Value Range Analysis for Higher-Order Programs

We develop a value range analysis for higher-order programs. The analysis extracts a nugget that characterizes the value bindings resulting from program execution. This abstraction can be fed into a theorem prover to extract non-trivial inductive properties about programs, including the range of values assigned to variables during program execution. The paper incorporates several new technical developments, including a novel prune-rerun technique for approximating higher-order recursive functions. The nugget extracted from the analysis condenses higher-order programs into a first-order rule-based system. We show how the nugget can be interpreted as an inductively defined structure, and can be simply and directly encoded in the Isabelle/HOL theorem prover, where nontrivial properties of the program can be verified.