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Probabilistic Lambda-calculus and Quantitative Program Analysis

Alessandra Di Pierro, Chris Hankin, Herbert Wiklicky

Journal Article
Journal of Logic and Computation
Volume 15
Issue 2
pp.159–179
April, 2005
Oxford University Press
ISSN 0955-792X
DOI 10.1093/logcom/exi008
Abstract

We show how the framework of probabilistic abstract interpretation can be applied to statically analyse a probabilistic version of the {lambda}-calculus. The resulting analysis allows for a more speculative use of its outcomes based on the consideration of statistically defined quantities. After introducing a linear operator based semantics for our probabilistic {lambda}-calculus {Lambda}p, and reviewing the framework of abstract interpretation and strictness analysis, we demonstrate our technique by constructing a probabilistic (first-order) strictness analysis for {Lambda}p.

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