Program Sketching Using Lifted Analysis for Numerical Program Families

Abstract

This work presents a novel approach for synthesizing numerical program sketches using lifted (family-based ) static program analysis. In particular, our approach leverages a lifted static analysis based on abstract interpretation, which is used for analyzing program families with numerical features. It takes as input the common code base, which encodes all variants of a program family, and produces precise results for all variants in a single analysis run. The elements of the underlying lifted analysis domain are decision trees, in which decision nodes are labeled with linear constraints defined over numerical features and leaf nodes belong to a given single-program analysis domain.We encode a program sketch as a program family such that holes correspond to numerical features and all possible sketch realizations correspond to variants in the program family. Then, we preform a lifted analysis of the family, so that only those variants that satisfy all assertions under all possible inputs represent correct realizations of holes in the sketch.We have implemented an experimental program synthesizer for resolving C sketches. It is based on a lifted static analyzer for #if-based C program families, which uses the numerical domains from the APRON library. An evaluation yields promising results. Moreover, our approach provides speedups in some cases against the popular sketching tool Sketch and can solve some numerical benchmarks that Sketch cannot handle.

Model Sketching by Abstraction Refinement for Lifted Model Checking (Extended Version)

“…In contrast to Boolean features that have only two values, numerical features can have a range of numbers as explicit values. Hence, the model sketching problem reduces to selecting correct variants (family members) from the resulting model family [8]. The automated analysis of such families for finding a correct variant is challenging since in addition to the state-space explosion affecting each family member, the family size (i.e., the number of variants) typically grows exponentially in the number of features.…”