Abstract
As we have done for IMP, we would like to introduce the denotational semantics of HOFL, for which we need to develop a proper domain theory that is more sophisticated than the one presented in Chapter 5. In order to define the denotational semantics of IMP, we have shown that the semantic domain of commands, for which we need to apply the fixpoint theorem, has the required properties. The situation is more complicated for HOFL, because HOFL provides constructors for infinitely many term types, so there are infinitely many domains to be considered. We will handle this problem by showing, using structural induction, that the type constructors of HOFL correspond to domains which are equipped with adequate CPO ⊥ structures and that we can define useful continuous functions between them.
Order, unity and continuity are human inventions just as truly as catalogues and encyclopedias. (Bertrand Russell)
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Bruni, R., Montanari, U. (2017). Domain Theory. In: Models of Computation. Texts in Theoretical Computer Science. An EATCS Series. Springer, Cham. https://doi.org/10.1007/978-3-319-42900-7_8
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DOI: https://doi.org/10.1007/978-3-319-42900-7_8
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