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Abstract: . We give a new semantic foundation for type theories in the lineage of Martin-Lof's "polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational semantics of an untyped programming language. We show how to integrate classical set-theoretic objects, such as functions-as-graphs and equivalence classes, into this operational framework. The new semantics is... (Update)
Context of citations to this paper: More
.... that permits classical reasoning; however, the programs synthesized may contain oracles that cannot be executed (Howe, 1996; Howe, 1997). A. Ayari and D. Basin We would like to close with two areas where we see a need for further work. The first concerns the...
.... for the logic is a (countable) set of descriptions (of data and classes) The work will be primarily theoretical, building on our work in [11], but if successful it will be used for some of the applications discussed above. The work on particular logics just described, and the...
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2: Introduction to HOL: A Theorem Proving Environment for Higher-Oder Logic (context) - Gordon, Melham - 1993
2: Implementing Mathematics with the Nuprl Proof Development System - Constable - 1986
BibTeX entry: (Update)
Howe, D. J. (1997). A classical set-theoretic model of polymorphic extensional type theory. Submitted to Information and Computation. http://citeseer.ist.psu.edu/howe97classical.html More
@misc{ howe97classical,
author = "D. Howe",
title = "A classical set-theoretic model of polymorphic extensional type theory",
text = "Howe, D. J. (1997). A classical set-theoretic model of polymorphic extensional
type theory. Submitted to Information and Computation.",
year = "1997",
url = "citeseer.ist.psu.edu/howe97classical.html" }
Citations (may not include all citations):1074 The Definition of Standard ML (context) - Milner, Tofte et al. - 1990
592 Introduction to HOL: A Theorem Proving Environment for Highe.. (context) - Gordon, Melham - 1993
505 Implementing Mathematics with the Nuprl Proof Development Sy.. - Constable - 1986
152 Semantics of Programming Languages (context) - Gunter - 1992
150 Edinburgh LCF: A Mechanized Logic of Computation (context) - Gordon, Milner et al. - 1979
141 Constructive mathematics and computer programming (context) - Martin-Lof - 1982
94 Equality in lazy computation systems - Howe - 1989
75 Proving congruence of bisimulation in functional programming.. - Howe
39 A Non-Type-Theoretic Semantics for Type-Theoretic Language (context) - Allen - 1987
38 Functional Programming and Input/Output (context) - Gordon - 1994
19 Importing mathematics from HOL into Nuprl - Howe
15 Hybrid interactive theorem proving using Nuprl and HOL - Felty, Howe - 1997
12 Translating dependent type theory into higher order logic - Jacobs, Melham - 1993
4 An operational approach to combining classical set theory an.. - Howe, Stoller - 1994
3 Higher Order Logic Theorem Proving and Its Applications (context) - Schubert, Windley et al. - 1995
3 Introducing well-founded function definitions in HOL (context) - van der Voort - 1993
1 Inductive sets and families in Martin-Lof's type theory and .. (context) - Proof, manual et al. - 1990
1 Exploring abstract algebra in constructive type theory (context) - Jackson - 1994
1 On computational open-endedness in Martin-Lof's type theory (context) - Society - 1991
1 Paulin-Mohring (context) - Cornes, Courant et al. - 1995
1 The HOL logic extended with quantification over type variabl.. (context) - International, Logic et al. - 1993
1 Logical and computational aspects of programming with sets/b.. (context) - thesis, University et al. - 1991
Documents on the same site (ftp://ftp.research.bell-labs.com/dist/howe/): More
A Type Annotation Scheme for Nuprl - Douglas Howe Bell (1998) (Correct)
Proving Congruence of Bisimulation in Functional Programming.. - Howe (1996) (Correct)
Metavariables and Tactic Proofs - Howe (Correct)
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