diff -r c93ae0eb9631 -r a6fb4ddc05c7 doc-src/TutorialI/Advanced/Partial.thy --- a/doc-src/TutorialI/Advanced/Partial.thy Mon May 02 08:17:16 2005 +0200 +++ b/doc-src/TutorialI/Advanced/Partial.thy Mon May 02 10:56:13 2005 +0200 @@ -49,7 +49,7 @@ \index{recursion!guarded}% Neither \isacommand{primrec} nor \isacommand{recdef} allow to prefix an equation with a condition in the way ordinary definitions do -(see @{term minus} above). Instead we have to move the condition over +(see @{const minus} above). Instead we have to move the condition over to the right-hand side of the equation. Given a partial function $f$ that should satisfy the recursion equation $f(x) = t$ over its domain $dom(f)$, we turn this into the \isacommand{recdef} @@ -117,7 +117,7 @@ well-foundedness of the relation given to \isacommand{recdef} is immediate. Furthermore, each recursive call descends along that relation: the first argument stays unchanged and the second one descends along @{term"step1 -f"}. The proof requires unfolding the definition of @{term step1}, +f"}. The proof requires unfolding the definition of @{const step1}, as specified in the \isacommand{hints} above. Normally you will then derive the following conditional variant from @@ -157,7 +157,7 @@ x := s; while b(x) do x := c(x); return x \end{verbatim} In general, @{term s} will be a tuple or record. As an example -consider the following definition of function @{term find}: +consider the following definition of function @{const find}: *} constdefs find2 :: "('a \ 'a) \ 'a \ 'a" @@ -181,7 +181,7 @@ (premise~3). And each loop iteration must descend along a well-founded relation @{term r} (premises 4 and~5). -Let us now prove that @{term find2} does indeed find a fixed point. Instead +Let us now prove that @{const find2} does indeed find a fixed point. Instead of induction we apply the above while rule, suitably instantiated. Only the final premise of @{thm[source]while_rule} is left unproved by @{text auto} but falls to @{text simp}: