| 104 |      1 | \begin{thebibliography}{10}
 | 
|  |      2 | 
 | 
|  |      3 | \bibitem{abramsky90}
 | 
| 293 |      4 | Abramsky, S.,
 | 
|  |      5 | \newblock The lazy lambda calculus,
 | 
|  |      6 | \newblock In {\em Resesarch Topics in Functional Programming}, D.~A. Turner,
 | 
|  |      7 |   Ed. Addison-Wesley, 1977, pp.~65--116
 | 
| 104 |      8 | 
 | 
|  |      9 | \bibitem{aczel77}
 | 
| 293 |     10 | Aczel, P.,
 | 
|  |     11 | \newblock An introduction to inductive definitions,
 | 
|  |     12 | \newblock In {\em Handbook of Mathematical Logic}, J.~Barwise, Ed.
 | 
|  |     13 |   North-Holland, 1977, pp.~739--782
 | 
| 104 |     14 | 
 | 
|  |     15 | \bibitem{aczel88}
 | 
| 293 |     16 | Aczel, P.,
 | 
|  |     17 | \newblock {\em Non-Well-Founded Sets},
 | 
|  |     18 | \newblock CSLI, 1988
 | 
| 104 |     19 | 
 | 
|  |     20 | \bibitem{bm79}
 | 
| 293 |     21 | Boyer, R.~S., Moore, J.~S.,
 | 
|  |     22 | \newblock {\em A Computational Logic},
 | 
|  |     23 | \newblock Academic Press, 1979
 | 
| 104 |     24 | 
 | 
|  |     25 | \bibitem{camilleri92}
 | 
| 293 |     26 | Camilleri, J., Melham, T.~F.,
 | 
| 104 |     27 | \newblock Reasoning with inductively defined relations in the {HOL} theorem
 | 
| 293 |     28 |   prover,
 | 
|  |     29 | \newblock Tech. Rep. 265, Comp. Lab., Univ. Cambridge, August 1992
 | 
| 104 |     30 | 
 | 
|  |     31 | \bibitem{davey&priestley}
 | 
| 293 |     32 | Davey, B.~A., Priestley, H.~A.,
 | 
|  |     33 | \newblock {\em Introduction to Lattices and Order},
 | 
|  |     34 | \newblock Cambridge Univ. Press, 1990
 | 
|  |     35 | 
 | 
|  |     36 | \bibitem{dybjer91}
 | 
|  |     37 | Dybjer, P.,
 | 
|  |     38 | \newblock Inductive sets and families in {Martin-L\"of's} type theory and their
 | 
|  |     39 |   set-theoretic semantics,
 | 
|  |     40 | \newblock In {\em Logical Frameworks}, G.~Huet, G.~Plotkin, Eds. Cambridge
 | 
|  |     41 |   Univ. Press, 1991, pp.~280--306
 | 
|  |     42 | 
 | 
|  |     43 | \bibitem{IMPS}
 | 
|  |     44 | Farmer, W.~M., Guttman, J.~D., Thayer, F.~J.,
 | 
|  |     45 | \newblock {IMPS}: An interactive mathematical proof system,
 | 
|  |     46 | \newblock {\em J. Auto. Reas. {\bf 11}}, 2 (1993), 213--248
 | 
| 104 |     47 | 
 | 
|  |     48 | \bibitem{hennessy90}
 | 
| 293 |     49 | Hennessy, M.,
 | 
| 104 |     50 | \newblock {\em The Semantics of Programming Languages: An Elementary
 | 
| 293 |     51 |   Introduction Using Structural Operational Semantics},
 | 
|  |     52 | \newblock Wiley, 1990
 | 
|  |     53 | 
 | 
|  |     54 | \bibitem{huet88}
 | 
|  |     55 | Huet, G.,
 | 
|  |     56 | \newblock Induction principles formalized in the {Calculus of Constructions},
 | 
|  |     57 | \newblock In {\em Programming of Future Generation Computers\/} (1988),
 | 
|  |     58 |   Elsevier, pp.~205--216
 | 
| 104 |     59 | 
 | 
|  |     60 | \bibitem{melham89}
 | 
| 293 |     61 | Melham, T.~F.,
 | 
|  |     62 | \newblock Automating recursive type definitions in higher order logic,
 | 
|  |     63 | \newblock In {\em Current Trends in Hardware Verification and Automated Theorem
 | 
|  |     64 |   Proving}, G.~Birtwistle, P.~A. Subrahmanyam, Eds. Springer, 1989,
 | 
|  |     65 |   pp.~341--386
 | 
|  |     66 | 
 | 
|  |     67 | \bibitem{milner-ind}
 | 
|  |     68 | Milner, R.,
 | 
|  |     69 | \newblock How to derive inductions in {LCF},
 | 
|  |     70 | \newblock note, Dept. Comp. Sci., Univ. Edinburgh, 1980
 | 
| 104 |     71 | 
 | 
|  |     72 | \bibitem{milner89}
 | 
| 293 |     73 | Milner, R.,
 | 
|  |     74 | \newblock {\em Communication and Concurrency},
 | 
|  |     75 | \newblock Prentice-Hall, 1989
 | 
|  |     76 | 
 | 
|  |     77 | \bibitem{monahan84}
 | 
|  |     78 | Monahan, B.~Q.,
 | 
|  |     79 | \newblock {\em Data Type Proofs using Edinburgh {LCF}},
 | 
|  |     80 | \newblock PhD thesis, University of Edinburgh, 1984
 | 
| 104 |     81 | 
 | 
|  |     82 | \bibitem{paulin92}
 | 
| 293 |     83 | Paulin-Mohring, C.,
 | 
|  |     84 | \newblock Inductive definitions in the system {Coq}: Rules and properties,
 | 
|  |     85 | \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon, Dec.
