lcp@460: \begin{thebibliography}{10}
lcp@460: 
lcp@460: \bibitem{andrews86}
lcp@460: Andrews, P.~B.,
lcp@460: \newblock {\em An Introduction to Mathematical Logic and Type Theory: To Truth
lcp@460:   Through Proof},
lcp@460: \newblock Academic Press, 1986
lcp@460: 
lcp@460: \bibitem{basin91}
lcp@460: Basin, D., Kaufmann, M.,
lcp@460: \newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison,
lcp@460: \newblock In {\em Logical Frameworks}, G.~Huet, G.~Plotkin, Eds. Cambridge
lcp@460:   Univ. Press, 1991, pp.~89--119
lcp@460: 
lcp@460: \bibitem{boyer86}
lcp@460: Boyer, R., Lusk, E., McCune, W., Overbeek, R., Stickel, M., Wos, L.,
lcp@460: \newblock Set theory in first-order logic: Clauses for {G\"odel's} axioms,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 2}}, 3 (1986), 287--327
lcp@460: 
lcp@460: \bibitem{bm88book}
lcp@460: Boyer, R.~S., Moore, J.~S.,
lcp@460: \newblock {\em A Computational Logic Handbook},
lcp@460: \newblock Academic Press, 1988
lcp@460: 
lcp@460: \bibitem{camilleri92}
lcp@460: Camilleri, J., Melham, T.~F.,
lcp@460: \newblock Reasoning with inductively defined relations in the {HOL} theorem
lcp@460:   prover,
lcp@460: \newblock Tech. Rep. 265, Comp. Lab., Univ. Cambridge, Aug. 1992
lcp@460: 
lcp@460: \bibitem{charniak80}
lcp@460: Charniak, E., Riesbeck, C.~K., McDermott, D.~V.,
lcp@460: \newblock {\em Artificial Intelligence Programming},
lcp@460: \newblock Lawrence Erlbaum Associates, 1980
lcp@460: 
lcp@460: \bibitem{church40}
lcp@460: Church, A.,
lcp@460: \newblock A formulation of the simple theory of types,
lcp@460: \newblock {\em J. Symb. Logic {\bf 5}\/} (1940), 56--68
lcp@460: 
lcp@460: \bibitem{coen92}
lcp@460: Coen, M.~D.,
lcp@460: \newblock {\em Interactive Program Derivation},
lcp@460: \newblock PhD thesis, University of Cambridge, 1992,
lcp@460: \newblock Computer Laboratory Technical Report 272
lcp@460: 
lcp@460: \bibitem{constable86}
lcp@460: {Constable et al.}, R.~L.,
lcp@460: \newblock {\em Implementing Mathematics with the Nuprl Proof Development
lcp@460:   System},
lcp@460: \newblock Prentice-Hall, 1986
lcp@460: 
lcp@460: \bibitem{davey&priestley}
lcp@460: Davey, B.~A., Priestley, H.~A.,
lcp@460: \newblock {\em Introduction to Lattices and Order},
lcp@460: \newblock Cambridge Univ. Press, 1990
lcp@460: 
lcp@460: \bibitem{dawson90}
lcp@460: Dawson, W.~M.,
lcp@460: \newblock {\em A Generic Logic Environment},
lcp@460: \newblock PhD thesis, Imperial College, London, 1990
lcp@460: 
lcp@460: \bibitem{debruijn72}
lcp@460: de~Bruijn, N.~G.,
lcp@460: \newblock Lambda calculus notation with nameless dummies, a tool for automatic
lcp@460:   formula manipulation, with application to the {Church-Rosser Theorem},
lcp@460: \newblock {\em Indag. Math. {\bf 34}\/} (1972), 381--392
lcp@460: 
lcp@460: \bibitem{devlin79}
lcp@460: Devlin, K.~J.,
lcp@460: \newblock {\em Fundamentals of Contemporary Set Theory},
lcp@460: \newblock Springer, 1979
lcp@460: 
lcp@460: \bibitem{coq}
lcp@460: {Dowek et al.}, G.,
