|
1 \begin{thebibliography}{10} |
|
2 |
|
3 \bibitem{andrews86} |
|
4 Andrews, P.~B., |
|
5 \newblock {\em An Introduction to Mathematical Logic and Type Theory: To Truth |
|
6 Through Proof}, |
|
7 \newblock Academic Press, 1986 |
|
8 |
|
9 \bibitem{basin91} |
|
10 Basin, D., Kaufmann, M., |
|
11 \newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison, |
|
12 \newblock In {\em Logical Frameworks}, G.~Huet, G.~Plotkin, Eds. Cambridge |
|
13 Univ. Press, 1991, pp.~89--119 |
|
14 |
|
15 \bibitem{boyer86} |
|
16 Boyer, R., Lusk, E., McCune, W., Overbeek, R., Stickel, M., Wos, L., |
|
17 \newblock Set theory in first-order logic: Clauses for {G\"odel's} axioms, |
|
18 \newblock {\em J. Auto. Reas. {\bf 2}}, 3 (1986), 287--327 |
|
19 |
|
20 \bibitem{bm88book} |
|
21 Boyer, R.~S., Moore, J.~S., |
|
22 \newblock {\em A Computational Logic Handbook}, |
|
23 \newblock Academic Press, 1988 |
|
24 |
|
25 \bibitem{camilleri92} |
|
26 Camilleri, J., Melham, T.~F., |
|
27 \newblock Reasoning with inductively defined relations in the {HOL} theorem |
|
28 prover, |
|
29 \newblock Tech. Rep. 265, Comp. Lab., Univ. Cambridge, Aug. 1992 |
|
30 |
|
31 \bibitem{charniak80} |
|
32 Charniak, E., Riesbeck, C.~K., McDermott, D.~V., |
|
33 \newblock {\em Artificial Intelligence Programming}, |
|
34 \newblock Lawrence Erlbaum Associates, 1980 |
|
35 |
|
36 \bibitem{church40} |
|
37 Church, A., |
|
38 \newblock A formulation of the simple theory of types, |
|
39 \newblock {\em J. Symb. Logic {\bf 5}\/} (1940), 56--68 |
|
40 |
|
41 \bibitem{coen92} |
|
42 Coen, M.~D., |
|
43 \newblock {\em Interactive Program Derivation}, |
|
44 \newblock PhD thesis, University of Cambridge, 1992, |
|
45 \newblock Computer Laboratory Technical Report 272 |
|
46 |
|
47 \bibitem{constable86} |
|
48 {Constable et al.}, R.~L., |
|
49 \newblock {\em Implementing Mathematics with the Nuprl Proof Development |
|
50 System}, |
|
51 \newblock Prentice-Hall, 1986 |
|
52 |
|
53 \bibitem{davey&priestley} |
|
54 Davey, B.~A., Priestley, H.~A., |
|
55 \newblock {\em Introduction to Lattices and Order}, |
|
56 \newblock Cambridge Univ. Press, 1990 |
|
57 |
|
58 \bibitem{dawson90} |
|
59 Dawson, W.~M., |
|
60 \newblock {\em A Generic Logic Environment}, |
|
61 \newblock PhD thesis, Imperial College, London, 1990 |
|
62 |
|
63 \bibitem{debruijn72} |
|
64 de~Bruijn, N.~G., |
|
65 \newblock Lambda calculus notation with nameless dummies, a tool for automatic |
|
66 formula manipulation, with application to the {Church-Rosser Theorem}, |
|
67 \newblock {\em Indag. Math. {\bf 34}\/} (1972), 381--392 |
|
68 |
|
69 \bibitem{devlin79} |
|
70 Devlin, K.~J., |
|
71 \newblock {\em Fundamentals of Contemporary Set Theory}, |
|
72 \newblock Springer, 1979 |
|
73 |
|
74 \bibitem{coq} |
|
75 {Dowek et al.}, G., |
|
76 \newblock The {Coq} proof assistant user's guide, |
|
77 \newblock Technical Report 134, INRIA-Rocquencourt, 1991 |
|
78 |
|
79 \bibitem{dummett} |
|
80 Dummett, M., |
|
81 \newblock {\em Elements of Intuitionism}, |
|
82 \newblock Oxford University Press, 1977 |
|
83 |
|
84 \bibitem{dyckhoff} |
|
85 Dyckhoff, R., |
|
86 \newblock Contraction-free sequent calculi for intuitionistic logic, |
|
87 \newblock {\em J. Symb. Logic {\bf 57}}, 3 (1992), 795--807 |
