Amb Breaks Well-Pointedness, Ground Amb Doesn't

McCarthy's amb operator has no known denotational semantics, and its basic operational properties - the context lemma, the compatibility of refinement similarity and convex bisimilarity - have long been open. In this paper, we give a single example program that demonstrates the failure of each of these properties. This shows that there cannot be any well-pointed denotational semantics.However, we show that, if amb is given at ground type only, then all of these operational properties do hold.