# HG changeset patch
# User haftmann
# Date 1266916275 -3600
# Node ID 870dfea4f9c0775cc7918779d1f891fda20cce50
# Parent  fbdc860d87a37bb70a663607df3bb5dabba1c47b
dropped axclass; dropped Id; session theory Hoare.thy

diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/Examples.thy
--- a/src/HOL/Hoare/Examples.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/Examples.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -1,12 +1,11 @@
 (*  Title:      HOL/Hoare/Examples.thy
-    ID:         $Id$
     Author:     Norbert Galm
     Copyright   1998 TUM
 
 Various examples.
 *)
 
-theory Examples imports Hoare Arith2 begin
+theory Examples imports Hoare_Logic Arith2 begin
 
 (*** ARITHMETIC ***)
 
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/ExamplesAbort.thy
--- a/src/HOL/Hoare/ExamplesAbort.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/ExamplesAbort.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -1,12 +1,11 @@
 (*  Title:      HOL/Hoare/ExamplesAbort.thy
-    ID:         $Id$
     Author:     Tobias Nipkow
     Copyright   1998 TUM
 
 Some small examples for programs that may abort.
 *)
 
-theory ExamplesAbort imports HoareAbort begin
+theory ExamplesAbort imports Hoare_Logic_Abort begin
 
 lemma "VARS x y z::nat
  {y = z & z \<noteq> 0} z \<noteq> 0 \<rightarrow> x := y div z {x = 1}"
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/HeapSyntax.thy
--- a/src/HOL/Hoare/HeapSyntax.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/HeapSyntax.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -3,7 +3,7 @@
     Copyright   2002 TUM
 *)
 
-theory HeapSyntax imports Hoare Heap begin
+theory HeapSyntax imports Hoare_Logic Heap begin
 
 subsection "Field access and update"
 
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/HeapSyntaxAbort.thy
--- a/src/HOL/Hoare/HeapSyntaxAbort.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/HeapSyntaxAbort.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -3,7 +3,7 @@
     Copyright   2002 TUM
 *)
 
-theory HeapSyntaxAbort imports HoareAbort Heap begin
+theory HeapSyntaxAbort imports Hoare_Logic_Abort Heap begin
 
 subsection "Field access and update"
 
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/Hoare.thy
--- a/src/HOL/Hoare/Hoare.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/Hoare.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -1,245 +1,9 @@
-(*  Title:      HOL/Hoare/Hoare.thy
-    Author:     Leonor Prensa Nieto & Tobias Nipkow
-    Copyright   1998 TUM
-
-Sugared semantic embedding of Hoare logic.
-Strictly speaking a shallow embedding (as implemented by Norbert Galm
-following Mike Gordon) would suffice. Maybe the datatype com comes in useful
-later.
+(*  Author:     Tobias Nipkow
+    Copyright   1998-2003 TUM
 *)
 
 theory Hoare
-imports Main
-uses ("hoare_tac.ML")
+imports Examples ExamplesAbort Pointers0 Pointer_Examples Pointer_ExamplesAbort SchorrWaite Separation
 begin
 
