论文标题
奇妙的形态和在哪里找到它们：递归计划指南
Fantastic Morphisms and Where to Find Them: A Guide to Recursion Schemes
论文作者
论文摘要
结构化的递归方案已广泛用于构造，优化和推理有关电感和共同诱导数据类型的程序的推理。它们的平淡形式，命令和变形，表现力受到限制。因此，已经提出了许多概括，这进一步导致了结构化递归方案的几个统一框架。但是，现有的统一框架的工作通常集中在分类基础上，因此对于愿意在实践中应用递归方案但并未精通类别理论的从业者来说，可能是无法访问的。为了填补这一空白，该说明性论文从实际的角度介绍了结构化的递归方案：在具体编程示例的背景下，各种递归方案是动机和解释的。这些递归方案的分类双重二元组也被解释了。
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus many generalisations have been proposed, which further lead to several unifying frameworks of structured recursion schemes. However, the existing work on unifying frameworks typically focuses on the categorical foundation, and thus is perhaps inaccessible to practitioners who are willing to apply recursion schemes in practice but are not versed in category theory. To fill this gap, this expository paper introduces structured recursion schemes from a practical point of view: a variety of recursion schemes are motivated and explained in contexts of concrete programming examples. The categorical duals of these recursion schemes are also explained.
