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阿格达中的可数子集

[英]Countable subsets in Agda

原文 2017-11-22 10:23:03 4 1 agda/ countable

I need to express the countable property over a specific subset defined by a certain predicate P. My first idea was to explicitly state that there exists a function f which is bijective between my subset and, let's say, the natural numbers. 我需要表达由谓词P定义的特定子集的可数属性。我的第一个想法是明确声明存在一个函数f，该函数在我的子集与自然数之间是双射的。 Is there another more general way to express that property in the standard library ? 在标准库中还有另一种更通用的方式来表达该属性吗？

Thank you in advance 先感谢您

1 个解决方案

If you are using a set that is isomorphic to the natural numbers why don't you just use the natural numbers? 如果您使用的是与自然数同构的集合，为什么不使用自然数呢？

There is no way to distinguish isomorphic sets and in HoTT (or cubical agda) isomorphic sets are equal. 无法区分同构集，并且在HoTT（或立方agda）中，同构集是相等的。 Hence asking for a set that is isomorphic to Nat is the same as asking for a number that is equal to 3. 因此，要求与Nat同构的集合与要求等于3的数字相同。