Abstract Intepretation and recursive behaviour of logic programs

Abstract

We propose a general abstract interpretation based on the recursive behaviour study of Prolog programs. This abstract interpretation allows both the dataflow analysis of a program execution and the automatic derivation of some program properties.

First, we introduce a new notion: the limited-unfolding loop (abbreviated to lul). Roughly speaking, a tree t satisfies a lul m iff the leaf of the branch corresponding to the unfolding of the loop m is labelled with a constant. Instead of a term-groundedness analysis, our study can be seen as a “branch-groundedness” analysis. A finite set of luls can be regarded as a type which may be associated with a variable. Thus, a new algebra of atoms is built and substitution, unification (lub) and anti-unification (gib) operations are redefined in an easy way.

Then, a general abstract resolution (called abstract OLDT resolution) based on the work of H. Tamaki and T. Sato is presented. This abstract resolution always terminates and allows the collection of some information about the concrete resolution (i.e., the standard Prolog interpretation) of all program.

The three stages for our Prolog program abstract interpretation are: 1) computation of a finite set of “significant” luls by looking into the structure of a given Prolog program. 2) abstract resolution from a given call-pattern. 3) analysis of the abstract structure (result of the previous step) for establishing properties like, e.g., solution pattern(s), termination, boundedness, determinism, complexity, ...

This work is supported by the “GRECO de la programmation du CNRS”