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Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
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…
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…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
Can a machine write good poetry? Any positive answer raises fundamental questions about the nature and value of art. We report a seven-month poetry workshop in which a large language model was shaped into a digital poet through iterative…
Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods either focus on theorem-only NL-to-FL…
Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of…
We provide an approach for generating beautiful poetry. Our sonnet-generation algorithm includes several novel elements that improve over the state of the art, leading to metrical, rhyming poetry with many human-like qualities. These novel…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…
We present Lean Refactor, a plug-and-play retrieval-augmented agentic framework for multi-objective, controllable, and version-robust refactoring of Lean proofs. LLM-generated proofs are notoriously correct-but-verbose and brittle across…
Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants. Such "hammer" tech- niques complement traditional proof assistant automation as…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
Formal verification offers a path to provably correct software, but writing verified code remains expensive enough that the technique is rarely used in production. Recent large language models can accelerate this work, and recent benchmarks…
This thesis delves into a fortiori arguments in deductive reasoning, underscoring their relevance in various domains such as law, philosophy, and artificial intelligence. The research is centred on employing GPT-3.5-turbo to automate the…
Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node…