Can I use where in Haskell to find function parameter given the function output?

Question

This is my program:

modify :: Integer -> Integer
modify a = a + 100

x = x where modify(x) = 101

In ghci, this compiles successfully but when I try to print x the terminal gets stuck. Is it not possible to find input from function output in Haskell?

Answer 1

x = x where modify(x) = 101

is valid syntax but is equivalent to

x = x where f y = 101

where x = x is a recursive definition, which will get stuck in an infinite loop (or generate a <<loop>> exception), and f y = 101 is a definition of a local function, completely unrelated to the modify function defined elsewhere.

If you turn on warnings you should get a message saying "warning: the local definition of modify shadows the outer binding", pointing at the issue.

Further, there is no way to invert a function like you'd like to do. First, the function might not be injective. Second, even if it were such, there is no easy way to invert an arbitrary function. We could try all the possible inputs but that would be extremely inefficient.