-types
-    'a bexp = "'a set"
-    'a assn = "'a set"
-
-datatype
- 'a com = Basic "'a \<Rightarrow> 'a"
-   | 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)
-
-abbreviation annskip ("SKIP") where "SKIP == Basic id"
-
-types 'a sem = "'a => 'a => bool"
-
-consts iter :: "nat => 'a bexp => 'a sem => 'a sem"
-primrec
-"iter 0 b S = (%s s'. s ~: b & (s=s'))"
-"iter (Suc n) b S = (%s s'. s : b & (? s''. S s s'' & iter n b S s'' s'))"
-
-consts Sem :: "'a com => 'a sem"
-primrec
-"Sem(Basic f) s s' = (s' = f s)"
-"Sem(c1;c2) s s' = (? s''. Sem c1 s s'' & Sem c2 s'' s')"
-"Sem(IF b THEN c1 ELSE c2 FI) s s' = ((s  : b --> Sem c1 s s') &
-                                      (s ~: b --> Sem c2 s s'))"
-"Sem(While b x c) s s' = (? n. iter n b (Sem c) s s')"
-
-constdefs Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool"
-  "Valid p c q == !s s'. Sem c s s' --> s : p --> s' : q"
-
-
-
-(** parse translations **)
-
-syntax
-  "_assign"  :: "id => 'b => 'a com"        ("(2_ :=/ _)" [70,65] 61)
-
-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)
-ML {*
-
-local
-
-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 @{const_syntax split} $ abs (x, mk_abstuple xs body);
-
-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 @{const_syntax 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
-*}
-
-(* 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"   (* FIXME !? *)
-  | bexp_tr b xs = Syntax.const @{const_syntax Collect} $ mk_abstuple xs b;
-
-fun assn_tr r xs = Syntax.const @{const_syntax Collect} $ mk_abstuple xs r;
-*}
-(* com_tr *)
-ML{*
-fun com_tr (Const(@{syntax_const "_assign"},_) $ Free (a,_) $ e) xs =
-      Syntax.const @{const_syntax Basic} $ mk_fexp a e xs
-  | com_tr (Const (@{const_syntax Basic},_) $ f) xs = Syntax.const @{const_syntax Basic} $ f
-  | com_tr (Const (@{const_syntax Seq},_) $ c1 $ c2) xs =
-      Syntax.const @{const_syntax Seq} $ com_tr c1 xs $ com_tr c2 xs
-  | com_tr (Const (@{const_syntax Cond},_) $ b $ c1 $ c2) xs =
-      Syntax.const @{const_syntax Cond} $ bexp_tr b xs $ com_tr c1 xs $ com_tr c2 xs
-  | com_tr (Const (@{const_syntax While},_) $ b $ I $ c) xs =
-      Syntax.const @{const_syntax 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 *)    (* FIXME does not handle "_idtdummy" *)
-ML{*
-local
-
-fun var_tr(Free(a,_)) = (a,Bound 0) (* Bound 0 = dummy term *)
-  | var_tr(Const (@{syntax_const "_constrain"}, _) $ (Free (a,_)) $ T) = (a,T);
-
-fun vars_tr (Const (@{syntax_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 @{const_syntax 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 {* [(@{syntax_const "_hoare_vars"}, hoare_vars_tr)] *}
-
-
-(*****************************************************************************)
-
-(*** print translations ***)
-ML{*
-fun dest_abstuple (Const (@{const_syntax 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 (@{const_syntax split},_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
-  | abs2list (Abs(x,T,t)) = [Free (x, T)]
-  | abs2list _ = [];
-
-fun mk_ts (Const (@{const_syntax split},_) $ (Abs(x,_,t))) = mk_ts t
-  | mk_ts (Abs(x,_,t)) = mk_ts t
-  | mk_ts (Const (@{const_syntax Pair},_) $ a $ b) = a::(mk_ts b)
-  | mk_ts t = [t];
-
-fun mk_vts (Const (@{const_syntax 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 (@{const_syntax split},_) $ (Abs(x,_,t))) = true
-  | is_f (Abs(x,_,t)) = true
-  | is_f t = false;
-*}
-
-(* assn_tr' & bexp_tr'*)
-ML{*
-fun assn_tr' (Const (@{const_syntax Collect},_) $ T) = dest_abstuple T
-  | assn_tr' (Const (@{const_syntax inter}, _) $
-        (Const (@{const_syntax Collect},_) $ T1) $ (Const (@{const_syntax Collect},_) $ T2)) =
-      Syntax.const @{const_syntax inter} $ dest_abstuple T1 $ dest_abstuple T2
-  | assn_tr' t = t;
-
-fun bexp_tr' (Const (@{const_syntax 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 @{syntax_const "_assign"} $ fst which $ snd which
-    else Syntax.const @{const_syntax annskip}
-  end;
-
-fun com_tr' (Const (@{const_syntax Basic},_) $ f) =
-      if is_f f then mk_assign f
-      else Syntax.const @{const_syntax Basic} $ f
-  | com_tr' (Const (@{const_syntax Seq},_) $ c1 $ c2) =
-      Syntax.const @{const_syntax Seq} $ com_tr' c1 $ com_tr' c2
-  | com_tr' (Const (@{const_syntax Cond},_) $ b $ c1 $ c2) =
-      Syntax.const @{const_syntax Cond} $ bexp_tr' b $ com_tr' c1 $ com_tr' c2
-  | com_tr' (Const (@{const_syntax While},_) $ b $ I $ c) =
