Related papers: Formalizing Chemical Physics using the Lean Theore…
Cell injection is an approach used for the delivery of small sample substances into a biological cell and is widely used in drug development, gene injection, intracytoplasmic sperm injection (ICSI) and in-virto fertilization (IVF). Robotic…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about…
Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often…
We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…
Chemical reactors are dynamic systems that can be described by systems of ordinary differential equations (ODEs). Reactor safety, regulatory compliance, and economics depend on whether certain states are reachable by the reactor, and are…
A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…
This study aims to observe if the theorem prover Lean positively influences students' understanding of mathematical proving. To this end, we perform a pilot study concerning freshmen students at the University of Zurich (UZH). While doing…
Numerical and symbolic methods for optimization are used extensively in engineering, industry, and finance. Various methods are used to reduce problems of interest to ones that are amenable to solution by such software. We develop a…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
Lean is an increasingly popular proof assistant based on dependent type theory. Despite its success, it still lacks important automation features present in more seasoned proof assistants, such as the Sledgehammer tactic in Isabelle/HOL. A…
We introduce our Leanabell-Prover-V2, a 7B large language models (LLMs) that can produce formal theorem proofs in Lean 4, with verifier-integrated Long Chain-of-Thoughts (CoT). Following our previous work Leanabell-Prover-V1, we continual…
In this paper we present a new "external checker" for the Lean theorem prover, written in Lean itself. This is the first complete typechecker for Lean 4 other than the reference implementation in C++ used by Lean itself, and our new checker…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
We show that the principles of a ''complete physical theory'' and the conclusions of the standard quantum mechanics do not irreconcilably contradict each other as is commonly believed. In the algebraic approach, we formulate axioms that…
Recent years have seen a significant increase in the use of machine intelligence for predicting electronic structure, molecular force fields, and the physicochemical properties of various condensed systems. However, substantial challenges…
We introduce MetaChem, a language for representing and implementing Artificial Chemistries. We motivate the need for modularisation and standardisation in representation of artificial chemistries. We describe a mathematical formalism for…
Proof Designer is a computer software program designed to help Mathematics students learn to write mathematical proofs. Under the guidance of the user, Proof Designer assists in writing outlines of proofs in elementary set theory. Proof…
Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to…