1 \begin{thebibliography}{10} |
1 \begin{thebibliography}{10} |
2 |
2 |
3 \bibitem{abramsky90} |
3 \bibitem{abramsky90} |
4 Abramsky, S., |
4 Abramsky, S., |
5 \newblock The lazy lambda calculus, |
5 \newblock The lazy lambda calculus, |
6 \newblock In {\em Resesarch Topics in Functional Programming}, D.~A. Turner, |
6 \newblock In {\em Research Topics in Functional Programming}, D.~A. Turner, Ed. |
7 Ed. Addison-Wesley, 1977, pp.~65--116 |
7 Addison-Wesley, 1977, pp.~65--116 |
8 |
8 |
9 \bibitem{aczel77} |
9 \bibitem{aczel77} |
10 Aczel, P., |
10 Aczel, P., |
11 \newblock An introduction to inductive definitions, |
11 \newblock An introduction to inductive definitions, |
12 \newblock In {\em Handbook of Mathematical Logic}, J.~Barwise, Ed. |
12 \newblock In {\em Handbook of Mathematical Logic}, J.~Barwise, Ed. |
35 |
35 |
36 \bibitem{dybjer91} |
36 \bibitem{dybjer91} |
37 Dybjer, P., |
37 Dybjer, P., |
38 \newblock Inductive sets and families in {Martin-L\"of's} type theory and their |
38 \newblock Inductive sets and families in {Martin-L\"of's} type theory and their |
39 set-theoretic semantics, |
39 set-theoretic semantics, |
40 \newblock In {\em Logical Frameworks}, G.~Huet, G.~Plotkin, Eds. Cambridge |
40 \newblock In {\em Logical Frameworks}, G.~Huet G.~Plotkin, Eds. Cambridge Univ. |
41 Univ. Press, 1991, pp.~280--306 |
41 Press, 1991, pp.~280--306 |
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42 |
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43 \bibitem{types94} |
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44 Dybjer, P., Nordstr{\"om}, B., Smith, J., Eds., |
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45 \newblock {\em Types for Proofs and Programs: International Workshop {TYPES |
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46 '94}}, |
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47 \newblock LNCS 996. Springer, published 1995 |
42 |
48 |
43 \bibitem{IMPS} |
49 \bibitem{IMPS} |
44 Farmer, W.~M., Guttman, J.~D., Thayer, F.~J., |
50 Farmer, W.~M., Guttman, J.~D., Thayer, F.~J., |
45 \newblock {IMPS}: An interactive mathematical proof system, |
51 \newblock {IMPS}: An interactive mathematical proof system, |
46 \newblock {\em J. Auto. Reas. {\bf 11}}, 2 (1993), 213--248 |
52 \newblock {\em J. Auto. Reas. {\bf 11}}, 2 (1993), 213--248 |
47 |
53 |
48 \bibitem{frost95} |
54 \bibitem{frost95} |
49 Frost, J., |
55 Frost, J., |
50 \newblock A case study of co-induction in {Isabelle}, |
56 \newblock A case study of co-induction in {Isabelle}, |
51 \newblock Tech. Rep. 359, Comp. Lab., Univ. Cambridge, Feb. 1995 |
57 \newblock Tech. Rep. 359, Comp. Lab., Univ. Cambridge, Feb. 1995 |
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58 |
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59 \bibitem{gimenez-codifying} |
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60 Gim{\'e}nez, E., |
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61 \newblock Codifying guarded definitions with recursive schemes, |
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62 \newblock In Dybjer et~al. \cite{types94}, pp.~39--59 |
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63 |
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64 \bibitem{gunter-trees} |
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65 Gunter, E.~L., |
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66 \newblock A broader class of trees for recursive type definitions for {HOL}, |
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67 \newblock In {\em Higher Order Logic Theorem Proving and Its Applications: HUG |
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68 '93\/} (Published 1994), J.~Joyce C.~Seger, Eds., LNCS 780, Springer, |
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69 pp.~141--154 |
52 |
70 |
53 \bibitem{hennessy90} |
71 \bibitem{hennessy90} |
54 Hennessy, M., |
72 Hennessy, M., |
55 \newblock {\em The Semantics of Programming Languages: An Elementary |
73 \newblock {\em The Semantics of Programming Languages: An Elementary |
56 Introduction Using Structural Operational Semantics}, |
74 Introduction Using Structural Operational Semantics}, |
58 |
76 |
59 \bibitem{huet88} |
77 \bibitem{huet88} |
60 Huet, G., |
78 Huet, G., |
61 \newblock Induction principles formalized in the {Calculus of Constructions}, |
79 \newblock Induction principles formalized in the {Calculus of Constructions}, |
62 \newblock In {\em Programming of Future Generation Computers\/} (1988), |
80 \newblock In {\em Programming of Future Generation Computers\/} (1988), |
63 K.~Fuchi, M.~Nivat, Eds., Elsevier, pp.~205--216 |
81 K.~Fuchi M.~Nivat, Eds., Elsevier, pp.~205--216 |
64 |
82 |
65 \bibitem{melham89} |
83 \bibitem{melham89} |
66 Melham, T.~F., |
84 Melham, T.~F., |
67 \newblock Automating recursive type definitions in higher order logic, |
85 \newblock Automating recursive type definitions in higher order logic, |
68 \newblock In {\em Current Trends in Hardware Verification and Automated Theorem |
86 \newblock In {\em Current Trends in Hardware Verification and Automated Theorem |
