
    Pages 193-218

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 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

Authors and affiliations

  • Dirk┬áDraheim
    • 1
  1. 1.Large-Scale Systems GroupTallinn University of TechnologyTallinnEstonia

Bibliographic information

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