doc-src/Logics/logics.bbl
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     8 
     8 
     9 \bibitem{basin91}
     9 \bibitem{basin91}
    10 David Basin and Matt Kaufmann.
    10 David Basin and Matt Kaufmann.
    11 \newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison.
    11 \newblock The {Boyer-Moore} prover and {Nuprl}: An experimental comparison.
    12 \newblock In {G\'erard} Huet and Gordon Plotkin, editors, {\em Logical
    12 \newblock In {G\'erard} Huet and Gordon Plotkin, editors, {\em Logical
    13   Frameworks}, pages 89--119. Cambridge University Press, 1991.
    13   Frameworks}, pages 89--119. 1991.
    14 
    14 
    15 \bibitem{boyer86}
    15 \bibitem{boyer86}
    16 Robert Boyer, Ewing Lusk, William McCune, Ross Overbeek, Mark Stickel, and
    16 Robert Boyer, Ewing Lusk, William McCune, Ross Overbeek, Mark Stickel, and
    17   Lawrence Wos.
    17   Lawrence Wos.
    18 \newblock Set theory in first-order logic: Clauses for {G\"odel's} axioms.
    18 \newblock Set theory in first-order logic: Clauses for {G\"odel's} axioms.
    19 \newblock {\em Journal of Automated Reasoning}, 2(3):287--327, 1986.
    19 \newblock 2(3):287--327, 1986.
    20 
    20 
    21 \bibitem{camilleri92}
    21 \bibitem{camilleri92}
    22 J.~Camilleri and T.~F. Melham.
    22 J.~Camilleri and T.~F. Melham.
    23 \newblock Reasoning with inductively defined relations in the {HOL} theorem
    23 \newblock Reasoning with inductively defined relations in the {HOL} theorem
    24   prover.
    24   prover.
    25 \newblock Technical Report 265, University of Cambridge Computer Laboratory,
    25 \newblock Technical Report 265, August 1992.
    26   August 1992.
       
    27 
    26 
    28 \bibitem{church40}
    27 \bibitem{church40}
    29 Alonzo Church.
    28 Alonzo Church.
    30 \newblock A formulation of the simple theory of types.
    29 \newblock A formulation of the simple theory of types.
    31 \newblock {\em Journal of Symbolic Logic}, 5:56--68, 1940.
    30 \newblock 5:56--68, 1940.
       
    31 
       
    32 \bibitem{coen92}
       
    33 Martin~D. Coen.
       
    34 \newblock {\em Interactive Program Derivation}.
       
    35 \newblock PhD thesis, University of Cambridge, 1992.
       
    36 \newblock Computer Laboratory Technical Report 272.
       
    37 
       
    38 \bibitem{constable86}
       
    39 R.~L. {Constable et al.}
       
    40 \newblock {\em Implementing Mathematics with the Nuprl Proof Development
       
    41   System}.
       
    42 \newblock 1986.
       
    43 
       
    44 \bibitem{davey&priestley}
       
    45 B.~A. Davey and H.~A. Priestley.
       
    46 \newblock {\em Introduction to Lattices and Order}.
       
    47 \newblock 1990.
       
    48 
       
    49 \bibitem{devlin79}
       
    50 Keith~J. Devlin.
       
    51 \newblock {\em Fundamentals of Contemporary Set Theory}.
       
    52 \newblock Springer, 1979.
    32 
    53 
    33 \bibitem{dummett}
    54 \bibitem{dummett}
    34 Michael Dummett.
    55 Michael Dummett.
    35 \newblock {\em Elements of Intuitionism}.
    56 \newblock {\em Elements of Intuitionism}.
    36 \newblock Oxford University Press, 1977.
    57 \newblock Oxford University Press, 1977.
    37 
    58 
    38 \bibitem{dyckhoff}
    59 \bibitem{dyckhoff}
    39 Roy Dyckhoff.
    60 Roy Dyckhoff.
    40 \newblock Contraction-free sequent calculi for intuitionistic logic.
    61 \newblock Contraction-free sequent calculi for intuitionistic logic.
    41 \newblock {\em Journal of Symbolic Logic}, 57(3):795--807, 1992.
    62 \newblock 57(3):795--807, 1992.
    42 
    63 
    43 \bibitem{felty91a}
    64 \bibitem{felty91a}
    44 Amy Felty.
    65 Amy Felty.
    45 \newblock A logic program for transforming sequent proofs to natural deduction
    66 \newblock A logic program for transforming sequent proofs to natural deduction
    46   proofs.
    67   proofs.
    49 \newblock LNAI 475.
    70 \newblock LNAI 475.
    50 
    71 
    51 \bibitem{frost93}
    72 \bibitem{frost93}
    52 Jacob Frost.
    73 Jacob Frost.
    53 \newblock A case study of co-induction in {Isabelle HOL}.
    74 \newblock A case study of co-induction in {Isabelle HOL}.
    54 \newblock Technical Report 308, University of Cambridge Computer Laboratory,
    75 \newblock Technical Report 308, August 1993.
    55   August 1993.
       
