--- a/doc-src/TutorialI/Recdef/Nested1.thy Mon Oct 09 09:33:45 2000 +0200
+++ b/doc-src/TutorialI/Recdef/Nested1.thy Mon Oct 09 10:18:21 2000 +0200
@@ -4,12 +4,12 @@
consts trev :: "('a,'b)term \<Rightarrow> ('a,'b)term";
text{*\noindent
-Although the definition of @{term"trev"} is quite natural, we will have
+Although the definition of @{term trev} is quite natural, we will have
overcome a minor difficulty in convincing Isabelle of is termination.
It is precisely this difficulty that is the \textit{raison d'\^etre} of
this subsection.
-Defining @{term"trev"} by \isacommand{recdef} rather than \isacommand{primrec}
+Defining @{term trev} by \isacommand{recdef} rather than \isacommand{primrec}
simplifies matters because we are now free to use the recursion equation
suggested at the end of \S\ref{sec:nested-datatype}:
*};
@@ -19,22 +19,22 @@
"trev (App f ts) = App f (rev(map trev ts))";
text{*\noindent
-Remember that function @{term"size"} is defined for each \isacommand{datatype}.
+Remember that function @{term size} is defined for each \isacommand{datatype}.
However, the definition does not succeed. Isabelle complains about an
unproved termination condition
@{term[display]"t : set ts --> size t < Suc (term_list_size ts)"}
-where @{term"set"} returns the set of elements of a list
+where @{term set} returns the set of elements of a list
and @{text"term_list_size :: term list \<Rightarrow> nat"} is an auxiliary
function automatically defined by Isabelle
-(when @{text"term"} was defined). First we have to understand why the
-recursive call of @{term"trev"} underneath @{term"map"} leads to the above
-condition. The reason is that \isacommand{recdef} ``knows'' that @{term"map"}
-will apply @{term"trev"} only to elements of @{term"ts"}. Thus the above
-condition expresses that the size of the argument @{term"t : set ts"} of any
-recursive call of @{term"trev"} is strictly less than @{term"size(App f ts) =
+(when @{text term} was defined). First we have to understand why the
+recursive call of @{term trev} underneath @{term map} leads to the above
+condition. The reason is that \isacommand{recdef} ``knows'' that @{term map}
+will apply @{term trev} only to elements of @{term ts}. Thus the above
+condition expresses that the size of the argument @{prop"t : set ts"} of any
+recursive call of @{term trev} is strictly less than @{prop"size(App f ts) =
Suc(term_list_size ts)"}. We will now prove the termination condition and
continue with our definition. Below we return to the question of how
-\isacommand{recdef} ``knows'' about @{term"map"}.
+\isacommand{recdef} ``knows'' about @{term map}.
*};
(*<*)