Dependency Analysis of Functional Specifications with Algebraic Data Structures

摘要

In the context of interactive formal verification of complex systems, much effort is spent on proving the preservation of the systems invariants. However, most operations have a localized effect on the system, which only really impacts few invariants at the same time. Identifying those invariants that are unaffected by an operation can substantially ease the proof burden for the programmer. We present a dependency analysis for a strongly-typed, functional language, which computes a conservative approximation of the input fragments on which the operations depend. It is a flow-sensitive interprocedural analysis that handles arrays, structures and variant data types. For the latter, it simultaneously computes a subset of possible constructors. We have validated the scalability of the analysis to complex transition systems by applying it to a functional specification of the MINIX operating system.