-      Syntax.const @{const_syntax While} $ bexp_tr' b $ assn_tr' I $ com_tr' c
-  | com_tr' t = t;
-
-fun spec_tr' [p, c, q] =
-  Syntax.const @{syntax_const "_hoare"} $ assn_tr' p $ com_tr' c $ assn_tr' q
-*}
-
-print_translation {* [(@{const_syntax 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
-
-
-lemma Compl_Collect: "-(Collect b) = {x. ~(b x)}"
-  by blast
-
-lemmas AbortRule = SkipRule  -- "dummy version"
-use "hoare_tac.ML"
-
-method_setup vcg = {*
-  Scan.succeed (fn ctxt => SIMPLE_METHOD' (hoare_tac ctxt (K all_tac))) *}
-  "verification condition generator"
-
-method_setup vcg_simp = {*
-  Scan.succeed (fn ctxt =>
-    SIMPLE_METHOD' (hoare_tac ctxt (asm_full_simp_tac (simpset_of ctxt)))) *}
-  "verification condition generator plus simplification"
-
-end
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/HoareAbort.thy
--- a/src/HOL/Hoare/HoareAbort.thy	Tue Feb 23 10:11:12 2010 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,269 +0,0 @@
-(*  Title:      HOL/Hoare/HoareAbort.thy
-    Author:     Leonor Prensa Nieto & Tobias Nipkow
-    Copyright   2003 TUM
-
-Like Hoare.thy, but with an Abort statement for modelling run time errors.
-*)
-
-theory HoareAbort
-imports Main
-uses ("hoare_tac.ML")
-begin
-
-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)
-
-abbreviation annskip ("SKIP") where "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 = (\<lambda>s s'. s \<notin> Some ` b \<and> s=s')"
-"iter (Suc n) b S =
-  (\<lambda>s s'. s \<in> Some ` b \<and> (\<exists>s''. S s s'' \<and> 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' = (\<exists>s''. Sem c1 s s'' \<and> 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 \<in> b \<longrightarrow> Sem c1 s s') \<and> (t \<notin> b \<longrightarrow> Sem c2 s s')))"
-"Sem(While b x c) s s' =
- (if s = None then s' = None else \<exists>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"
-
-
-
-(** parse translations **)
-
-syntax
-  "_assign"  :: "id => 'b => 'a com"        ("(2_ :=/ _)" [70,65] 61)
-
-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)
-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 @{const_syntax 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 @{const_syntax 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"   (* FIXME !? *)
-  | bexp_tr b xs = Syntax.const @{const_syntax Collect} $ mk_abstuple xs b;
-
-fun assn_tr r xs = Syntax.const @{const_syntax Collect} $ mk_abstuple xs r;
-*}
-(* com_tr *)
-ML{*
-fun com_tr (Const (@{syntax_const "_assign"},_) $ Free (a,_) $ e) xs =
-      Syntax.const @{const_syntax Basic} $ mk_fexp a e xs
-  | com_tr (Const (@{const_syntax Basic},_) $ f) xs = Syntax.const @{const_syntax Basic} $ f
-  | com_tr (Const (@{const_syntax Seq},_) $ c1 $ c2) xs =
-      Syntax.const @{const_syntax Seq} $ com_tr c1 xs $ com_tr c2 xs
-  | com_tr (Const (@{const_syntax Cond},_) $ b $ c1 $ c2) xs =
-      Syntax.const @{const_syntax Cond} $ bexp_tr b xs $ com_tr c1 xs $ com_tr c2 xs
-  | com_tr (Const (@{const_syntax While},_) $ b $ I $ c) xs =
-      Syntax.const @{const_syntax 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 *)  (* FIXME does not handle "_idtdummy" *)
-ML{*
-local
-
-fun var_tr (Free (a, _)) = (a, Bound 0) (* Bound 0 = dummy term *)
-  | var_tr (Const (@{syntax_const "_constrain"}, _) $ Free (a, _) $ T) = (a, T);
-
-fun vars_tr (Const (@{syntax_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 @{const_syntax 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 {* [(@{syntax_const "_hoare_vars"}, hoare_vars_tr)] *}
-
-
-(*****************************************************************************)
-
-(*** print translations ***)
-ML{*
-fun dest_abstuple (Const (@{const_syntax 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 (@{const_syntax split},_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
-  | abs2list (Abs(x,T,t)) = [Free (x, T)]
-  | abs2list _ = [];
-
-fun mk_ts (Const (@{const_syntax split},_) $ (Abs(x,_,t))) = mk_ts t
-  | mk_ts (Abs(x,_,t)) = mk_ts t
-  | mk_ts (Const (@{const_syntax Pair},_) $ a $ b) = a::(mk_ts b)
-  | mk_ts t = [t];
-
-fun mk_vts (Const (@{const_syntax 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 (@{const_syntax split},_) $ (Abs(x,_,t))) = true
-  | is_f (Abs(x,_,t)) = true
-  | is_f t = false;
-*}
-
-(* assn_tr' & bexp_tr'*)
-ML{*
-fun assn_tr' (Const (@{const_syntax Collect},_) $ T) = dest_abstuple T
