doc-src/Logics/logics.toc
changeset 136 a9015b16a0e5
parent 104 d8205bb279a7
child 359 b5a2e9503a7a
     1.1 --- a/doc-src/Logics/logics.toc	Mon Nov 22 11:27:04 1993 +0100
     1.2 +++ b/doc-src/Logics/logics.toc	Mon Nov 22 11:28:25 1993 +0100
     1.3 @@ -16,85 +16,85 @@
     1.4  \contentsline {subsection}{Derived rules versus definitions}{20}
     1.5  \contentsline {chapter}{\numberline {3}Zermelo-Fraenkel set theory}{23}
     1.6  \contentsline {section}{\numberline {3.1}Which version of axiomatic set theory?}{23}
     1.7 -\contentsline {section}{\numberline {3.2}The syntax of set theory}{25}
     1.8 -\contentsline {section}{\numberline {3.3}Binding operators}{25}
     1.9 +\contentsline {section}{\numberline {3.2}The syntax of set theory}{24}
    1.10 +\contentsline {section}{\numberline {3.3}Binding operators}{26}
    1.11  \contentsline {section}{\numberline {3.4}The Zermelo-Fraenkel axioms}{28}
    1.12  \contentsline {section}{\numberline {3.5}From basic lemmas to function spaces}{33}
    1.13 -\contentsline {subsection}{Fundamental lemmas}{33}
    1.14 -\contentsline {subsection}{Unordered pairs and finite sets}{36}
    1.15 -\contentsline {subsection}{Subset and lattice properties}{36}
    1.16 +\contentsline {subsection}{Fundamental lemmas}{34}
    1.17 +\contentsline {subsection}{Unordered pairs and finite sets}{34}
    1.18 +\contentsline {subsection}{Subset and lattice properties}{37}
    1.19  \contentsline {subsection}{Ordered pairs}{37}
    1.20  \contentsline {subsection}{Relations}{37}
    1.21 -\contentsline {subsection}{Functions}{40}
    1.22 -\contentsline {section}{\numberline {3.6}Further developments}{40}
    1.23 -\contentsline {section}{\numberline {3.7}Simplification rules}{47}
    1.24 -\contentsline {section}{\numberline {3.8}The examples directory}{48}
    1.25 -\contentsline {section}{\numberline {3.9}A proof about powersets}{49}
    1.26 -\contentsline {section}{\numberline {3.10}Monotonicity of the union operator}{51}
    1.27 -\contentsline {section}{\numberline {3.11}Low-level reasoning about functions}{52}
    1.28 -\contentsline {chapter}{\numberline {4}Higher-order logic}{55}
    1.29 -\contentsline {section}{\numberline {4.1}Syntax}{55}
    1.30 -\contentsline {subsection}{Types}{55}
    1.31 -\contentsline {subsection}{Binders}{58}
    1.32 -\contentsline {section}{\numberline {4.2}Rules of inference}{58}
    1.33 -\contentsline {section}{\numberline {4.3}Generic packages}{62}
    1.34 -\contentsline {section}{\numberline {4.4}A formulation of set theory}{63}
    1.35 -\contentsline {subsection}{Syntax of set theory}{63}
    1.36 -\contentsline {subsection}{Axioms and rules of set theory}{69}
    1.37 -\contentsline {subsection}{Derived rules for sets}{69}
    1.38 -\contentsline {section}{\numberline {4.5}Types}{69}
    1.39 -\contentsline {subsection}{Product and sum types}{74}
    1.40 -\contentsline {subsection}{The type of natural numbers, $nat$}{74}
    1.41 -\contentsline {subsection}{The type constructor for lists, $\alpha \pcomma list$}{74}
    1.42 -\contentsline {subsection}{The type constructor for lazy lists, $\alpha \pcomma llist$}{78}
    1.43 -\contentsline {section}{\numberline {4.6}Classical proof procedures}{78}
    1.44 -\contentsline {section}{\numberline {4.7}The examples directory}{78}
    1.45 -\contentsline {section}{\numberline {4.8}Example: deriving the conjunction rules}{79}
    1.46 -\contentsline {subsection}{The introduction rule}{79}
    1.47 -\contentsline {subsection}{The elimination rule}{80}
    1.48 -\contentsline {section}{\numberline {4.9}Example: Cantor's Theorem}{81}
    1.49 -\contentsline {chapter}{\numberline {5}First-order sequent calculus}{83}
    1.50 -\contentsline {section}{\numberline {5.1}Unification for lists}{83}
    1.51 -\contentsline {section}{\numberline {5.2}Syntax and rules of inference}{84}
    1.52 -\contentsline {section}{\numberline {5.3}Tactics for the cut rule}{84}
    1.53 -\contentsline {section}{\numberline {5.4}Tactics for sequents}{88}
    1.54 -\contentsline {section}{\numberline {5.5}Packaging sequent rules}{89}
