haskell - Defining a function by equations with different number of arguments

Question

I noticed today that such a definition

safeDivide x 0 = x
safeDivide = (/)

is not possible. I am just curious what the (good) reason behind this is. There must be a very good one (it's Haskell after all :)).

Note: I am not looking suggestions for alternative implementations to the code above, it's a simple example to demonstrate my point.

Answer 1

I think it's mainly for consistency so that all clauses can be read in the same manner, so to speak; i.e. every RHS is at the same position in the type of the function. I think would mask quite a few silly errors if you allowed this, too.

There's also a slight semantic quirk: say the compiler padded out such clauses to have the same number of patterns as the other clauses; i.e. your example would become

safeDivide x 0 = x
safeDivide x y = (/) x y

Now consider if the second line had instead been safeDivide = undefined; in the absence of the previous clause, safeDivide would be ⊥, but thanks to the eta-expansion performed here, it's x y -> if y == 0 then x else ⊥ — so safeDivide = undefined does not actually define safeDivide to be ⊥! This seems confusing enough to justify banning such clauses, IMO.