# HG changeset patch
# User nipkow
# Date 1047391464 -3600
# Node ID 11d7c5a8dbb79bc98ffa4e991f51e22bab40fdda
# Parent  f5d08c341216aa1af328317cee13045f25f82321
*** empty log message ***

diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/Examples.thy
--- a/src/HOL/Hoare/Examples.thy	Tue Mar 11 15:04:24 2003 +0100
+++ b/src/HOL/Hoare/Examples.thy	Tue Mar 11 15:04:24 2003 +0100
@@ -45,7 +45,7 @@
 lemma Euclid_GCD: "VARS a b
  {0<A & 0<B}
  a := A; b := B;
- WHILE  a~=b
+ WHILE  a \<noteq> b
  INV {0<a & 0<b & gcd A B = gcd a b}
  DO IF a<b THEN b := b-a ELSE a := a-b FI OD
  {a = gcd A B}"
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/ExamplesAbort.thy
--- a/src/HOL/Hoare/ExamplesAbort.thy	Tue Mar 11 15:04:24 2003 +0100
+++ b/src/HOL/Hoare/ExamplesAbort.thy	Tue Mar 11 15:04:24 2003 +0100
@@ -1,3 +1,12 @@
+(*  Title:      HOL/Hoare/ExamplesAbort.thy
+    ID:         $Id$
+    Author:     Tobias Nipkow
+    Copyright   1998 TUM
+
+Some small examples for programs that may abort.
+Currently only show the absence of abort.
+*)
+
 theory ExamplesAbort = HoareAbort:
 
 syntax guarded_com :: "'bool \<Rightarrow> 'a com \<Rightarrow> 'a com"  ("_ \<rightarrow> _" 60)
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/Hoare.thy
--- a/src/HOL/Hoare/Hoare.thy	Tue Mar 11 15:04:24 2003 +0100
+++ b/src/HOL/Hoare/Hoare.thy	Tue Mar 11 15:04:24 2003 +0100
@@ -60,7 +60,7 @@
 ML{*
 
 local
-fun free a = Free(a,dummyT)
+
 fun abs((a,T),body) =
   let val a = absfree(a, dummyT, body)
   in if T = Bound 0 then a else Const(Syntax.constrainAbsC,dummyT) $ a $ T end
@@ -70,9 +70,9 @@
   | mk_abstuple (x::xs) body =
       Syntax.const "split" $ abs (x, mk_abstuple xs body);
 
-fun mk_fbody a e [x as (b,_)] = if a=b then e else free b
+fun mk_fbody a e [x as (b,_)] = if a=b then e else Syntax.free b
   | mk_fbody a e ((b,_)::xs) =
-      Syntax.const "Pair" $ (if a=b then e else free b) $ mk_fbody a e xs;
+      Syntax.const "Pair" $ (if a=b then e else Syntax.free b) $ mk_fbody a e xs;
 
 fun mk_fexp a e xs = mk_abstuple xs (mk_fbody a e xs)
 end
@@ -193,6 +193,38 @@
 
 print_translation {* [("Valid", spec_tr')] *}
 
+lemma SkipRule: "p \<subseteq> q \<Longrightarrow> Valid p (Basic id) q"
+by (auto simp:Valid_def)
+
+lemma BasicRule: "p \<subseteq> {s. f s \<in> q} \<Longrightarrow> Valid p (Basic f) q"
+by (auto simp:Valid_def)
+
+lemma SeqRule: "Valid P c1 Q \<Longrightarrow> Valid Q c2 R \<Longrightarrow> Valid P (c1;c2) R"
+by (auto simp:Valid_def)
+
+lemma CondRule:
+ "p \<subseteq> {s. (s \<in> b \<longrightarrow> s \<in> w) \<and> (s \<notin> b \<longrightarrow> s \<in> w')}
+  \<Longrightarrow> Valid w c1 q \<Longrightarrow> Valid w' c2 q \<Longrightarrow> Valid p (Cond b c1 c2) q"
+by (auto simp:Valid_def)
+
+lemma iter_aux: "! s s'. Sem c s s' --> s : I & s : b --> s' : I ==>
+       (\<And>s s'. s : I \<Longrightarrow> iter n b (Sem c) s s' \<Longrightarrow> s' : I & s' ~: b)";
+apply(induct n)
+ apply clarsimp
+apply(simp (no_asm_use))
+apply blast
+done
+
+lemma WhileRule:
+ "p \<subseteq> i \<Longrightarrow> Valid (i \<inter> b) c i \<Longrightarrow> i \<inter> (-b) \<subseteq> q \<Longrightarrow> Valid p (While b i c) q"
+apply (clarsimp simp:Valid_def)
+apply(drule iter_aux)
+  prefer 2 apply assumption
+ apply blast
+apply blast
+done
+
+
 use "hoare.ML"
 
 method_setup vcg = {*
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/HoareAbort.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Hoare/HoareAbort.thy	Tue Mar 11 15:04:24 2003 +0100
@@ -0,0 +1,250 @@
+(*  Title:      HOL/Hoare/HoareAbort.thy
+    ID:         $Id$
+    Author:     Leonor Prensa Nieto & Tobias Nipkow
+    Copyright   2003 TUM
+
+Like Hoare.thy, but with an Abort statement for modelling run time errors.
+*)
+
+theory HoareAbort  = Main
+files ("hoareAbort.ML"):
+
+types
+    'a bexp = "'a set"
+    'a assn = "'a set"
+
+datatype
+ 'a com = Basic "'a \<Rightarrow> 'a"
+   | Abort
+   | Seq "'a com" "'a com"               ("(_;/ _)"      [61,60] 60)
+   | Cond "'a bexp" "'a com" "'a com"    ("(1IF _/ THEN _ / ELSE _/ FI)"  [0,0,0] 61)
+   | While "'a bexp" "'a assn" "'a com"  ("(1WHILE _/ INV {_} //DO _ /OD)"  [0,0,0] 61)
+  
+syntax
+  "@assign"  :: "id => 'b => 'a com"        ("(2_ :=/ _)" [70,65] 61)
+  "@annskip" :: "'a com"                    ("SKIP")
+
+translations
+            "SKIP" == "Basic id"
+
+types 'a sem = "'a option => 'a option => bool"
+
+consts iter :: "nat => 'a bexp => 'a sem => 'a sem"
+primrec
+"iter 0 b S = (%s s'. s ~: Some ` b & (s=s'))"
+"iter (Suc n) b S = (%s s'. s : Some ` b & (? s''. S s s'' & iter n b S s'' s'))"
+
+consts Sem :: "'a com => 'a sem"
+primrec
+"Sem(Basic f) s s' = (case s of None \<Rightarrow> s' = None | Some t \<Rightarrow> s' = Some(f t))"
+"Sem Abort s s' = (s' = None)"
+"Sem(c1;c2) s s' = (? s''. Sem c1 s s'' & Sem c2 s'' s')"
+"Sem(IF b THEN c1 ELSE c2 FI) s s' =
+ (case s of None \<Rightarrow> s' = None
+  | Some t \<Rightarrow> ((t : b --> Sem c1 s s') & (t ~: b --> Sem c2 s s')))"
+"Sem(While b x c) s s' =
+ (if s = None then s' = None
+  else EX n. iter n b (Sem c) s s')"
+
+constdefs Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool"
+  "Valid p c q == \<forall>s s'. Sem c s s' \<longrightarrow> s : Some ` p \<longrightarrow> s' : Some ` q"
+
+
+syntax
+ "@hoare_vars" :: "[idts, 'a assn,'a com,'a assn] => bool"
+                 ("VARS _// {_} // _ // {_}" [0,0,55,0] 50)
+syntax ("" output)
+ "@hoare"      :: "['a assn,'a com,'a assn] => bool"
+                 ("{_} // _ // {_}" [0,55,0] 50)
+
+(** parse translations **)
+
+ML{*
+
+local
+fun free a = Free(a,dummyT)
+fun abs((a,T),body) =
+  let val a = absfree(a, dummyT, body)
+  in if T = Bound 0 then a else Const(Syntax.constrainAbsC,dummyT) $ a $ T end
+in
+
+fun mk_abstuple [x] body = abs (x, body)
+  | mk_abstuple (x::xs) body =
+      Syntax.const "split" $ abs (x, mk_abstuple xs body);
+
+fun mk_fbody a e [x as (b,_)] = if a=b then e else free b
+  | mk_fbody a e ((b,_)::xs) =
+      Syntax.const "Pair" $ (if a=b then e else free b) $ mk_fbody a e xs;
+
+fun mk_fexp a e xs = mk_abstuple xs (mk_fbody a e xs)
+end
+*}
+
+(* bexp_tr & assn_tr *)
+(*all meta-variables for bexp except for TRUE are translated as if they
+  were boolean expressions*)
+ML{*
+fun bexp_tr (Const ("TRUE", _)) xs = Syntax.const "TRUE"
+  | bexp_tr b xs = Syntax.const "Collect" $ mk_abstuple xs b;
+  
+fun assn_tr r xs = Syntax.const "Collect" $ mk_abstuple xs r;
+*}
+(* com_tr *)
+ML{*
+fun com_tr (Const("@assign",_) $ Free (a,_) $ e) xs =
+      Syntax.const "Basic" $ mk_fexp a e xs
+  | com_tr (Const ("Basic",_) $ f) xs = Syntax.const "Basic" $ f