-  | assn_tr' (Const (@{const_syntax inter},_) $ (Const (@{const_syntax Collect},_) $ T1) $
-        (Const (@{const_syntax Collect},_) $ T2)) =
-      Syntax.const @{const_syntax inter} $ dest_abstuple T1 $ dest_abstuple T2
-  | assn_tr' t = t;
-
-fun bexp_tr' (Const (@{const_syntax 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 @{syntax_const "_assign"} $ fst which $ snd which
-    else Syntax.const @{const_syntax annskip}
-  end;
-
-fun com_tr' (Const (@{const_syntax Basic},_) $ f) =
-      if is_f f then mk_assign f else Syntax.const @{const_syntax Basic} $ f
-  | com_tr' (Const (@{const_syntax Seq},_) $ c1 $ c2) =
-      Syntax.const @{const_syntax Seq} $ com_tr' c1 $ com_tr' c2
-  | com_tr' (Const (@{const_syntax Cond},_) $ b $ c1 $ c2) =
-      Syntax.const @{const_syntax Cond} $ bexp_tr' b $ com_tr' c1 $ com_tr' c2
-  | com_tr' (Const (@{const_syntax While},_) $ b $ I $ c) =
-      Syntax.const @{const_syntax While} $ bexp_tr' b $ assn_tr' I $ com_tr' c
-  | com_tr' t = t;
-
-fun spec_tr' [p, c, q] =
-  Syntax.const @{syntax_const "_hoare"} $ assn_tr' p $ com_tr' c $ assn_tr' q
-*}
-
-print_translation {* [(@{const_syntax 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' \<longrightarrow> s \<in> Some ` (I \<inter> b) \<longrightarrow> s' \<in> Some ` I \<Longrightarrow>
-  (\<And>s s'. s \<in> Some ` I \<Longrightarrow> iter n b (Sem c) s s' \<Longrightarrow> s' \<in> 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)
-
-
-subsection {* Derivation of the proof rules and, most importantly, the VCG tactic *}
-
-lemma Compl_Collect: "-(Collect b) = {x. ~(b x)}"
-  by blast
-
-use "hoare_tac.ML"
-
-method_setup vcg = {*
-  Scan.succeed (fn ctxt => SIMPLE_METHOD' (hoare_tac ctxt (K all_tac))) *}
-  "verification condition generator"
-
-method_setup vcg_simp = {*
-  Scan.succeed (fn ctxt =>
-    SIMPLE_METHOD' (hoare_tac ctxt (asm_full_simp_tac (simpset_of ctxt)))) *}
-  "verification condition generator plus simplification"
-
-(* Special syntax for guarded statements and guarded array updates: *)
-
-syntax
-  guarded_com :: "bool \<Rightarrow> 'a com \<Rightarrow> 'a com"  ("(2_ \<rightarrow>/ _)" 71)
-  array_update :: "'a list \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> 'a com"  ("(2_[_] :=/ _)" [70, 65] 61)
-translations
-  "P \<rightarrow> c" == "IF P THEN c ELSE CONST Abort FI"
-  "a[i] := v" => "(i < CONST length a) \<rightarrow> (a := CONST list_update a i v)"
-  (* reverse translation not possible because of duplicate "a" *)
-
-text{* Note: there is no special syntax for guarded array access. Thus
-you must write @{text"j < length a \<rightarrow> a[i] := a!j"}. *}
-
-end
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/Hoare_Logic.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Hoare/Hoare_Logic.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -0,0 +1,245 @@
+(*  Title:      HOL/Hoare/Hoare.thy
+    Author:     Leonor Prensa Nieto & Tobias Nipkow
+    Copyright   1998 TUM
+
+Sugared semantic embedding of Hoare logic.
+Strictly speaking a shallow embedding (as implemented by Norbert Galm
+following Mike Gordon) would suffice. Maybe the datatype com comes in useful
+later.
+*)
+
+theory Hoare_Logic
+imports Main
+uses ("hoare_tac.ML")
+begin
+
+types
+    'a bexp = "'a set"
+    'a assn = "'a set"
+
+datatype
+ 'a com = Basic "'a \<Rightarrow> 'a"
+   | 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)
+
+abbreviation annskip ("SKIP") where "SKIP == Basic id"
+
+types 'a sem = "'a => 'a => bool"
+
+consts iter :: "nat => 'a bexp => 'a sem => 'a sem"
+primrec
+"iter 0 b S = (%s s'. s ~: b & (s=s'))"
+"iter (Suc n) b S = (%s s'. s : b & (? s''. S s s'' & iter n b S s'' s'))"
+
+consts Sem :: "'a com => 'a sem"
+primrec
+"Sem(Basic f) s s' = (s' = f s)"
+"Sem(c1;c2) s s' = (? s''. Sem c1 s s'' & Sem c2 s'' s')"
+"Sem(IF b THEN c1 ELSE c2 FI) s s' = ((s  : b --> Sem c1 s s') &
+                                      (s ~: b --> Sem c2 s s'))"
+"Sem(While b x c) s s' = (? n. iter n b (Sem c) s s')"
+
+constdefs Valid :: "'a bexp \<Rightarrow> 'a com \<Rightarrow> 'a bexp \<Rightarrow> bool"
+  "Valid p c q == !s s'. Sem c s s' --> s : p --> s' : q"
+
+
+
+(** parse translations **)
+
+syntax
+  "_assign"  :: "id => 'b => 'a com"        ("(2_ :=/ _)" [70,65] 61)
+
+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)
+ML {*
+
+local
+
+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 @{const_syntax split} $ abs (x, mk_abstuple xs body);
