--- a/doc-src/Logics/logics.toc Mon Nov 22 11:27:04 1993 +0100
+++ b/doc-src/Logics/logics.toc Mon Nov 22 11:28:25 1993 +0100
@@ -16,85 +16,85 @@
\contentsline {subsection}{Derived rules versus definitions}{20}
\contentsline {chapter}{\numberline {3}Zermelo-Fraenkel set theory}{23}
\contentsline {section}{\numberline {3.1}Which version of axiomatic set theory?}{23}
-\contentsline {section}{\numberline {3.2}The syntax of set theory}{25}
-\contentsline {section}{\numberline {3.3}Binding operators}{25}
+\contentsline {section}{\numberline {3.2}The syntax of set theory}{24}
+\contentsline {section}{\numberline {3.3}Binding operators}{26}
\contentsline {section}{\numberline {3.4}The Zermelo-Fraenkel axioms}{28}
\contentsline {section}{\numberline {3.5}From basic lemmas to function spaces}{33}
-\contentsline {subsection}{Fundamental lemmas}{33}
-\contentsline {subsection}{Unordered pairs and finite sets}{36}
-\contentsline {subsection}{Subset and lattice properties}{36}
+\contentsline {subsection}{Fundamental lemmas}{34}
+\contentsline {subsection}{Unordered pairs and finite sets}{34}
+\contentsline {subsection}{Subset and lattice properties}{37}
\contentsline {subsection}{Ordered pairs}{37}
\contentsline {subsection}{Relations}{37}
-\contentsline {subsection}{Functions}{40}
-\contentsline {section}{\numberline {3.6}Further developments}{40}
-\contentsline {section}{\numberline {3.7}Simplification rules}{47}
-\contentsline {section}{\numberline {3.8}The examples directory}{48}
-\contentsline {section}{\numberline {3.9}A proof about powersets}{49}
-\contentsline {section}{\numberline {3.10}Monotonicity of the union operator}{51}
-\contentsline {section}{\numberline {3.11}Low-level reasoning about functions}{52}
-\contentsline {chapter}{\numberline {4}Higher-order logic}{55}
-\contentsline {section}{\numberline {4.1}Syntax}{55}
-\contentsline {subsection}{Types}{55}
-\contentsline {subsection}{Binders}{58}
-\contentsline {section}{\numberline {4.2}Rules of inference}{58}
-\contentsline {section}{\numberline {4.3}Generic packages}{62}
-\contentsline {section}{\numberline {4.4}A formulation of set theory}{63}
-\contentsline {subsection}{Syntax of set theory}{63}
-\contentsline {subsection}{Axioms and rules of set theory}{69}
-\contentsline {subsection}{Derived rules for sets}{69}
-\contentsline {section}{\numberline {4.5}Types}{69}
-\contentsline {subsection}{Product and sum types}{74}
-\contentsline {subsection}{The type of natural numbers, $nat$}{74}
-\contentsline {subsection}{The type constructor for lists, $\alpha \pcomma list$}{74}
-\contentsline {subsection}{The type constructor for lazy lists, $\alpha \pcomma llist$}{78}
-\contentsline {section}{\numberline {4.6}Classical proof procedures}{78}
-\contentsline {section}{\numberline {4.7}The examples directory}{78}
-\contentsline {section}{\numberline {4.8}Example: deriving the conjunction rules}{79}
-\contentsline {subsection}{The introduction rule}{79}
-\contentsline {subsection}{The elimination rule}{80}
-\contentsline {section}{\numberline {4.9}Example: Cantor's Theorem}{81}
-\contentsline {chapter}{\numberline {5}First-order sequent calculus}{83}
-\contentsline {section}{\numberline {5.1}Unification for lists}{83}
-\contentsline {section}{\numberline {5.2}Syntax and rules of inference}{84}
-\contentsline {section}{\numberline {5.3}Tactics for the cut rule}{84}
-\contentsline {section}{\numberline {5.4}Tactics for sequents}{88}
-\contentsline {section}{\numberline {5.5}Packaging sequent rules}{89}
-\contentsline {section}{\numberline {5.6}Proof procedures}{89}
