--- a/src/HOL/IMP/Big_Step.thy Thu Nov 03 10:29:05 2011 +1100
+++ b/src/HOL/IMP/Big_Step.thy Thu Nov 03 15:54:19 2011 +1100
@@ -4,6 +4,7 @@
subsection "Big-Step Semantics of Commands"
+text_raw{*\begin{isaverbatimwrite}\newcommand{\BigStepdef}{% *}
inductive
big_step :: "com \<times> state \<Rightarrow> state \<Rightarrow> bool" (infix "\<Rightarrow>" 55)
where
@@ -20,6 +21,7 @@
WhileFalse: "\<not>bval b s \<Longrightarrow> (WHILE b DO c,s) \<Rightarrow> s" |
WhileTrue: "\<lbrakk> bval b s\<^isub>1; (c,s\<^isub>1) \<Rightarrow> s\<^isub>2; (WHILE b DO c, s\<^isub>2) \<Rightarrow> s\<^isub>3 \<rbrakk> \<Longrightarrow>
(WHILE b DO c, s\<^isub>1) \<Rightarrow> s\<^isub>3"
+text_raw{*}\end{isaverbatimwrite}*}
schematic_lemma ex: "(''x'' ::= N 5; ''y'' ::= V ''x'', s) \<Rightarrow> ?t"
apply(rule Semi)
@@ -126,9 +128,11 @@
in @{text s'} iff @{text c'} started in the same @{text s} also terminates
in the same @{text s'}}. Formally:
*}
+text_raw{*\begin{isaverbatimwrite}\newcommand{\BigStepEquiv}{% *}
abbreviation
equiv_c :: "com \<Rightarrow> com \<Rightarrow> bool" (infix "\<sim>" 50) where
"c \<sim> c' == (\<forall>s t. (c,s) \<Rightarrow> t = (c',s) \<Rightarrow> t)"
+text_raw{*}\end{isaverbatimwrite}*}
text {*
Warning: @{text"\<sim>"} is the symbol written \verb!\ < s i m >! (without spaces).
@@ -196,7 +200,7 @@
text {* Luckily, such lengthy proofs are seldom necessary. Isabelle can
prove many such facts automatically. *}
-lemma
+lemma while_unfold:
"(WHILE b DO c) \<sim> (IF b THEN c; WHILE b DO c ELSE SKIP)"
by blast
@@ -214,15 +218,17 @@
subsection "Execution is deterministic"
text {* This proof is automatic. *}
+text_raw{*\begin{isaverbatimwrite}\newcommand{\BigStepDeterministic}{% *}
theorem big_step_determ: "\<lbrakk> (c,s) \<Rightarrow> t; (c,s) \<Rightarrow> u \<rbrakk> \<Longrightarrow> u = t"
-apply (induction arbitrary: u rule: big_step.induct)
-apply blast+
-done
+ by (induction arbitrary: u rule: big_step.induct) blast+
+text_raw{*}\end{isaverbatimwrite}*}
+
text {*
This is the proof as you might present it in a lecture. The remaining
cases are simple enough to be proved automatically:
*}
+text_raw{*\begin{isaverbatimwrite}\newcommand{\BigStepDet2}{% *}
theorem
"(c,s) \<Rightarrow> t \<Longrightarrow> (c,s) \<Rightarrow> t' \<Longrightarrow> t' = t"
proof (induction arbitrary: t' rule: big_step.induct)
@@ -242,6 +248,6 @@
from c IHc have "s1' = s1" by blast
with w IHw show "t' = t" by blast
qed blast+ -- "prove the rest automatically"
-
+text_raw{*}\end{isaverbatimwrite}*}
end