Related papers: Metamath Zero: The Cartesian Theorem Prover
The purpose of this article is to give a presentation of the method of forcing aimed at someone with a minimal knowledge of set theory and logic. The emphasis will be on how the method can be used to prove theorems in ZFC.
We introduce Goedel-Prover, an open-source language model that achieves state-of-the-art (as of April 5 2025) performance in automated formal proof generation for mathematical problems. A key challenge in this field is the scarcity of…
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…
This paper introduces the theory and practice of formal verification of self-assembling systems. We interpret a well-studied abstraction of nanomolecular self assembly, the Abstract Tile Assembly Model (aTAM), into Computation Tree Logic…
Type soundness is an important property of modern programming languages. In this paper we explore the idea that "well-typed languages are sound": the idea that the appropriate typing discipline over language specifications guarantees that…
Recently, researchers have been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted…
This article revisits standard theorems from elementary number theory from a constructive, algorithmic, and proof-theoretic perspective, framed within the theory of computable functionals TCF. Key examples include B\'ezout's identity, the…
One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the…
In a previously published ENTCS paper (Santos et al. (2016)), we introduced a sequent calculus called $\mathbf{LMT^{\rightarrow}}$ for Minimal Implicational Propositional Logic ($\mathbf{LMT^{\rightarrow}}$). This calculus provides a proof…
Large language models (LLMs) have demonstrated remarkable progress in code generation, but many existing benchmarks are approaching saturation and offer little guarantee on the trustworthiness of the generated programs. To improve…
Formal program verification is a longstanding goal in the field. We present the first quantitative comparison of the two primary compiler verification approaches, credible compilation/translation validation and full verification. Working…
In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this…
A proof of quantumness (PoQ) allows a classical verifier to efficiently test if a quantum machine is performing a computation that is infeasible for any classical machine. In this work, we propose a new approach for constructing PoQ…
As one of the longest-running computer-assisted formal mathematics projects, large tracts of mathematical knowledge have been formalized with the help of the Mizar system. Because Mizar is based on first-order classical logic and set…
Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form…
We introduce a machine learning approach to model checking temporal logic, with application to formal hardware verification. Model checking answers the question of whether every execution of a given system satisfies a desired temporal logic…
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…
In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…