-\contentsline {subsection}{Method A}{90}
-\contentsline {subsection}{Method B}{90}
-\contentsline {section}{\numberline {5.7}A simple example of classical reasoning}{91}
-\contentsline {section}{\numberline {5.8}A more complex proof}{92}
-\contentsline {chapter}{\numberline {6}Constructive Type Theory}{95}
-\contentsline {section}{\numberline {6.1}Syntax}{96}
-\contentsline {section}{\numberline {6.2}Rules of inference}{96}
-\contentsline {section}{\numberline {6.3}Rule lists}{101}
-\contentsline {section}{\numberline {6.4}Tactics for subgoal reordering}{104}
-\contentsline {section}{\numberline {6.5}Rewriting tactics}{105}
-\contentsline {section}{\numberline {6.6}Tactics for logical reasoning}{105}
-\contentsline {section}{\numberline {6.7}A theory of arithmetic}{106}
-\contentsline {section}{\numberline {6.8}The examples directory}{106}
-\contentsline {section}{\numberline {6.9}Example: type inference}{108}
-\contentsline {section}{\numberline {6.10}An example of logical reasoning}{109}
-\contentsline {section}{\numberline {6.11}Example: deriving a currying functional}{112}
-\contentsline {section}{\numberline {6.12}Example: proving the Axiom of Choice}{113}
-\contentsline {chapter}{\numberline {7}Defining Logics}{118}
-\contentsline {section}{\numberline {7.1}Precedence grammars}{118}
-\contentsline {section}{\numberline {7.2}Basic syntax}{119}
-\contentsline {subsection}{Logical types and default syntax}{120}
-\contentsline {subsection}{Lexical matters *}{121}
-\contentsline {subsection}{Inspecting syntax *}{121}
-\contentsline {section}{\numberline {7.3}Abstract syntax trees}{123}
-\contentsline {subsection}{Parse trees to asts}{125}
-\contentsline {subsection}{Asts to terms *}{126}
-\contentsline {subsection}{Printing of terms *}{126}
-\contentsline {section}{\numberline {7.4}Mixfix declarations}{128}
-\contentsline {subsection}{Infixes}{130}
-\contentsline {subsection}{Binders}{130}
-\contentsline {section}{\numberline {7.5}Syntactic translations (macros)}{131}
-\contentsline {subsection}{Specifying macros}{132}
-\contentsline {subsection}{Applying rules}{133}
-\contentsline {subsection}{Rewriting strategy}{135}
-\contentsline {subsection}{More examples}{135}
-\contentsline {section}{\numberline {7.6}Translation functions *}{138}
-\contentsline {subsection}{A simple example *}{139}
-\contentsline {section}{\numberline {7.7}Example: some minimal logics}{140}
+\contentsline {subsection}{Functions}{38}
+\contentsline {section}{\numberline {3.6}Further developments}{41}
+\contentsline {section}{\numberline {3.7}Simplification rules}{49}
+\contentsline {section}{\numberline {3.8}The examples directory}{49}
+\contentsline {section}{\numberline {3.9}A proof about powersets}{52}
+\contentsline {section}{\numberline {3.10}Monotonicity of the union operator}{54}
+\contentsline {section}{\numberline {3.11}Low-level reasoning about functions}{55}
+\contentsline {chapter}{\numberline {4}Higher-order logic}{58}
+\contentsline {section}{\numberline {4.1}Syntax}{58}
+\contentsline {subsection}{Types}{58}
+\contentsline {subsection}{Binders}{61}
+\contentsline {section}{\numberline {4.2}Rules of inference}{61}
+\contentsline {section}{\numberline {4.3}Generic packages}{65}
+\contentsline {section}{\numberline {4.4}A formulation of set theory}{66}
+\contentsline {subsection}{Syntax of set theory}{66}
+\contentsline {subsection}{Axioms and rules of set theory}{72}
+\contentsline {subsection}{Derived rules for sets}{72}
+\contentsline {section}{\numberline {4.5}Types}{72}
+\contentsline {subsection}{Product and sum types}{77}