lcp@460: \newblock The {Coq} proof assistant user's guide,
lcp@460: \newblock Technical Report 134, INRIA-Rocquencourt, 1991
lcp@460: 
lcp@460: \bibitem{dummett}
lcp@460: Dummett, M.,
lcp@460: \newblock {\em Elements of Intuitionism},
lcp@460: \newblock Oxford University Press, 1977
lcp@460: 
lcp@460: \bibitem{dyckhoff}
lcp@460: Dyckhoff, R.,
lcp@460: \newblock Contraction-free sequent calculi for intuitionistic logic,
lcp@460: \newblock {\em J. Symb. Logic {\bf 57}}, 3 (1992), 795--807
lcp@460: 
lcp@460: \bibitem{felty91a}
lcp@460: Felty, A.,
lcp@460: \newblock A logic program for transforming sequent proofs to natural deduction
lcp@460:   proofs,
lcp@460: \newblock In {\em Extensions of Logic Programming\/} (1991),
lcp@460:   P.~Schroeder-Heister, Ed., Springer, pp.~157--178,
lcp@460: \newblock LNAI 475
lcp@460: 
lcp@460: \bibitem{felty93}
lcp@460: Felty, A.,
lcp@460: \newblock Implementing tactics and tacticals in a higher-order logic
lcp@460:   programming language,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 11}}, 1 (1993), 43--82
lcp@460: 
lcp@460: \bibitem{frost93}
lcp@460: Frost, J.,
lcp@460: \newblock A case study of co-induction in {Isabelle HOL},
lcp@460: \newblock Tech. Rep. 308, Comp. Lab., Univ. Cambridge, Aug. 1993
lcp@460: 
lcp@460: \bibitem{OBJ}
lcp@460: Futatsugi, K., Goguen, J., Jouannaud, J.-P., Meseguer, J.,
lcp@460: \newblock Principles of {OBJ2},
lcp@460: \newblock In {\em Princ. Prog. Lang.\/} (1985), pp.~52--66
lcp@460: 
lcp@460: \bibitem{gallier86}
lcp@460: Gallier, J.~H.,
lcp@460: \newblock {\em Logic for Computer Science: Foundations of Automatic Theorem
lcp@460:   Proving},
lcp@460: \newblock Harper \& Row, 1986
lcp@460: 
lcp@460: \bibitem{mgordon-hol}
lcp@460: Gordon, M. J.~C., Melham, T.~F.,
lcp@460: \newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher
lcp@460:   Order Logic},
lcp@460: \newblock Cambridge Univ. Press, 1993
lcp@460: 
lcp@460: \bibitem{halmos60}
lcp@460: Halmos, P.~R.,
lcp@460: \newblock {\em Naive Set Theory},
lcp@460: \newblock Van Nostrand, 1960
lcp@460: 
lcp@460: \bibitem{harper-jacm}
lcp@460: Harper, R., Honsell, F., Plotkin, G.,
lcp@460: \newblock A framework for defining logics,
lcp@460: \newblock {\em J.~ACM {\bf 40}}, 1 (1993), 143--184
lcp@460: 
lcp@460: \bibitem{haskell-tutorial}
lcp@460: Hudak, P., Fasel, J.~H.,
lcp@460: \newblock A gentle introduction to {Haskell},
lcp@460: \newblock {\em {SIGPLAN} {\bf 27}}, 5 (May 1992)
lcp@460: 
lcp@460: \bibitem{haskell-report}
lcp@460: Hudak, P., Jones, S.~P., Wadler, P.,
lcp@460: \newblock Report on the programming language {Haskell}: A non-strict, purely
lcp@460:   functional language,
lcp@460: \newblock {\em {SIGPLAN} {\bf 27}}, 5 (May 1992),
lcp@460: \newblock Version 1.2
lcp@460: 
lcp@460: \bibitem{huet75}
lcp@460: Huet, G.~P.,
lcp@460: \newblock A unification algorithm for typed $\lambda$-calculus,
lcp@460: \newblock {\em Theoretical Comput. Sci. {\bf 1}\/} (1975), 27--57
lcp@460: 
lcp@460: \bibitem{huet78}
lcp@460: Huet, G.~P., Lang, B.,
