\begin{thebibliography}{10}
\bibitem{andrews86}
Peter~B. Andrews.
\newblock {\em An Introduction to Mathematical Logic and Type Theory: To Truth
Through Proof}.
\newblock Academic Press, 1986.
\bibitem{basin91}
David Basin and Matt Kaufmann.
\newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison.
\newblock In {G\'erard} Huet and Gordon Plotkin, editors, {\em Logical
Frameworks}, pages 89--119. 1991.
\bibitem{boyer86}
Robert Boyer, Ewing Lusk, William McCune, Ross Overbeek, Mark Stickel, and
Lawrence Wos.
\newblock Set theory in first-order logic: Clauses for {G\"odel's} axioms.
\newblock 2(3):287--327, 1986.
\bibitem{camilleri92}
J.~Camilleri and T.~F. Melham.
\newblock Reasoning with inductively defined relations in the {HOL} theorem
prover.
\newblock Technical Report 265, August 1992.
\bibitem{church40}
Alonzo Church.
\newblock A formulation of the simple theory of types.
\newblock 5:56--68, 1940.
\bibitem{coen92}
Martin~D. Coen.
\newblock {\em Interactive Program Derivation}.
\newblock PhD thesis, University of Cambridge, 1992.
\newblock Computer Laboratory Technical Report 272.
\bibitem{constable86}
R.~L. {Constable et al.}
\newblock {\em Implementing Mathematics with the Nuprl Proof Development
System}.
\newblock 1986.
\bibitem{davey&priestley}
B.~A. Davey and H.~A. Priestley.
\newblock {\em Introduction to Lattices and Order}.
\newblock 1990.
\bibitem{devlin79}
Keith~J. Devlin.
\newblock {\em Fundamentals of Contemporary Set Theory}.
\newblock Springer, 1979.
\bibitem{dummett}
Michael Dummett.
\newblock {\em Elements of Intuitionism}.
\newblock Oxford University Press, 1977.
\bibitem{dyckhoff}
Roy Dyckhoff.
\newblock Contraction-free sequent calculi for intuitionistic logic.
\newblock 57(3):795--807, 1992.
\bibitem{felty91a}
Amy Felty.
\newblock A logic program for transforming sequent proofs to natural deduction
proofs.
\newblock In Peter Schroeder-Heister, editor, {\em Extensions of Logic
Programming}, pages 157--178. Springer, 1991.
\newblock LNAI 475.
\bibitem{frost93}
Jacob Frost.
\newblock A case study of co-induction in {Isabelle HOL}.
\newblock Technical Report 308, August 1993.
\bibitem{gallier86}
J.~H. Gallier.
\newblock {\em Logic for Computer Science: Foundations of Automatic Theorem
Proving}.
\newblock Harper \& Row, 1986.
\bibitem{mgordon-hol}
M.~J.~C. Gordon and T.~F. Melham.
\newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher
Order Logic}.
\newblock 1993.
\bibitem{halmos60}
Paul~R. Halmos.
\newblock {\em Naive Set Theory}.
\newblock Van Nostrand, 1960.
\bibitem{huet78}
G.~P. Huet and B.~Lang.
\newblock Proving and applying program transformations expressed with
second-order patterns.
\newblock {\em Acta Informatica}, 11:31--55, 1978.
\bibitem{alf}
Lena Magnusson and Bengt {Nordstr\"om}.
\newblock The {ALF} proof editor and its proof engine.
\newblock In {\em : International Workshop {TYPES '93}}, pages 213--237.
Springer, published 1994.
\newblock LNCS 806.
\bibitem{mw81}
Zohar Manna and Richard Waldinger.
\newblock Deductive synthesis of the unification algorithm.
\newblock {\em Science of Computer Programming}, 1(1):5--48, 1981.
\bibitem{martinlof84}
Per Martin-L\"of.
\newblock {\em Intuitionistic type theory}.
