The Nuggetizer: Abstracting Away Higher-Orderness for Program Verification

Abstract

Abstract. We develop a static analysis which distills first-order computational structure from higher-order functional programs. The analysis condenses higher-order programs into a first-order rule-based system, a nugget, that characterizes all value bindings that may arise from program execution. Theorem provers are limited in their ability to automatically reason about higher-order programs; nuggets address this problem, being inductively defined structures that can be simply and directly encoded in a theorem prover. The theorem prover can then prove non-trivial program properties, such as the range of values assignable to particular variables at runtime. Our analysis is flow-and path-sensitive, and incorporates a novel prune-rerun analysis technique to approximate higher-order recursive computations.