69 Proving}, G.~Birtwistle, P.~A. Subrahmanyam, Eds. Springer, 1989, |
87 Proving}, G.~Birtwistle P.~A. Subrahmanyam, Eds. Springer, 1989, pp.~341--386 |
70 pp.~341--386 |
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71 |
88 |
72 \bibitem{milner-ind} |
89 \bibitem{milner-ind} |
73 Milner, R., |
90 Milner, R., |
74 \newblock How to derive inductions in {LCF}, |
91 \newblock How to derive inductions in {LCF}, |
75 \newblock note, Dept. Comp. Sci., Univ. Edinburgh, 1980 |
92 \newblock note, Dept. Comp. Sci., Univ. Edinburgh, 1980 |
90 \newblock PhD thesis, University of Edinburgh, 1984 |
107 \newblock PhD thesis, University of Edinburgh, 1984 |
91 |
108 |
92 \bibitem{nipkow-CR} |
109 \bibitem{nipkow-CR} |
93 Nipkow, T., |
110 Nipkow, T., |
94 \newblock More {Church-Rosser} proofs (in {Isabelle/HOL}), |
111 \newblock More {Church-Rosser} proofs (in {Isabelle/HOL}), |
95 \newblock In {\em Automated Deduction --- {CADE}-13\/} (1996), M.~McRobbie, |
112 \newblock In {\em Automated Deduction --- {CADE}-13\/} (1996), M.~McRobbie |
96 J.~Slaney, Eds., LNAI, Springer, p.~?, |
113 J.~Slaney, Eds., LNAI, Springer, p.~?, |
97 \newblock in press |
114 \newblock in press |
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115 |
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116 \bibitem{pvs-language} |
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117 Owre, S., Shankar, N., Rushby, J.~M., |
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118 \newblock {\em The {PVS} specification language}, |
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119 \newblock Computer Science Laboratory, SRI International, Menlo Park, CA, Apr. |
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120 1993, |
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121 \newblock Beta release |
98 |
122 |
99 \bibitem{paulin92} |
123 \bibitem{paulin92} |
100 Paulin-Mohring, C., |
124 Paulin-Mohring, C., |
101 \newblock Inductive definitions in the system {Coq}: Rules and properties, |
125 \newblock Inductive definitions in the system {Coq}: Rules and properties, |
102 \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon, Dec. |
126 \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon, Dec. |
129 \newblock In press |
153 \newblock In press |
130 |
154 |
131 \bibitem{paulson-final} |
155 \bibitem{paulson-final} |
132 Paulson, L.~C., |
156 Paulson, L.~C., |
133 \newblock A concrete final coalgebra theorem for {ZF} set theory, |
157 \newblock A concrete final coalgebra theorem for {ZF} set theory, |
134 \newblock In {\em Types for Proofs and Programs: International Workshop {TYPES |
158 \newblock In Dybjer et~al. \cite{types94}, pp.~120--139 |
135 '94}\/} (published 1995), P.~Dybjer, B.~Nordstr{\"om},, J.~Smith, Eds., LNCS |
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136 996, Springer, pp.~120--139 |
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137 |
159 |
138 \bibitem{paulson-gr} |
160 \bibitem{paulson-gr} |
139 Paulson, L.~C., Gr\c{a}bczewski, K., |
161 Paulson, L.~C., Gr\c{a}bczewski, K., |
140 \newblock Mechanizing set theory: Cardinal arithmetic and the axiom of choice, |
162 \newblock Mechanizing set theory: Cardinal arithmetic and the axiom of choice, |
141 \newblock {\em J. Auto. Reas.\/} (1996), |
163 \newblock {\em J. Auto. Reas.\/} (1996), |
155 |
177 |
156 \bibitem{saaltink-fme} |
178 \bibitem{saaltink-fme} |
157 Saaltink, M., Kromodimoeljo, S., Pase, B., Craigen, D., Meisels, I., |
179 Saaltink, M., Kromodimoeljo, S., Pase, B., Craigen, D., Meisels, I., |
158 \newblock An {EVES} data abstraction example, |
180 \newblock An {EVES} data abstraction example, |
159 \newblock In {\em FME '93: Industrial-Strength Formal Methods\/} (1993), |
181 \newblock In {\em FME '93: Industrial-Strength Formal Methods\/} (1993), |
160 J.~C.~P. Woodcock, P.~G. Larsen, Eds., LNCS 670, Springer, pp.~578--596 |
182 J.~C.~P. Woodcock P.~G. Larsen, Eds., LNCS 670, Springer, pp.~578--596 |
161 |
183 |
162 \bibitem{slind-tfl} |
184 \bibitem{slind-tfl} |
163 Slind, K., |
185 Slind, K., |
164 \newblock Function definition in higher-order logic, |
186 \newblock Function definition in higher-order logic, |
165 \newblock In {\em Theorem Proving in Higher Order Logics\/} (1996), J.~von |
187 \newblock In {\em Theorem Proving in Higher Order Logics\/} (1996), J.~von |
168 |
190 |
169 \bibitem{szasz93} |
191 \bibitem{szasz93} |
170 Szasz, N., |
192 Szasz, N., |
171 \newblock A machine checked proof that {Ackermann's} function is not primitive |
193 \newblock A machine checked proof that {Ackermann's} function is not primitive |
172 recursive, |
194 recursive, |
173 \newblock In {\em Logical Environments}, G.~Huet, G.~Plotkin, Eds. Cambridge |
195 \newblock In {\em Logical Environments}, G.~Huet G.~Plotkin, Eds. Cambridge |
174 Univ. Press, 1993, pp.~317--338 |
196 Univ. Press, 1993, pp.~317--338 |
175 |
197 |
176 \bibitem{voelker95} |
198 \bibitem{voelker95} |
177 V\"olker, N., |
199 V\"olker, N., |
178 \newblock On the representation of datatypes in {Isabelle/HOL}, |
200 \newblock On the representation of datatypes in {Isabelle/HOL}, |