Related papers: Capturing properties of planar diagrams in Lean pr…
Just as humans can become disoriented in featureless deserts or thick fogs, not all environments are conducive to the Localization Accuracy and Stability (LAS) of autonomous robots. This paper introduces an efficient framework designed to…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
The proof assistant Lean has support for abstract polynomials, but this is not necessarily the same as support for computations with polynomials. Lean is also a functional programming language, so it should be possible to implement…
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 formulate learning guided Automated Theorem Proving as Partial Label Learning, building the first bridge across these fields of research and providing a theoretical framework for dealing with alternative proofs during learning. We use…
Advanced driver assistance systems have improved comfort, safety, and efficiency of modern vehicles. However, sensor limitations lead to noisy lane estimates that pose a significant challenge in developing performant control architectures.…
Pattern-Oriented Analysis and Design (POAD) is the practice of building complex software by applying proven designs to specific problem domains. Although a great deal of research and practice has been devoted to formalizing existing design…
The automation offered by modern program proof tools goes hand in hand with the capability to interact with the tool when the verification fails. The SPARK proof tool tries to help the user by providing the right information, so that the…
In the present article, we show the existence of a coupled fixed point for an order preserving mapping in a preordered left K-complete quasi-pseudometric space using a preorder induced by an appropriate function. We also define the concept…
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…
We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Adversarial images highlight how vulnerable modern image classifiers are to perturbations outside of their training set. Human oversight might mitigate this weakness, but depends on humans understanding the AI well enough to predict when it…
In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…
This paper introduces a framework for Planning while Learning where an agent is given a goal to achieve in an environment whose behavior is only partially known to the agent. We discuss the tractability of various plan-design processes. We…
Autoformalization, the process of transforming informal mathematical language into formal specifications and proofs remains a difficult task for state-of-the-art (large) language models. Existing works point to competing explanations for…