diff -r 493308514ea8 -r a9015b16a0e5 doc-src/Logics/logics.toc --- 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}