Ralf Hemmecke wrote:
> (13) -> u(x:Integer): Integer->Integer==(y:Integer):Integer+->gcd(x,y)
>
> is unacceptable to you?

I dislike to be forced to use the two notions :
and == for the outside function and +-> for the inner one.

And I can neither use fct2 x == (fct3 y == gcd (x,y)) only with ==.

But this syntax seems less fine because this is a definition of fct2, 
and the résult of fct2 3 adds  a definition : "the name" fct3 of this 
function.
anonymousFunction is as near as possible from mathematic functions.

Mathematics have only one description of function.

Elementry use of axiom should also allow (before optimisation)
function inside function with +-> (only) or with == (only),
and doesn't force the user to use the two syntax.

Your example shows that axiom allows to "currify" 2 variables with this 
syntax, but how do you create a 3-variable function ?

fct := x +-> (y +-> (z +-> gcd (x,y,z)))

fct 4    is a 2-variable function.
fct 4 6 is a 1-variable function
fct 4 6 8 = 2

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