Towards a Deductive Verification Infrastructure for Weighted Programming

2026-08-19

AI Summary

本文提出一种基于加权断言语言和中间验证语言的演绎验证框架，用于解决加权程序的验证问题，支持自动量化消除。

Abstract

Weighted programs extend guarded commands with trace weights drawn from a semiring, or more generally a monoid-module. Varying this algebra gives one programmatic syntax for a variety of quantitative and symbolic models. Weakest-preweighting semantics provides a compositional basis for reasoning about those programs. We present a deductive verification framework based on a weighted assertion language and an intermediate verification language. Its weight domains are ordered structures with implication and coimplication, which let verification conditions express lower- and upper-bound obligations internally. We prove sound translations of core commands and reusable encodings for various proof rules applying to procedure calls and loops. To facilitate automation, we prove soundness of a quantifier elimination procedure for our assertion language. A prototype in the Caesar verifier checks case studies for probabilistic queueing costs, recursive database provenance with cyclic dependencies, clearance bounds for networks of arbitrary size, and formal-language reasoning about lock-freedom of a compare-and-swap counter.

Problem

• weighted programs
• deductive verification
• weakest-preweighting semantics
• semiring
• monoid-module

Innovation

• weighted programs
• deductive verification framework
• quantifier elimination procedure
• semiring