diff -r 6417de2029b0 -r b254d5ad6dd4 doc-src/TutorialI/Advanced/document/WFrec.tex --- a/doc-src/TutorialI/Advanced/document/WFrec.tex Fri Jan 12 16:05:12 2001 +0100 +++ b/doc-src/TutorialI/Advanced/document/WFrec.tex Fri Jan 12 16:07:20 2001 +0100 @@ -30,11 +30,11 @@ 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 -example, \cite{Baader-Nipkow}. +example, Baader and Nipkow~\cite{Baader-Nipkow}. Each \isacommand{recdef} definition should be accompanied (after the name of the function) by a well-founded relation on the argument type of the -function. The HOL library formalizes some of the most important +function. HOL formalizes some of the most important constructions of well-founded relations (see \S\ref{sec:Well-founded}). For example, \isa{measure\ f} is always well-founded, and the lexicographic product of two well-founded relations is again well-founded, which we relied @@ -50,7 +50,7 @@ {\isachardoublequote}contrived{\isacharparenleft}{\isadigit{0}}{\isacharcomma}{\isadigit{0}}{\isacharcomma}{\isadigit{0}}{\isacharparenright}\ \ \ \ \ {\isacharequal}\ {\isadigit{0}}{\isachardoublequote}% \begin{isamarkuptext}% Lexicographic products of measure functions already go a long -way. Furthermore you may embed some type in an +way. Furthermore, you may embed a type in an existing well-founded relation via the inverse image construction \isa{inv{\isacharunderscore}image}. All these constructions are known to \isacommand{recdef}. Thus you will never have to prove well-foundedness of any relation composed solely of these building blocks. But of course the proof of