src/HOL/IMP/VC.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/IMP/VC.thy	Tue Jan 23 10:59:35 1996 +0100
@@ -0,0 +1,45 @@
+(*  Title: 	HOL/IMP/VC.thy
+    ID:         $Id$
+    Author: 	Tobias Nipkow
+    Copyright   1996 TUM
+
+acom: annotated commands
+vc:   verification-conditions
+wp:   weakest (liberal) precondition
+*)
+
+VC  =  Hoare +
+
+datatype  acom = Askip
+               | Aass   loc aexp
+               | Asemi  acom acom
+               | Aif    bexp acom acom
+               | Awhile bexp assn acom
+
+consts
+  vc,wp :: acom => assn => assn
+  astrip :: acom => com
+
+primrec wp acom
+  wp_Askip  "wp Askip Q = Q"
+  wp_Aass   "wp (Aass x a) Q = (%s.Q(s[A a s/x]))"
+  wp_Asemi  "wp (Asemi c d) Q = wp c (wp d Q)"
+  wp_Aif    "wp (Aif b c d) Q = (%s. (B b s-->wp c Q s)&(~B b s-->wp d Q s))" 
+  wp_Awhile "wp (Awhile b I c) Q = I"
+
+primrec vc acom
+  vc_Askip  "vc Askip Q = (%s.True)"
+  vc_Aass   "vc (Aass x a) Q = (%s.True)"
+  vc_Asemi  "vc (Asemi c d) Q = (%s. vc c (wp d Q) s & vc d Q s)"
+  vc_Aif    "vc (Aif b c d) Q = (%s. vc c Q s & vc d Q s)" 
+  vc_Awhile "vc (Awhile b I c) Q = (%s. (I s & ~B b s --> Q s) &
+                              (I s & B b s --> wp c I s) & vc c I s)"
+
+primrec astrip acom
+  astrip_Askip  "astrip Askip = skip"
+  astrip_Aass   "astrip (Aass x a) = (x:=a)"
+  astrip_Asemi  "astrip (Asemi c d) = (astrip c;astrip d)"
+  astrip_Aif    "astrip (Aif b c d) = ifC b (astrip c) (astrip d)"
+  astrip_Awhile "astrip (Awhile b I c) = whileC b (astrip c)"
+  
+end