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Comment by mneary | Hacker News Reader

Function composition is very different from passing one function into another and the latter is definitely a concept that most Algebra 2 students would not be able to grok.

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I knew I was making a strong assertion when I mentioned function composition. I'm grateful for your feedback, but perhaps you could elaborate? I don't see why they have to be "very different". I think you called me on a certain case, but an example like this demonstrates that they are not so "very different":

    def a(b):
        m = 0
        return b(m)

Or even:

    def a(b):
        m = b(1)
        return m+7

I don't see how these are not a form of function composition. I'm definitely no expert. But I'd really appreciate an elaboration so I can learn from any mistake I'm making.

Function composition is a single, special case of a function accepting functional arguments. You could define the compose operator as below:

    compose : (a -> b) -> (b -> c) -> (a -> c)
    a `compose` b = \x -> b(a(x))

However, there is a whole spectrum of additionally possible functions which can be built to accept functions as arguments. Here's a couple of example:

    partial3 : (Integer -> Integer -> Integer) -> (Integer -> Integer)
    partial3 f = f 3
    map : [a] -> (a -> b) -> [b]
    map [] f = []
    map (x:xs) f = (f x):(map xs f)

The first one takes a function and applies an argument, 3; the next one takes a list and a function and maps the list using the provided function. The idea of functions as arguments is a very powerful one, and from my understanding one with which people sometimes struggle.

One way to look at function composition is that it is a function to which you pass two functions and out comes a function:

  compose :: (b -> c) -> (a -> b) -> a -> c
  compose f g x = f (g x)

I'm not sure about the math curriculum in USA but in linear algebra you have functions that operate on functions.

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