    56 
       
    57 \bibitem{OBJ}
       
    58 K.~Futatsugi, J.A. Goguen, Jean-Pierre Jouannaud, and J.~Meseguer.
       
    59 \newblock Principles of {OBJ2}.
       
    60 \newblock In {\em Symposium on Principles of Programming Languages}, pages
       
    61   52--66, 1985.
       
    62 
    76 
    63 \bibitem{gallier86}
    77 \bibitem{gallier86}
    64 J.~H. Gallier.
    78 J.~H. Gallier.
    65 \newblock {\em Logic for Computer Science: Foundations of Automatic Theorem
    79 \newblock {\em Logic for Computer Science: Foundations of Automatic Theorem
    66   Proving}.
    80   Proving}.
    67 \newblock Harper \& Row, 1986.
    81 \newblock Harper \& Row, 1986.
    68 
    82 
    69 \bibitem{mgordon88a}
    83 \bibitem{mgordon-hol}
    70 Michael J.~C. Gordon.
    84 M.~J.~C. Gordon and T.~F. Melham.
    71 \newblock {HOL}: A proof generating system for higher-order logic.
    85 \newblock {\em Introduction to {HOL}: A Theorem Proving Environment for Higher
    72 \newblock In Graham Birtwistle and P.~A. Subrahmanyam, editors, {\em {VLSI}
    86   Order Logic}.
    73   Specification, Verification and Synthesis}, pages 73--128. Kluwer Academic
    87 \newblock 1993.
    74   Publishers, 1988.
       
    75 
    88 
    76 \bibitem{halmos60}
    89 \bibitem{halmos60}
    77 Paul~R. Halmos.
    90 Paul~R. Halmos.
    78 \newblock {\em Naive Set Theory}.
    91 \newblock {\em Naive Set Theory}.
    79 \newblock Van Nostrand, 1960.
    92 \newblock Van Nostrand, 1960.
    82 G.~P. Huet and B.~Lang.
    95 G.~P. Huet and B.~Lang.
    83 \newblock Proving and applying program transformations expressed with
    96 \newblock Proving and applying program transformations expressed with
    84   second-order patterns.
    97   second-order patterns.
    85 \newblock {\em Acta Informatica}, 11:31--55, 1978.
    98 \newblock {\em Acta Informatica}, 11:31--55, 1978.
    86 
    99 
       
   100 \bibitem{alf}
       
   101 Lena Magnusson and Bengt {Nordstr\"om}.
       
   102 \newblock The {ALF} proof editor and its proof engine.
       
   103 \newblock In {\em : International Workshop {TYPES '93}}, pages 213--237.
       
   104   Springer, published 1994.
       
   105 \newblock LNCS 806.
       
   106 
    87 \bibitem{mw81}
   107 \bibitem{mw81}
    88 Zohar Manna and Richard Waldinger.
   108 Zohar Manna and Richard Waldinger.
    89 \newblock Deductive synthesis of the unification algorithm.
   109 \newblock Deductive synthesis of the unification algorithm.
    90 \newblock {\em Science of Computer Programming}, 1(1):5--48, 1981.
   110 \newblock {\em Science of Computer Programming}, 1(1):5--48, 1981.
    91 
   111 
    92 \bibitem{martinlof84}
   112 \bibitem{martinlof84}
    93 Per Martin-L\"of.
   113 Per Martin-L\"of.
    94 \newblock {\em Intuitionistic type theory}.
   114 \newblock {\em Intuitionistic type theory}.
    95 \newblock Bibliopolis, 1984.
   115 \newblock Bibliopolis, 1984.
    96 
   116 
       
   117 \bibitem{melham89}
       
   118 Thomas~F. Melham.
       
   119 \newblock Automating recursive type definitions in higher order logic.
       
   120 \newblock In Graham Birtwistle and P.~A. Subrahmanyam, editors, {\em Current
       
   121   Trends in Hardware Verification and Automated Theorem Proving}, pages
       
   122   341--386. Springer, 1989.
       
