Related papers: HolPy: Interactive Theorem Proving in Python

We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…

QuaPy is an open-source framework for performing quantification (a.k.a. supervised prevalence estimation), written in Python. Quantification is the task of training quantifiers via supervised learning, where a quantifier is a predictor that…

Combinatorial group testing reduces screening costs and turnaround time but remains challenging to apply due to design complexity, varying applicability, and lack of implementation tools. Here we present PoolPy, a unified end-to-end…

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…

Scientific inference is often undermined by the vast but rarely explored "multiverse" of defensible modelling choices, which can generate results as variable as the phenomena under study. We introduce RobustiPy, an open-source Python…

Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…

Array programming provides a powerful, compact, expressive syntax for accessing, manipulating, and operating on data in vectors, matrices, and higher-dimensional arrays. NumPy is the primary array programming library for the Python…

Discovering novel high-level concepts is one of the most important steps needed for human-level AI. In inductive logic programming (ILP), discovering novel high-level concepts is known as predicate invention (PI). Although seen as crucial…

InferPy is a Python package for probabilistic modeling with deep neural networks. It defines a user-friendly API that trades-off model complexity with ease of use, unlike other libraries whose focus is on dealing with very general…

We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP…

We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…

IntLevPy provides a comprehensive description of the IntLevPy Package, a Python library designed for simulating and analyzing intermittent and L\'evy processes. The package includes functionalities for process simulation, including full…

We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on…

PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…

Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…

Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…

We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…

We propose to extend the Dafny system with an interactive proof mode. We present a motivating example, how the IPM works, including the main design choices we make, and a prototype implementation.

I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…