在纯函数语言中，是否有一个算法来获得逆函数？ [英] In pure functional languages, is there an algorithm to get the inverse function?

问题描述

在像Haskell这样的纯函数语言中，有一个算法来获取函数的逆函数，当它是双射的时候（编辑）？

In pure functional languages like Haskell, is there an algorithm to get the inverse of a function, (edit) when it is bijective? And is there a specific way to program your function so it is?

推荐答案

在某些情况下，是的！有一篇美丽的文章，名为双向免费！其中讨论了一些情况 - 当你的函数有足够的多态性 - 在这里有可能，完全自动地导出一个反函数。 （它还讨论了当函数不是多态时，使问题变得困难。）

In some cases, yes! There's a beautiful paper called Bidirectionalization for Free! which discusses a few cases -- when your function is sufficiently polymorphic -- where it is possible, completely automatically to derive an inverse function. (It also discusses what makes the problem hard when the functions are not polymorphic.)

在函数可逆的情况下得到的是反函数输入）;在其他情况下，你得到一个函数，试图合并旧的输入值和新的输出值。

What you get out in the case your function is invertible is the inverse (with a spurious input); in other cases, you get a function which tries to "merge" an old input value and a new output value.

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