diff -r c94db1a96f4e -r 6b0b6b471855 doc-src/TutorialI/Recdef/document/simplification.tex --- a/doc-src/TutorialI/Recdef/document/simplification.tex Thu Aug 17 21:07:25 2000 +0200 +++ b/doc-src/TutorialI/Recdef/document/simplification.tex Fri Aug 18 10:34:08 2000 +0200 @@ -18,7 +18,7 @@ \begin{quote} \begin{isabelle}% -n\ {\isasymnoteq}\ 0\ {\isasymLongrightarrow}\ m\ mod\ n\ <\ n +\mbox{n}\ {\isasymnoteq}\ 0\ {\isasymLongrightarrow}\ \mbox{m}\ mod\ \mbox{n}\ <\ \mbox{n} \end{isabelle}% \end{quote} @@ -33,7 +33,7 @@ \begin{quote} \begin{isabelle}% -gcd\ (m,\ n)\ =\ k +gcd\ (\mbox{m},\ \mbox{n})\ =\ \mbox{k} \end{isabelle}% \end{quote} @@ -41,7 +41,7 @@ \begin{quote} \begin{isabelle}% -(if\ n\ =\ 0\ then\ m\ else\ gcd\ (n,\ m\ mod\ n))\ =\ k +(if\ \mbox{n}\ =\ 0\ then\ \mbox{m}\ else\ gcd\ (\mbox{n},\ \mbox{m}\ mod\ \mbox{n}))\ =\ \mbox{k} \end{isabelle}% \end{quote} @@ -49,11 +49,11 @@ \begin{quote} \begin{isabelle}% -(n\ =\ 0\ {\isasymlongrightarrow}\ m\ =\ k)\ {\isasymand}\ (n\ {\isasymnoteq}\ 0\ {\isasymlongrightarrow}\ gcd\ (n,\ m\ mod\ n)\ =\ k) +(\mbox{n}\ =\ 0\ {\isasymlongrightarrow}\ \mbox{m}\ =\ \mbox{k})\ {\isasymand}\ (\mbox{n}\ {\isasymnoteq}\ 0\ {\isasymlongrightarrow}\ gcd\ (\mbox{n},\ \mbox{m}\ mod\ \mbox{n})\ =\ \mbox{k}) \end{isabelle}% \end{quote} -Since the recursive call \isa{gcd\ (n,\ m\ mod\ n)} is no longer protected by +Since the recursive call \isa{gcd\ (\mbox{n},\ \mbox{m}\ mod\ \mbox{n})} is no longer protected by an \isa{if}, it is unfolded again, which leads to an infinite chain of simplification steps. Fortunately, this problem can be avoided in many different ways.