Teaching Code LLMs to Reason with Intermediate Formal Specifications

Unlike natural-language specifications, executable formal specifications provide machine-checkable constraints for verifying, debugging, and repairing code. However, writing such specifications is labor-intensive, and existing LLM-based methods mainly infer whole-program pre/postconditions, missing the intermediate semantic commitments that programmers rely on when reasoning about an algorithm. Our study further shows that prompting current CodeLLMs often produces executable assertions that are syntactically invalid, trivial, or too weak to reject behavior-changing faults. In this paper, we study executable checkpoint specification generation, where assertions are inserted at meaningful internal program points to describe expected intermediate states. We introduce SpecCoder, a verification-guided CodeLLM training framework that learns from validated reference programs, behavior-changing mutants, and multi-turn specification-refinement traces. SpecCoder selects specifications that hold on correct executions while rejecting faulty executions, turning specifications from passive annotations into executable evidence. To evaluate this setting, we introduce HumanExec, a benchmark built from recent Codeforces competitive programming problems with test suites, reference solutions, and human buggy submissions, supporting three tasks: specification generation, program correctness checking, and program repair. Experiments on HumanExec show that SpecCoder substantially improves checkpoint-specification quality over base CodeLLMs. Across Qwen2.5-Coder models, SpecCoder improves inline-specification correctness by up to 55.8%, completeness by up to 358.1%, and executable assertion validity by up to 26.6%. These gains further translate to downstream correctness reasoning and repair, showing that executable checkpoints provide fine-grained evidence for reliable verification.

SpecRLBench: A Benchmark for Generalization in Specification-Guided Reinforcement Learning

Specification-guided reinforcement learning (RL) provides a principled framework for encoding complex, temporally extended tasks using formal specifications such as linear temporal logic (LTL). While recent methods have shown promising results, their ability to generalize across unseen specifications and diverse environments remains insufficiently understood. In this work, we introduce SpecRLBench, a benchmark designed to evaluate the generalization capabilities of LTL-based specification-guided RL methods. The benchmark spans multiple difficulty levels across navigation and manipulation domains, incorporating both static and dynamic environments, diverse robot dynamics, and varied observation modalities. Through extensive empirical evaluation, we characterize the strengths and limitations of existing approaches and reveal the challenges that emerge as specification and environment complexity increase. SpecRLBench provides a structured platform for systematic comparison and supports the development of more generalizable specification-guided RL methods. Code is available at https://github.com/BU-DEPEND-Lab/SpecRLBench.