--- a/doc-src/ind-defs.toc Wed Mar 23 13:05:12 1994 +0100
+++ b/doc-src/ind-defs.toc Wed Mar 23 15:21:41 1994 +0100
@@ -1,33 +1,22 @@
\contentsline {section}{\numberline {1}Introduction}{1}
-\contentsline {section}{\numberline {2}Fixedpoint operators}{2}
-\contentsline {section}{\numberline {3}Elements of an inductive or co-inductive definition}{2}
+\contentsline {section}{\numberline {2}Fixedpoint operators}{1}
+\contentsline {section}{\numberline {3}Elements of an inductive or coinductive definition}{2}
\contentsline {subsection}{\numberline {3.1}The form of the introduction rules}{2}
\contentsline {subsection}{\numberline {3.2}The fixedpoint definitions}{3}
-\contentsline {subsection}{\numberline {3.3}Mutual recursion}{4}
+\contentsline {subsection}{\numberline {3.3}Mutual recursion}{3}
\contentsline {subsection}{\numberline {3.4}Proving the introduction rules}{4}
\contentsline {subsection}{\numberline {3.5}The elimination rule}{4}
-\contentsline {section}{\numberline {4}Induction and co-induction rules}{5}
-\contentsline {subsection}{\numberline {4.1}The basic induction rule}{5}
+\contentsline {section}{\numberline {4}Induction and coinduction rules}{4}
+\contentsline {subsection}{\numberline {4.1}The basic induction rule}{4}
\contentsline {subsection}{\numberline {4.2}Mutual induction}{5}
-\contentsline {subsection}{\numberline {4.3}Co-induction}{6}
-\contentsline {section}{\numberline {5}Examples of inductive and co-inductive definitions}{6}
-\contentsline {subsection}{\numberline {5.1}The finite set operator}{7}
-\contentsline {subsection}{\numberline {5.2}Lists of $n$ elements}{7}
-\contentsline {subsection}{\numberline {5.3}A demonstration of {\ptt mk\unhbox \voidb@x \kern .06em \vbox {\hrule width.3em}cases}}{9}
-\contentsline {subsection}{\numberline {5.4}A co-inductive definition: bisimulations on lazy lists}{9}
-\contentsline {subsection}{\numberline {5.5}The accessible part of a relation}{10}
-\contentsline {subsection}{\numberline {5.6}The primitive recursive functions}{11}
-\contentsline {section}{\numberline {6}Datatypes and co-datatypes}{13}
-\contentsline {subsection}{\numberline {6.1}Constructors and their domain}{13}
-\contentsline {subsection}{\numberline {6.2}The case analysis operator}{14}
-\contentsline {subsection}{\numberline {6.3}Example: lists and lazy lists}{15}
-\contentsline {subsection}{\numberline {6.4}Example: mutual recursion}{16}
-\contentsline {subsection}{\numberline {6.5}A four-constructor datatype}{18}
-\contentsline {subsection}{\numberline {6.6}Proving freeness theorems}{19}
-\contentsline {section}{\numberline {7}Conclusions and future work}{20}
-\contentsline {section}{\numberline {A}Inductive and co-inductive definitions: users guide}{22}
-\contentsline {subsection}{\numberline {A.1}The result structure}{22}
-\contentsline {subsection}{\numberline {A.2}The argument structure}{23}
-\contentsline {section}{\numberline {B}Datatype and co-datatype definitions: users guide}{24}
-\contentsline {subsection}{\numberline {B.1}The result structure}{24}
-\contentsline {subsection}{\numberline {B.2}The argument structure}{24}
+\contentsline {subsection}{\numberline {4.3}Coinduction}{5}
+\contentsline {section}{\numberline {5}Examples of inductive and coinductive definitions}{6}
+\contentsline {subsection}{\numberline {5.1}The finite set operator}{6}
+\contentsline {subsection}{\numberline {5.2}Lists of $n$ elements}{6}
+\contentsline {subsection}{\numberline {5.3}A coinductive definition: bisimulations on lazy lists}{7}
+\contentsline {subsection}{\numberline {5.4}The accessible part of a relation}{8}
+\contentsline {subsection}{\numberline {5.5}The primitive recursive functions}{9}
+\contentsline {section}{\numberline {6}Datatypes and codatatypes}{11}
+\contentsline {subsection}{\numberline {6.1}Constructors and their domain}{11}
+\contentsline {subsection}{\numberline {6.2}The case analysis operator}{11}
+\contentsline {section}{\numberline {7}Conclusions and future work}{12}