diff -r 499637e8f2c6 -r 0376cccd9118 doc-src/TutorialI/Recdef/document/termination.tex --- a/doc-src/TutorialI/Recdef/document/termination.tex Wed Oct 11 09:09:06 2000 +0200 +++ b/doc-src/TutorialI/Recdef/document/termination.tex Wed Oct 11 10:44:42 2000 +0200 @@ -9,7 +9,7 @@ measure of the argument goes down in each recursive call. As a result, $f$\isa{{\isachardot}simps} will contain the defining equations (or variants derived from them) as theorems. For example, look (via \isacommand{thm}) at -\isa{sep{\isachardot}simps} and \isa{sep\isadigit{1}{\isachardot}simps} to see that they define +\isa{sep{\isachardot}simps} and \isa{sep{\isadigit{1}}{\isachardot}simps} to see that they define the same function. What is more, those equations are automatically declared as simplification rules. @@ -19,7 +19,7 @@ \end{isamarkuptext}% \isacommand{consts}\ f\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}nat{\isasymtimes}nat\ {\isasymRightarrow}\ nat{\isachardoublequote}\isanewline \isacommand{recdef}\ f\ {\isachardoublequote}measure{\isacharparenleft}{\isasymlambda}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}\ x{\isacharminus}y{\isacharparenright}{\isachardoublequote}\isanewline -\ \ {\isachardoublequote}f{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ x\ {\isasymle}\ y\ then\ x\ else\ f{\isacharparenleft}x{\isacharcomma}y{\isacharplus}\isadigit{1}{\isacharparenright}{\isacharparenright}{\isachardoublequote}% +\ \ {\isachardoublequote}f{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ x\ {\isasymle}\ y\ then\ x\ else\ f{\isacharparenleft}x{\isacharcomma}y{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isacharparenright}{\isachardoublequote}% \begin{isamarkuptext}% \noindent is not proved automatically (although maybe it should be). Isabelle prints a @@ -43,7 +43,7 @@ \end{isamarkuptext}% \isacommand{consts}\ g\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequote}nat{\isasymtimes}nat\ {\isasymRightarrow}\ nat{\isachardoublequote}\isanewline \isacommand{recdef}\ g\ {\isachardoublequote}measure{\isacharparenleft}{\isasymlambda}{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}{\isachardot}\ x{\isacharminus}y{\isacharparenright}{\isachardoublequote}\isanewline -\ \ {\isachardoublequote}g{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ x\ {\isasymle}\ y\ then\ x\ else\ g{\isacharparenleft}x{\isacharcomma}y{\isacharplus}\isadigit{1}{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isanewline +\ \ {\isachardoublequote}g{\isacharparenleft}x{\isacharcomma}y{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ x\ {\isasymle}\ y\ then\ x\ else\ g{\isacharparenleft}x{\isacharcomma}y{\isacharplus}{\isadigit{1}}{\isacharparenright}{\isacharparenright}{\isachardoublequote}\isanewline {\isacharparenleft}\isakeyword{hints}\ recdef{\isacharunderscore}simp{\isacharcolon}\ termi{\isacharunderscore}lem{\isacharparenright}% \begin{isamarkuptext}% \noindent @@ -51,7 +51,7 @@ the stated recursion equation for \isa{g} and they are simplification rules. Thus we can automatically prove% \end{isamarkuptext}% -\isacommand{theorem}\ {\isachardoublequote}g{\isacharparenleft}\isadigit{1}{\isacharcomma}\isadigit{0}{\isacharparenright}\ {\isacharequal}\ g{\isacharparenleft}\isadigit{1}{\isacharcomma}\isadigit{1}{\isacharparenright}{\isachardoublequote}\isanewline +\isacommand{theorem}\ {\isachardoublequote}g{\isacharparenleft}{\isadigit{1}}{\isacharcomma}{\isadigit{0}}{\isacharparenright}\ {\isacharequal}\ g{\isacharparenleft}{\isadigit{1}}{\isacharcomma}{\isadigit{1}}{\isacharparenright}{\isachardoublequote}\isanewline \isacommand{apply}{\isacharparenleft}simp{\isacharparenright}\isanewline \isacommand{done}% \begin{isamarkuptext}%