Static analysis of functional languages

Static analysis is the name given to a number of compile time analysis techniques used to automatically generate information which can lead to improvements in the execution performance of function languages. This thesis provides an introduction to these techniques and their implementation. The abstract interpretation framework is an example of a technique used to extract information from a program by providing the program with an alternate semantics and evaluating this program over a non-standard domain. The elements of this domain represent certain properties of interest. This framework is examined in detail, as well as various extensions and variants of it. The use of binary logical relations and program logics as alternative formulations of the framework , and partial equivalence relations as an extension to it, are also looked at. The projection analysis framework determines how much of a sub-expression can be evaluated by examining the context in which the expression is to be evaluated, and provides an elegant method for finding particular types of information from data structures. This is also examined. The most costly operation in implementing an analysis is the computation of fixed points. Methods developed to make this process more efficient are looked at. This leads to the final chapter which highlights the dependencies and relationships between the different frameworks and their mathematical disciplines.KMBT_22

The tensor product in Wadler's analysis of lists

AbstractWe consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation of Wadler's strictness analysis for lists using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation