Andrzej Borzyszkowski, Ryszard Kubiak, Jacek Leszczylowski, Stefan Sokolowski  Home/Search
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Abstract: this paper is to present such system of sets that may serve as a foundation for denotations of type expressions of a programming language. In this system there is no selfapplication and its existence is consistent with any classical set theory. Still, it is rich enough to contain high-order functions, polymorphism and dependent types. Also recursion operators as well as those needed to build types defined by recursive equations are present. 1 Basic notions (Update)
Context of citations to this paper: More
.... is expected to contain polymorphic and dependent types, with the already established hierarchical semantics developed in [BKS 88] and [BKLS 88] The denotational model of the definitional language is constructed in a structured way. First, we define the algebra of domains and...
...our immediate concern, but extending SDDP with Sigma dependent types should be easy. The type system of SDDP is based on considerations from [2]. It generalises the ramified 2 type system from [5] see also [10] Therefore, it generalises also the two level type system of the...
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How to Reconcile Subtypes, Dependent Types and Deep.. - Sokolowski (1991) (Correct)
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0.2: Type Checking with Universes - Harper, Pollack (1991) (Correct)
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BibTeX entry: (Update)
Borzyszkowski, A. M., R. Kubiak, J. Leszczy/lowski and S. Soko/lowski. "Towards a set-theoretic type theory". Submitted to Theoretical Computer Science , 1988. http://citeseer.ist.psu.edu/borzyszkowski88towards.html More
@techreport{ owski88towards,
author = "Andrzej Borzyszkowski, Ryszard Kubiak, Jacek Leszczy\l owski and Stefan Sokolowski",
title = "{Towards a set-theoretic Type Theory}",
month = "September",
address = "P.O.\ Box 562, 80-252 Gdansk, Poland",
year = "1988",
url = "citeseer.ist.psu.edu/borzyszkowski88towards.html" }
Citations (may not include all citations):505 Implementing Mathematics with the Nuprl Proof Development Sy.. - Constable - 1986
325 Towards a theory of type structure (context) - Reynolds - 1974
141 Constructive Mathematics and Computer Programming (context) - Martin-Lof - 1982
132 Interpr'etation fonctionelle et 'elimination des coupures da.. (context) - Girard - 1972
71 An intuitionistic theory of types: predicative part (context) - Martin-Lof - 1973
50 Polymorphism is not set-theoretic (context) - Reynolds - 1984
37 A kernel language for abstract data types and modules (context) - Burstall, Lampson - 1984
33 Domain Theoretic Models of Polymorphism - Coquand, Gunter et al.
22 Extensional models for Polymorphism (context) - Breazu-Tannen, Coquand - 1987
13 Ergebnisse der Mathematik und ihrer Grenzgebiete (context) - Beeson, Constructive - 1985
12 Polymorphism is set-theoretic, constructively (context) - Pitts - 1987
10 A Polymorphic -calculus with Type:Type (context) - Cardelli
10 Type' Is Not a Type: Preliminary Report (context) - Meyer, Reinhold - 1986
1 What is a model of the -calculus (context) - Meyer
1 The semantics of second order polymorphic -calculus (context) - Bruce, Meyer - 1984
1 University of Edinburgh (context) - in, LFCS et al. - 1986
1 A set-theoretic model for a polymorphic typed -calculus. A c.. (context) - Borzyszkowski, Kubiak et al.
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