lcp@460: \newblock Proving and applying program transformations expressed with
lcp@460:   second-order patterns,
lcp@460: \newblock {\em Acta Inf. {\bf 11}\/} (1978), 31--55
lcp@460: 
lcp@460: \bibitem{mural}
lcp@460: Jones, C.~B., Jones, K.~D., Lindsay, P.~A., Moore, R.,
lcp@460: \newblock {\em Mural: A Formal Development Support System},
lcp@460: \newblock Springer, 1991
lcp@460: 
lcp@460: \bibitem{alf}
lcp@460: Magnusson, L., {Nordstr\"om}, B.,
lcp@460: \newblock The {ALF} proof editor and its proof engine,
lcp@460: \newblock In {\em Types for Proofs and Programs: International Workshop {TYPES
lcp@460:   '93}\/} (published 1994), Springer, pp.~213--237,
lcp@460: \newblock LNCS 806
lcp@460: 
lcp@460: \bibitem{mw81}
lcp@460: Manna, Z., Waldinger, R.,
lcp@460: \newblock Deductive synthesis of the unification algorithm,
lcp@460: \newblock {\em Sci. Comput. Programming {\bf 1}}, 1 (1981), 5--48
lcp@460: 
lcp@460: \bibitem{martin-nipkow}
lcp@460: Martin, U., Nipkow, T.,
lcp@460: \newblock Ordered rewriting and confluence,
lcp@460: \newblock In {\em 10th Conf. Auto. Deduct.\/} (1990), M.~E. Stickel, Ed.,
lcp@460:   Springer, pp.~366--380,
lcp@460: \newblock LNCS 449
lcp@460: 
lcp@460: \bibitem{martinlof84}
lcp@460: Martin-L\"of, P.,
lcp@460: \newblock {\em Intuitionistic type theory},
lcp@460: \newblock Bibliopolis, 1984
lcp@460: 
lcp@460: \bibitem{melham89}
lcp@460: Melham, T.~F.,
lcp@460: \newblock Automating recursive type definitions in higher order logic,
lcp@460: \newblock In {\em Current Trends in Hardware Verification and Automated Theorem
lcp@460:   Proving}, G.~Birtwistle, P.~A. Subrahmanyam, Eds. Springer, 1989,
lcp@460:   pp.~341--386
lcp@460: 
lcp@460: \bibitem{miller-mixed}
lcp@460: Miller, D.,
lcp@460: \newblock Unification under a mixed prefix,
lcp@460: \newblock {\em J. Symb. Comput. {\bf 14}}, 4 (1992), 321--358
lcp@460: 
lcp@460: \bibitem{milner-coind}
lcp@460: Milner, R., Tofte, M.,
lcp@460: \newblock Co-induction in relational semantics,
lcp@460: \newblock {\em Theoretical Comput. Sci. {\bf 87}\/} (1991), 209--220
lcp@460: 
lcp@460: \bibitem{nipkow-prehofer}
lcp@460: Nipkow, T., Prehofer, C.,
lcp@460: \newblock Type checking type classes,
lcp@460: \newblock In {\em 20th Princ. Prog. Lang.\/} (1993), ACM Press, pp.~409--418,
lcp@460: \newblock Revised version to appear in \bgroup\em J. Func. Prog.\egroup
lcp@460: 
lcp@460: \bibitem{noel}
lcp@460: {No\"el}, P.,
lcp@460: \newblock Experimenting with {Isabelle} in {ZF} set theory,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 10}}, 1 (1993), 15--58
lcp@460: 
lcp@460: \bibitem{nordstrom90}
lcp@460: {Nordstr\"om}, B., Petersson, K., Smith, J.,
lcp@460: \newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction},
lcp@460: \newblock Oxford University Press, 1990
lcp@460: 
lcp@460: \bibitem{paulin92}
lcp@460: Paulin-Mohring, C.,
lcp@460: \newblock Inductive definitions in the system {Coq}: Rules and properties,
lcp@460: \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon, Dec.
