Relating Full Abstraction Results for Different Programming Languages

We prove that Plotkin's model of bottomless cpos and partial continuous functions [19] is fully abstract for PCFv, a call-by-yalue version of the language PCF [17]. This settles a ‘folk theorem’ which has occasionally been misunderstood. We then show that the (known) full abstraction results for lazy PCF [2] and PCF with control [22] can be derived as corollaries from this theorem. Such a connection is particularly surprising, because observational congruence—the central notion in the definition of full abstraction—is usually not preserved by many known translations between different programming languages. We expect that new full abstraction theorems for some extensions of PCFv can be derived in the same way.

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