Jianqiu Zhao

Marisa Kirisame, Thomas J. Porter, Ruqing Yang et al.

Live programming systems aim to quickly show programmers the dynamic impacts of program edits. To do so, they re-execute the program whenever it is edited, which poses a computational challenge when programs become large or complex. This has led to the need for incrementality in the implementation of live program interpreters. This paper introduces Chordata, an incremental program interpreter based on shortcut memoization, which learns repeated patterns of computation, called shortcuts, by observing executions of previous versions of a program. It can then apply these shortcuts when the same or a structurally similar program fragment is re-executed. This paper contributes a formal semantics of shortcut memoization for any language with a rewrite-based semantics, with mechanized proofs of key correctness properties. We then express a variant of the Hazel live programming system, expressed as a CEK machine, in Chordata, and develop a number of practical heuristics to learn high-value shortcuts. We evaluate the resulting system on editing traces of students solving simple programming problems. Chordata achieves a speedup of 13.03\times compared to baseline with a 19.97\times memory overhead. For smaller changes and for more complex programs, Chordata achieves even greater speedups. Furthermore, we show that Chordata is capable of providing a speedup even within a single execution, with a faster speedup on a larger input.

Yichi Zhou, Jianqiu Zhao, Yongxin Zhang et al.

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in specialized languages like Lean 4 remains a significant challenge for these models, limiting their application in complex theorem proving and automated verification. Current approaches typically require specializing models through fine-tuning on dedicated formal corpora, incurring high costs for data collection and training. In this work, we introduce \textbf{Delta Prover}, an agent-based framework that orchestrates the interaction between a general-purpose LLM and the Lean 4 proof environment. Delta Prover leverages the reflection and reasoning capabilities of general-purpose LLMs to interactively construct formal proofs in Lean 4, circumventing the need for model specialization. At its core, the agent integrates two novel, interdependent components: an algorithmic framework for reflective decomposition and iterative proof repair, and a custom Domain-Specific Language (DSL) built upon Lean 4 for streamlined subproblem management. \textbf{Delta Prover achieves a state-of-the-art 95.9\% success rate on the miniF2F-test benchmark, surpassing all existing approaches, including those requiring model specialization.} Furthermore, Delta Prover exhibits a significantly stronger test-time scaling law compared to standard Best-of-N proof strategies. Crucially, our findings demonstrate that general-purpose LLMs, when guided by an effective agentic structure, possess substantial untapped theorem-proving capabilities. This presents a computationally efficient alternative to specialized models for robust automated reasoning in formal environments.