There are also the monoid "laws" (not checked in Haskell):

    empty `smash` x = x -- left identity
    x `smash` empty = x -- right identity
    (x `smash` y) `smash` z = x `smash` (y `smash` z) -- associativity

Your definition doesn't fit any of these. (Edit: you've rewritten to meet the first two; but it is not associative.)