Probabilistic λ-calculus and Quantitative Program Analysis

Authors:
Alessandra Di Pierro;Chris Hankin;Herbert Wiklicky
Affiliations:
Università di Pisa, Dipartimento di Informatica, Largo Bruno Pontecorvo, 3, 56127 Pisa, Italy. E-mail: dipierro@di.unipi.it,;Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2AZ, UK. E-mail: clh@doc.ic.ac.uk, herbert@doc.ic.ac.uk;Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2AZ, UK. E-mail: clh@doc.ic.ac.uk, herbert@doc.ic.ac.uk
Venue:
Journal of Logic and Computation
Year:
2005

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Abstract

We show how the framework of probabilistic abstract interpretation can be applied to statically analyse a probabilistic version of the λ-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 λ-calculus Λp, and reviewing the framework of abstract interpretation and strictness analysis, we demonstrate our technique by constructing a probabilistic (first-order) strictness analysis for Λp.