@MISC{Bloom88lcfshould, author = {Bard Bloom and Jon G. Riecke}, title = {LCF Should Be Lifted}, year = {1988} }

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Abstract

: When observing termination of closed terms at all types in Plotkin's interpreter for PCF [11], the standard cpo model A V is not adequate. We define a new model, A Y , with lifted functional types and prove its adequacy for this notion of observation. We prove that with the addition of a parallel conditional and a convergence testing operator to the language, the model becomes fully abstract; with the addition of an existential-like operator, the language becomes universal. Using the model as a guide, we develop a sound logic for the language. 1 Introduction The denotational semantics most appropriate for a programming language depends crucially upon the observations one makes about computations. In general, an observation is some important behavior of the interpreter [8]. For example, in the arithmetic, higher-order programming language PCF [11, 13], one usually chooses to observe the results of arithmetic expressions---that a term of integer type reduces to a numeral. One may also...