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OnlineProver is an interactive proof assistant tailored for the educational setting. Its main features include a user-friendly interface for editing and checking proofs. The user interface provides feedback directly within the derivation,…
New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In…
ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented…
We present an implementation of tree neural networks within the proof assistant HOL4. Their architecture makes them naturally suited for approximating functions whose domain is a set of formulas. We measure the performance of our…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
We introduce DeepSeek-Prover-V1.5, an open-source language model designed for theorem proving in Lean 4, which enhances DeepSeek-Prover-V1 by optimizing both training and inference processes. Pre-trained on DeepSeekMath-Base with…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
I describe the TreeBanker, a graphical tool for the supervised training involved in domain customization of the disambiguation component of a speech- or language-understanding system. The TreeBanker presents a user, who need not be a system…
Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
We present a tool that automates termination proofs for recursive definitions by mining existing termination theorems.
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations of higher-dimensional proofs, assists in their…
Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and…
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…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…