Erlang does it very much like GP's suggestion with the one downside of being 'noisy' with its punctuation (some might say 'clearer'):

  factorial(0) -> 1;
  factorial(N) -> N * factorial(N-1).

  factorial(Foo, 0) -> .. ;
  factorial(Foo, Bar) -> .. .

Semicolons separate partial definitions for a single function of a single arity, and periods end those definitions. Removing the punctuation might make parsing a bit more difficult (will there be more partial definitions?), so it's understandable to not offer it.