Question

I am trying to write a higher-order Racket function that takes a first-order function of one variable and returns its inverse. I know that it has to start off something like this:

(let [(inverse (lambda (f)
                 (lambda (y)
                   ... )))])

I figured this because inverse must take a function which returns a function which takes a y and returns x such that (= (f x) y). In other words, the contract for inverse is something like:

; inverse : (number? -> number?) -> (number? -> number?)

I’m just stumped trying to figure out what goes where the elipses are?

EDIT:
In response to people saying this is impossible, I am willing to accept an inverse function that when given y returns a possible x. In response to comments about the function not having an inverse, please note the contract that I have for f. It is a (number? -> number?) mapping, and therefore has an inverse.

Answer 1

For the general case, given an arbitrary function f you can’t tell what’s its inverse function. Even worse, a given function might not have an inverse at all – for example: the input function could perform an MD5 hash, which has no inverse. Sorry, your question has no answer.