BRIDGE: Building Representations In Domain Guided Program Synthesis

TL;DR

BRIDGE is a structured prompting framework that enhances multi-artifact program synthesis in Lean by decomposing generation into interconnected domains, improving correctness and efficiency.

Contribution

It introduces a domain-guided, multi-artifact synthesis approach that significantly improves correctness, sample efficiency, and learnability over existing methods.

Findings

BRIDGE improves Lean executable correctness by up to 1.5x.

It is roughly 2x more sample efficient at similar generation lengths.

Specification-oriented prompting boosts Python pass rates by up to 17.5 percentage points.

Abstract

Large language models can generate plausible code, but remain brittle for formal verification in proof assistants such as Lean. A central scalability challenge is that verified synthesis requires consistent artifacts across several coupled domains: executable code, formal specifications, theorem statements, and proof attempts. Existing approaches often treat these artifacts separately. We present BRIDGE, a structured prompting framework for multi-artifact program synthesis. BRIDGE decomposes generation into three interconnected domains: Code, Specification, and Theorem/Proof, and uses domain-specific intermediate reasoning to connect them. In Lean, BRIDGE often follows a code-first workflow, using the generated implementation as a semantic anchor for downstream specification, theorem statement, and proof-attempt generation. Across 178 algorithmic problems and five LLMs, BRIDGE improves Lean executable correctness by up to nearly 1.5x over direct prompting and can be roughly 2x more sample efficient at comparable generation lengths. We further find that specification-oriented prompting improves Python pass rates by up to 17.5 percentage points. Beyond inference-time prompting, supervised fine-tuning on BRIDGE-style reasoning traces yields nearly 1.5x higher Lean pass success than code-only fine-tuning, suggesting that these intermediate representations provide a learnable inductive bias. BRIDGE provides a practical framework for scaling verified synthesis while highlighting the remaining gap between executable correctness and full formal proof generation.