+  | com_tr (Const ("Seq",_) $ c1 $ c2) xs =
+      Syntax.const "Seq" $ com_tr c1 xs $ com_tr c2 xs
+  | com_tr (Const ("Cond",_) $ b $ c1 $ c2) xs =
+      Syntax.const "Cond" $ bexp_tr b xs $ com_tr c1 xs $ com_tr c2 xs
+  | com_tr (Const ("While",_) $ b $ I $ c) xs =
+      Syntax.const "While" $ bexp_tr b xs $ assn_tr I xs $ com_tr c xs
+  | com_tr t _ = t (* if t is just a Free/Var *)
+*}
+
+(* triple_tr *)
+ML{*
+local
+
+fun var_tr(Free(a,_)) = (a,Bound 0) (* Bound 0 = dummy term *)
+  | var_tr(Const ("_constrain", _) $ (Free (a,_)) $ T) = (a,T);
+
+fun vars_tr (Const ("_idts", _) $ idt $ vars) = var_tr idt :: vars_tr vars
+  | vars_tr t = [var_tr t]
+
+in
+fun hoare_vars_tr [vars, pre, prg, post] =
+      let val xs = vars_tr vars
+      in Syntax.const "Valid" $
+         assn_tr pre xs $ com_tr prg xs $ assn_tr post xs
+      end
+  | hoare_vars_tr ts = raise TERM ("hoare_vars_tr", ts);
+end
+*}
+
+parse_translation {* [("@hoare_vars", hoare_vars_tr)] *}
+
+
+(*****************************************************************************)
+
+(*** print translations ***)
+ML{*
+fun dest_abstuple (Const ("split",_) $ (Abs(v,_, body))) =
+                            subst_bound (Syntax.free v, dest_abstuple body)
+  | dest_abstuple (Abs(v,_, body)) = subst_bound (Syntax.free v, body)
+  | dest_abstuple trm = trm;
+
+fun abs2list (Const ("split",_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
+  | abs2list (Abs(x,T,t)) = [Free (x, T)]
+  | abs2list _ = [];
+
+fun mk_ts (Const ("split",_) $ (Abs(x,_,t))) = mk_ts t
+  | mk_ts (Abs(x,_,t)) = mk_ts t
+  | mk_ts (Const ("Pair",_) $ a $ b) = a::(mk_ts b)
+  | mk_ts t = [t];
+
+fun mk_vts (Const ("split",_) $ (Abs(x,_,t))) = 
+           ((Syntax.free x)::(abs2list t), mk_ts t)
+  | mk_vts (Abs(x,_,t)) = ([Syntax.free x], [t])
+  | mk_vts t = raise Match;
+  
+fun find_ch [] i xs = (false, (Syntax.free "not_ch",Syntax.free "not_ch" ))
+  | find_ch ((v,t)::vts) i xs = if t=(Bound i) then find_ch vts (i-1) xs
+              else (true, (v, subst_bounds (xs,t)));
+  
+fun is_f (Const ("split",_) $ (Abs(x,_,t))) = true
+  | is_f (Abs(x,_,t)) = true
+  | is_f t = false;
+*}
+
+(* assn_tr' & bexp_tr'*)
+ML{*  
+fun assn_tr' (Const ("Collect",_) $ T) = dest_abstuple T
+  | assn_tr' (Const ("op Int",_) $ (Const ("Collect",_) $ T1) $ 
+                                   (Const ("Collect",_) $ T2)) =  
+            Syntax.const "op Int" $ dest_abstuple T1 $ dest_abstuple T2
+  | assn_tr' t = t;
+
+fun bexp_tr' (Const ("Collect",_) $ T) = dest_abstuple T 
+  | bexp_tr' t = t;
+*}
+
+(*com_tr' *)
+ML{*
+fun mk_assign f =
+  let val (vs, ts) = mk_vts f;
+      val (ch, which) = find_ch (vs~~ts) ((length vs)-1) (rev vs)
+  in if ch then Syntax.const "@assign" $ fst(which) $ snd(which)
+     else Syntax.const "@skip" end;
+
+fun com_tr' (Const ("Basic",_) $ f) = if is_f f then mk_assign f
+                                           else Syntax.const "Basic" $ f
