
diff -r f51d4a302962 -r 5386df44a037 src/Doc/Tutorial/Misc/case_exprs.thy
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+++ b/src/Doc/Tutorial/Misc/case_exprs.thy	Tue Aug 28 18:57:32 2012 +0200
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+(*<*)
+theory case_exprs imports Main begin
+(*>*)
+
+text{*
+\subsection{Case Expressions}
+\label{sec:case-expressions}\index{*case expressions}%
+HOL also features \isa{case}-expressions for analyzing
+elements of a datatype. For example,
+@{term[display]"case xs of [] => [] | y#ys => y"}
+evaluates to @{term"[]"} if @{term"xs"} is @{term"[]"} and to @{term"y"} if 
+@{term"xs"} is @{term"y#ys"}. (Since the result in both branches must be of
+the same type, it follows that @{term y} is of type @{typ"'a list"} and hence
+that @{term xs} is of type @{typ"'a list list"}.)
+
+In general, case expressions are of the form
+\[
+\begin{array}{c}
+@{text"case"}~e~@{text"of"}\ pattern@1~@{text"\<Rightarrow>"}~e@1\ @{text"|"}\ \dots\
+ @{text"|"}~pattern@m~@{text"\<Rightarrow>"}~e@m
+\end{array}
+\]
+Like in functional programming, patterns are expressions consisting of
+datatype constructors (e.g. @{term"[]"} and @{text"#"})
+and variables, including the wildcard ``\verb$_$''.
+Not all cases need to be covered and the order of cases matters.
+However, one is well-advised not to wallow in complex patterns because
+complex case distinctions tend to induce complex proofs.
+
+\begin{warn}
+Internally Isabelle only knows about exhaustive case expressions with
+non-nested patterns: $pattern@i$ must be of the form
+$C@i~x@ {i1}~\dots~x@ {ik@i}$ and $C@1, \dots, C@m$ must be exactly the
+constructors of the type of $e$.
+%
+More complex case expressions are automatically
+translated into the simpler form upon parsing but are not translated
+back for printing. This may lead to surprising output.
+\end{warn}
+
+\begin{warn}
+Like @{text"if"}, @{text"case"}-expressions may need to be enclosed in
+parentheses to indicate their scope.
+\end{warn}
+
+\subsection{Structural Induction and Case Distinction}
+\label{sec:struct-ind-case}
+\index{case distinctions}\index{induction!structural}%
+Induction is invoked by \methdx{induct_tac}, as we have seen above; 
+it works for any datatype.  In some cases, induction is overkill and a case
+distinction over all constructors of the datatype suffices.  This is performed
+by \methdx{case_tac}.  Here is a trivial example:
+*}
+
+lemma "(case xs of [] \<Rightarrow> [] | y#ys \<Rightarrow> xs) = xs";
+apply(case_tac xs);
+
+txt{*\noindent
+results in the proof state
+@{subgoals[display,indent=0,margin=65]}
+which is solved automatically:
+*}
+
+apply(auto)
+(*<*)done(*>*)
+text{*
+Note that we do not need to give a lemma a name if we do not intend to refer
+to it explicitly in the future.
+Other basic laws about a datatype are applied automatically during
+simplification, so no special methods are provided for them.
+
+\begin{warn}
+  Induction is only allowed on free (or \isasymAnd-bound) variables that
+  should not occur among the assumptions of the subgoal; see
+  \S\ref{sec:ind-var-in-prems} for details. Case distinction
+  (@{text"case_tac"}) works for arbitrary terms, which need to be
+  quoted if they are non-atomic. However, apart from @{text"\<And>"}-bound
+  variables, the terms must not contain variables that are bound outside.
+  For example, given the goal @{prop"\<forall>xs. xs = [] \<or> (\<exists>y ys. xs = y#ys)"},
+  @{text"case_tac xs"} will not work as expected because Isabelle interprets
+  the @{term xs} as a new free variable distinct from the bound
+  @{term xs} in the goal.
+\end{warn}
+*}
+
+(*<*)
+end
+(*>*)