    1.55 -\contentsline {section}{\numberline {5.6}Proof procedures}{89}
    1.56 -\contentsline {subsection}{Method A}{90}
    1.57 -\contentsline {subsection}{Method B}{90}
    1.58 -\contentsline {section}{\numberline {5.7}A simple example of classical reasoning}{91}
    1.59 -\contentsline {section}{\numberline {5.8}A more complex proof}{92}
    1.60 -\contentsline {chapter}{\numberline {6}Constructive Type Theory}{95}
    1.61 -\contentsline {section}{\numberline {6.1}Syntax}{96}
    1.62 -\contentsline {section}{\numberline {6.2}Rules of inference}{96}
    1.63 -\contentsline {section}{\numberline {6.3}Rule lists}{101}
    1.64 -\contentsline {section}{\numberline {6.4}Tactics for subgoal reordering}{104}
    1.65 -\contentsline {section}{\numberline {6.5}Rewriting tactics}{105}
    1.66 -\contentsline {section}{\numberline {6.6}Tactics for logical reasoning}{105}
    1.67 -\contentsline {section}{\numberline {6.7}A theory of arithmetic}{106}
    1.68 -\contentsline {section}{\numberline {6.8}The examples directory}{106}
    1.69 -\contentsline {section}{\numberline {6.9}Example: type inference}{108}
    1.70 -\contentsline {section}{\numberline {6.10}An example of logical reasoning}{109}
    1.71 -\contentsline {section}{\numberline {6.11}Example: deriving a currying functional}{112}
    1.72 -\contentsline {section}{\numberline {6.12}Example: proving the Axiom of Choice}{113}
    1.73 -\contentsline {chapter}{\numberline {7}Defining Logics}{118}
    1.74 -\contentsline {section}{\numberline {7.1}Precedence grammars}{118}
    1.75 -\contentsline {section}{\numberline {7.2}Basic syntax}{119}
    1.76 -\contentsline {subsection}{Logical types and default syntax}{120}
    1.77 -\contentsline {subsection}{Lexical matters *}{121}
    1.78 -\contentsline {subsection}{Inspecting syntax *}{121}
    1.79 -\contentsline {section}{\numberline {7.3}Abstract syntax trees}{123}
    1.80 -\contentsline {subsection}{Parse trees to asts}{125}
    1.81 -\contentsline {subsection}{Asts to terms *}{126}
    1.82 -\contentsline {subsection}{Printing of terms *}{126}
    1.83 -\contentsline {section}{\numberline {7.4}Mixfix declarations}{128}
    1.84 -\contentsline {subsection}{Infixes}{130}
    1.85 -\contentsline {subsection}{Binders}{130}
    1.86 -\contentsline {section}{\numberline {7.5}Syntactic translations (macros)}{131}
    1.87 -\contentsline {subsection}{Specifying macros}{132}
    1.88 -\contentsline {subsection}{Applying rules}{133}
    1.89 -\contentsline {subsection}{Rewriting strategy}{135}
    1.90 -\contentsline {subsection}{More examples}{135}
    1.91 -\contentsline {section}{\numberline {7.6}Translation functions *}{138}
    1.92 -\contentsline {subsection}{A simple example *}{139}
    1.93 -\contentsline {section}{\numberline {7.7}Example: some minimal logics}{140}
    1.94 +\contentsline {subsection}{Functions}{38}
    1.95 +\contentsline {section}{\numberline {3.6}Further developments}{41}
    1.96 +\contentsline {section}{\numberline {3.7}Simplification rules}{49}
    1.97 +\contentsline {section}{\numberline {3.8}The examples directory}{49}
    1.98 +\contentsline {section}{\numberline {3.9}A proof about powersets}{52}
    1.99 +\contentsline {section}{\numberline {3.10}Monotonicity of the union operator}{54}
   1.100 +\contentsline {section}{\numberline {3.11}Low-level reasoning about functions}{55}
   1.101 +\contentsline {chapter}{\numberline {4}Higher-order logic}{58}
   1.102 +\contentsline {section}{\numberline {4.1}Syntax}{58}
   1.103 +\contentsline {subsection}{Types}{58}
   1.104 +\contentsline {subsection}{Binders}{61}
   1.105 +\contentsline {section}{\numberline {4.2}Rules of inference}{61}
   1.106 +\contentsline {section}{\numberline {4.3}Generic packages}{65}
   1.107 +\contentsline {section}{\numberline {4.4}A formulation of set theory}{66}
   1.108 +\contentsline {subsection}{Syntax of set theory}{66}
   1.109 +\contentsline {subsection}{Axioms and rules of set theory}{72}
   1.110 +\contentsline {subsection}{Derived rules for sets}{72}
   1.111 +\contentsline {section}{\numberline {4.5}Types}{72}