+  | com_tr' (Const ("Seq",_) $ c1 $ c2) = Syntax.const "Seq" $
+                                                 com_tr' c1 $ com_tr' c2
+  | com_tr' (Const ("Cond",_) $ b $ c1 $ c2) = Syntax.const "Cond" $
+                                           bexp_tr' b $ com_tr' c1 $ com_tr' c2
+  | com_tr' (Const ("While",_) $ b $ I $ c) = Syntax.const "While" $
+                                               bexp_tr' b $ assn_tr' I $ com_tr' c
+  | com_tr' t = t;
+
+
+fun spec_tr' [p, c, q] =
+  Syntax.const "@hoare" $ assn_tr' p $ com_tr' c $ assn_tr' q
+*}
+
+print_translation {* [("Valid", spec_tr')] *}
+
+(*** The proof rules ***)
+
+lemma SkipRule: "p \<subseteq> q \<Longrightarrow> Valid p (Basic id) q"
+by (auto simp:Valid_def)
+
+lemma BasicRule: "p \<subseteq> {s. f s \<in> q} \<Longrightarrow> Valid p (Basic f) q"
+by (auto simp:Valid_def)
+
+lemma SeqRule: "Valid P c1 Q \<Longrightarrow> Valid Q c2 R \<Longrightarrow> Valid P (c1;c2) R"
+by (auto simp:Valid_def)
+
+lemma CondRule:
+ "p \<subseteq> {s. (s \<in> b \<longrightarrow> s \<in> w) \<and> (s \<notin> b \<longrightarrow> s \<in> w')}
+  \<Longrightarrow> Valid w c1 q \<Longrightarrow> Valid w' c2 q \<Longrightarrow> Valid p (Cond b c1 c2) q"
+by (fastsimp simp:Valid_def image_def)
+
+lemma iter_aux: "! s s'. Sem c s s' --> s : Some ` (I \<inter> b) --> s' : Some ` I ==>
+       (\<And>s s'. s : Some ` I \<Longrightarrow> iter n b (Sem c) s s' \<Longrightarrow> s' : Some ` (I \<inter> -b))";
+apply(unfold image_def)
+apply(induct n)
+ apply clarsimp
+apply(simp (no_asm_use))
+apply blast
+done
+
+lemma WhileRule:
+ "p \<subseteq> i \<Longrightarrow> Valid (i \<inter> b) c i \<Longrightarrow> i \<inter> (-b) \<subseteq> q \<Longrightarrow> Valid p (While b i c) q"
+apply(simp add:Valid_def)
+apply(simp (no_asm) add:image_def)
+apply clarify
+apply(drule iter_aux)
+  prefer 2 apply assumption
+ apply blast
+apply blast
+done
+
+lemma AbortRule: "p \<subseteq> {s. False} \<Longrightarrow> Valid p Abort q"
+by(auto simp:Valid_def)
+
+use "hoareAbort.ML"
+
+method_setup vcg = {*
+  Method.no_args
+    (Method.SIMPLE_METHOD' HEADGOAL (hoare_tac (K all_tac))) *}
+  "verification condition generator"
+
+method_setup vcg_simp = {*
+  Method.ctxt_args (fn ctxt =>
+    Method.METHOD (fn facts => 
+      hoare_tac (asm_full_simp_tac (Simplifier.get_local_simpset ctxt))1)) *}
+  "verification condition generator plus simplification"
+
+end
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/ROOT.ML
--- a/src/HOL/Hoare/ROOT.ML	Tue Mar 11 15:04:24 2003 +0100
+++ b/src/HOL/Hoare/ROOT.ML	Tue Mar 11 15:04:24 2003 +0100
@@ -5,5 +5,6 @@
 *)
 
 time_use_thy "Examples";
+time_use_thy "ExamplesAbort";
 time_use_thy "Pointers0";
 time_use_thy "Pointer_Examples";
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/Separation.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Hoare/Separation.thy	Tue Mar 11 15:04:24 2003 +0100
