Probabilistic λ-calculus and Quantitative Program Analysis
نویسندگان
چکیده
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 .
منابع مشابه
λ - calculus and Quantitative Program Analysis ( Extended
In this paper we show how the framework of probabilistic abstract interpretation can be applied to statically analyse a probabilistic λ-calculus. We start by reviewing the classical framework of abstract interpretation. We choose to use (first-order) strictness analysis as our running example. We present the definition of probabilistic abstract interpretation and use it to construct a probabili...
متن کاملQuantitative Behavioural Reasoning for Higher-order Effectful Programs: Applicative Distances (Extended Version)
Behavioural preorders and equivalences for higher-order languages have been extensively studied in the last decades, often leading to rich and satisfactory theories. However, in presence of effectful computations ordinary behavioural relations can be too discriminating, as highlighted by probabilistic higher-order languages. An elegant way to avoid such problem is to move from qualitative, bool...
متن کاملOn Probabilistic Applicative Bisimulation and Call-by-Value λ-Calculi
Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is generalized to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more sur...
متن کاملProbabilistic Applicative Bisimulation and Call-by-Value λ-Calculi (Long Version)
Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is generalized to a typed, call-by-value, lambda-calculus. Surprisingly, the obtained relation coincides with context equivalence, contrary to what happens when call-by-name evaluation is considered. Even more sur...
متن کاملQuantitative Analysis and Model Checking
Many notions of models in computer science provide quantitative information, or uncertainties, which necessitate a quantitative model checking paradigm. We present such a framework for reactive and generative systems based on a non-standard interpretation of the modal mu-calculus, where x: / x: are interpreted as least/greatest fixed points over the infinite lattice of maps from states to the u...
متن کامل