   123 
    97 \bibitem{milner-coind}
   124 \bibitem{milner-coind}
    98 Robin Milner and Mads Tofte.
   125 Robin Milner and Mads Tofte.
    99 \newblock Co-induction in relational semantics.
   126 \newblock Co-induction in relational semantics.
   100 \newblock {\em Theoretical Computer Science}, 87:209--220, 1991.
   127 \newblock {\em Theoretical Computer Science}, 87:209--220, 1991.
   101 
   128 
   102 \bibitem{noel}
   129 \bibitem{noel}
   103 Philippe {No\"el}.
   130 Philippe {No\"el}.
   104 \newblock Experimenting with {Isabelle} in {ZF} set theory.
   131 \newblock Experimenting with {Isabelle} in {ZF} set theory.
   105 \newblock {\em Journal of Automated Reasoning}, 10(1):15--58, 1993.
   132 \newblock 10(1):15--58, 1993.
   106 
   133 
   107 \bibitem{nordstrom90}
   134 \bibitem{nordstrom90}
   108 Bengt {Nordstr\"om}, Kent Petersson, and Jan Smith.
   135 Bengt {Nordstr\"om}, Kent Petersson, and Jan Smith.
   109 \newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}.
   136 \newblock {\em Programming in {Martin-L\"of}'s Type Theory. An Introduction}.
   110 \newblock Oxford University Press, 1990.
   137 \newblock Oxford University Press, 1990.
   113 Christine Paulin-Mohring.
   140 Christine Paulin-Mohring.
   114 \newblock Inductive definitions in the system {Coq}: Rules and properties.
   141 \newblock Inductive definitions in the system {Coq}: Rules and properties.
   115 \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon,
   142 \newblock Research Report 92-49, LIP, Ecole Normale Sup\'erieure de Lyon,
   116   December 1992.
   143   December 1992.
   117 
   144 
   118 \bibitem{paulson-set-I}
       
   119 Lawrence~C. Paulson.
       
   120 \newblock Set theory for verification: {I}. {From} foundations to functions.
       
   121 \newblock {\em Journal of Automated Reasoning}.
       
   122 \newblock In press; draft available as Report 271, University of Cambridge
       
   123   Computer Laboratory.
       
   124 
       
   125 \bibitem{paulson85}
   145 \bibitem{paulson85}
   126 Lawrence~C. Paulson.
   146 Lawrence~C. Paulson.
   127 \newblock Verifying the unification algorithm in {LCF}.
   147 \newblock Verifying the unification algorithm in {LCF}.
   128 \newblock {\em Science of Computer Programming}, 5:143--170, 1985.
   148 \newblock {\em Science of Computer Programming}, 5:143--170, 1985.
   129 
   149 
   130 \bibitem{paulson87}
   150 \bibitem{paulson87}
   131 Lawrence~C. Paulson.
   151 Lawrence~C. Paulson.
   132 \newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}.
   152 \newblock {\em Logic and Computation: Interactive proof with Cambridge LCF}.
   133 \newblock Cambridge University Press, 1987.
   153 \newblock 1987.
   134 
   154 
   135 \bibitem{paulson-COLOG}
   155 \bibitem{paulson-COLOG}
   136 Lawrence~C. Paulson.
   156 Lawrence~C. Paulson.
   137 \newblock A formulation of the simple theory of types (for {Isabelle}).
   157 \newblock A formulation of the simple theory of types (for {Isabelle}).
   138 \newblock In P.~Martin-L\"of and G.~Mints, editors, {\em COLOG-88:
   158 \newblock In P.~Martin-L\"of and G.~Mints, editors, {\em COLOG-88:
   139   International Conference on Computer Logic}, Tallinn, 1990. Estonian Academy
   159   International Conference on Computer Logic}, Tallinn, 1990. Estonian Academy
   140   of Sciences, Springer.
   160   of Sciences, Springer.
   141 \newblock LNCS 417.
   161 \newblock LNCS 417.
   142 
   162 
   143 \bibitem{paulson91}
       
   144 Lawrence~C. Paulson.
       
   145 \newblock {\em {ML} for the Working Programmer}.
       
   146 \newblock Cambridge University Press, 1991.
       
