doc-src/TutorialI/Misc/asm_simp.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/doc-src/TutorialI/Misc/asm_simp.thy	Wed Apr 19 11:56:31 2000 +0200
@@ -0,0 +1,49 @@
+(*<*)
+theory asm_simp = Main:;
+
+(*>*)text{*
+By default, assumptions are part of the simplification process: they are used
+as simplification rules and are simplified themselves. For example:
+*}
+
+lemma "\\<lbrakk> xs @ zs = ys @ xs; [] @ xs = [] @ [] \\<rbrakk> \\<Longrightarrow> ys = zs";
+apply simp.;
+
+text{*\noindent
+The second assumption simplifies to \isa{xs = []}, which in turn
+simplifies the first assumption to \isa{zs = ys}, thus reducing the
+conclusion to \isa{ys = ys} and hence to \isa{True}.
+
+In some cases this may be too much of a good thing and may lead to
+nontermination:
+*}
+
+lemma "\\<forall>x. f x = g (f (g x)) \\<Longrightarrow> f [] = f [] @ []";
+
+txt{*\noindent
+cannot be solved by an unmodified application of \isa{simp} because the
+simplification rule \isa{f x = g(f(g x))} extracted from the assumption
+does not terminate. Isabelle notices certain simple forms of
+nontermination but not this one. The problem can be circumvented by
+explicitly telling the simplifier to ignore the assumptions:
+*}
+
+apply(simp no_asm:).;
+
+text{*\noindent
+There are three modifiers that influence the treatment of assumptions:
+\begin{description}
+\item[\isaindexbold{no_asm:}] means that assumptions are completely ignored.
+\item[\isaindexbold{no_asm_simp:}] means that the assumptions are not simplified but
+  are used in the simplification of the conclusion.
+\item[\isaindexbold{no_asm_use:}] means that the assumptions are simplified
+but are not
+  used in the simplification of each other or the conclusion.
+\end{description}
+Neither \isa{no_asm_simp:} nor \isa{no_asm_use:} allow to simplify the above
+problematic subgoal.
+
+Note that only one of the above modifiers is allowed, and it must precede all
+other modifiers.
+*}
+(*<*)end(*>*)