Technically, Ruby doesn’t have functions, but methods. However, a Ruby method behaves almost identically to functions in other language:

def double(n)
  n * 2
end

This normal method/function takes a parameter n, doubles it and returns the value. Now let’s define a higher order function (or method):

def triple(n)
  lambda {3 * n}
end

Instead of returning a number, triple returns a method. You can test it using the Interactive Ruby Shell:

$ irb --simple-prompt
>> def double(n)
>>   n * 2
>> end
=> :double
>> def triple(n)
>>   lambda {3 * n}
>> end
=> :triple
>> double(2)
=> 4
>> triple(2)
=> #<Proc:0x007fd07f07bdc0@(irb):7 (lambda)>

If you want to actually get the tripled number, you need to call (or “reduce”) the lambda:

triple_two = triple(2)
triple_two.call # => 6

Or more concisely:

triple(2).call

Currying and Partial Applications

This is not useful in terms of defining very basic functionality, but it is useful if you want to have methods/functions that are not instantly called or reduced. For example, let’s say you want to define methods that add a number by a specific number (for example add_one(2) = 3). If you had to define a ton of these you could do:

def add_one(n)
  n + 1
end

def add_two(n)
  n + 2
end

However, you could also do this:

add = -> (a, b) { a + b }
add_one = add.curry.(1)
add_two = add.curry.(2)

Using lambda calculus we can say that add is (λa.(λb.(a+b))). Currying is a way of partially applying add. So add.curry.(1), is (λa.(λb.(a+b)))(1) which can be reduced to (λb.(1+b)). Partial application means that we passed one argument to add but left the other argument to be supplied later. The output is a specialized method.

More useful examples of currying

Let’s say we have really big general formula, that if we specify certain arguments to it, we can get specific formulae from it. Consider this formula:

f(x, y, z) = sin(x\\*y)*sin(y\\*z)*sin(z\\*x)