doc-src/ind-defs.toc
author nipkow
Mon Jan 29 22:25:45 2001 +0100 (2001-01-29)
changeset 10995 ef0b521698b7
parent 294 058343877e3a
permissions -rw-r--r--
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     1 \contentsline {section}{\numberline {1}Introduction}{1}
     2 \contentsline {section}{\numberline {2}Fixedpoint operators}{1}
     3 \contentsline {section}{\numberline {3}Elements of an inductive or coinductive definition}{2}
     4 \contentsline {subsection}{\numberline {3.1}The form of the introduction rules}{2}
     5 \contentsline {subsection}{\numberline {3.2}The fixedpoint definitions}{3}
     6 \contentsline {subsection}{\numberline {3.3}Mutual recursion}{3}
     7 \contentsline {subsection}{\numberline {3.4}Proving the introduction rules}{4}
     8 \contentsline {subsection}{\numberline {3.5}The elimination rule}{4}
     9 \contentsline {section}{\numberline {4}Induction and coinduction rules}{4}
    10 \contentsline {subsection}{\numberline {4.1}The basic induction rule}{4}
    11 \contentsline {subsection}{\numberline {4.2}Mutual induction}{5}
    12 \contentsline {subsection}{\numberline {4.3}Coinduction}{5}
    13 \contentsline {section}{\numberline {5}Examples of inductive and coinductive definitions}{6}
    14 \contentsline {subsection}{\numberline {5.1}The finite set operator}{6}
    15 \contentsline {subsection}{\numberline {5.2}Lists of $n$ elements}{6}
    16 \contentsline {subsection}{\numberline {5.3}A coinductive definition: bisimulations on lazy lists}{7}
    17 \contentsline {subsection}{\numberline {5.4}The accessible part of a relation}{8}
    18 \contentsline {subsection}{\numberline {5.5}The primitive recursive functions}{9}
    19 \contentsline {section}{\numberline {6}Datatypes and codatatypes}{11}
    20 \contentsline {subsection}{\numberline {6.1}Constructors and their domain}{11}
    21 \contentsline {subsection}{\numberline {6.2}The case analysis operator}{11}
    22 \contentsline {section}{\numberline {7}Conclusions and future work}{12}