Are functions the same as closures in this case?

General Usage Performance
1

Are these functions/closures examples:

function main()

  a = 1.0
  b = 5.0

  function f1(t)
    return a * t + b
  end

  f2(t) = a * t + b

  f3 = t -> a * t + b

  solver(f1, f2, f3)
  return nothing
end

the same with respect to performance?

Is this correct:

  1. f1 is a function.
  2. f2 is a function (?)
  3. f3 is a closure.

In the solver function, if we evaluate each function, they will have the same performance?

Thanks!

2

All of these are closures.

3

And they are all functions too (so f isa Function will give true), just different syntax to do the same thing.

4

okay, but a closure builds a struct with captured variables as elements, while I do not know what a function does.

5

Each function is an instance of its own type (a subtype of Function), so log isa typeof(log) is true and typeof(log) <: Function is also true. Function is an abstract type in Julia. Structs can be made subtypes of Function and can be made callable using the syntax:

struct MyStruct <: Function end
(s::MyStruct)(args...) = println(args...)

s = MyStruct(); s(1) is equivalent to println(1).

I don’t know if this answers your question, but others might be able to comment better on lowering and compilation techniques used for closures and functions.

6

This is good enough!

As always, thanks a lot for your help!

7

From a programming language theory perspective the issue is how to resolve free variables in the body of a function.

function f1(t)
   return a * t + b
end

has 2 free variables, a and b. But it was defined in a context where those free variables were bound, and so a closure captures those bindings into a structure.

For a function defined at the “toplevel”, then you can resolve the free variables as global variables. So in some sense a function at toplevel is a closure whose bindings are the toplevel bindings.

8

A non-closure function is also a struct with captured variables as fields. It’s just has zero fields.

9

Thanks @yuyichao and @dlakelan!