What is the name of feature that allows separate function implementations for different values of parameters?

Question

In some programming languages one can specify the function implementation for particular values of arguments:

factorial[x] = x * factorial[x-1]
factorial[0] = 1

Calling the function with 0 will use the second definition while calling it with 3 will use the first definition.

I am aware that this is a kind of function overloading, but if I would search for languages with function overloading, I will find a lot that don't have this feature but only overload depending on arity or types. Is there a more specific name for this?

Answer 1

Such case-by-case functions are known as piecewise functions in mathematics. For example, in Scala they can be implemented using case statements like so

val factorial: Int => Int = {
  case 0 => 1
  case x => x * factorial(x - 1)
}

which outputs

factorial(4) // res1: Int = 24

This is a form of function definition using pattern matching.

Similarly, in Haskell we can define a function using pattern matching like so

factorial :: Integer -> Integer 
factorial 0 = 1
factorial x = x * factorial (x - 1)