code to treat differentiate as a first class higher order function

[Eskatrem]

I added a macro @define to store the code of a function when creating it, and another one @makeDerivative to create functions that are derivatives. It becomes possible to do:

julia> @define myFunction x cos(x*x)
(anonymous function)

julia> myDer = @makeDerivative myFunction x
(anonymous function)

julia> myDer(sqrt(pi))
-2.0083812473182306e-15

julia> myDer2 = @makeDerivative((x_x_sin(x)),x)
(anonymous function)

julia> myDer2(pi)
-9.869604401089358

[johnmyleswhite]

I think this needs some revision.

(1) I don't want to introduce a global variable to get this functionality. Why does anything need to be cached here?

(2) It's not conventional in Julia to introduce a type with untyped fields. Please specify which types you have in mind.

[johnmyleswhite]

This code also doesn't pass tests.

[ivarne]

Why did you remove this?

[mlubin]

What's the point of coming up with a strange new syntax for defining functions? The source for any function is accessible via code_lowered.

[ivarne]

With code_lowered you need to supply types for the arguments, and you get a altered expression tree. I'm unsure if that is a problem though.

[mlubin]

Supplying types is unavoidable because of multiple dispatch. I agree that the output of code_lowered is pretty ugly, but it's definitely parseable. We should do the heavy lifting for users instead of making them define functions in an awkward way.

[Eskatrem]

Sorry, I didn't realize my code was that messy. I'll address the other issues mentioned by @johnmyleswhite and @ivarne, but I was trying to play with code_lowered, and I can't get the AST of my function. If I write in a file:

function test(x)
    x*x
end

I get in the REPL:

julia> code_lowered(test,())
0-element Array{Any,1}

And writing the function straight in the REPL returns a similar result. Not sure if that matters, but the version of Julia I am running is julia version 0.2.0-rc4+16.

[mlubin]

You need to provide a tuple corresponding to the input types, e.g.,

julia> code_lowered(test,(Float64,))
1-element Array{Any,1}:
 :($(Expr(:lambda, {:x}, {{},{{:x,:Any,0}},{}}, quote  # none, line 2:
        return *(x,x)
    end)))