How does one write the Pythagoras Theorem in Scala?

Question

The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

This is Pythagoras\'s Theore

Answer 1

The most obvious way:

type Num = {
  def +(a: Num): Num
  def *(a: Num): Num
}

def pyth[A <: Num](a: A, b: A)(sqrt: A=>A) = sqrt(a * a + b * b)

// usage
pyth(3, 4)(Math.sqrt)

This is horrible for many reasons. First, we have the problem of the recursive type, Num. This is only allowed if you compile this code with the -Xrecursive option set to some integer value (5 is probably more than sufficient for numbers). Second, the type Num is structural, which means that any usage of the members it defines will be compiled into corresponding reflective invocations. Putting it mildly, this version of pyth is obscenely inefficient, running on the order of several hundred thousand times slower than a conventional implementation. There's no way around the structural type though if you want to define pyth for any type which defines +, * and for which there exists a sqrt function.

Finally, we come to the most fundamental issue: it's over-complicated. Why bother implementing the function in this way? Practically speaking, the only types it will ever need to apply to are real Scala numbers. Thus, it's easiest just to do the following:

def pyth(a: Double, b: Double) = Math.sqrt(a * a + b * b)

All problems solved! This function is usable on values of type Double, Int, Float, even odd ones like Short thanks to the marvels of implicit conversion. While it is true that this function is technically less flexible than our structurally-typed version, it is vastly more efficient and eminently more readable. We may have lost the ability to calculate the Pythagrean theorem for unforeseen types defining + and *, but I don't think you're going to miss that ability.