diff --git a/src/HOL/Imperative_HOL/Array.thy b/src/HOL/Imperative_HOL/Array.thy
--- a/src/HOL/Imperative_HOL/Array.thy
+++ b/src/HOL/Imperative_HOL/Array.thy
@@ -1,499 +1,499 @@
 (*  Title:      HOL/Imperative_HOL/Array.thy
     Author:     John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen
 *)
 
 section \<open>Monadic arrays\<close>
 
 theory Array
 imports Heap_Monad
 begin
 
 subsection \<open>Primitives\<close>
 
 definition present :: "heap \<Rightarrow> 'a::heap array \<Rightarrow> bool" where
   "present h a \<longleftrightarrow> addr_of_array a < lim h"
 
 definition get :: "heap \<Rightarrow> 'a::heap array \<Rightarrow> 'a list" where
   "get h a = map from_nat (arrays h (TYPEREP('a)) (addr_of_array a))"
 
 definition set :: "'a::heap array \<Rightarrow> 'a list \<Rightarrow> heap \<Rightarrow> heap" where
   "set a x = arrays_update (\<lambda>h. h(TYPEREP('a) := ((h(TYPEREP('a))) (addr_of_array a:=map to_nat x))))"
 
 definition alloc :: "'a list \<Rightarrow> heap \<Rightarrow> 'a::heap array \<times> heap" where
   "alloc xs h = (let
      l = lim h;
      r = Array l;
      h'' = set r xs (h\<lparr>lim := l + 1\<rparr>)
    in (r, h''))"
 
 definition length :: "heap \<Rightarrow> 'a::heap array \<Rightarrow> nat" where
   "length h a = List.length (get h a)"
   
 definition update :: "'a::heap array \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> heap \<Rightarrow> heap" where
   "update a i x h = set a ((get h a)[i:=x]) h"
 
 definition noteq :: "'a::heap array \<Rightarrow> 'b::heap array \<Rightarrow> bool" (infix "=!!=" 70) where
   "r =!!= s \<longleftrightarrow> TYPEREP('a) \<noteq> TYPEREP('b) \<or> addr_of_array r \<noteq> addr_of_array s"
 
 
 subsection \<open>Monad operations\<close>
 
 definition new :: "nat \<Rightarrow> 'a::heap \<Rightarrow> 'a array Heap" where
   [code del]: "new n x = Heap_Monad.heap (alloc (replicate n x))"
 
 definition of_list :: "'a::heap list \<Rightarrow> 'a array Heap" where
   [code del]: "of_list xs = Heap_Monad.heap (alloc xs)"
 
 definition make :: "nat \<Rightarrow> (nat \<Rightarrow> 'a::heap) \<Rightarrow> 'a array Heap" where
   [code del]: "make n f = Heap_Monad.heap (alloc (map f [0 ..< n]))"
 
 definition len :: "'a::heap array \<Rightarrow> nat Heap" where
   [code del]: "len a = Heap_Monad.tap (\<lambda>h. length h a)"
 
 definition nth :: "'a::heap array \<Rightarrow> nat \<Rightarrow> 'a Heap" where
   [code del]: "nth a i = Heap_Monad.guard (\<lambda>h. i < length h a)
     (\<lambda>h. (get h a ! i, h))"
 
 definition upd :: "nat \<Rightarrow> 'a \<Rightarrow> 'a::heap array \<Rightarrow> 'a::heap array Heap" where
   [code del]: "upd i x a = Heap_Monad.guard (\<lambda>h. i < length h a)
     (\<lambda>h. (a, update a i x h))"
 
 definition map_entry :: "nat \<Rightarrow> ('a::heap \<Rightarrow> 'a) \<Rightarrow> 'a array \<Rightarrow> 'a array Heap" where
   [code del]: "map_entry i f a = Heap_Monad.guard (\<lambda>h. i < length h a)
     (\<lambda>h. (a, update a i (f (get h a ! i)) h))"
 
 definition swap :: "nat \<Rightarrow> 'a \<Rightarrow> 'a::heap array \<Rightarrow> 'a Heap" where
   [code del]: "swap i x a = Heap_Monad.guard (\<lambda>h. i < length h a)
     (\<lambda>h. (get h a ! i, update a i x h))"
 
 definition freeze :: "'a::heap array \<Rightarrow> 'a list Heap" where
   [code del]: "freeze a = Heap_Monad.tap (\<lambda>h. get h a)"
 
 
 subsection \<open>Properties\<close>
 
 text \<open>FIXME: Does there exist a "canonical" array axiomatisation in
 the literature?\<close>
 
