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Comment by kian | Hacker News Reader

I think f: X->Y could be fairly thought of as labeling the function X->Y with f.

f: X->Y means f maps an input from domain X (set of all real numbers, say) to output range Y (set of all positive real numbers, say, f could be 'abs').

I think you might be thinking it's LX.Y (L for lambda)? But consider X=Y, LX.X is the identity function, some f: X->X could be the identity function, but it could also be anything else that returns a value of the same type as its argument - it could be 'add1' in this example of X being the reals, for example.

I'm not quite sure why this seems to be so controversial, except for the light abuse of notation in my english. Saying that f: X->Y means f maps an input from domain X to output in range Y is to say that we are defining a function -- and labeling it f, since it could just as easily be labeled g and still be the same function. Defining is naming -- naming is labeling [with scope].

It's not defining a function though, it's describing (by one aspect) a whole class of functions.

Take:

    f: ints -> ints

f can be 'add1', 'identity', 'double', etc.

If you know that, and calling it 'defining a function' is just loose English (you didn't mean completely defining) then fine, but that's what's confusing people.

It read to me like you thought it was equivalent to a function definition in code, X & Y described what would actually happen over different inputs, so I was just trying to explain, didn't mean to offend if you knew already.

Oooh, I see what you're saying. For want of an "s". Yes, in this context, I am aware that it is a whole class of functions -- and that f is a label being affixed to that class of functions. Sorry for the confusion -- that makes much more sense now.

No offense received -- was just genuinely confused as to why it netted two comments and a few downvotes for a seemingly uncontroversial statement. But then again, we're talking mathematical logic here, so loose english is of course reasonably discouraged.

Thanks for the clarification, and I hope you have a great evening!

X->Y is not a function. f is.

label the function going from X->Y would be how I was intending that to be read. I'm well aware that X->Y is a type signature ;)

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