author | wenzelm |
Wed, 07 May 1997 18:39:04 +0200 | |
changeset 3140 | fb987fb6a489 |
parent 2933 | f842a75d9624 |
child 3488 | 32f90fe0f3f9 |
permissions | -rw-r--r-- |
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\begin{thebibliography}{10} |
2 |
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598 | 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 |
||
104 | 9 |
\bibitem{andrews86} |
10 |
Peter~B. Andrews. |
|
11 |
\newblock {\em An Introduction to Mathematical Logic and Type Theory: To Truth |
|
12 |
Through Proof}. |
|
13 |
\newblock Academic Press, 1986. |
|
14 |
||
114 | 15 |
\bibitem{basin91} |
16 |
David Basin and Matt Kaufmann. |
|
17 |
\newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison. |
|
18 |
\newblock In {G\'erard} Huet and Gordon Plotkin, editors, {\em Logical |
|
598 | 19 |
Frameworks}, pages 89--119. Cambridge University Press, 1991. |
114 | 20 |
|
104 | 21 |
\bibitem{boyer86} |
22 |
Robert Boyer, Ewing Lusk, William McCune, Ross Overbeek, Mark Stickel, and |
|
23 |
Lawrence Wos. |
|
1536 | 24 |
\newblock Set theory in first-order logic: Clauses for {G\"{o}del's} axioms. |
598 | 25 |
\newblock {\em Journal of Automated Reasoning}, 2(3):287--327, 1986. |
114 | 26 |
|
27 |
\bibitem{camilleri92} |
|
28 |
J.~Camilleri and T.~F. Melham. |
|
29 |
\newblock Reasoning with inductively defined relations in the {HOL} theorem |
|
30 |
prover. |
|
598 | 31 |
\newblock Technical Report 265, Computer Laboratory, University of Cambridge, |
32 |
August 1992. |
|
104 | 33 |
|
34 |
\bibitem{church40} |
|
35 |
Alonzo Church. |
|
36 |
\newblock A formulation of the simple theory of types. |
|
598 | 37 |
\newblock {\em Journal of Symbolic Logic}, 5:56--68, 1940. |
359 | 38 |
|
39 |
\bibitem{coen92} |
|
40 |
Martin~D. Coen. |
|
41 |
\newblock {\em Interactive Program Derivation}. |
|
707 | 42 |
\newblock PhD thesis, University of Cambridge, November 1992. |
359 | 43 |
\newblock Computer Laboratory Technical Report 272. |
44 |
||
45 |
\bibitem{constable86} |
|
630 | 46 |
R.~L. Constable et~al. |
359 | 47 |
\newblock {\em Implementing Mathematics with the Nuprl Proof Development |
48 |
System}. |
|
598 | 49 |
\newblock Prentice-Hall, 1986. |
359 | 50 |
|
51 |
\bibitem{davey&priestley} |
|
52 |
B.~A. Davey and H.~A. Priestley. |
|
53 |
\newblock {\em Introduction to Lattices and Order}. |
|
598 | 54 |
\newblock Cambridge University Press, 1990. |
359 | 55 |
|
56 |
\bibitem{devlin79} |
|
57 |
Keith~J. Devlin. |
|
58 |
\newblock {\em Fundamentals of Contemporary Set Theory}. |
|
59 |
\newblock Springer, 1979. |
|
104 | 60 |
|
61 |
\bibitem{dummett} |
|
62 |
Michael Dummett. |
|
63 |
\newblock {\em Elements of Intuitionism}. |
|
114 | 64 |
\newblock Oxford University Press, 1977. |
104 | 65 |
|
66 |
\bibitem{dyckhoff} |
|
67 |
Roy Dyckhoff. |
|
68 |
\newblock Contraction-free sequent calculi for intuitionistic logic. |
|
598 | 69 |
\newblock {\em Journal of Symbolic Logic}, 57(3):795--807, 1992. |
104 | 70 |
|
71 |
\bibitem{felty91a} |
|
72 |
Amy Felty. |
|
73 |
\newblock A logic program for transforming sequent proofs to natural deduction |
|
74 |
proofs. |
|
75 |
\newblock In Peter Schroeder-Heister, editor, {\em Extensions of Logic |
|
1399 | 76 |
Programming}, LNAI 475, pages 157--178. Springer, 1991. |
104 | 77 |
|
114 | 78 |
\bibitem{frost93} |
79 |
Jacob Frost. |
|
80 |
\newblock A case study of co-induction in {Isabelle HOL}. |
|
598 | 81 |
\newblock Technical Report 308, Computer Laboratory, University of Cambridge, |
82 |
August 1993. |
|
104 | 83 |
|
84 |
\bibitem{gallier86} |
|
85 |
J.~H. Gallier. |