|
88 |
|
89 \bibitem{felty91a} |
|
90 Felty, A., |
|
91 \newblock A logic program for transforming sequent proofs to natural deduction |
|
92 proofs, |
|
93 \newblock In {\em Extensions of Logic Programming\/} (1991), |
|
94 P.~Schroeder-Heister, Ed., Springer, pp.~157--178, |
|
95 \newblock LNAI 475 |
|
96 |
|
97 \bibitem{felty93} |
|
98 Felty, A., |
|
99 \newblock Implementing tactics and tacticals in a higher-order logic |
|
100 programming language, |
|
101 \newblock {\em J. Auto. Reas. {\bf 11}}, 1 (1993), 43--82 |
|
102 |
|
103 \bibitem{frost93} |
|
104 Frost, J., |
|
105 \newblock A case study of co-induction in {Isabelle HOL}, |
|
106 \newblock Tech. Rep. 308, Comp. Lab., Univ. Cambridge, Aug. 1993 |
|
107 |
|
108 \bibitem{OBJ} |
|
109 Futatsugi, K., Goguen, J., Jouannaud, J.-P., Meseguer, J., |
|
110 \newblock Principles of {OBJ2}, |
|
111 \newblock In {\em Princ. Prog. Lang.\/} (1985), pp.~52--66 |
|
112 |
|
113 \bibitem{gallier86} |
|
114 Gallier, J.~H., |
|
115 \newblock {\em Logic for Computer Science: Foundations of Automatic Theorem |
|
116 Proving}, |
|
117 \newblock Harper \& Row, 1986 |
|
118 |
|
119 \bibitem{mgordon-hol} |
|
120 Gordon, M. J.~C., Melham, T.~F., |
|
121 \newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher |
|
122 Order Logic}, |
|
123 \newblock Cambridge Univ. Press, 1993 |
|
124 |
|
125 \bibitem{halmos60} |
|
126 Halmos, P.~R., |
|
127 \newblock {\em Naive Set Theory}, |
|
128 \newblock Van Nostrand, 1960 |
|
129 |
|
130 \bibitem{harper-jacm} |
|
131 Harper, R., Honsell, F., Plotkin, G., |
|
132 \newblock A framework for defining logics, |
|
133 \newblock {\em J.~ACM {\bf 40}}, 1 (1993), 143--184 |
|
134 |
|
135 \bibitem{haskell-tutorial} |
|
136 Hudak, P., Fasel, J.~H., |
|
137 \newblock A gentle introduction to {Haskell}, |
|
138 \newblock {\em {SIGPLAN} {\bf 27}}, 5 (May 1992) |
|
139 |
|
140 \bibitem{haskell-report} |
|
141 Hudak, P., Jones, S.~P., Wadler, P., |
|
142 \newblock Report on the programming language {Haskell}: A non-strict, purely |
|
143 functional language, |
|
144 \newblock {\em {SIGPLAN} {\bf 27}}, 5 (May 1992), |
|
145 \newblock Version 1.2 |
|
146 |
|
147 \bibitem{huet75} |
|
148 Huet, G.~P., |
|
149 \newblock A unification algorithm for typed $\lambda$-calculus, |
|
150 \newblock {\em Theoretical Comput. Sci. {\bf 1}\/} (1975), 27--57 |
|
151 |
|
152 \bibitem{huet78} |
|
153 Huet, G.~P., Lang, B., |
|
154 \newblock Proving and applying program transformations expressed with |
|
155 second-order patterns, |
|
156 \newblock {\em Acta Inf. {\bf 11}\/} (1978), 31--55 |
|
157 |
|
158 \bibitem{mural} |
|
159 Jones, C.~B., Jones, K.~D., Lindsay, P.~A., Moore, R., |
|
160 \newblock {\em Mural: A Formal Development Support System}, |
|
161 \newblock Springer, 1991 |
|
162 |
|
163 \bibitem{alf} |
|
164 Magnusson, L., {Nordstr\"om}, B., |
|
165 \newblock The {ALF} proof editor and its proof engine, |
|
166 \newblock In {\em Types for Proofs and Programs: International Workshop {TYPES |
|
167 '93}\/} (published 1994), Springer, pp.~213--237, |
|
168 \newblock LNCS 806 |
|
169 |
|
170 \bibitem{mw81} |
|
171 Manna, Z., Waldinger, R., |
|
172 \newblock Deductive synthesis of the unification algorithm, |
|
