A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to automatically discover interesting conjectures about a given set of functions. QuickSpec works by interleaving term generation with random testing to form candidate conjectures. This is made tractable by starting from small sizes and ensuring that only terms that are irreducible with respect to already discovered conjectures are considered. QuickSpec has been successfully applied to generate lemmas for automated inductive theorem proving as well as to generate specifications of functional programs. We give an overview of typical use-cases of QuickSpec, as well as demonstrating how to easily connect it to a theorem prover of the user's choice.

中文翻译：

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猜想、检验和证明：理论探索概述

数学推理的一个关键组成部分是能够对手头的问题域提出有趣的猜想。在本文中，我们简要概述了一个名为 QuickSpec 的理论探索系统，该系统能够自动发现关于给定函数集的有趣猜想。QuickSpec 的工作原理是将术语生成与随机测试交错以形成候选猜想。通过从小尺寸开始并确保仅考虑相对于已发现的猜想不可约的项，这变得易于处理。QuickSpec 已成功应用于生成用于自动归纳定理证明的引理以及生成功能程序的规范。我们概述了 QuickSpec 的典型用例，