Geometry Problem Solving (GPS) is a fundamental task in mathematical reasoning, with applications in intelligent education and automated theorem proving. Existing neuro-symbolic solvers often rely on two restrictive assumptions: textual conditions are expressed as atomic geometric statements, and target derivation can be reduced to eager elimination of intermediate variables. These assumptions break down in realistic problems, where coupled geometric descriptions lead to combinatorial growth in parsing patterns, and nonlinear constraints make explicit elimination inefficient or even intractable. We propose RIGOR, a neuro-symbolic GPS framework based on Atomic Semantic Normalization and Declarative Constraint Reasoning. RIGOR uses a Geometric Semantic Normalizer trained on our newly constructed GSN-15K dataset to normalize geometric texts into atomic statements for reliable formalization. It then adopts a Declarative Symbolic Engine that globally accumulates derived geometric constraints and determines target values through constraint entailment, while also reconstructing proof-grounded reasoning traces. Experiments on multiple standard GPS benchmarks show that RIGOR outperforms state-of-the-art methods while producing interpretable derivations. Our project is available at https://github.com/dongyuhang22/RIGOR.

Constraint programming (CP) is a crucial technology for solving real-world constraint optimization problems (COPs), with the advantages of rich modeling semantics and high solving efficiency. Using large language models (LLMs) to generate formal modeling automatically for COPs is becoming a promising approach, which aims to build trustworthy neuro-symbolic AI with the help of symbolic solvers. However, CP has received less attention compared to works based on operations research (OR) models. We introduce ConstraintLLM, the first LLM specifically designed for CP modeling, which is trained on an open-source LLM with multi-instruction supervised fine-tuning. We propose the Constraint-Aware Retrieval Module (CARM) to increase the in-context learning capabilities, which is integrated in a Tree-of-Thoughts (ToT) framework with guided self-correction mechanism. Moreover, we construct and release IndusCP, the first industrial-level benchmark for CP modeling, which contains 140 challenging tasks from various domains. Our experiments demonstrate that ConstraintLLM achieves state-of-the-art solving accuracy across multiple benchmarks and outperforms the baselines by 2x on the new IndusCP benchmark. Code and data are available at: https://github.com/william4s/ConstraintLLM.