src/HOL/IMP/Def_Ass_Big.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/IMP/Def_Ass_Big.thy	Mon Jun 06 16:29:38 2011 +0200
@@ -0,0 +1,31 @@
+(* Author: Tobias Nipkow *)
+
+theory Def_Ass_Big imports Com Def_Ass_Exp
+begin
+
+subsection "Initialization-Sensitive Big Step Semantics"
+
+inductive
+  big_step :: "(com \<times> state option) \<Rightarrow> state option \<Rightarrow> bool" (infix "\<Rightarrow>" 55)
+where
+None: "(c,None) \<Rightarrow> None" |
+Skip: "(SKIP,s) \<Rightarrow> s" |
+AssignNone: "aval a s = None \<Longrightarrow> (x ::= a, Some s) \<Rightarrow> None" |
+Assign: "aval a s = Some i \<Longrightarrow> (x ::= a, Some s) \<Rightarrow> Some(s(x := Some i))" |
+Semi:   "(c\<^isub>1,s\<^isub>1) \<Rightarrow> s\<^isub>2 \<Longrightarrow> (c\<^isub>2,s\<^isub>2) \<Rightarrow> s\<^isub>3 \<Longrightarrow> (c\<^isub>1;c\<^isub>2,s\<^isub>1) \<Rightarrow> s\<^isub>3" |
+
+IfNone:  "bval b s = None \<Longrightarrow> (IF b THEN c\<^isub>1 ELSE c\<^isub>2,Some s) \<Rightarrow> None" |
+IfTrue:  "\<lbrakk> bval b s = Some True;  (c\<^isub>1,Some s) \<Rightarrow> s' \<rbrakk> \<Longrightarrow>
+  (IF b THEN c\<^isub>1 ELSE c\<^isub>2,Some s) \<Rightarrow> s'" |
+IfFalse: "\<lbrakk> bval b s = Some False;  (c\<^isub>2,Some s) \<Rightarrow> s' \<rbrakk> \<Longrightarrow>
+  (IF b THEN c\<^isub>1 ELSE c\<^isub>2,Some s) \<Rightarrow> s'" |
+
+WhileNone: "bval b s = None \<Longrightarrow> (WHILE b DO c,Some s) \<Rightarrow> None" |
+WhileFalse: "bval b s = Some False \<Longrightarrow> (WHILE b DO c,Some s) \<Rightarrow> Some s" |
+WhileTrue:
+  "\<lbrakk> bval b s = Some True;  (c,Some s) \<Rightarrow> s';  (WHILE b DO c,s') \<Rightarrow> s'' \<rbrakk> \<Longrightarrow>
+  (WHILE b DO c,Some s) \<Rightarrow> s''"
+
+lemmas big_step_induct = big_step.induct[split_format(complete)]
+
+end