arXiv subjects

Jasmin Blanchette

Publications and source records attributed to Jasmin Blanchette.

8 recordsLinked to original sources

arXiv2026

Tao's Equational Proof Challenge Accepted (Technical Report)

In the context of the Equational Theories Project, Terence Tao posed the challenge of finding alternatives to a complicated 62-step proof found by the Vampire superposition prover. We introduce a proof minimization tool called Krympa. Using a combination of brute force and heuristics, and exploiting both Vampire and the Twee equational prover, the tool reduces the 62-step proof to 20 steps, each corresponding to a rewrite. In an empirical evaluation, it also performs well on 1431 equational problems originating from the same project, reducing in particular a 151-step proof to only 10 steps.

cs.LO↗

arXiv2025

Optimistic Higher-Order Superposition

The $λ$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional extensionality axiom. In the present work, we introduce an "optimistic" version of $λ$-superposition that addresses these two issues. Specifically, our new calculus delays explosive unification problems using constraints stored along with the clauses, and it applies functional extensionality in a more targeted way. The calculus is sound and refutationally complete with respect to a Henkin semantics. We have yet to implement it in a prover, but examples suggest that it will outperform, or at least usefully complement, the original $λ$-superposition calculus.

cs.LO↗

arXiv2025

Term Orders for Optimistic Lambda-Superposition

We introduce $λ$KBO and $λ$LPO, two variants of the Knuth-Bendix order (KBO) and the lexicographic path order (LPO) designed for use with the $λ$-superposition calculus. We establish the desired properties via encodings into the familiar first-order KBO and LPO.

cs.LO↗

arXiv2025

Exploiting Instantiations from Paramodulation Proofs in Isabelle/HOL

Metis is an ordered paramodulation prover built into the Isabelle/HOL proof assistant. It attempts to close the current goal using a given list of lemmas. Typically these lemmas are found by Sledgehammer, a tool that integrates external automatic provers. We present a new tool that analyzes successful Metis proofs to derive variable instantiations. These increase Sledgehammer's success rate, improve the speed of Sledgehammer-generated proofs, and help users understand why a goal follows from the lemmas.

cs.LO↗

arXiv2024

Closure Properties of General Grammars -- Formally Verified

We formalized general (i.e., type-0) grammars using the Lean 3 proof assistant. We defined basic notions of rewrite rules and of words derived by a grammar, and used grammars to show closure of the class of type-0 languages under four operations: union, reversal, concatenation, and the Kleene star. The literature mostly focuses on Turing machine arguments, which are possibly more difficult to formalize. For the Kleene star, we could not follow the literature and came up with our own grammar-based construction.

cs.FL↗

arXiv2023

SAT-Inspired Higher-Order Eliminations

We generalize several propositional preprocessing techniques to higher-order logic, building on existing first-order generalizations. These techniques eliminate literals, clauses, or predicate symbols from the problem, with the aim of making it more amenable to automatic proof search. We also introduce a new technique, which we call quasipure literal elimination, that strictly subsumes pure literal elimination. The new techniques are implemented in the Zipperposition theorem prover. Our evaluation shows that they sometimes help prove problems originating from Isabelle formalizations and the TPTP library.

cs.LO↗

arXiv2021

Superposition for Lambda-Free Higher-Order Logic

We introduce refutationally complete superposition calculi for intentional and extensional clausal $λ$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the $λ$-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.

cs.LO↗

arXiv2021

Superposition with Lambdas

We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $βη$-equivalence classes of $λ$-terms and rely on higher-order unification to achieve refutational completeness. We implemented the calculus in the Zipperposition prover and evaluated it on TPTP and Isabelle benchmarks. The results suggest that superposition is a suitable basis for higher-order reasoning.

cs.LO↗