@@ -0,0 +1,90 @@
+theory Separation = HoareAbort:
+
+types heap = "(nat \<Rightarrow> nat option)"
+
+
+text{* The semantic definition of a few connectives: *}
+
+constdefs
+ R:: "heap \<Rightarrow> heap \<Rightarrow> heap \<Rightarrow> bool"
+"R h h1 h2 == dom h1 \<inter> dom h2 = {} \<and> h = h1 ++ h2"
+
+ star:: "(heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool) \<Rightarrow> (heap \<Rightarrow> bool)"
+"star P Q == \<lambda>h. \<exists>h1 h2. R h h1 h2 \<and> P h1 \<and> Q h2"
+
+ singl:: "heap \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool"
+"singl h x y == dom h = {x} & h x = Some y"
+
+lemma "VARS x y z w h
+ {star (%h. singl h x y) (%h. singl h z w) h}
+ SKIP
+ {x \<noteq> z}"
+apply vcg
+apply(auto simp:star_def R_def singl_def)
+done
+
+text{* To suppress the heap parameter of the connectives, we assume it
+is always called H and add/remove it upon parsing/printing. Thus
+every pointer program needs to have a program variable H, and
+assertions should not contain any locally bound Hs - otherwise they
+may bind the implicit H. *}
+
+text{* Nice input syntax: *}
+
+syntax
+ "@singl" :: "nat \<Rightarrow> nat \<Rightarrow> bool" ("[_ \<mapsto> _]")
+ "@star" :: "bool \<Rightarrow> bool \<Rightarrow> bool" (infixl "**" 60)
+
+ML{*
+fun singl_tr [p,q] = Syntax.const "singl" $ Syntax.free "H" $ p $ q
+  | singl_tr ts = raise TERM ("singl_tr", ts);
+fun star_tr [P,Q] = Syntax.const "star" $
+      absfree("H",dummyT,P) $ absfree("H",dummyT,Q) $ Syntax.free "H"
+  | star_tr ts = raise TERM ("star_tr", ts);
+*}
+
+parse_translation {* [("@singl", singl_tr),("@star", star_tr)] *}
+
+lemma "VARS H x y z w
+ {[x\<mapsto>y] ** [z\<mapsto>w]}
+ SKIP
+ {x \<noteq> z}"
+apply vcg
+apply(auto simp:star_def R_def singl_def)
+done
+
+text{* Nice output syntax: *}
+
+ML{*
+fun singl_tr' [_,p,q] = Syntax.const "@singl" $ p $ q
+fun star_tr' [Abs(_,_,P),Abs(_,_,Q),_] = Syntax.const "@star" $ P $ Q
+*}
+
+print_translation {* [("singl", singl_tr'),("star", star_tr')] *}
+
+lemma "VARS H x y z w
+ {[x\<mapsto>y] ** [z\<mapsto>w]}
+ SKIP
+ {x \<noteq> z}"
+apply vcg
+apply(auto simp:star_def R_def singl_def)
+done
+
+
+consts llist :: "(heap * nat)set"
+inductive llist
+intros
+empty: "(%n. None, 0) : llist"
+cons: "\<lbrakk> R h h1 h2; pto h1 p q; (h2,q):llist \<rbrakk> \<Longrightarrow> (h,p):llist"
+
+lemma "VARS p q h
+ {(h,p) : llist}
+ h := h(q \<mapsto> p)
+ {(h,q) : llist}"
+apply vcg
+apply(rule_tac "h1.0" = "%n. if n=q then Some p else None" in llist.cons)
+prefer 3 apply assumption
+prefer 2 apply(simp add:singl_def dom_def)
+apply(simp add:R_def dom_def)
+
+
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/hoare.ML
--- a/src/HOL/Hoare/hoare.ML	Tue Mar 11 15:04:24 2003 +0100
+++ b/src/HOL/Hoare/hoare.ML	Tue Mar 11 15:04:24 2003 +0100
@@ -6,54 +6,11 @@
 Derivation of the proof rules and, most importantly, the VCG tactic.