+\contentsline {subsection}{The type of natural numbers, $nat$}{77}
+\contentsline {subsection}{The type constructor for lists, $\alpha \pcomma list$}{77}
+\contentsline {subsection}{The type constructor for lazy lists, $\alpha \pcomma llist$}{81}
+\contentsline {section}{\numberline {4.6}Classical proof procedures}{81}
+\contentsline {section}{\numberline {4.7}The examples directories}{81}
+\contentsline {section}{\numberline {4.8}Example: deriving the conjunction rules}{82}
+\contentsline {subsection}{The introduction rule}{82}
+\contentsline {subsection}{The elimination rule}{83}
+\contentsline {section}{\numberline {4.9}Example: Cantor's Theorem}{84}
+\contentsline {chapter}{\numberline {5}First-order sequent calculus}{87}
+\contentsline {section}{\numberline {5.1}Unification for lists}{87}
+\contentsline {section}{\numberline {5.2}Syntax and rules of inference}{88}
+\contentsline {section}{\numberline {5.3}Tactics for the cut rule}{88}
+\contentsline {section}{\numberline {5.4}Tactics for sequents}{93}
+\contentsline {section}{\numberline {5.5}Packaging sequent rules}{93}
+\contentsline {section}{\numberline {5.6}Proof procedures}{94}
+\contentsline {subsection}{Method A}{95}
+\contentsline {subsection}{Method B}{95}
+\contentsline {section}{\numberline {5.7}A simple example of classical reasoning}{95}
+\contentsline {section}{\numberline {5.8}A more complex proof}{97}
+\contentsline {chapter}{\numberline {6}Constructive Type Theory}{99}
+\contentsline {section}{\numberline {6.1}Syntax}{100}
+\contentsline {section}{\numberline {6.2}Rules of inference}{100}
+\contentsline {section}{\numberline {6.3}Rule lists}{105}
+\contentsline {section}{\numberline {6.4}Tactics for subgoal reordering}{108}
+\contentsline {section}{\numberline {6.5}Rewriting tactics}{109}
+\contentsline {section}{\numberline {6.6}Tactics for logical reasoning}{109}
+\contentsline {section}{\numberline {6.7}A theory of arithmetic}{110}
+\contentsline {section}{\numberline {6.8}The examples directory}{110}
+\contentsline {section}{\numberline {6.9}Example: type inference}{112}
+\contentsline {section}{\numberline {6.10}An example of logical reasoning}{113}
+\contentsline {section}{\numberline {6.11}Example: deriving a currying functional}{116}
+\contentsline {section}{\numberline {6.12}Example: proving the Axiom of Choice}{117}
+\contentsline {chapter}{\numberline {7}Defining Logics}{121}
+\contentsline {section}{\numberline {7.1}Precedence grammars}{121}
+\contentsline {section}{\numberline {7.2}Basic syntax}{122}
+\contentsline {subsection}{Logical types and default syntax}{123}
+\contentsline {subsection}{Lexical matters *}{124}
+\contentsline {subsection}{Inspecting syntax *}{124}
+\contentsline {section}{\numberline {7.3}Abstract syntax trees}{126}
+\contentsline {subsection}{Parse trees to asts}{128}
+\contentsline {subsection}{Asts to terms *}{129}
+\contentsline {subsection}{Printing of terms *}{129}
+\contentsline {section}{\numberline {7.4}Mixfix declarations}{130}
+\contentsline {subsection}{Infixes}{133}
+\contentsline {subsection}{Binders}{133}
+\contentsline {section}{\numberline {7.5}Syntactic translations (macros)}{134}
+\contentsline {subsection}{Specifying macros}{135}
+\contentsline {subsection}{Applying rules}{136}
+\contentsline {subsection}{Rewriting strategy}{138}
+\contentsline {subsection}{More examples}{138}
+\contentsline {section}{\numberline {7.6}Translation functions *}{141}
+\contentsline {subsection}{A simple example *}{142}
+\contentsline {section}{\numberline {7.7}Example: some minimal logics}{143}