Function Creation via Partial Application

Partial application is a way to create a function by passing only some arguments to a method. The _ character stands in for missing arguments and becomes an argument to the created function. It only applies to a single method, list, or dictionary call, not to a more complex nested expression.

for example:

f = _ + 2;

f is now a function of one argument.

f.value(7);

it is equivalent to having written:

f = {|x| x + 2 };

(except that there is no name 'x' declared)

g = Point(_, _);

g is a function of two arguments.

g.value(3, 4);

Here are some example usages of this in a collect message. Below each is written the equivalent function.

(1..8).collect(_.isPrime);

(1..8).collect {|x| x.isPrime };

(1..8).collect(_.hash);

(1..8).collect {|x| x.hash };

(1..8).collect([\a, \b, _]);

(1..8).collect {|x| [\a, \b, x] };

(1..8).collect((a:_));

(1..8).collect {|x| (a:x) };

(1..8).collect(Polar(_, pi));

(1..8).collect {|x| Polar(x, pi) };

(1..8).collect((1.._));

(1..8).collect {|x| (1..x) };

f = (a:_, b:_); // f is a two argument function

g = f.(_, 5);   // g is a partial application of f

g.(7);          // get the answer

// equivalent to this:

f = {|x, y| (a:x, b:y) }

g = {|z| f.(z, 5) };

g.value(7);

An example of what you can't do:

(1..8).collect( Point(100 * _, 50) ); // nested expression won't work.

// only the * gets partially applied, not the surrounding expression.

(1..8).collect {|x| Point(100 * x, 50) }; // need to use a function for this.