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.