   147 
       
   148 \bibitem{paulson-coind}
   163 \bibitem{paulson-coind}
   149 Lawrence~C. Paulson.
   164 Lawrence~C. Paulson.
   150 \newblock Co-induction and co-recursion in higher-order logic.
   165 \newblock Co-induction and co-recursion in higher-order logic.
   151 \newblock Technical Report 304, University of Cambridge Computer Laboratory,
   166 \newblock Technical Report 304, July 1993.
   152   July 1993.
       
   153 
   167 
   154 \bibitem{paulson-fixedpt}
   168 \bibitem{paulson-fixedpt}
   155 Lawrence~C. Paulson.
   169 Lawrence~C. Paulson.
   156 \newblock A fixedpoint approach to implementing (co-)inductive definitions.
   170 \newblock A fixedpoint approach to implementing (co)inductive definitions.
   157 \newblock Technical report, University of Cambridge Computer Laboratory, 1993.
   171 \newblock Technical Report 320, December 1993.
   158 \newblock Draft.
   172 
       
   173 \bibitem{paulson-set-I}
       
   174 Lawrence~C. Paulson.
       
   175 \newblock Set theory for verification: {I}. {From} foundations to functions.
       
   176 \newblock 11(3):353--389, 1993.
   159 
   177 
   160 \bibitem{paulson-set-II}
   178 \bibitem{paulson-set-II}
   161 Lawrence~C. Paulson.
   179 Lawrence~C. Paulson.
   162 \newblock Set theory for verification: {II}. {Induction} and recursion.
   180 \newblock Set theory for verification: {II}. {Induction} and recursion.
   163 \newblock Technical Report 312, University of Cambridge Computer Laboratory,
   181 \newblock Technical Report 312, 1993.
   164   1993.
   182 
       
   183 \bibitem{paulson-final}
       
   184 Lawrence~C. Paulson.
       
   185 \newblock A concrete final coalgebra theorem for {ZF} set theory.
       
   186 \newblock Technical report, 1994.
   165 
   187 
   166 \bibitem{pelletier86}
   188 \bibitem{pelletier86}
   167 F.~J. Pelletier.
   189 F.~J. Pelletier.
   168 \newblock Seventy-five problems for testing automatic theorem provers.
   190 \newblock Seventy-five problems for testing automatic theorem provers.
   169 \newblock {\em Journal of Automated Reasoning}, 2:191--216, 1986.
   191 \newblock 2:191--216, 1986.
   170 \newblock Errata, JAR 4 (1988), 235--236.
   192 \newblock Errata, JAR 4 (1988), 235--236.
   171 
   193 
   172 \bibitem{plaisted90}
   194 \bibitem{plaisted90}
   173 David~A. Plaisted.
   195 David~A. Plaisted.
   174 \newblock A sequent-style model elimination strategy and a positive refinement.
   196 \newblock A sequent-style model elimination strategy and a positive refinement.
   175 \newblock {\em Journal of Automated Reasoning}, 6(4):389--402, 1990.
   197 \newblock 6(4):389--402, 1990.
   176 
   198 
   177 \bibitem{quaife92}
   199 \bibitem{quaife92}
   178 Art Quaife.
   200 Art Quaife.
   179 \newblock Automated deduction in {von Neumann-Bernays-G\"odel} set theory.
   201 \newblock Automated deduction in {von Neumann-Bernays-G\"odel} set theory.
   180 \newblock {\em Journal of Automated Reasoning}, 8(1):91--147, 1992.
   202 \newblock 8(1):91--147, 1992.
   181 
   203 
   182 \bibitem{suppes72}
   204 \bibitem{suppes72}
   183 Patrick Suppes.
   205 Patrick Suppes.
   184 \newblock {\em Axiomatic Set Theory}.
   206 \newblock {\em Axiomatic Set Theory}.
   185 \newblock Dover, 1972.
   207 \newblock Dover, 1972.
   195 \newblock Addison-Wesley, 1991.
   217 \newblock Addison-Wesley, 1991.
   196 
   218 
   197 \bibitem{principia}
   219 \bibitem{principia}
   198 A.~N. Whitehead and B.~Russell.
   220 A.~N. Whitehead and B.~Russell.
   199 \newblock {\em Principia Mathematica}.
   221 \newblock {\em Principia Mathematica}.
   200 \newblock Cambridge University Press, 1962.
   222 \newblock 1962.
   201 \newblock Paperback edition to *56, abridged from the 2nd edition (1927).
   223 \newblock Paperback edition to *56, abridged from the 2nd edition (1927).
   202 
   224 
   203 \end{thebibliography}
   225 \end{thebibliography}