Dot syntax for anonymous functions

General Usage
1

Hi,
in mathematics we use this syntax of • to represent (anonymous) functions. For instance ||•|| is then equivalent to writing x |–> ||x||.

My question is, is there such syntax in julia?

If not, I’d love to see the, for instance, bullet operator handle this shorthand in a future release. Do you agree?

2

See https://github.com/JuliaLang/julia/pull/24990

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3

Oh okay, thanks.

4

They seem to have problems regarding how the “_” syntax should be used, more important, their representation does not seem well defined anymore, as for instance

A,B,C = rand(5), rand(5), rand(5)
maximum(_[1], [A,B,C])

could mean maximum(x -> x[1], [A,B,C]), but also x -> maximum(x[1], [A,B,C]), hence where x is itself is an array of functions.

Therefore I just wanted to implement my own macro as follows:

  • the replacement would be achieved by writing @x(:x + 3), meaning x -> x + 3
  • similarly @x(f(:x, :y, 7, :x)) means (x,y) -> f(x, y, 7, x)

We then can automatically create problem cases like the ones above and by using composition ∘ or |> we can create arbitrary complex functions, like @x(f(:x, :y, 7)) |> @x(:x^2) |> @x(print("The solution is $(:x).")).

How do I write such a macro and do you have a neater syntax idea?

5

By writing

macro x(f)
    f.args = replace(f.args, :(:x) => :x)
    return :(x -> $f)
end

I got a little of the functionality. One can for instance do this

julia> rdim = @x(rand(5, :x)) # 5 × x random arrays

julia> rdim(1)
5×1 Array{Float64,2}:
 0.9939828371497994
 0.773338508907532
 0.8633776655992123
 0.22892379107363436
 0.39529414038536226

julia> rdim(3)
5×3 Array{Float64,2}:
 0.146573  0.108516  0.327287
 0.105098  0.111566  0.942984
 0.713338  0.69219   0.877718
 0.243916  0.561024  0.569137
 0.787741  0.970282  0.0878656
6

You can find examples on this forum (search for partial application macro or something similar), and even some packages like

(I think there are others, but I can’t recall the names).

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