--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/IMP/Def_Init_Small.thy Thu Nov 22 08:23:13 2012 +0100
@@ -0,0 +1,27 @@
+(* Author: Tobias Nipkow *)
+
+theory Def_Init_Small
+imports Star Com Def_Init_Exp
+begin
+
+subsection "Initialization-Sensitive Small Step Semantics"
+
+inductive
+ small_step :: "(com \<times> state) \<Rightarrow> (com \<times> state) \<Rightarrow> bool" (infix "\<rightarrow>" 55)
+where
+Assign: "aval a s = Some i \<Longrightarrow> (x ::= a, s) \<rightarrow> (SKIP, s(x := Some i))" |
+
+Seq1: "(SKIP;c,s) \<rightarrow> (c,s)" |
+Seq2: "(c\<^isub>1,s) \<rightarrow> (c\<^isub>1',s') \<Longrightarrow> (c\<^isub>1;c\<^isub>2,s) \<rightarrow> (c\<^isub>1';c\<^isub>2,s')" |
+
+IfTrue: "bval b s = Some True \<Longrightarrow> (IF b THEN c\<^isub>1 ELSE c\<^isub>2,s) \<rightarrow> (c\<^isub>1,s)" |
+IfFalse: "bval b s = Some False \<Longrightarrow> (IF b THEN c\<^isub>1 ELSE c\<^isub>2,s) \<rightarrow> (c\<^isub>2,s)" |
+
+While: "(WHILE b DO c,s) \<rightarrow> (IF b THEN c; WHILE b DO c ELSE SKIP,s)"
+
+lemmas small_step_induct = small_step.induct[split_format(complete)]
+
+abbreviation small_steps :: "com * state \<Rightarrow> com * state \<Rightarrow> bool" (infix "\<rightarrow>*" 55)
+where "x \<rightarrow>* y == star small_step x y"
+
+end