Related papers: HolPy: Interactive Theorem Proving in Python

The usage of the high-level scripting language Python has enabled new mechanisms for data interrogation, discovery and visualization of scientific data. We present yt, an open source, community-developed astrophysical analysis and…

Dynamic languages, such as Python and Javascript, trade static typing for developer flexibility and productivity. Lack of static typing can cause run-time exceptions and is a major factor for weak IDE support. To alleviate these issues, PEP…

Often user interfaces of theorem proving systems focus on assisting particularly trained and skilled users, i.e., proof experts. As a result, the systems are difficult to use for non-expert users. This paper describes a paper and pencil HCI…

CurvPy is an open-source Python library for automated curve fitting and regression analysis, aiming to make advanced statistical and machine learning techniques more accessible. This paper explores the mathematical foundations and…

The paradigm of Tabled Logic Programming (TLP) is now supported by a number of Prolog systems, including XSB, YAP Prolog, B-Prolog, Mercury, ALS, and Ciao. The reasons for this are partly theoretical: tabling ensures termination and optimal…

We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics…

Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…

Using the programming language Haskell, we introduce an implementation of propositional calculus, number theory, and a simple imperative language that can evaluate arithmetic and boolean expressions. Finally, we provide an implementation of…

In order to handle the complexity and heterogeneity of mod- ern instruction set architectures, analysis platforms share a common design, the adoption of hardware-independent intermediate representa- tions. The usage of these platforms to…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…

Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…

NIFTY, "Numerical Information Field Theory", is a software package designed to enable the development of signal inference algorithms that operate regardless of the underlying spatial grid and its resolution. Its object-oriented framework is…

Molly is a program that compiles cryptographic protocol roles written in a high-level notation into straight-line programs in an intermediate-level imperative language, suitable for implementation in a conventional programming language. We…

A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…

SkyPy is an open-source Python package for simulating the astrophysical sky. It comprises a library of physical and empirical models across a range of observables and a command-line script to run end-to-end simulations. The library provides…

We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We…

Information theory has been very successful in obtaining performance limits for various problems such as communication, compression and hypothesis testing. Likewise, stochastic control theory provides a characterization of optimal policies…

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of…

The use of a functional language to implement proof strategies as proof tactics in interactive theorem provers, often provides short, concise and elegant implementations. Whilst being elegant, the use of higher order features and combinator…