+
+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 @{const_syntax 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
+*}
+
+(* 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"   (* FIXME !? *)
+  | bexp_tr b xs = Syntax.const @{const_syntax Collect} $ mk_abstuple xs b;
+
+fun assn_tr r xs = Syntax.const @{const_syntax Collect} $ mk_abstuple xs r;
+*}
+(* com_tr *)
+ML{*
+fun com_tr (Const(@{syntax_const "_assign"},_) $ Free (a,_) $ e) xs =
+      Syntax.const @{const_syntax Basic} $ mk_fexp a e xs
+  | com_tr (Const (@{const_syntax Basic},_) $ f) xs = Syntax.const @{const_syntax Basic} $ f
+  | com_tr (Const (@{const_syntax Seq},_) $ c1 $ c2) xs =
+      Syntax.const @{const_syntax Seq} $ com_tr c1 xs $ com_tr c2 xs
+  | com_tr (Const (@{const_syntax Cond},_) $ b $ c1 $ c2) xs =
+      Syntax.const @{const_syntax Cond} $ bexp_tr b xs $ com_tr c1 xs $ com_tr c2 xs
+  | com_tr (Const (@{const_syntax While},_) $ b $ I $ c) xs =
+      Syntax.const @{const_syntax 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 *)    (* FIXME does not handle "_idtdummy" *)
+ML{*
+local
+
+fun var_tr(Free(a,_)) = (a,Bound 0) (* Bound 0 = dummy term *)
+  | var_tr(Const (@{syntax_const "_constrain"}, _) $ (Free (a,_)) $ T) = (a,T);
+
+fun vars_tr (Const (@{syntax_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 @{const_syntax 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 {* [(@{syntax_const "_hoare_vars"}, hoare_vars_tr)] *}
+
+
+(*****************************************************************************)
+
+(*** print translations ***)
+ML{*
+fun dest_abstuple (Const (@{const_syntax 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 (@{const_syntax split},_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
+  | abs2list (Abs(x,T,t)) = [Free (x, T)]
+  | abs2list _ = [];
+
+fun mk_ts (Const (@{const_syntax split},_) $ (Abs(x,_,t))) = mk_ts t
+  | mk_ts (Abs(x,_,t)) = mk_ts t
+  | mk_ts (Const (@{const_syntax Pair},_) $ a $ b) = a::(mk_ts b)
+  | mk_ts t = [t];
+
+fun mk_vts (Const (@{const_syntax 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 (@{const_syntax split},_) $ (Abs(x,_,t))) = true
+  | is_f (Abs(x,_,t)) = true
+  | is_f t = false;
+*}
+
+(* assn_tr' & bexp_tr'*)
+ML{*
+fun assn_tr' (Const (@{const_syntax Collect},_) $ T) = dest_abstuple T
+  | assn_tr' (Const (@{const_syntax inter}, _) $
+        (Const (@{const_syntax Collect},_) $ T1) $ (Const (@{const_syntax Collect},_) $ T2)) =
+      Syntax.const @{const_syntax inter} $ dest_abstuple T1 $ dest_abstuple T2
+  | assn_tr' t = t;
+
+fun bexp_tr' (Const (@{const_syntax 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 @{syntax_const "_assign"} $ fst which $ snd which
+    else Syntax.const @{const_syntax annskip}
+  end;
+
+fun com_tr' (Const (@{const_syntax Basic},_) $ f) =
+      if is_f f then mk_assign f
+      else Syntax.const @{const_syntax Basic} $ f
+  | com_tr' (Const (@{const_syntax Seq},_) $ c1 $ c2) =
+      Syntax.const @{const_syntax Seq} $ com_tr' c1 $ com_tr' c2
+  | com_tr' (Const (@{const_syntax Cond},_) $ b $ c1 $ c2) =
+      Syntax.const @{const_syntax Cond} $ bexp_tr' b $ com_tr' c1 $ com_tr' c2
+  | com_tr' (Const (@{const_syntax While},_) $ b $ I $ c) =
+      Syntax.const @{const_syntax While} $ bexp_tr' b $ assn_tr' I $ com_tr' c
+  | com_tr' t = t;
+
+fun spec_tr' [p, c, q] =
+  Syntax.const @{syntax_const "_hoare"} $ assn_tr' p $ com_tr' c $ assn_tr' q
+*}
+
+print_translation {* [(@{const_syntax 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
+
+
+lemma Compl_Collect: "-(Collect b) = {x. ~(b x)}"
+  by blast
+
+lemmas AbortRule = SkipRule  -- "dummy version"
+use "hoare_tac.ML"
+
+method_setup vcg = {*
+  Scan.succeed (fn ctxt => SIMPLE_METHOD' (hoare_tac ctxt (K all_tac))) *}
+  "verification condition generator"
+
+method_setup vcg_simp = {*
+  Scan.succeed (fn ctxt =>
+    SIMPLE_METHOD' (hoare_tac ctxt (asm_full_simp_tac (simpset_of ctxt)))) *}
+  "verification condition generator plus simplification"
+
+end
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/Pointer_Examples.thy
--- a/src/HOL/Hoare/Pointer_Examples.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/Pointer_Examples.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -1,5 +1,4 @@
 (*  Title:      HOL/Hoare/Pointers.thy
-    ID:         $Id$
     Author:     Tobias Nipkow
     Copyright   2002 TUM
 
