Numeric operations on value objects in Ruby

Here’s a little Ruby puzzle. Imagine you have a Value class that wraps a number, and implements numeric operations. How would you go about implementing the class in a way that lets you do something like 2 + Value.new(3) and returns Value.new(5)?

To start with, let’s describe what the Value class looks like:

class Value
  attr_reader :num

  def initialize(num)
    @num = num
  end

  def +(other)
    Value.new(self.num + other.num)
  end

  # other operations: -, *, /
end

This will allow you do to things like this:

Value.new(2) + Value.new(3)  #=> #<Value(5)

Changing this class to accept a numeric value on the right hand side is pretty straightforward. We can change the + method on Value to wrap non-Value arguments as value objects.

def +(other)
  other = other.is_a?(value) ? other : Value.new(other)
  Value.new(self.num + other.num)
end

Value.new(3) + 2 #=> #<Value(5)>

However, this doesn’t work in reverse. This is because when we write 2 + something, Ruby calls the + method on the integer, so this is equivalent to 2.+(something). Integer#+ doesn’t know how to handle Values so we’ll see this exception:

2 + Value.new(3)
#=> 🔥 Value can't be coerced into Integer (TypeError)

The first idea that came to my mind when thinking of a way to do this in reverse was to monkeypatch Numeric.

class Numeric
  def +(other)
    if other.is_a?(Value)
      Value.new(self) + other
    else
      super
    end
  end
end

Monkeypatching core classes is a terrible idea, so let’s look for another way. The error message we saw earlier (“Value can’t be coerced into Integer”) gives us a clue about what to do. There must be a way to coerce Value into Integer.

Can we define to_i on Value? Nope, same error. Defining to_f doesn’t help either.

Next let’s look at how + is implemented on Integer. When you perform an arithmetic operation on an integer and it doesn’t know what to do with the argument, it calls coerce on that object. This method should return a 2-element array containing the objects modified into compatible types. It then calls + on the resulting objects.

We can now define a Value#coerce method, that returns a tuple. Ther first element here should be the number wrapped into a Value object, and the second should be the value object being added to it.

def coerce(n)
  [Value.new(n), self]
end

# And now this works!
2 + Value.new(3) #=> <Value(5)>

There’s one gotcha to note here: it might be tempting to return [self, n] here because self.+(n) can handle both numbers and Values. However, the coerce method is used for all numeric operations, including - and / where the order of arguments matters (x/y is not the same as y/x), so it’s important to return the values in the same order.

Python

I came across this problem while working through Andrej Karpathy’s neural networks course and trying to reimplement his micrograd package written in Python.

Python takes a different approach to this, and lets you define magic methods for numeric operations. For a similar Value class written in Python, you would do something like this:

class Value:
  # ...

  # Value(2) + Value(3)
  def __add__(other):
    Value(self.num + other.num)

  # 2 + Value(3)
  def __radd__(other):
    return self + other


2 + Value(3) #=> Value(5)

I prefer the Ruby approach, because you don’t need to implement these magic methods for all numeric operations. However, the explicitness of magic methods means that we don’t need to worry about returning the operands in an incorrect order.

If you want to compare the Value class in the two languages, you can see them here:

• Original Python implementation
• Ruby implementation

I looked around to find real life usage of coerce, and found that the the money gem uses coerce to allow adding numbers and Money objects.