lcp@460:   1992
lcp@460: 
lcp@460: \bibitem{paulson85}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock Verifying the unification algorithm in {LCF},
lcp@460: \newblock {\em Sci. Comput. Programming {\bf 5}\/} (1985), 143--170
lcp@460: 
lcp@460: \bibitem{paulson87}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock {\em Logic and Computation: Interactive proof with Cambridge LCF},
lcp@460: \newblock Cambridge Univ. Press, 1987
lcp@460: 
lcp@460: \bibitem{paulson89}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock The foundation of a generic theorem prover,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 5}}, 3 (1989), 363--397
lcp@460: 
lcp@460: \bibitem{paulson-COLOG}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock A formulation of the simple theory of types (for {Isabelle}),
lcp@460: \newblock In {\em COLOG-88: International Conference on Computer Logic\/}
lcp@460:   (Tallinn, 1990), P.~Martin-L\"of, G.~Mints, Eds., Estonian Academy of
lcp@460:   Sciences, Springer,
lcp@460: \newblock LNCS 417
lcp@460: 
lcp@460: \bibitem{paulson700}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock {Isabelle}: The next 700 theorem provers,
lcp@460: \newblock In {\em Logic and Computer Science}, P.~Odifreddi, Ed. Academic
lcp@460:   Press, 1990, pp.~361--386
lcp@460: 
lcp@460: \bibitem{paulson91}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock {\em {ML} for the Working Programmer},
lcp@460: \newblock Cambridge Univ. Press, 1991
lcp@460: 
lcp@460: \bibitem{paulson-coind}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock Co-induction and co-recursion in higher-order logic,
lcp@460: \newblock Tech. Rep. 304, Comp. Lab., Univ. Cambridge, July 1993
lcp@460: 
lcp@460: \bibitem{paulson-fixedpt}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock A fixedpoint approach to implementing (co)inductive definitions,
lcp@460: \newblock Tech. Rep. 320, Comp. Lab., Univ. Cambridge, Dec. 1993
lcp@460: 
lcp@460: \bibitem{paulson-set-I}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock Set theory for verification: {I}. {From} foundations to functions,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 11}}, 3 (1993), 353--389
lcp@460: 
lcp@460: \bibitem{paulson-set-II}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock Set theory for verification: {II}. {Induction} and recursion,
lcp@460: \newblock Tech. Rep. 312, Comp. Lab., Univ. Cambridge, 1993
lcp@460: 
lcp@460: \bibitem{paulson-final}
lcp@460: Paulson, L.~C.,
lcp@460: \newblock A concrete final coalgebra theorem for {ZF} set theory,
lcp@460: \newblock Tech. rep., Comp. Lab., Univ. Cambridge, 1994
lcp@460: 
lcp@460: \bibitem{pelletier86}
lcp@460: Pelletier, F.~J.,
lcp@460: \newblock Seventy-five problems for testing automatic theorem provers,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 2}\/} (1986), 191--216,
lcp@460: \newblock Errata, JAR 4 (1988), 235--236
lcp@460: 
lcp@460: \bibitem{plaisted90}
lcp@460: Plaisted, D.~A.,
lcp@460: \newblock A sequent-style model elimination strategy and a positive refinement,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 6}}, 4 (1990), 389--402
lcp@460: 
lcp@460: \bibitem{quaife92}
lcp@460: Quaife, A.,
lcp@460: \newblock Automated deduction in {von Neumann-Bernays-G\"odel} set theory,
lcp@460: \newblock {\em J. Auto. Reas. {\bf 8}}, 1 (1992), 91--147
lcp@460: 
lcp@460: \bibitem{sawamura92}
lcp@460: Sawamura, H., Minami, T., Ohashi, K.,
lcp@460: \newblock Proof methods based on sheet of thought in {EUODHILOS},
lcp@460: \newblock Research Report IIAS-RR-92-6E, International Institute for Advanced
lcp@460:   Study of Social Information Science, Fujitsu Laboratories, 1992
lcp@460: 
lcp@460: \bibitem{suppes72}
lcp@460: Suppes, P.,
lcp@460: \newblock {\em Axiomatic Set Theory},
lcp@460: \newblock Dover, 1972
lcp@460: 
lcp@460: \bibitem{takeuti87}
lcp@460: Takeuti, G.,
lcp@460: \newblock {\em Proof Theory}, 2nd~ed.,
lcp@460: \newblock North Holland, 1987
lcp@460: 
lcp@460: \bibitem{thompson91}
lcp@460: Thompson, S.,
lcp@460: \newblock {\em Type Theory and Functional Programming},
lcp@460: \newblock Addison-Wesley, 1991
lcp@460: 
lcp@460: \bibitem{principia}
lcp@460: Whitehead, A.~N., Russell, B.,
lcp@460: \newblock {\em Principia Mathematica},
lcp@460: \newblock Cambridge Univ. Press, 1962,
lcp@460: \newblock Paperback edition to *56, abridged from the 2nd edition (1927)
lcp@460: 
lcp@460: \bibitem{wos-bledsoe}
lcp@460: Wos, L.,
lcp@460: \newblock Automated reasoning and {Bledsoe's} dream for the field,
lcp@460: \newblock In {\em Automated Reasoning: Essays in Honor of {Woody Bledsoe}},
lcp@460:   R.~S. Boyer, Ed. Kluwer Academic Publishers, 1991, pp.~297--342
lcp@460: 
lcp@460: \end{thebibliography}