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Abstract: We present a general axiomatic construction of models of FPC, a recursively typed lambda-calculus with call-byvalue operational semantics. Our method of construction is to obtain such models as full subcategories of categorical models of intuitionistic set theory. This allows us to obtain a notion of model that encompasses both domain-theoretic and realizability models. We show that the existence of solutions to recursive domain equations, needed for the interpretation of recursive types,... (Update)
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...to assume Axiom N in general. The use of a natural numbers object in P represents an improvement over the conference version of the paper, [42], in which Axiom N is assumed. First we have to show that the category P has a natural numbers object. By Theorem 1, every bred...
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BibTeX entry: (Update)
A.K. Simpson. Computational Adequacy for Recursive Types in Models of Intuitionistic Set Theory. In Proc. 17th IEEE Symposium on Logic in Computer Science, 2002. http://citeseer.ist.psu.edu/article/simpson02computational.html More
@misc{ simpson02computational,
author = "A. Simpson",
title = "Computational Adequacy for Recursive Types in Models of Intuitionistic
Set Theory",
text = "A.K. Simpson. Computational Adequacy for Recursive Types in Models of Intuitionistic
Set Theory. In Proc. 17th IEEE Symposium on Logic in Computer Science, 2002.",
year = "2002",
url = "citeseer.ist.psu.edu/article/simpson02computational.html" }
Citations (may not include all citations):306 LCF considered as a programming language (context) - Plotkin - 1977
150 The category-theoretic solution of recursive domain equation.. (context) - Smyth, Plotkin - 1982
59 Axiomatic Domain Theory in Categories of Partial Maps (context) - Fiore - 1996
58 Algebraically complete categories (context) - Freyd - 1990
54 Games and Full Abstraction for a Functional Metalanguage wit.. (context) - McCusker - 1998
46 Recursive types reduced to inductive types (context) - Freyd - 1990
45 First steps in synthetic domain theory (context) - Hyland - 1990
39 The effective topos (context) - Hyland - 1982
38 Categorical Logic and Type Theory (context) - Jacobs - 1999
36 Remarks on algebraically compact categories (context) - Freyd - 1992
28 The fixed point property in synthetic domain theory (context) - Taylor - 1991
26 Tripos theory (context) - Hyland, Johnstone et al. - 1980
25 Recursive types in Kleisli categories - Simpson - 1992
24 Denotational semantics with partial functions (context) - Plotkin - 1985
19 General synthetic domain theory --- a logical approach - Reus, Streicher - 1999
17 Relating theories of the #-calculus (context) - Scott - 1980
16 Complete cuboidal sets in axiomatic domain theory - Fiore, Plotkin et al. - 1997
14 Algebraic Set Theory (context) - Joyal, Moerdijk - 1995
13 An extension of models of axiomatic domain theory to models .. - Fiore, Plotkin - 1997
12 Computational adequacy in an elementary topos - Simpson - 1999
12 Effective domains and intrinsic structure (context) - Phoa - 1990
9 A presentation of the initial lift algebra (context) - Jibladze - 1997
9 A uniform account of domain theory in realizability models (context) - Longley, Simpson - 1997
9 Department of Computer Science (context) - Longley, Language et al. - 1995
7 Elementary axioms for categories of classes (context) - Simpson - 1999
7 Continuity and Effectivity in Topoi (context) - Rosolini - 1986
6 From term models to domains (context) - Phoa - 1994
5 Cambridge University Press (context) - Taylor - 1999
5 examples in synthetic domain theory (context) - van Oosten, Simpson et al. - 2000
5 Theoretical Computer Science (context) - Fiore, Rosolini - 2001
4 Information and Computation (context) - Freyd, Mulry et al. - 1992
4 Intuitionistic set theory (context) - Scedrov - 1985
3 Building domains from graph models (context) - Phoa - 1992
3 the adequacy of PER models (context) - Amadio - 1993
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