Semantics of the Probabilistic Typed Lambda Calculus
Springer Berlin (Verlag)
978-3-642-55197-0 (ISBN)
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.
Dirk Draheim holds a Diploma in Computer Science from the Technische Universität Berlin since 1994 and a PhD in Computer Science from the Freie Universität Berlin since 2002. Since 1999 he gives lectures on Software Engineering at the Freie Universität Berlin. From 2004 to 2006 he was a research associate in the project "Typed User Interfaces", which is granted by the German Research Foundation DFG. In summer 2006 he was lecturer in human-computer interaction at the University of Auckland. Since summer 2006 until autumn 2008 he was senior researcher at the SCCH (Software Competence Center Hagenberg) in the position of the Area Manager Database Technology. Furthermore, he was guest professor in software engineering at the University of Mannheim in winter 2006 and guest lecturer in applied computer science at the Johannes Kepler University Linz in summer 2007 and summer 2008. Since autumn 2008 he is head of the IT department of the University of Innsbruck. Dirk Draheim is interested in system modeling, semantic web, web applications, and databases. Together with Gerald Weber he is organizer and program committee chair of the International Conference "Trends of Enterprise Application Architecture . He is member of ACM.
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.
| Erscheint lt. Verlag | 10.3.2017 |
|---|---|
| Zusatzinfo | VIII, 218 p. 6 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Informatik ► Theorie / Studium ► Compilerbau |
| Mathematik / Informatik ► Mathematik | |
| Schlagworte | Computability • Denotational Semantics • inductive logics • Lambda Calculus • markov chains • probabilistic computation • Probability Theory • Programming language theory • randomized algorithms • verification by model checking |
| ISBN-10 | 3-642-55197-1 / 3642551971 |
| ISBN-13 | 978-3-642-55197-0 / 9783642551970 |
| Zustand | Neuware |
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