1.1 --- a/doc-src/TutorialI/Inductive/document/Star.tex Wed Oct 18 17:19:18 2000 +0200
1.2 +++ b/doc-src/TutorialI/Inductive/document/Star.tex Wed Oct 18 17:19:24 2000 +0200
1.3 @@ -6,6 +6,7 @@
1.4 %
1.5 \begin{isamarkuptext}%
1.6 \label{sec:rtc}
1.7 +
1.8 {\bf Say something about inductive relations as opposed to sets? Or has that
1.9 been said already? If not, explain induction!}
1.10
1.11 @@ -13,7 +14,7 @@
1.12 closure of a relation. This concept was already introduced in
1.13 \S\ref{sec:rtrancl}, but it was not shown how it is defined. In fact,
1.14 the operator \isa{{\isacharcircum}{\isacharasterisk}} is not defined inductively but via a least
1.15 -fixed point because at that point in the theory hierarchy
1.16 +fixpoint because at that point in the theory hierarchy
1.17 inductive definitions are not yet available. But now they are:%
1.18 \end{isamarkuptext}%
1.19 \isacommand{consts}\ rtc\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}{\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}set{\isachardoublequote}\ \ \ {\isacharparenleft}{\isachardoublequote}{\isacharunderscore}{\isacharasterisk}{\isachardoublequote}\ {\isacharbrackleft}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isadigit{0}}{\isacharbrackright}\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isacharparenright}\isanewline
1.20 @@ -26,9 +27,8 @@
1.21 The function \isa{rtc} is annotated with concrete syntax: instead of
1.22 \isa{rtc\ r} we can read and write {term"r*"}. The actual definition
1.23 consists of two rules. Reflexivity is obvious and is immediately declared an
1.24 -equivalence rule. Thus the automatic tools will apply it automatically. The
1.25 -second rule, \isa{rtc{\isacharunderscore}step}, says that we can always add one more
1.26 -\isa{r}-step to the left. Although we could make \isa{rtc{\isacharunderscore}step} an
1.27 +equivalence. Thus the automatic tools will apply it automatically. The second
1.28 +rule, \isa{rtc{\isacharunderscore}step}, says that we can always add one more \isa{r}-step to the left. Although we could make \isa{rtc{\isacharunderscore}step} an
1.29 introduction rule, this is dangerous: the recursion slows down and may
1.30 even kill the automatic tactics.
1.31