   1.112 +\contentsline {subsection}{Product and sum types}{77}
   1.113 +\contentsline {subsection}{The type of natural numbers, $nat$}{77}
   1.114 +\contentsline {subsection}{The type constructor for lists, $\alpha \pcomma list$}{77}
   1.115 +\contentsline {subsection}{The type constructor for lazy lists, $\alpha \pcomma llist$}{81}
   1.116 +\contentsline {section}{\numberline {4.6}Classical proof procedures}{81}
   1.117 +\contentsline {section}{\numberline {4.7}The examples directories}{81}
   1.118 +\contentsline {section}{\numberline {4.8}Example: deriving the conjunction rules}{82}
   1.119 +\contentsline {subsection}{The introduction rule}{82}
   1.120 +\contentsline {subsection}{The elimination rule}{83}
   1.121 +\contentsline {section}{\numberline {4.9}Example: Cantor's Theorem}{84}
   1.122 +\contentsline {chapter}{\numberline {5}First-order sequent calculus}{87}
   1.123 +\contentsline {section}{\numberline {5.1}Unification for lists}{87}
   1.124 +\contentsline {section}{\numberline {5.2}Syntax and rules of inference}{88}
   1.125 +\contentsline {section}{\numberline {5.3}Tactics for the cut rule}{88}
   1.126 +\contentsline {section}{\numberline {5.4}Tactics for sequents}{93}
   1.127 +\contentsline {section}{\numberline {5.5}Packaging sequent rules}{93}
   1.128 +\contentsline {section}{\numberline {5.6}Proof procedures}{94}
   1.129 +\contentsline {subsection}{Method A}{95}
   1.130 +\contentsline {subsection}{Method B}{95}
   1.131 +\contentsline {section}{\numberline {5.7}A simple example of classical reasoning}{95}
   1.132 +\contentsline {section}{\numberline {5.8}A more complex proof}{97}
   1.133 +\contentsline {chapter}{\numberline {6}Constructive Type Theory}{99}
   1.134 +\contentsline {section}{\numberline {6.1}Syntax}{100}
   1.135 +\contentsline {section}{\numberline {6.2}Rules of inference}{100}
   1.136 +\contentsline {section}{\numberline {6.3}Rule lists}{105}
   1.137 +\contentsline {section}{\numberline {6.4}Tactics for subgoal reordering}{108}
   1.138 +\contentsline {section}{\numberline {6.5}Rewriting tactics}{109}
   1.139 +\contentsline {section}{\numberline {6.6}Tactics for logical reasoning}{109}
   1.140 +\contentsline {section}{\numberline {6.7}A theory of arithmetic}{110}
   1.141 +\contentsline {section}{\numberline {6.8}The examples directory}{110}
   1.142 +\contentsline {section}{\numberline {6.9}Example: type inference}{112}
   1.143 +\contentsline {section}{\numberline {6.10}An example of logical reasoning}{113}
   1.144 +\contentsline {section}{\numberline {6.11}Example: deriving a currying functional}{116}
   1.145 +\contentsline {section}{\numberline {6.12}Example: proving the Axiom of Choice}{117}
   1.146 +\contentsline {chapter}{\numberline {7}Defining Logics}{121}
   1.147 +\contentsline {section}{\numberline {7.1}Precedence grammars}{121}
   1.148 +\contentsline {section}{\numberline {7.2}Basic syntax}{122}
   1.149 +\contentsline {subsection}{Logical types and default syntax}{123}
   1.150 +\contentsline {subsection}{Lexical matters *}{124}
   1.151 +\contentsline {subsection}{Inspecting syntax *}{124}
   1.152 +\contentsline {section}{\numberline {7.3}Abstract syntax trees}{126}
   1.153 +\contentsline {subsection}{Parse trees to asts}{128}
   1.154 +\contentsline {subsection}{Asts to terms *}{129}
   1.155 +\contentsline {subsection}{Printing of terms *}{129}
   1.156 +\contentsline {section}{\numberline {7.4}Mixfix declarations}{130}
   1.157 +\contentsline {subsection}{Infixes}{133}
   1.158 +\contentsline {subsection}{Binders}{133}
   1.159 +\contentsline {section}{\numberline {7.5}Syntactic translations (macros)}{134}
   1.160 +\contentsline {subsection}{Specifying macros}{135}
   1.161 +\contentsline {subsection}{Applying rules}{136}
   1.162 +\contentsline {subsection}{Rewriting strategy}{138}
   1.163 +\contentsline {subsection}{More examples}{138}
   1.164 +\contentsline {section}{\numberline {7.6}Translation functions *}{141}
   1.165 +\contentsline {subsection}{A simple example *}{142}
   1.166 +\contentsline {section}{\numberline {7.7}Example: some minimal logics}{143}