Quantitative Program Sketching using Lifted Static Analysis

Abstract

We present a novel approach for resolving numerical program sketches under Boolean and quantitative objectives. The input is a program sketch, which represents a partial program with missing numerical parameters (holes). The aim is to automatically synthesize values for the parameters, such that the resulting complete program satisfies: a Boolean (qualitative) specification given in the form of assertions; and a quantitative specification that estimates the number of execution steps to termination and which the synthesizer is expected to optimize.To address the above quantitative sketching problem, we encode a program sketch as a program family (a.k.a. software product line) and analyze it by the specifically designed lifted analysis algorithms based on abstract interpretation. In particular, we use a combination of forward (numerical) and backward (termination) lifted analysis of program families to find the variants (family members) that satisfy all assertions, and moreover are optimal with respect to the given quantitative objective. Such obtained variants represent “correct & optimal” sketch realizations.We present a prototype implementation of our approach within the FamilySketcher tool for resolving C sketches with numerical types. We have evaluated our approach on a set of benchmarks, and experimental results confirm the effectiveness of our approach.