相关论文: Designing a Theorem Prover
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…
LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
Generating code from natural-language requirements has become a primary route for LLM-assisted software development. Although LLMs can successfully complete small programming tasks, generating an entire complex project remains unreliable…
Probing classifiers have emerged as one of the prominent methodologies for interpreting and analyzing deep neural network models of natural language processing. The basic idea is simple -- a classifier is trained to predict some linguistic…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
Static verification relying on an automated theorem prover can be very slow and brittle: since static verification is undecidable, correct code may not pass a particular static verifier. In this work we use metaprogramming to generate code…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…