\newblock Bibliopolis, 1984.
\bibitem{melham89}
Thomas~F. Melham.
\newblock Automating recursive type definitions in higher order logic.
\newblock In Graham Birtwistle and P.~A. Subrahmanyam, editors, {\em Current
Trends in Hardware Verification and Automated Theorem Proving}, pages
341--386. Springer, 1989.
\bibitem{milner-coind}
Robin Milner and Mads Tofte.
\newblock Co-induction in relational semantics.
\newblock {\em Theoretical Computer Science}, 87:209--220, 1991.
\bibitem{noel}
Philippe {No\"el}.
\newblock Experimenting with {Isabelle} in {ZF} set theory.
\newblock 10(1):15--58, 1993.
\bibitem{nordstrom90}
Bengt {Nordstr\"om}, Kent Petersson, and Jan Smith.
\newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}.
\newblock Oxford University Press, 1990.
\bibitem{paulin92}
Christine Paulin-Mohring.
\newblock Inductive definitions in the system {Coq}: Rules and properties.
\newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon,
December 1992.
\bibitem{paulson85}
Lawrence~C. Paulson.
\newblock Verifying the unification algorithm in {LCF}.
\newblock {\em Science of Computer Programming}, 5:143--170, 1985.
\bibitem{paulson87}
Lawrence~C. Paulson.
\newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}.
\newblock 1987.
\bibitem{paulson-COLOG}
Lawrence~C. Paulson.
\newblock A formulation of the simple theory of types (for {Isabelle}).
\newblock In P.~Martin-L\"of and G.~Mints, editors, {\em COLOG-88:
International Conference on Computer Logic}, Tallinn, 1990. Estonian Academy
of Sciences, Springer.
\newblock LNCS 417.
\bibitem{paulson-coind}
Lawrence~C. Paulson.
\newblock Co-induction and co-recursion in higher-order logic.
\newblock Technical Report 304, July 1993.
\bibitem{paulson-fixedpt}
Lawrence~C. Paulson.
\newblock A fixedpoint approach to implementing (co)inductive definitions.
\newblock Technical Report 320, December 1993.
\bibitem{paulson-set-I}
Lawrence~C. Paulson.
\newblock Set theory for verification: {I}. {From} foundations to functions.
\newblock 11(3):353--389, 1993.
\bibitem{paulson-set-II}
Lawrence~C. Paulson.
\newblock Set theory for verification: {II}. {Induction} and recursion.
\newblock Technical Report 312, 1993.
\bibitem{paulson-final}
Lawrence~C. Paulson.
\newblock A concrete final coalgebra theorem for {ZF} set theory.
\newblock Technical report, 1994.
\bibitem{pelletier86}
F.~J. Pelletier.
\newblock Seventy-five problems for testing automatic theorem provers.
\newblock 2:191--216, 1986.
\newblock Errata, JAR 4 (1988), 235--236.
\bibitem{plaisted90}
David~A. Plaisted.
\newblock A sequent-style model elimination strategy and a positive refinement.
\newblock 6(4):389--402, 1990.
\bibitem{quaife92}
Art Quaife.
\newblock Automated deduction in {von Neumann-Bernays-G\"odel} set theory.
\newblock 8(1):91--147, 1992.
\bibitem{suppes72}
Patrick Suppes.
\newblock {\em Axiomatic Set Theory}.
\newblock Dover, 1972.
\bibitem{takeuti87}
G.~Takeuti.
\newblock {\em Proof Theory}.
\newblock North Holland, 2nd edition, 1987.
\bibitem{thompson91}
Simon Thompson.
\newblock {\em Type Theory and Functional Programming}.
\newblock Addison-Wesley, 1991.
\bibitem{principia}
A.~N. Whitehead and B.~Russell.
\newblock {\em Principia Mathematica}.
\newblock 1962.
\newblock Paperback edition to *56, abridged from the 2nd edition (1927).
\end{thebibliography}