Trying to create a Function that checks whether 2 Functions are Equal Haskell

Question

checkEquality :: (Enum a, Eq b) => (a->b) -> (a->b) -> Bool

checkEquality f g = if f == g then True else False

I am trying to create a Function that will check if two Functions are equal but I can't seem to figure what exactly to do when typing the Function. I would appreciate if I can get some pointers as to what to do. What I have tried so far is up there

by equality it means the functions produce the same answer like X^2 = x * x

Take a look at this: https://stackoverflow.com/questions/17045941/how-to-compare-two-functions-for-equivalence-as-in-%CE%BBx-2x-%CE%BBx-xx — shree.pat18, Oct 17 '21 at 08:59

score 0 · Answer 1 · answered Oct 17 '21 at 09:36

While the answers so far are correct in that it's not possible to do in general, it is almost possible to do in your case. It seems to me like you were given this as a task, so I'll only give you some hints/pointers:

it's not possible to do in general, for two arbitrary functions of type a -> b - so it must mean that you're supposed to use something additional that you've been provided
in mathematics, for two functions to be, it is often considered enough for them to be equal "on all points", i.e. for all input values x, f(x) == g(x)
in your case, you can indeed check that the results are equal - you have an Eq b, allowing you to compare the results of two functions of type a -> b
the only thing you need to figure out is - do you have something else, which would allow you to check all values of type a?

The answer is no, but only because I don't think it's possible to do without an additional constraint on what a should be (what other instances it should have) - you can already "go through" values of type a by using Enum, but you don't really know "where to start".

Trying to create a Function that checks whether 2 Functions are Equal Haskell

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