1 \begin{thebibliography}{10} |
|
2 |
|
3 \bibitem{abrial93} |
|
4 J.~R. Abrial and G.~Laffitte. |
|
5 \newblock Towards the mechanization of the proofs of some classical theorems of |
|
6 set theory. |
|
7 \newblock preprint, February 1993. |
|
8 |
|
9 \bibitem{basin91} |
|
10 David Basin and Matt Kaufmann. |
|
11 \newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison. |
|
12 \newblock In {G\'erard} Huet and Gordon Plotkin, editors, {\em Logical |
|
13 Frameworks}, pages 89--119. Cambridge University Press, 1991. |
|
14 |
|
15 \bibitem{boyer86} |
|
16 Robert Boyer, Ewing Lusk, William McCune, Ross Overbeek, Mark Stickel, and |
|
17 Lawrence Wos. |
|
18 \newblock Set theory in first-order logic: Clauses for {G\"{o}del's} axioms. |
|
19 \newblock {\em J. Auto. Reas.}, 2(3):287--327, 1986. |
|
20 |
|
21 \bibitem{camilleri92} |
|
22 J.~Camilleri and T.~F. Melham. |
|
23 \newblock Reasoning with inductively defined relations in the {HOL} theorem |
|
24 prover. |
|
25 \newblock Technical Report 265, Computer Laboratory, University of Cambridge, |
|
26 August 1992. |
|
27 |
|
28 \bibitem{davey&priestley} |
|
29 B.~A. Davey and H.~A. Priestley. |
|
30 \newblock {\em Introduction to Lattices and Order}. |
|
31 \newblock Cambridge University Press, 1990. |
|
32 |
|
33 \bibitem{devlin79} |
|
34 Keith~J. Devlin. |
|
35 \newblock {\em Fundamentals of Contemporary Set Theory}. |
|
36 \newblock Springer, 1979. |
|
37 |
|
38 \bibitem{dummett} |
|
39 Michael Dummett. |
|
40 \newblock {\em Elements of Intuitionism}. |
|
41 \newblock Oxford University Press, 1977. |
|
42 |
|
43 \bibitem{dyckhoff} |
|
44 Roy Dyckhoff. |
|
45 \newblock Contraction-free sequent calculi for intuitionistic logic. |
|
46 \newblock {\em J. Symb. Logic}, 57(3):795--807, 1992. |
|
47 |
|
48 \bibitem{halmos60} |
|
49 Paul~R. Halmos. |
|
50 \newblock {\em Naive Set Theory}. |
|
51 \newblock Van Nostrand, 1960. |
|
52 |
|
53 \bibitem{kunen80} |
|
54 Kenneth Kunen. |
|
55 \newblock {\em Set Theory: An Introduction to Independence Proofs}. |
|
56 \newblock North-Holland, 1980. |
|
57 |
|
58 \bibitem{noel} |
|
59 Philippe No{\"e}l. |
|
60 \newblock Experimenting with {Isabelle} in {ZF} set theory. |
|
61 \newblock {\em J. Auto. Reas.}, 10(1):15--58, 1993. |
|
62 |
|
63 \bibitem{paulin-tlca} |
|
64 Christine Paulin-Mohring. |
|
65 \newblock Inductive definitions in the system {Coq}: Rules and properties. |
|
66 \newblock In M.~Bezem and J.F. Groote, editors, {\em Typed Lambda Calculi and |
|
67 Applications}, LNCS 664, pages 328--345. Springer, 1993. |
|
68 |
|
69 \bibitem{paulson87} |
|
70 Lawrence~C. Paulson. |
|
71 \newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}. |
|
72 \newblock Cambridge University Press, 1987. |
|
73 |
|
74 \bibitem{paulson-set-I} |
|
75 Lawrence~C. Paulson. |
|
76 \newblock Set theory for verification: {I}. {From} foundations to functions. |
|
77 \newblock {\em J. Auto. Reas.}, 11(3):353--389, 1993. |
|
78 |
|
79 \bibitem{paulson-CADE} |
|
80 Lawrence~C. Paulson. |
|
81 \newblock A fixedpoint approach to implementing (co)inductive definitions. |
|
82 \newblock In Alan Bundy, editor, {\em Automated Deduction --- {CADE}-12 |
|
83 International Conference}, LNAI 814, pages 148--161. Springer, 1994. |
|
84 |
|
85 \bibitem{paulson-set-II} |
|
86 Lawrence~C. Paulson. |
|
87 \newblock Set theory for verification: {II}. {Induction} and recursion. |
|
88 \newblock {\em J. Auto. Reas.}, 15(2):167--215, 1995. |
|
89 |
|
90 \bibitem{paulson-generic} |
|
91 Lawrence~C. Paulson. |
|
92 \newblock Generic automatic proof tools. |
|
93 \newblock In Robert Veroff, editor, {\em Automated Reasoning and its |
|
94 Applications: Essays in Honor of {Larry Wos}}, chapter~3. MIT Press, 1997. |
|
95 |
|
96 \bibitem{paulson-mscs} |
|
97 Lawrence~C. Paulson. |
|
98 \newblock Final coalgebras as greatest fixed points in zf set theory. |
|
99 \newblock {\em Mathematical Structures in Computer Science}, 9, 1999. |
|
100 \newblock in press. |
|
101 |
|
102 \bibitem{quaife92} |
|
103 Art Quaife. |
|
104 \newblock Automated deduction in {von Neumann-Bernays-G\"{o}del} set theory. |
|
105 \newblock {\em J. Auto. Reas.}, 8(1):91--147, 1992. |
|
106 |
|
107 \bibitem{suppes72} |
|
108 Patrick Suppes. |
|
109 \newblock {\em Axiomatic Set Theory}. |
|
110 \newblock Dover, 1972. |
|
111 |
|
112 \bibitem{principia} |
|
113 A.~N. Whitehead and B.~Russell. |
|
114 \newblock {\em Principia Mathematica}. |
|
115 \newblock Cambridge University Press, 1962. |
|
116 \newblock Paperback edition to *56, abridged from the 2nd edition (1927). |
|
117 |
|
118 \bibitem{winskel93} |
|
119 Glynn Winskel. |
|
120 \newblock {\em The Formal Semantics of Programming Languages}. |
|
121 \newblock MIT Press, 1993. |
|
122 |
|
123 \end{thebibliography} |
|