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...

Software architecture has an important impact on maintainability. One of its key functions is to restrict dependencies between system components. However, there are few objective criteria to quantify how well a given architecture does so. In this paper, we propose an objective measure for architecture strictness and report the findings of our case study on architecture strictness with nine real...

We show that compiler optimisations based on strictness analysis can be expressed formally in the functional framework using continuations. This formal presentation has two beneets: it allows us to give a rigorous correctness proof of the optimised compiler; and it exposes the various optimisations made possible by a strictness analysis.

The concept of strictness of morphological operators is discussed, and it is shown that the ordinary morphological operators have extreme strictness which leads to sensitivity to noise and digital artifacts. Based on this observation new morphological operators that generalize the ordinary morphological operators, are de ned. The generalized operators have controllable strictness and so excessi...

The extraction of strictness information marks an indispensable element of an eecient compilation of lazy functional languages like Haskell. Based on the method of abstract reduction we have developed an eecient strictness analyser for a core language of Haskell. It is completely written in Haskell and compares favourably with known implementations. The implementation is based on the G #-machin...

This article examines the association between three dimensions of perceived parenting--warmth, strictness, and expectation--and adult cognitive and socioeconomic achievement outcomes. Structural equation models (N = 7,035) were used to examine simultaneously the influence of parenting on adult achievement while controlling for the influence of parental socioeconomic circumstances. Very low and ...

This paper describes a method for finding the least fixed points of higher-order functions over finite domains using symbolic manipulation. Fixed point finding is an essential component in the calculation of abstract semantics of functional programs, providing the foundation for program analyses based on abstract interpretation. Previous methods for fixed point finding have primarily used seman...

Abstract. Explicit enforcement of strictness is used by functional programmers for many different purposes. Few functional programmers, however, are aware that explicitly enforcing strictness has serious consequences for (formal) reasoning about their programs. Some vague “folklore” knowledge has emerged concerning the correspondence between lazy and strict evaluation but this is based on exper...

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 frame...

We show that compiler optimisations based on strictness analysis can be expressed formally in the functional framework using continuations. This formal presentation has two beneets: it allows us to give a rigorous correctness proof of the optimised compiler; and it exposes the various optimisations made possible by a strictness analysis. These beneets are especially signiicant in the presence o...