Abstract
It is well known that for many non-deterministic programming languages there is no continuous fully abstract fixpoint semantics. This is usually attributed to “problems with continuity”, that is, the assumption that the semantic functions should be continuous supposedly plays a role in the difficulties of giving a fully abstract fixpoint semantics. We show that for a large class of non-deterministic programming languages there is no fully abstract least fixpoint semantics even if one considers arbitrary functions (not necessarily continuous) over arbitrary partial orders (not necessarily complete).
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