A type theoretic interpretation of constructive domain theory
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.
scientific article; zbMATH DE number 934093
scientific article