SeCaV: A Sequent Calculus Verifier in Isabelle/HOL
Asta Halkj{\ae}r From (Technical University of Denmark), Frederik, Krogsdal Jacobsen (Technical University of Denmark), J{\o}rgen Villadsen, (Technical University of Denmark)
TL;DR
SeCaV is a formal sequent calculus verifier implemented in Isabelle/HOL, offering transparent proof checking and an online tool for expanding derivations, enhancing teaching and understanding of first-order logic.
Contribution
The paper introduces SeCaV, a novel sequent calculus verifier in Isabelle/HOL, with an online unshortener tool, providing formal proofs and interactive features for logic verification.
Findings
Formalized soundness and completeness proofs.
Interactive proof checking with Isabelle/HOL.
Effective teaching tool for logic derivations.
Abstract
We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof checker for our SeCaV derivations. The interactive features of Isabelle/HOL make our system transparent. For instance, the user can simply click on a side condition to see its exact definition. Our formalized soundness and completeness proofs pertain exactly to the calculus as exposed to the user and not just to some model of our tool. Users can also write their derivations in the SeCaV Unshortener, which provides a lighter syntax, and expand them for later verification. We have used both tools in our teaching.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.