 *)
 
-(*** The proof rules ***)
-
-Goalw [thm "Valid_def"] "p <= q ==> Valid p (Basic id) q";
-by (Auto_tac);
-qed "SkipRule";
-
-Goalw [thm "Valid_def"] "p <= {s. (f s):q} ==> Valid p (Basic f) q";
-by (Auto_tac);
-qed "BasicRule";
-
-Goalw [thm "Valid_def"] "Valid P c1 Q ==> Valid Q c2 R ==> Valid P (c1;c2) R";
-by (Asm_simp_tac 1);
-by (Blast_tac 1);
-qed "SeqRule";
-
-Goalw [thm "Valid_def"]
- "p <= {s. (s:b --> s:w) & (s~:b --> s:w')} \
-\ ==> Valid w c1 q ==> Valid w' c2 q \
-\ ==> Valid p (Cond b c1 c2) q";
-by (Asm_simp_tac 1);
-by (Blast_tac 1);
-qed "CondRule";
-
-Goal "! s s'. Sem c s s' --> s : I Int b --> s' : I ==> \
-\     ! s s'. s : I --> iter n b (Sem c) s s' --> s' : I & s' ~: b";
-by (induct_tac "n" 1);
- by (Asm_simp_tac 1);
-by (Simp_tac 1);
-by (Blast_tac 1);
-val lemma = result() RS spec RS spec RS mp RS mp;
-
-Goalw [thm "Valid_def"]
- "p <= i ==> Valid (i Int b) c i ==> i Int (-b) <= q \
-\ ==> Valid p (While b j c) q";
-by (Asm_simp_tac 1);
-by (Clarify_tac 1);
-by (dtac lemma 1);
-by (assume_tac 2);
-by (Blast_tac 1);
-by (Blast_tac 1);
-qed "WhileRule'";
-
-Goal
- "p <= i ==> Valid (i Int b) c i ==> i Int (-b) <= q \
-\ ==> Valid p (While b i c) q";
-by (rtac WhileRule' 1);
-by (ALLGOALS assume_tac);
-qed "WhileRule";
+val SkipRule = thm"SkipRule";
+val BasicRule = thm"BasicRule";
+val SeqRule = thm"SeqRule";
+val CondRule = thm"CondRule";
+val WhileRule = thm"WhileRule";
 
 (*** The tactics ***)
 
@@ -191,7 +148,8 @@
 
 (** HoareRuleTac **)
 
-fun WlpTac Mlem tac i = rtac SeqRule i THEN  HoareRuleTac Mlem tac false (i+1)
+fun WlpTac Mlem tac i =
+  rtac SeqRule i THEN  HoareRuleTac Mlem tac false (i+1)
 and HoareRuleTac Mlem tac pre_cond i st = st |>
         (*abstraction over st prevents looping*)
     ( (WlpTac Mlem tac i THEN HoareRuleTac Mlem tac pre_cond i)
diff -r f5d08c341216 -r 11d7c5a8dbb7 src/HOL/Hoare/hoareAbort.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Hoare/hoareAbort.ML	Tue Mar 11 15:04:24 2003 +0100
@@ -0,0 +1,177 @@
+(*  Title:      HOL/Hoare/Hoare.ML
+    ID:         $Id$
+    Author:     Leonor Prensa Nieto & Tobias Nipkow
+    Copyright   1998 TUM
+
+Derivation of the proof rules and, most importantly, the VCG tactic.
