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Fast and Loose Reasoning is Morally Correct
, 2006
"... Functional programmers often reason about programs as if they were written in a total language, expecting the results to carry over to nontotal (partial) languages. We justify such reasoning. ..."
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Functional programmers often reason about programs as if they were written in a total language, expecting the results to carry over to nontotal (partial) languages. We justify such reasoning.
Cpo's Do Not Form a Cpo, and Yet Recursion Works
 In VDM ’91, volume 551 of LNCS
, 1991
"... We consider type universes as examples of regular algebras in the area of denotational semantics. The paper concentrates on our method which was used implicitly to prove that the interesting domain equations have solutions in the domain universes underlying MetaSoft, cf. [BBP90], and BSI/VDM, cf ..."
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We consider type universes as examples of regular algebras in the area of denotational semantics. The paper concentrates on our method which was used implicitly to prove that the interesting domain equations have solutions in the domain universes underlying MetaSoft, cf. [BBP90], and BSI/VDM, cf. [TW90]. Technically speaking the method allows to prove regularity of a universe. It is demonstrated by means of an example that the method applies even to universes which are essentially regular, i.e., which are neither cpo's, nor the images of the initial regular algebra. 1 Introduction 1.1 The Problem It is a usual practice in the area of programming languages to assign types to the manipulated objects. The typing procedure yields the first, naive, explanation of the notion of type: each type stands for the set of objects that have the type assigned to them. Consequently, one demands that the type forming operators should also be interpreted as operations on sets. It was discovere...