We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model into a full model for a set of assertions or returns an explanation (a model interpolant) when no solution exists. This mode of interaction fits well into the model-constructing satisfiability (MCSAT) framework of SMT. We use it to develop an interpolation procedure for any MCSAT-supported theory. In particular, this method leads to an effective interpolation procedure for nonlinear real arithmetic. We evaluate the new procedure by integrating it into a model checker and comparing it with state-of-art model-checking tools for nonlinear arithmetic.

中文翻译：

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非线性算术的插值和模型检查

我们为可满足性模理论 (SMT) 提出了一种新的基于模型的插值程序。该过程使用了一种与 SMT 求解器交互的新模式，我们称之为以模型为模求解。这要么将给定的部分模型扩展为一组断言的完整模型，要么在不存在解决方案时返回解释（模型插值）。这种交互模式非常适合 SMT 的模型构建可满足性 (MCSAT) 框架。我们使用它为任何 MCSAT 支持的理论开发插值程序。特别地，该方法导致了非线性实数算术的有效插值过程。我们通过将新程序集成到模型检查器中并将其与用于非线性算法的最先进的模型检查工具进行比较来评估新程序。