|
86 |
\newblock {\em Logic for Computer Science: Foundations of Automatic Theorem |
|
87 |
Proving}. |
|
88 |
\newblock Harper \& Row, 1986. |
|
89 |
||
359 | 90 |
\bibitem{mgordon-hol} |
91 |
M.~J.~C. Gordon and T.~F. Melham. |
|
92 |
\newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher |
|
93 |
Order Logic}. |
|
598 | 94 |
\newblock Cambridge University Press, 1993. |
104 | 95 |
|
96 |
\bibitem{halmos60} |
|
97 |
Paul~R. Halmos. |
|
98 |
\newblock {\em Naive Set Theory}. |
|
99 |
\newblock Van Nostrand, 1960. |
|
100 |
||
101 |
\bibitem{huet78} |
|
102 |
G.~P. Huet and B.~Lang. |
|
103 |
\newblock Proving and applying program transformations expressed with |
|
104 |
second-order patterns. |
|
105 |
\newblock {\em Acta Informatica}, 11:31--55, 1978. |
|
106 |
||
598 | 107 |
\bibitem{kunen80} |
108 |
Kenneth Kunen. |
|
109 |
\newblock {\em Set Theory: An Introduction to Independence Proofs}. |
|
110 |
\newblock North-Holland, 1980. |
|
111 |
||
359 | 112 |
\bibitem{alf} |
1536 | 113 |
Lena Magnusson and Bengt {Nordstr\"{o}m}. |
359 | 114 |
\newblock The {ALF} proof editor and its proof engine. |
1444 | 115 |
\newblock In Henk Barendregt and Tobias Nipkow, editors, {\em Types for Proofs |
116 |
and Programs: International Workshop {TYPES '93}}, LNCS 806, pages 213--237. |
|
117 |
Springer, published 1994. |
|
359 | 118 |
|
114 | 119 |
\bibitem{mw81} |
120 |
Zohar Manna and Richard Waldinger. |
|
121 |
\newblock Deductive synthesis of the unification algorithm. |
|
122 |
\newblock {\em Science of Computer Programming}, 1(1):5--48, 1981. |
|
123 |
||
104 | 124 |
\bibitem{martinlof84} |
125 |
Per Martin-L\"of. |
|
126 |
\newblock {\em Intuitionistic type theory}. |
|
127 |
\newblock Bibliopolis, 1984. |
|
128 |
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\bibitem{milner78} |
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|
130 |
Robin Milner. |
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131 |
\newblock A theory of type polymorphism in programming. |
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132 |
\newblock {\em Journal of Computer and System Sciences}, 17:348--375, 1978. |
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133 |
|
114 | 134 |
\bibitem{milner-coind} |
135 |
Robin Milner and Mads Tofte. |
|
136 |
\newblock Co-induction in relational semantics. |
|
137 |
\newblock {\em Theoretical Computer Science}, 87:209--220, 1991. |
|
104 | 138 |
|
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139 |
\bibitem{nazareth-nipkow} |
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|
140 |
Dieter Nazareth and Tobias Nipkow. |
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|
141 |
\newblock Formal verification of algorithm {W}: The monomorphic case. |
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|
142 |
\newblock In J.~von Wright, J.~Grundy, and J.~Harrison, editors, {\em Theorem |
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143 |
Proving in Higher Order Logics: {TPHOLs} '96}, LNCS 1125, pages 331--345, |
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|
144 |
1996. |
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145 |
|
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146 |
\bibitem{Nipkow-CR} |
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|
147 |
Tobias Nipkow. |
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|
148 |
\newblock More {Church-Rosser} proofs (in {Isabelle/HOL}). |
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149 |
\newblock In Michael McRobbie and John~K. Slaney, editors, {\em Automated |
