A type theoretic interpretation of constructive domain theory
type: Item
instance of: scholarly article
title: A type theoretic interpretation of constructive domain theory
zbMATH Open document ID: 0861.03009
DOI: 10.1007/BF00252182
author: Michael Hedberg
published in: Journal of Automated Reasoning
publication date: 1996-10-13T00:00:00Z
review text: A well-pointed Cartesian closed category of semilattices and approximable mappings is constructed. The construction is completely formalized and checked using the interactive ``proof assistant'' ALF (developed by L. Augustsson, T. Coquand and B. Nordström). In fact, the general frame is that of P. Martin-Löf's type theory for \(\lambda\)-calculus, and the notion of domain ``interpreted'' in such theories is stronger than the ``classical'' one (D. Scott). The complete semilattices are generated by semilattices in the same way as Scott domains are generated by consistent semilattices.
Mathematics Subject Classification ID: 03B40
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 03F35
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 03-04
Mathematics Subject Classification ID: 68T15
Mathematics Subject Classification ID: 06A12
zbMATH DE Number: 934093
zbMATH Keywords: interactive proof assistant ALF
zbMATH Keywords: constructive type theory
zbMATH Keywords: Cartesian closed category
zbMATH Keywords: semilattices
zbMATH Keywords: approximable mappings
zbMATH Keywords: \(\lambda\)-calculus
zbMATH Keywords: domain
reviewed by: Cristian Masalagiu
MaRDI profile type: Publication
cites work: Q3912779
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description: scientific article; zbMATH DE number 934093