Semantics of the Probabilistic Typed Lambda Calculus
Markov Chain Semantics, Termination Behavior, and Denotational Semantics
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 establishes a Markov chain semantics 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. Path stoppability characterizes a broadened class of termination and allows for the computation of program runs that are otherwise considered as non-terminating. Lastly, the book defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains.