Verified code generation asks a large language model (LLM) to generate both an executable program and a machine-checkable proof that the program meets a formal specification, promising software that is correct by construction. The de facto workflow decouples the two halves of the problem: first synthesize a program, then attempt to prove it correct. We observe that this sequential pipeline can be both ineffective and inefficient in practice. A program generated without anticipating its proof can be subtly incorrect or structurally difficult to verify, forcing the LLM into brittle repair loops that alternate between patching the code and patching the proof. Inspired by Dijkstra's view that a program and its correctness argument should be developed hand in hand, we propose $P^3$, an LLM-based agentic workflow that first derives a unified program-and-proof plan from the specification, then elaborates the implementation and proof scaffold under this shared plan. To evaluate verified code generation in realistic settings, we further introduce Lean4Commit0, a repository-derived, library-level benchmark built by extracting core APIs from real-world software repositories and translating their requirements, including relational specifications across APIs, into Lean tasks. Using four frontier LLM backends, we evaluate $P^3$ on Verina, AlgoVeri, and our Lean4Commit0 benchmark, where it achieves the highest solve rate in every benchmark--model setting. Compared with the stronger baseline, it improves solve rates by 4.6--11.2 percentage points and reduces per-task API cost by up to roughly 40\% and wall-clock time by up to roughly 37\% on the difficult subset of each benchmark. A targeted ablation further shows gains of 3.3--8.3 points over implementation-only planning, isolating the benefit of planning the program and proof jointly.
Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort. Large language models (LLMs) promise to generate these proofs automatically, yet existing approaches wire a fixed, human-designed proof strategy into the system and constrain the model to follow it (retrieving premises and predicting tactics one step at a time, or splitting goals by divide-and-conquer), and still prove only a fraction of their target theorems. We show that imposing such a strategy is unnecessary and limiting. Handing the whole lemma to a general LLM code agent (for example, Claude Code), free to choose its own approach, and wrapping it in a verification harness is both simpler and more effective, achieving full coverage: every targeted lemma proved, with no failures and no Coq expert intervention. The agent writes the proofs under feedback and hard constraints from the harness that keep each one sound (accepted only when the prover's kernel closes it), complete (no obligation left unproved or silently dropped), and terminating (no divergent tactics). We evaluate this harness plus code agent along three dimensions. (1) Core logic: on Iris, the state-of-the-art separation logic for concurrent and memory-manipulating programs, Aria proves all 4,257 lemmas of the four core modules and the 217 lemmas verifying Rust's standard libraries built on it, fully automatically. (2) Comparison with prior LLM provers: on reglang, where prior provers manage barely one in eight, Aria proves all 318. (3) Generality: on iris-lean, the unfinished Lean 4 port of Iris, it proves 72 not-yet-ported lemmas, showing the approach is not specific to Coq. A state-of-the-art model (Claude Opus 4.7) can write proofs for verified software development fully and automatically.
Shuangxiang Kan, Shuanglong Kan, Sebastian Ertel· 0 citations
Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability. LLM-based proof agents promise to ease this effort, but their heavy token consumption and API cost remain a major obstacle. We trace this cost to a shared root: current agents operate on serialized concrete syntax, emitting proofs as source text and recovering proof states through separate, line-number-based queries, so every edit shifts later lines and forces repeated relocation of errors and states. This same dependence on concrete syntax also blocks adoption of Minilang, a recent proof language that reaches SOTA on LLM-based proving but is too new for LLMs'training corpora. We address both problems by lifting the agent off source text and onto the abstract syntax tree (AST): the model supplies proofs as JSON representations of Minilang's AST -- native to tool-calling LLMs -- and drives the prover through a tree-edit model that fuses proof operations and states into one proof tree, so each operation carries its own subgoal's state, readable directly off the tree. We realize this design in \emph{Agent over AST} (AoA). Against Amazon's Isabelle Agent on miniF2F and NTP4VC-Pearl common success sets, AoA cuts API cost by 2.3--4.7x (normalized input-cache accounting), uses 2.9--6.9x fewer tokens and 3.9--8.9x fewer tool calls, and finishes 1.4--2.0x faster -- while also solving far more problems on the harder verification benchmark.
Qiyuan Xu, Joshua Ong Jun Leang, Renxi Wang et al.· 0 citations
On a new benchmark of 77 problems with an exact oracle, translation to Answer Set Programming is faithful on six of seven domains and fails only on aggregate coverage scheduling, which concentrates the translation tax in one diagnosable pattern.
Due to token and cognitive limits, Large Language Models (LLMs) typically perform program reasoning over incomplete code fragments/prompts rather than complete programs. Such reasoning therefore must rely on {assumptions about omitted code and context. As a result, the meaning of an inference over a program fragment is not absolute, but depends on an implicit completion model describing how the fragment may be refined into a complete program. In this paper, we introduce completion semantics for LLM-based program reasoning. We formalize incomplete programs as denoting a space of possible refinements and define the correctness of existential inferences relative to a completion model. Under this view, a reported bug is correct whenever there exists a completion within the model that witnesses the bug. This perspective explains why many LLM-generated reports are neither simply correct nor incorrect, but instead depend on assumptions about omitted context. We have instantiated our approach in the form of a witness-generation workflow that concretizes completions underlying an inference by constructing executable refinements of the original program fragment. Witnesses serve both as evidence for existential claims and as a mechanism for exposing the assumptions required to support them. We evaluate our approach on real-world LLM-generated bug reports and program-analysis tasks. Our results show that witness generation effectively distinguishes inferences supported by plausible completions from those requiring unrealistic assumptions, providing a practical mechanism for validating reasoning over incomplete programs.
Zhiyuan Liu, Yihe Li, Trevor E. Carlson et al.· 0 citations
LLM-based agents excel at software engineering tasks where an existing codebase provides context, but constructing a program from scratch remains fundamentally harder. Recent benchmarks such as ProgramBench quantify this gap: given only natural-language documentation and an execute-only binary as a behavioral oracle, even frontier models solve fewer than 1% of instances. Existing frameworks conflate documentation reading, behavioral exploration, and code synthesis into a single pass, causing agents to probe insufficiently, lose behavioral intent as context drifts, and propagate early misinterpretations into the final implementation. Inspired by classical requirements engineering, we argue that behavioral specification elicitation should be a first-class phase that precedes implementation. We present SpecFirst, a two-stage framework that forces the specification elicitation before code synthesis. A dedicated spec agent first probes the binary and combines observations with documentation into a structured specification. Next, a code synthesis agent then uses this specification to drive implementation. This decomposition resolves documentation ambiguities before coding begins and provides a stable behavioral reference throughout synthesis. We evaluate SpecFirst on all 200 ProgramBench instances across four models spanning two families and an order of magnitude of capability. SpecFirst consistently outperforms the single-loop baseline, improving test pass rates by 6.9%-21.3% and binary exploration coverage by 9.4%-18.5%, all statistically significant. Behavioral analysis on code synthesis further shows that a prior specification enables earlier and more sustained code construction. Our results demonstrate that an explicit requirements-engineering phase is an effective paradigm for from-scratch program construction.
Yihao Chen, Shi Chang, Feng Lin et al.· 0 citations