Shorthand for operations?

Question

Mathematica has a large number of built-in symbols, and I am unsure when there is a shorthand for the operation I am trying to perform.

Question 1:

Is there a shorthand for the function Join[#,#] &? Here I only need the operation to apply to lists.

Question 2:

Is there a shorthand for a function which swaps out one operation with another:

f[bool_, a_, b_] := If[bool, a + b, a - b]

Answer 1

I can't think of a way to improve Join[#, #] &. Merely as a game you could use:

{##, ##} & @@ {1, 2, 3}

{1, 2, 3, 1, 2, 3}

However this is inadvisable because it will unpack packed arrays and it loses the original Head.

For the second case if the arguments are long, rather than just a and b, it can be shorter to use:

If[bool, Plus, Subtract][a, b]

Somewhat related: List manipulation to build a functional expression.

You could also use two separate definitions:

f[True,  a_, b_] := a + b
f[False, a_, b_] := a - b

Neither is an improvement in your example but each has its place I believe.