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/Pointers0.thy
--- a/src/HOL/Hoare/Pointers0.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/Pointers0.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -9,12 +9,12 @@
 - in fact in some case they appear to get (a bit) more complicated.
 *)
 
-theory Pointers0 imports Hoare begin
+theory Pointers0 imports Hoare_Logic begin
 
 subsection "References"
 
-axclass ref < type
-consts Null :: "'a::ref"
+class ref =
+  fixes Null :: 'a
 
 subsection "Field access and update"
 
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/ROOT.ML
--- a/src/HOL/Hoare/ROOT.ML	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/ROOT.ML	Tue Feb 23 10:11:15 2010 +0100
@@ -1,8 +1,2 @@
-(*  Title:      HOL/Hoare/ROOT.ML
-    ID:         $Id$
-    Author:     Tobias Nipkow
-    Copyright   1998-2003 TUM
-*)
 
-use_thys ["Examples", "ExamplesAbort", "Pointers0", "Pointer_Examples",
-  "Pointer_ExamplesAbort", "SchorrWaite", "Separation"];
+use_thy "Hoare";
diff -r fbdc860d87a3 -r 870dfea4f9c0 src/HOL/Hoare/Separation.thy
--- a/src/HOL/Hoare/Separation.thy	Tue Feb 23 10:11:12 2010 +0100
+++ b/src/HOL/Hoare/Separation.thy	Tue Feb 23 10:11:15 2010 +0100
@@ -12,7 +12,7 @@
 
 *)
 
-theory Separation imports HoareAbort SepLogHeap begin
+theory Separation imports Hoare_Logic_Abort SepLogHeap begin
 
 text{* The semantic definition of a few connectives: *}