Related papers: Towards Autoformalization of Mathematics and Code …
In mathematical proof education, there remains a need for interventions that help students learn to write mathematical proofs. Research has shown that timely feedback can be very helpful to students learning new skills. While for many years…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
In this paper we share several experiments trying to automatically translate informal mathematics into formal mathematics. In our context informal mathematics refers to human-written mathematical sentences in the LaTeX format; and formal…
In this paper, we present a formalization of Kozen's propositional modal $\mu$-calculus, in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higher-order abstract syntax in inductive sets in…
Autoformalization aims to produce formal statements that compile and faithfully preserve the intended meaning of informal mathematics. Yet standard single-output evaluation protocols collapse a many-to-many problem into a single-output…
Using the measurement-based quantum computation model, we construct interactive proofs with non-communicating quantum provers and a classical verifier. Our construction gives interactive proofs for all languages in BQP with a polynomial…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
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…
If a code base is so big and complicated that complete mechanical verification is intractable, can we still apply and benefit from verification methods? We show that by allowing a deliberate mechanized formalization gap we can shrink and…
One of the effective model checking methods is to utilize the efficient decision procedure of SAT (or SMT) solvers. In a SAT-based model checking, a system and its property are encoded into a set of logic formulas and the safety is checked…
This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support…
MapReduce frameworks are widely used for the implementation of distributed algorithms. However, translating imperative algorithms into these frameworks requires significant structural changes to the algorithm. As the costs of running faulty…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
We address the problem of translating informal mathematical proofs expressed in natural language into formal proofs in Lean4 under a constrained computational budget. Our approach is grounded in two key insights. First, informal proofs tend…
In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of…
Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on…
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…