Abstract

In this paper, we describe design principles for certified programs of fraction arithmetic over any domain with the greatest common divisor (GCD) function. This is a small part of the DoCon-A library of certified programs, which is designed by the author of this paper. In this system, programs include definitions of the corresponding mathematical notions and proofs for the main properties of the methods implemented. These proofs are checked by the compiler. A purely functional programming language Agda, which supports dependent types, is used. A technique to generate formal machine-checked proofs for a certain optimized method of fraction addition is described.

中文翻译：

---

关于GCD域上分数算法的机器检查证明

摘要

在本文中，我们描述了具有最大公约数（GCD）函数的任何域上分数算术认证程序的设计原理。这是由本文作者设计的DoCon-A认证程序库的一小部分。在该系统中，程序包括相应数学概念的定义以及所实现方法的主要属性的证明。这些证明由编译器检查。使用纯函数式编程语言Agda，它支持依赖类型。描述了一种为分数添加的某些优化方法生成形式化的机器检查证明的技术。