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|
150 |
Deduction --- {CADE}-13 International Conference}, LNAI 1104, pages 733--747. |
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151 |
Springer, 1996. |
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|
152 |
|
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153 |
\bibitem{nipkow-IMP} |
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|
154 |
Tobias Nipkow. |
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|
155 |
\newblock Winskel is (almost) right: Towards a mechanized semantics textbook. |
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156 |
\newblock In V.~Chandru and V.~Vinay, editors, {\em Foundations of Software |
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|
157 |
Technology and Theoretical Computer Science}, volume 1180 of {\em LNCS}, |
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|
158 |
pages 180--192. Springer, 1996. |
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|
159 |
|
104 | 160 |
\bibitem{noel} |
643 | 161 |
Philippe No{\"e}l. |
104 | 162 |
\newblock Experimenting with {Isabelle} in {ZF} set theory. |
598 | 163 |
\newblock {\em Journal of Automated Reasoning}, 10(1):15--58, 1993. |
104 | 164 |
|
165 |
\bibitem{nordstrom90} |
|
166 |
Bengt {Nordstr\"om}, Kent Petersson, and Jan Smith. |
|
167 |
\newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}. |
|
114 | 168 |
\newblock Oxford University Press, 1990. |
169 |
||
170 |
\bibitem{paulin92} |
|
171 |
Christine Paulin-Mohring. |
|
172 |
\newblock Inductive definitions in the system {Coq}: Rules and properties. |
|
173 |
\newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon, |
|
174 |
December 1992. |
|
175 |
||
176 |
\bibitem{paulson85} |
|
177 |
Lawrence~C. Paulson. |
|
178 |
\newblock Verifying the unification algorithm in {LCF}. |
|
179 |
\newblock {\em Science of Computer Programming}, 5:143--170, 1985. |
|
104 | 180 |
|
181 |
\bibitem{paulson87} |
|
182 |
Lawrence~C. Paulson. |
|
183 |
\newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}. |
|
598 | 184 |
\newblock Cambridge University Press, 1987. |
104 | 185 |
|
359 | 186 |
\bibitem{paulson-set-I} |
187 |
Lawrence~C. Paulson. |
|
188 |
\newblock Set theory for verification: {I}. {From} foundations to functions. |
|
598 | 189 |
\newblock {\em Journal of Automated Reasoning}, 11(3):353--389, 1993. |
114 | 190 |
|
598 | 191 |
\bibitem{paulson-CADE} |
192 |
Lawrence~C. Paulson. |
|
193 |
\newblock A fixedpoint approach to implementing (co)inductive definitions. |
|
2495 | 194 |
\newblock In Alan Bundy, editor, {\em Automated Deduction --- {CADE}-12 |
195 |
International Conference}, LNAI 814, pages 148--161. Springer, 1994. |
|
1399 | 196 |
|
197 |
\bibitem{paulson-set-II} |
|
198 |
Lawrence~C. Paulson. |
|
199 |
\newblock Set theory for verification: {II}. {Induction} and recursion. |
|
200 |
\newblock {\em Journal of Automated Reasoning}, 15(2):167--215, 1995. |
|
878 | 201 |
|
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202 |
\bibitem{paulson-ns} |
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|
203 |
Lawrence~C. Paulson. |
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|
204 |
\newblock Mechanized proofs of security protocols: {Needham-Schroeder} with |
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|
205 |
public keys. |
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|
206 |
\newblock Technical Report 413, Computer Laboratory, University of Cambridge, |
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|
207 |
January 1997. |