173 \newblock {\em Sci. Comput. Programming {\bf 1}}, 1 (1981), 5--48 |
|
174 |
|
175 \bibitem{martin-nipkow} |
|
176 Martin, U., Nipkow, T., |
|
177 \newblock Ordered rewriting and confluence, |
|
178 \newblock In {\em 10th Conf. Auto. Deduct.\/} (1990), M.~E. Stickel, Ed., |
|
179 Springer, pp.~366--380, |
|
180 \newblock LNCS 449 |
|
181 |
|
182 \bibitem{martinlof84} |
|
183 Martin-L\"of, P., |
|
184 \newblock {\em Intuitionistic type theory}, |
|
185 \newblock Bibliopolis, 1984 |
|
186 |
|
187 \bibitem{melham89} |
|
188 Melham, T.~F., |
|
189 \newblock Automating recursive type definitions in higher order logic, |
|
190 \newblock In {\em Current Trends in Hardware Verification and Automated Theorem |
|
191 Proving}, G.~Birtwistle, P.~A. Subrahmanyam, Eds. Springer, 1989, |
|
192 pp.~341--386 |
|
193 |
|
194 \bibitem{miller-mixed} |
|
195 Miller, D., |
|
196 \newblock Unification under a mixed prefix, |
|
197 \newblock {\em J. Symb. Comput. {\bf 14}}, 4 (1992), 321--358 |
|
198 |
|
199 \bibitem{milner-coind} |
|
200 Milner, R., Tofte, M., |
|
201 \newblock Co-induction in relational semantics, |
|
202 \newblock {\em Theoretical Comput. Sci. {\bf 87}\/} (1991), 209--220 |
|
203 |
|
204 \bibitem{nipkow-prehofer} |
|
205 Nipkow, T., Prehofer, C., |
|
206 \newblock Type checking type classes, |
|
207 \newblock In {\em 20th Princ. Prog. Lang.\/} (1993), ACM Press, pp.~409--418, |
|
208 \newblock Revised version to appear in \bgroup\em J. Func. Prog.\egroup |
|
209 |
|
210 \bibitem{noel} |
|
211 {No\"el}, P., |
|
212 \newblock Experimenting with {Isabelle} in {ZF} set theory, |
|
213 \newblock {\em J. Auto. Reas. {\bf 10}}, 1 (1993), 15--58 |
|
214 |
|
215 \bibitem{nordstrom90} |
|
216 {Nordstr\"om}, B., Petersson, K., Smith, J., |
|
217 \newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}, |
|
218 \newblock Oxford University Press, 1990 |
|
219 |
|
220 \bibitem{paulin92} |
|
221 Paulin-Mohring, C., |
|
222 \newblock Inductive definitions in the system {Coq}: Rules and properties, |
|
223 \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon, Dec. |
|
224 1992 |
|
225 |
|
226 \bibitem{paulson85} |
|
227 Paulson, L.~C., |
|
228 \newblock Verifying the unification algorithm in {LCF}, |
|
229 \newblock {\em Sci. Comput. Programming {\bf 5}\/} (1985), 143--170 |
|
230 |
|
231 \bibitem{paulson87} |
|
232 Paulson, L.~C., |
|
233 \newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}, |
|
234 \newblock Cambridge Univ. Press, 1987 |
|
235 |
|
236 \bibitem{paulson89} |
|
237 Paulson, L.~C., |
|
238 \newblock The foundation of a generic theorem prover, |
|
239 \newblock {\em J. Auto. Reas. {\bf 5}}, 3 (1989), 363--397 |
|
240 |
|
241 \bibitem{paulson-COLOG} |
|
242 Paulson, L.~C., |
|
243 \newblock A formulation of the simple theory of types (for {Isabelle}), |
|
244 \newblock In {\em COLOG-88: International Conference on Computer Logic\/} |
|
245 (Tallinn, 1990), P.~Martin-L\"of, G.~Mints, Eds., Estonian Academy of |
|
246 Sciences, Springer, |
|
247 \newblock LNCS 417 |
|
248 |
|
249 \bibitem{paulson700} |
|
250 Paulson, L.~C., |
|
251 \newblock {Isabelle}: The next 700 theorem provers, |
|
252 \newblock In {\em Logic and Computer Science}, P.~Odifreddi, Ed. Academic |
|
253 Press, 1990, pp.~361--386 |
