# HG changeset patch # User paulson # Date 975947388 -3600 # Node ID b9c290f0343d2c8f7614c42f78a97334e0bcbd16 # Parent 92d3cbea80b2ce77503038032349fdc5b0dd23a4 auto update diff -r 92d3cbea80b2 -r b9c290f0343d doc-src/TutorialI/Advanced/document/WFrec.tex --- a/doc-src/TutorialI/Advanced/document/WFrec.tex Fri Dec 01 20:24:08 2000 +0100 +++ b/doc-src/TutorialI/Advanced/document/WFrec.tex Mon Dec 04 17:29:48 2000 +0100 @@ -25,9 +25,8 @@ In general, \isacommand{recdef} supports termination proofs based on arbitrary well-founded relations as introduced in \S\ref{sec:Well-founded}. This is called \textbf{well-founded -recursion}\indexbold{recursion!well-founded}\index{well-founded -recursion|see{recursion, well-founded}}. Clearly, a function definition is -total iff the set of all pairs $(r,l)$, where $l$ is the argument on the +recursion}\indexbold{recursion!well-founded}. Clearly, a function definition +is total iff the set of all pairs $(r,l)$, where $l$ is the argument on the left-hand side of an equation and $r$ the argument of some recursive call on the corresponding right-hand side, induces a well-founded relation. For a systematic account of termination proofs via well-founded relations see, for diff -r 92d3cbea80b2 -r b9c290f0343d doc-src/TutorialI/Types/document/Pairs.tex --- a/doc-src/TutorialI/Types/document/Pairs.tex Fri Dec 01 20:24:08 2000 +0100 +++ b/doc-src/TutorialI/Types/document/Pairs.tex Mon Dec 04 17:29:48 2000 +0100 @@ -154,7 +154,8 @@ \begin{isamarkuptxt}% \noindent \begin{isabelle}% -\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ b\ aa\ ba{\isachardot}\ swap\ {\isacharparenleft}swap\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}aa{\isacharcomma}\ ba{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}aa{\isacharcomma}\ ba{\isacharparenright}% +\ {\isadigit{1}}{\isachardot}\ {\isasymAnd}a\ b\ aa\ ba{\isachardot}\isanewline +\ \ \ \ \ \ \ swap\ {\isacharparenleft}swap\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}aa{\isacharcomma}\ ba{\isacharparenright}\ {\isasymlongrightarrow}\ {\isacharparenleft}a{\isacharcomma}\ b{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}aa{\isacharcomma}\ ba{\isacharparenright}% \end{isabelle}% \end{isamarkuptxt}% \isacommand{apply}\ simp\isanewline