+*)
+
+val SkipRule = thm"SkipRule";
+val BasicRule = thm"BasicRule";
+val AbortRule = thm"AbortRule";
+val SeqRule = thm"SeqRule";
+val CondRule = thm"CondRule";
+val WhileRule = thm"WhileRule";
+
+(*** The tactics ***)
+
+(*****************************************************************************)
+(** The function Mset makes the theorem                                     **)
+(** "?Mset <= {(x1,...,xn). ?P (x1,...,xn)} ==> ?Mset <= {s. ?P s}",        **)
+(** where (x1,...,xn) are the variables of the particular program we are    **)
+(** working on at the moment of the call                                    **)
+(*****************************************************************************)
+
+local open HOLogic in
+
+(** maps (%x1 ... xn. t) to [x1,...,xn] **)
+fun abs2list (Const ("split",_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
+  | abs2list (Abs(x,T,t)) = [Free (x, T)]
+  | abs2list _ = [];
+
+(** maps {(x1,...,xn). t} to [x1,...,xn] **)
+fun mk_vars (Const ("Collect",_) $ T) = abs2list T
+  | mk_vars _ = [];
+
+(** abstraction of body over a tuple formed from a list of free variables. 
+Types are also built **)
+fun mk_abstupleC []     body = absfree ("x", unitT, body)
+  | mk_abstupleC (v::w) body = let val (n,T) = dest_Free v
+                               in if w=[] then absfree (n, T, body)
+        else let val z  = mk_abstupleC w body;
+                 val T2 = case z of Abs(_,T,_) => T
+                        | Const (_, Type (_,[_, Type (_,[T,_])])) $ _ => T;
+       in Const ("split", (T --> T2 --> boolT) --> mk_prodT (T,T2) --> boolT) 
+          $ absfree (n, T, z) end end;
+
+(** maps [x1,...,xn] to (x1,...,xn) and types**)
+fun mk_bodyC []      = HOLogic.unit
+  | mk_bodyC (x::xs) = if xs=[] then x 
+               else let val (n, T) = dest_Free x ;
+                        val z = mk_bodyC xs;
+                        val T2 = case z of Free(_, T) => T
+                                         | Const ("Pair", Type ("fun", [_, Type
+                                            ("fun", [_, T])])) $ _ $ _ => T;
+                 in Const ("Pair", [T, T2] ---> mk_prodT (T, T2)) $ x $ z end;
+
+fun dest_Goal (Const ("Goal", _) $ P) = P;
+
+(** maps a goal of the form:
+        1. [| P |] ==> VARS x1 ... xn {._.} _ {._.} or to [x1,...,xn]**) 
+fun get_vars thm = let  val c = dest_Goal (concl_of (thm));
+                        val d = Logic.strip_assums_concl c;
+                        val Const _ $ pre $ _ $ _ = dest_Trueprop d;
+      in mk_vars pre end;
+
+
+(** Makes Collect with type **)
+fun mk_CollectC trm = let val T as Type ("fun",[t,_]) = fastype_of trm 
+                      in Collect_const t $ trm end;
+
+fun inclt ty = Const ("op <=", [ty,ty] ---> boolT);
+
+(** Makes "Mset <= t" **)
+fun Mset_incl t = let val MsetT = fastype_of t 
+                 in mk_Trueprop ((inclt MsetT) $ Free ("Mset", MsetT) $ t) end;
+
+
+fun Mset thm = let val vars = get_vars(thm);
+                   val varsT = fastype_of (mk_bodyC vars);
+                   val big_Collect = mk_CollectC (mk_abstupleC vars 
+                         (Free ("P",varsT --> boolT) $ mk_bodyC vars));
+                   val small_Collect = mk_CollectC (Abs("x",varsT,
+                           Free ("P",varsT --> boolT) $ Bound 0));
+                   val impl = implies $ (Mset_incl big_Collect) $ 
+                                          (Mset_incl small_Collect);
+   in Tactic.prove (Thm.sign_of_thm thm) ["Mset", "P"] [] impl (K (CLASET' blast_tac 1)) end;
+
+end;
+
+
+(*****************************************************************************)
+(** Simplifying:                                                            **)
+(** Some useful lemmata, lists and simplification tactics to control which  **)
+(** theorems are used to simplify at each moment, so that the original      **)
