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Set Theory for Verification: II - Induction and Recursion (2000)

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by Lawrence C. Paulson
Venue:Journal of Automated Reasoning
Citations:40 - 20 self
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@ARTICLE{Paulson00settheory,
    author = {Lawrence C. Paulson},
    title = {Set Theory for Verification: II - Induction and Recursion},
    journal = {Journal of Automated Reasoning},
    year = {2000},
    volume = {15},
    pages = {167--215}
}

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Abstract

A theory of recursive definitions has been mechanized in Isabelle's Zermelo-Fraenkel (ZF) set theory. The objective is to support the formalization of particular recursive definitions for use in verification, semantics proofs and other computational reasoning.

Citations

1497 The Definition of Standard ML - Milner, Tofte, et al. - 1997
909 Introduction to Lattices and Order - Davey, Priestley - 1990
505 A Computational Logic - Boyer, Moore - 1979
242 Programming in Martin-Löf’s Type Theory. An Introduction - Nordström, Petersson, et al. - 1990
218 The lazy lambda calculus - Abramsky - 1990
123 Intuitionistic type theory. Bibliopolis - Martin-Löf - 1984
114 Naive Set Theory - Halmos - 1960
99 Inductively defined types - Coquand, Paulin - 1988
69 Automating recursive type definitions in higher order logic - Melham - 1989
59 Axiomatic Set Theory - Suppes - 1960
45 Non-resolution Theorem Proving - Bledsoe - 1977
44 A fixedpoint approach to implementing (co)inductive definitions - Paulson - 1994
41 Set theory for verification: I. From foundations to functions - Paulson - 1993
40 Reasoning with inductively defined relations in the HOL theorem prover - Camilleri, Melham - 1992
33 Waldinger: Deductive Synthesis of the Unification Algorithm - Manna, R - 1981
26 Terminating general recursion - Nordström - 1988
18 Constructing recursion operators in intuitionistic type theory - Paulson - 1986
12 Fundamentals of Contemporary Set Theory - Devlin - 1979
12 Experimenting with Isabelle in ZF set theory - Noël - 1990
12 A concrete final coalgebra theorem for ZF set theory - Paulson - 1990
6 The identification of propositions and types in Martin-Lof's type theory: A programming example - Smith - 1983
5 Generalized rules for quantifiers and the completeness of the intuitionistic operators - Schroeder-Heister - 1984
3 Proofs and Types. Cambridge Univ - Girard - 1989
3 Ontic: Language specification and user’s manual - Givan, McAllester, et al. - 1992
3 Student use of an interactive theorem prover - McDonald, Suppes - 1984
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