关于算法的定义
Towards a Definition of an Algorithm
摘要：
我们将算法定义为实现或表达该算法的程序集。所有程序的集合被划分为等价类。如果两个程序本质上是同一个程序，则它们是等价的。等价类的集合形成了算法的范畴。虽然程序集甚至不能形成一个类别，但算法集形成了一个具有额外结构的类别。我们给出的描述两个程序本质上相同的条件是一致性关系，它丰富了具有额外结构的算法的范畴。证明了这类算法的泛性质。
英文摘要：
We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of equivalence classes forms the category of algorithms. Although the set of programs does not even form a category, the set of algorithms form a category with extra structure. The conditions we give that describe when two programs are essentially the same turn out to be coherence relations that enrich the category of algorithms with extra structure. Universal properties of the category of algorithms are proved.
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