That is a very different behavior though. If my multiply function returns ADDs the input and returns an int it passes the type checker but is still wrong.
But if your multiply function fails to handle some special case that the tests don't catch (negatives, overflow/saturation, denorms, ...) then the tests are also wrong.
What you really want is to be able to state properties, e.g. "for all x/y, mul(x, 0) = 0, mul(x, 1) = x, mul(x, 2) = x + x, mul(x, y) = mul(y, x)", and so on. And working with these kinds of statements (via e.g. quickcheck or whatever) might generate tests, but feels a lot more like working with types. You're making proofs, not examples.
What you really want is to be able to state properties, e.g. "for all x/y, mul(x, 0) = 0, mul(x, 1) = x, mul(x, 2) = x + x, mul(x, y) = mul(y, x)", and so on. And working with these kinds of statements (via e.g. quickcheck or whatever) might generate tests, but feels a lot more like working with types. You're making proofs, not examples.