Towards a Trustworthy Semantics-Based Language Framework via Proof Generation

Abstract

We pursue the vision of an ideal language framework, where programming language designers only need to define the formal syntax and semantics of their languages, and all language tools are automatically generated by the framework. Due to the complexity of such a language framework, it is a big challenge to ensure its trustworthiness and to establish the correctness of the autogenerated language tools. In this paper, we propose an innovative approach based on proof generation. The key idea is to generate proof objects as correctness certificates for each individual task that the language tools conduct, on a case-by-case basis, and use a trustworthy proof checker to check the proof objects. This way, we avoid formally verifying the entire framework, which is practically impossible, and thus can make the language framework both practical and trustworthy. As a first step, we formalize program execution as mathematical proofs and generate their complete proof objects. The experimental result shows that the performance of our proof object generation and proof checking is very promising.

Mechanizing Matching Logic In Coq

“…• Exporting Metamath Proof Objects. An interesting way of combining advantages of both our Coq formalization and the Metamath formalization in [11] would be the ability to convert matching logic proofs in Coq to matching logic proofs in Metamath. One challenge here is posed by the fact that Metamath uses the traditional named representation of matching logic patterns, which is different from the locally nameless representation used in our Coq development.…”

“…This paper is not the only attempt that tries to formalize matching logic using a formal system. In [11], the authors propose a matching logic formalization based on Metamath [35], a formal language used to encode abstract mathematical axioms and theorems. The syntax and proof system of matching logic are defined in Metamath in a few hundreds lines of code [25].…”

Mechanizing Matching Logic In Coq

“…This paper is not the only attempt that tries to formalize matching logic using a formal system. In [6], the authors propose a matching logic formalization based on Metamath [31], a formal language used to encode abstract mathematical axioms and theorems. The syntax and proof system of matching logic are defined in Metamath in a few hundreds lines of code [21].…”

“…An interesting way of combining advantages of both our Coq formalization and the Metamath formalization in [6] would be the ability to convert matching logic proofs in Coq to matching logic proofs in Metamath. One challenge here is posed by the fact that Metamath uses nominal representation of matching logic patterns, which is different from the locally nameless representation used in our Coq development.…”

Proof-Carrying Parameters in Certified Symbolic Execution: The Case Study of Antiunification

“…A fair question that needs to be posed is how can we trust the proofs produced by the deductive verifier generated by K? Given the size of the K codebase (about half a million lines of code [6]) and its dynamics (new code committed every week), the formal verification of the implementation of K is out of question. The solution here is to do what other formal verification tools do: instrument K so that its automatically generated tools produce proof objects that can be independently checked by a trusted kernel.…”