|
254 |
|
255 \bibitem{paulson91} |
|
256 Paulson, L.~C., |
|
257 \newblock {\em {ML} for the Working Programmer}, |
|
258 \newblock Cambridge Univ. Press, 1991 |
|
259 |
|
260 \bibitem{paulson-coind} |
|
261 Paulson, L.~C., |
|
262 \newblock Co-induction and co-recursion in higher-order logic, |
|
263 \newblock Tech. Rep. 304, Comp. Lab., Univ. Cambridge, July 1993 |
|
264 |
|
265 \bibitem{paulson-fixedpt} |
|
266 Paulson, L.~C., |
|
267 \newblock A fixedpoint approach to implementing (co)inductive definitions, |
|
268 \newblock Tech. Rep. 320, Comp. Lab., Univ. Cambridge, Dec. 1993 |
|
269 |
|
270 \bibitem{paulson-set-I} |
|
271 Paulson, L.~C., |
|
272 \newblock Set theory for verification: {I}. {From} foundations to functions, |
|
273 \newblock {\em J. Auto. Reas. {\bf 11}}, 3 (1993), 353--389 |
|
274 |
|
275 \bibitem{paulson-set-II} |
|
276 Paulson, L.~C., |
|
277 \newblock Set theory for verification: {II}. {Induction} and recursion, |
|
278 \newblock Tech. Rep. 312, Comp. Lab., Univ. Cambridge, 1993 |
|
279 |
|
280 \bibitem{paulson-final} |
|
281 Paulson, L.~C., |
|
282 \newblock A concrete final coalgebra theorem for {ZF} set theory, |
|
283 \newblock Tech. rep., Comp. Lab., Univ. Cambridge, 1994 |
|
284 |
|
285 \bibitem{pelletier86} |
|
286 Pelletier, F.~J., |
|
287 \newblock Seventy-five problems for testing automatic theorem provers, |
|
288 \newblock {\em J. Auto. Reas. {\bf 2}\/} (1986), 191--216, |
|
289 \newblock Errata, JAR 4 (1988), 235--236 |
|
290 |
|
291 \bibitem{plaisted90} |
|
292 Plaisted, D.~A., |
|
293 \newblock A sequent-style model elimination strategy and a positive refinement, |
|
294 \newblock {\em J. Auto. Reas. {\bf 6}}, 4 (1990), 389--402 |
|
295 |
|
296 \bibitem{quaife92} |
|
297 Quaife, A., |
|
298 \newblock Automated deduction in {von Neumann-Bernays-G\"odel} set theory, |
|
299 \newblock {\em J. Auto. Reas. {\bf 8}}, 1 (1992), 91--147 |
|
300 |
|
301 \bibitem{sawamura92} |
|
302 Sawamura, H., Minami, T., Ohashi, K., |
|
303 \newblock Proof methods based on sheet of thought in {EUODHILOS}, |
|
304 \newblock Research Report IIAS-RR-92-6E, International Institute for Advanced |
|
305 Study of Social Information Science, Fujitsu Laboratories, 1992 |
|
306 |
|
307 \bibitem{suppes72} |
|
308 Suppes, P., |
|
309 \newblock {\em Axiomatic Set Theory}, |
|
310 \newblock Dover, 1972 |
|
311 |
|
312 \bibitem{takeuti87} |
|
313 Takeuti, G., |
|
314 \newblock {\em Proof Theory}, 2nd~ed., |
|
315 \newblock North Holland, 1987 |
|
316 |
|
317 \bibitem{thompson91} |
|
318 Thompson, S., |
|
319 \newblock {\em Type Theory and Functional Programming}, |
|
320 \newblock Addison-Wesley, 1991 |
|
321 |
|
322 \bibitem{principia} |
|
323 Whitehead, A.~N., Russell, B., |
|
324 \newblock {\em Principia Mathematica}, |
|
325 \newblock Cambridge Univ. Press, 1962, |
|
326 \newblock Paperback edition to *56, abridged from the 2nd edition (1927) |
|
327 |
|
328 \bibitem{wos-bledsoe} |
|
329 Wos, L., |
|
330 \newblock Automated reasoning and {Bledsoe's} dream for the field, |
|
331 \newblock In {\em Automated Reasoning: Essays in Honor of {Woody Bledsoe}}, |
|
332 R.~S. Boyer, Ed. Kluwer Academic Publishers, 1991, pp.~297--342 |
|
333 |
|
334 \end{thebibliography} |