Using the programming language Haskell, we introduce an implementation for a simple imperative language that can evaluate arithmetic and boolean expressions; step by step, we will expand the implementation starting from arithmetic expressions, to boolean expressions and then to imperative programs. As we expand the language, we will show several evaluation strategies, considering the normalization property and how it affects an implementation. Finally, we will provide a bottom-up implementation of Hoare's logic which will allow us to deduce facts about programs without the need for a full evaluation.

中文翻译：

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在Haskell中为命令式程序实现Hoare逻辑的教程

使用Haskell编程语言，我们介绍了一种简单的命令式语言的实现，该语言可以评估算术和布尔表达式。逐步地，我们将扩展实现，从算术表达式开始，到布尔表达式，再到命令式程序。在扩展语言时，我们将展示几种评估策略，其中考虑了归一化属性及其对实现的影响。最后，我们将提供自下而上的Hoare逻辑实现，这将使我们能够推断有关程序的事实，而无需进行全面评估。