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|
208 |
|
1682 | 209 |
\bibitem{paulson-coind} |
210 |
Lawrence~C. Paulson. |
|
211 |
\newblock Mechanizing coinduction and corecursion in higher-order logic. |
|
2933
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|
212 |
\newblock {\em Journal of Logic and Computation}, 7(2):175--204, March 1997. |
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213 |
|
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|
214 |
\bibitem{paulson-security} |
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|
215 |
Lawrence~C. Paulson. |
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|
216 |
\newblock Proving properties of security protocols by induction. |
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|
217 |
\newblock In {\em 10th Computer Security Foundations Workshop}. IEEE Computer |
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|
218 |
Society Press, 1997. |
1682 | 219 |
\newblock In press. |
220 |
||
878 | 221 |
\bibitem{paulson-COLOG} |
222 |
Lawrence~C. Paulson. |
|
223 |
\newblock A formulation of the simple theory of types (for {Isabelle}). |
|
224 |
\newblock In P.~Martin-L\"of and G.~Mints, editors, {\em COLOG-88: |
|
1399 | 225 |
International Conference on Computer Logic}, LNCS 417, pages 246--274, |
226 |
Tallinn, Published 1990. Estonian Academy of Sciences, Springer. |
|
227 |
||
228 |
\bibitem{paulson-final} |
|
229 |
Lawrence~C. Paulson. |
|
230 |
\newblock A concrete final coalgebra theorem for {ZF} set theory. |
|
1444 | 231 |
\newblock In Peter Dybjer, Bengt Nordstr{\"om}, and Jan Smith, editors, {\em |
232 |
Types for Proofs and Programs: International Workshop {TYPES '94}}, LNCS 996, |
|
233 |
pages 120--139. Springer, published 1995. |
|
114 | 234 |
|
104 | 235 |
\bibitem{pelletier86} |
236 |
F.~J. Pelletier. |
|
237 |
\newblock Seventy-five problems for testing automatic theorem provers. |
|
598 | 238 |
\newblock {\em Journal of Automated Reasoning}, 2:191--216, 1986. |
2933
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|
239 |
\newblock Errata, JAR 4 (1988), 235--236 and JAR 18 (1997), 135. |
104 | 240 |
|
241 |
\bibitem{plaisted90} |
|
242 |
David~A. Plaisted. |
|
243 |
\newblock A sequent-style model elimination strategy and a positive refinement. |
|
598 | 244 |
\newblock {\em Journal of Automated Reasoning}, 6(4):389--402, 1990. |
104 | 245 |
|
246 |
\bibitem{quaife92} |
|
247 |
Art Quaife. |
|
1536 | 248 |
\newblock Automated deduction in {von Neumann-Bernays-G\"{o}del} set theory. |
598 | 249 |
\newblock {\em Journal of Automated Reasoning}, 8(1):91--147, 1992. |
104 | 250 |
|
251 |
\bibitem{suppes72} |
|
252 |
Patrick Suppes. |
|
253 |
\newblock {\em Axiomatic Set Theory}. |
|
254 |
\newblock Dover, 1972. |
|
255 |
||
256 |
\bibitem{takeuti87} |
|
257 |
G.~Takeuti. |
|
258 |
\newblock {\em Proof Theory}. |
|
878 | 259 |
\newblock North-Holland, 2nd edition, 1987. |
104 | 260 |
|
261 |
\bibitem{thompson91} |
|
262 |
Simon Thompson. |
|
263 |
\newblock {\em Type Theory and Functional Programming}. |
|
264 |
\newblock Addison-Wesley, 1991. |
|
265 |
||
266 |
\bibitem{principia} |
|
267 |
A.~N. Whitehead and B.~Russell. |
|
268 |
\newblock {\em Principia Mathematica}. |
|
598 | 269 |
\newblock Cambridge University Press, 1962. |
104 | 270 |
\newblock Paperback edition to *56, abridged from the 2nd edition (1927). |
271 |
||
598 | 272 |
\bibitem{winskel93} |
273 |
Glynn Winskel. |
|
274 |
\newblock {\em The Formal Semantics of Programming Languages}. |
|
275 |
\newblock MIT Press, 1993. |
|
276 |
||
104 | 277 |
\end{thebibliography} |