--- a/CookBook/Tactical.thy	Thu Mar 12 18:39:10 2009 +0000
+++ b/CookBook/Tactical.thy	Fri Mar 13 01:15:55 2009 +0100
@@ -1762,9 +1762,9 @@
 
   Note that the actual response in this example is @{term "2 + 10 \<equiv> 2 + (10::nat)"}, 
   since the pretty-printer for @{ML_type cterm}s already beta-normalises terms.
-  But by the way how we constructed the term (using the function 
-  @{ML Thm.capply}, which is the application @{ML $} for @{ML_type cterm}s),
-  we can be sure the left-hand side must contain beta-redexes. Indeed
+  But how we constructed the term (using the function 
+  @{ML Thm.capply}, which is the application @{ML $} for @{ML_type cterm}s)
+  ensures that the left-hand side must contain beta-redexes. Indeed
   if we obtain the ``raw'' representation of the produced theorem, we
   can see the difference:
 
@@ -1808,7 +1808,7 @@
 
 text {* 
   You can see how this function works in the example rewriting 
-  the @{ML_type cterm} @{term "True \<and> (Foo \<longrightarrow> Bar)"} to @{term "Foo \<longrightarrow> Bar"}.
+  @{term "True \<and> (Foo \<longrightarrow> Bar)"} to @{term "Foo \<longrightarrow> Bar"}.
 
   @{ML_response_fake [display,gray]
 "let 
@@ -1861,6 +1861,14 @@
   does not fail, however, because the combinator @{ML Conv.else_conv} will then 
   try out @{ML Conv.all_conv}, which always succeeds.
 
+  The conversion combinator @{ML Conv.try_conv} constructs a conversion 
+  which is tried out on a term, but in case of failure just does nothing.
+  For example
+  
+  @{ML_response_fake [display,gray]
+  "Conv.try_conv (Conv.rewr_conv @{thm true_conj1}) @{cterm \"True \<or> P\"}"
+  "True \<or> P \<equiv> True \<or> P"}
+
   Apart from the function @{ML beta_conversion in Thm}, which is able to fully
   beta-normalise a term, the conversions so far are restricted in that they
   only apply to the outer-most level of a @{ML_type cterm}. In what follows we
@@ -2028,8 +2036,6 @@
   and simprocs; the advantage of conversions, however, is that you never have
   to worry about non-termination.
 
-  (FIXME: explain @{ML Conv.try_conv})
-
   \begin{exercise}\label{ex:addconversion}
   Write a tactic that does the same as the simproc in exercise
   \ref{ex:addsimproc}, but is based in conversions. That means replace terms
@@ -2038,7 +2044,7 @@
   \end{exercise}
 
   \begin{exercise}\label{ex:compare}
-  Compare your solutions of Exercises~\ref{addsimproc} and \ref{ex:addconversion},
+  Compare your solutions of Exercises~\ref{ex:addsimproc} and \ref{ex:addconversion},
   and try to determine which way of rewriting such terms is faster. For this you might 
   have to construct quite large terms. Also see Recipe \ref{rec:timing} for information 
   about timing.