Interesting Function Composition

var multBy2Add3:Function = add(3, mult(2));

trace(multBy2Add3(10));
// 10 * 2  = 20
//  20 + 3 = 23

var add2AndSquare = sq(add(2));

trace(add2AndSquare(8));
// 8 + 2 = 10
// 10 * 10 = 100

var multBy2_3times:Function = repeat(3,mult(2));

trace(multBy2_3times(3));
// 3 * 2 = 6;
// 6 * 2 = 12;
// 12 * 2 = 24

// you can also chain for even less readability
trace(sq(mult(5,add(1)))(4));
// 4 + 1 = 5
// 5 * 5 = 25;
// 25 * 25 = 625;

/*
outputs: 
12
100
24
625
*/

// function  composition
const F:Function = function(a:*):*{return a};
function mult(scalar:Number, f:Function=null):Function{
	if (f == null) f = F;
	 return function(n:Number){
		return f(n) * scalar;
	}
}

function add(off:Number, f:Function=null):Function{
	 if (f == null) f = F;
	 return function(n:Number){
		return f(n) + off;
	}
}
function sq(f:Function=null):Function{
	 if (f == null) f = F;
	 return function(n:Number){
		 var v:Number = f(n);
		return  v * v;
	}
}
function repeat(times:int, f:Function):Function {
	 if (f == null) f = F;
	 return function (n:Number){
		 var v:Number = n;
		 for (var i:int = 0; i<times; i++) v = f(v);
		 return v;
	 }
}

The above shows some interesting function composition… this demo contains the following functions:

mult();
add();
sq();
repeat();

These functions are designed to be combined to create new functions.