+(** input does not suffer any unexpected transformation                     **)
+(*****************************************************************************)
+
+Goal "-(Collect b) = {x. ~(b x)}";
+by (Fast_tac 1);
+qed "Compl_Collect";
+
+
+(**Simp_tacs**)
+
+val before_set2pred_simp_tac =
+  (simp_tac (HOL_basic_ss addsimps [Collect_conj_eq RS sym,Compl_Collect]));
+
+val split_simp_tac = (simp_tac (HOL_basic_ss addsimps [split_conv]));
+
+(*****************************************************************************)
+(** set2pred transforms sets inclusion into predicates implication,         **)
+(** maintaining the original variable names.                                **)
+(** Ex. "{x. x=0} <= {x. x <= 1}" -set2pred-> "x=0 --> x <= 1"              **)
+(** Subgoals containing intersections (A Int B) or complement sets (-A)     **)
+(** are first simplified by "before_set2pred_simp_tac", that returns only   **)
+(** subgoals of the form "{x. P x} <= {x. Q x}", which are easily           **)
+(** transformed.                                                            **)
+(** This transformation may solve very easy subgoals due to a ligth         **)
+(** simplification done by (split_all_tac)                                  **)
+(*****************************************************************************)
+
+fun set2pred i thm = let fun mk_string [] = ""
+                           | mk_string (x::xs) = x^" "^mk_string xs;
+                         val vars=get_vars(thm);
+                         val var_string = mk_string (map (fst o dest_Free) vars);
+      in ((before_set2pred_simp_tac i) THEN_MAYBE
+          (EVERY [rtac subsetI i, 
+                  rtac CollectI i,
+                  dtac CollectD i,
+                  (TRY(split_all_tac i)) THEN_MAYBE
+                  ((rename_tac var_string i) THEN
+                   (full_simp_tac (HOL_basic_ss addsimps [split_conv]) i)) ])) thm
+      end;
+
+(*****************************************************************************)
+(** BasicSimpTac is called to simplify all verification conditions. It does **)
+(** a light simplification by applying "mem_Collect_eq", then it calls      **)
+(** MaxSimpTac, which solves subgoals of the form "A <= A",                 **)
+(** and transforms any other into predicates, applying then                 **)
+(** the tactic chosen by the user, which may solve the subgoal completely.  **)
+(*****************************************************************************)
+
+fun MaxSimpTac tac = FIRST'[rtac subset_refl, set2pred THEN_MAYBE' tac];
+
+fun BasicSimpTac tac =
+  simp_tac
+    (HOL_basic_ss addsimps [mem_Collect_eq,split_conv] addsimprocs [record_simproc])
+  THEN_MAYBE' MaxSimpTac tac;
+
+(** HoareRuleTac **)
+
+fun WlpTac Mlem tac i =
+  rtac SeqRule i THEN  HoareRuleTac Mlem tac false (i+1)
+and HoareRuleTac Mlem tac pre_cond i st = st |>
+        (*abstraction over st prevents looping*)
+    ( (WlpTac Mlem tac i THEN HoareRuleTac Mlem tac pre_cond i)
+      ORELSE
+      (FIRST[rtac SkipRule i,
+             rtac AbortRule i,
+             EVERY[rtac BasicRule i,
+                   rtac Mlem i,
+                   split_simp_tac i],
+             EVERY[rtac CondRule i,
+                   HoareRuleTac Mlem tac false (i+2),
+                   HoareRuleTac Mlem tac false (i+1)],
+             EVERY[rtac WhileRule i,
+                   BasicSimpTac tac (i+2),
+                   HoareRuleTac Mlem tac true (i+1)] ] 
+       THEN (if pre_cond then (BasicSimpTac tac i) else rtac subset_refl i) ));
+
+
+(** tac:(int -> tactic) is the tactic the user chooses to solve or simplify **)
+(** the final verification conditions                                       **)
+ 
+fun hoare_tac tac i thm =
+  let val Mlem = Mset(thm)
+  in SELECT_GOAL(EVERY[HoareRuleTac Mlem tac true 1]) i thm end;