 | 
|  |     86 |   1992
 | 
| 104 |     87 | 
 | 
| 293 |     88 | \bibitem{paulson87}
 | 
|  |     89 | Paulson, L.~C.,
 | 
|  |     90 | \newblock {\em Logic and Computation: Interactive proof with Cambridge LCF},
 | 
|  |     91 | \newblock Cambridge Univ. Press, 1987
 | 
| 104 |     92 | 
 | 
|  |     93 | \bibitem{paulson91}
 | 
| 293 |     94 | Paulson, L.~C.,
 | 
|  |     95 | \newblock {\em {ML} for the Working Programmer},
 | 
|  |     96 | \newblock Cambridge Univ. Press, 1991
 | 
| 104 |     97 | 
 | 
|  |     98 | \bibitem{paulson-coind}
 | 
| 293 |     99 | Paulson, L.~C.,
 | 
|  |    100 | \newblock Co-induction and co-recursion in higher-order logic,
 | 
|  |    101 | \newblock Tech. Rep. 304, Comp. Lab., Univ. Cambridge, July 1993
 | 
| 104 |    102 | 
 | 
|  |    103 | \bibitem{isabelle-intro}
 | 
| 293 |    104 | Paulson, L.~C.,
 | 
|  |    105 | \newblock Introduction to {Isabelle},
 | 
|  |    106 | \newblock Tech. Rep. 280, Comp. Lab., Univ. Cambridge, 1993
 | 
|  |    107 | 
 | 
|  |    108 | \bibitem{paulson-set-I}
 | 
|  |    109 | Paulson, L.~C.,
 | 
|  |    110 | \newblock Set theory for verification: {I}. {From} foundations to functions,
 | 
|  |    111 | \newblock {\em J. Auto. Reas. {\bf 11}}, 3 (1993), 353--389
 | 
| 104 |    112 | 
 | 
|  |    113 | \bibitem{paulson-set-II}
 | 
| 293 |    114 | Paulson, L.~C.,
 | 
|  |    115 | \newblock Set theory for verification: {II}. {Induction} and recursion,
 | 
|  |    116 | \newblock Tech. Rep. 312, Comp. Lab., Univ. Cambridge, 1993
 | 
|  |    117 | 
 | 
|  |    118 | \bibitem{paulson-final}
 | 
|  |    119 | Paulson, L.~C.,
 | 
|  |    120 | \newblock A concrete final coalgebra theorem for {ZF} set theory,
 | 
|  |    121 | \newblock Tech. rep., Comp. Lab., Univ. Cambridge, 1994
 | 
| 104 |    122 | 
 | 
|  |    123 | \bibitem{pitts94}
 | 
| 293 |    124 | Pitts, A.~M.,
 | 
|  |    125 | \newblock A co-induction principle for recursively defined domains,
 | 
|  |    126 | \newblock {\em Theoretical Comput. Sci.\/} (1994),
 | 
|  |    127 | \newblock In press; available as Report 252, Comp. Lab., Univ. Cambridge
 | 
|  |    128 | 
 | 
|  |    129 | \bibitem{saaltink-fme}
 | 
|  |    130 | Saaltink, M., Kromodimoeljo, S., Pase, B., Craigen, D., Meisels, I.,
 | 
|  |    131 | \newblock An {EVES} data abstraction example,
 | 
|  |    132 | \newblock In {\em FME '93: Industrial-Strength Formal Methods\/} (1993),
 | 
|  |    133 |   J.~C.~P. Woodcock, P.~G. Larsen, Eds., Springer, pp.~578--596,
 | 
|  |    134 | \newblock LNCS 670
 | 
| 104 |    135 | 
 | 
|  |    136 | \bibitem{szasz93}
 | 
| 293 |    137 | Szasz, N.,
 | 
| 104 |    138 | \newblock A machine checked proof that {Ackermann's} function is not primitive
 | 
| 293 |    139 |   recursive,
 | 
|  |    140 | \newblock In {\em Logical Environments}, G.~Huet, G.~Plotkin, Eds. Cambridge
 | 
|  |    141 |   Univ. Press, 1993, pp.~317--338
 | 
| 104 |    142 | 
 | 
|  |    143 | \end{thebibliography}
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