 text \<open>Primitives\<close>
 
 lemma noteq_sym: "a =!!= b \<Longrightarrow> b =!!= a"
   and unequal [simp]: "a \<noteq> a' \<longleftrightarrow> a =!!= a'"
   unfolding noteq_def by auto
 
 lemma noteq_irrefl: "r =!!= r \<Longrightarrow> False"
   unfolding noteq_def by auto
 
 lemma present_alloc_noteq: "present h a \<Longrightarrow> a =!!= fst (alloc xs h)"
   by (simp add: present_def noteq_def alloc_def Let_def)
 
 lemma get_set_eq [simp]: "get (set r x h) r = x"
   by (simp add: get_def set_def o_def)
 
 lemma get_set_neq [simp]: "r =!!= s \<Longrightarrow> get (set s x h) r = get h r"
   by (simp add: noteq_def get_def set_def)
 
 lemma set_same [simp]:
   "set r x (set r y h) = set r x h"
   by (simp add: set_def)
 
 lemma set_set_swap:
   "r =!!= r' \<Longrightarrow> set r x (set r' x' h) = set r' x' (set r x h)"
   by (simp add: Let_def fun_eq_iff noteq_def set_def)
 
 lemma get_update_eq [simp]:
   "get (update a i v h) a = (get h a) [i := v]"
   by (simp add: update_def)
 
 lemma nth_update_neq [simp]:
   "a =!!= b \<Longrightarrow> get (update b j v h) a ! i = get h a ! i"
   by (simp add: update_def noteq_def)
 
 lemma get_update_elem_neqIndex [simp]:
   "i \<noteq> j \<Longrightarrow> get (update a j v h) a ! i = get h a ! i"
   by simp
 
 lemma length_update [simp]: 
   "length (update b i v h) = length h"
   by (simp add: update_def length_def set_def get_def fun_eq_iff)
 
 lemma update_swap_neq:
   "a =!!= a' \<Longrightarrow> 
   update a i v (update a' i' v' h) 
   = update a' i' v' (update a i v h)"
 apply (unfold update_def)
 apply simp
 apply (subst set_set_swap, assumption)
 apply (subst get_set_neq)
 apply (erule noteq_sym)
 apply simp
 done
 
 lemma update_swap_neqIndex:
   "\<lbrakk> i \<noteq> i' \<rbrakk> \<Longrightarrow> update a i v (update a i' v' h) = update a i' v' (update a i v h)"
   by (auto simp add: update_def set_set_swap list_update_swap)
 
 lemma get_alloc:
   "get (snd (alloc xs h)) (fst (alloc ys h)) = xs"
   by (simp add: Let_def split_def alloc_def)
 
 lemma length_alloc:
   "length (snd (alloc (xs :: 'a::heap list) h)) (fst (alloc (ys :: 'a list) h)) = List.length xs"
   by (simp add: Array.length_def get_alloc)
 
 lemma set:
   "set (fst (alloc ls h))
      new_ls (snd (alloc ls h))
        = snd (alloc new_ls h)"
   by (simp add: Let_def split_def alloc_def)
 
 lemma present_update [simp]: 
   "present (update b i v h) = present h"
   by (simp add: update_def present_def set_def get_def fun_eq_iff)
 
 lemma present_alloc [simp]:
   "present (snd (alloc xs h)) (fst (alloc xs h))"
   by (simp add: present_def alloc_def set_def Let_def)
 
 lemma not_present_alloc [simp]:
   "\<not> present h (fst (alloc xs h))"
   by (simp add: present_def alloc_def Let_def)
 
 
 text \<open>Monad operations\<close>
 
 lemma execute_new [execute_simps]:
   "execute (new n x) h = Some (alloc (replicate n x) h)"
   by (simp add: new_def execute_simps)
 
 lemma success_newI [success_intros]:
   "success (new n x) h"
   by (auto intro: success_intros simp add: new_def)
 
 lemma effect_newI [effect_intros]:
   assumes "(a, h') = alloc (replicate n x) h"
   shows "effect (new n x) h h' a"
   by (rule effectI) (simp add: assms execute_simps)
 
 lemma effect_newE [effect_elims]:
   assumes "effect (new n x) h h' r"
   obtains "r = fst (alloc (replicate n x) h)" "h' = snd (alloc (replicate n x) h)" 
     "get h' r = replicate n x" "present h' r" "\<not> present h r"
   using assms by (rule effectE) (simp add: get_alloc execute_simps)
 
 lemma execute_of_list [execute_simps]:
   "execute (of_list xs) h = Some (alloc xs h)"
   by (simp add: of_list_def execute_simps)
 
 lemma success_of_listI [success_intros]:
   "success (of_list xs) h"
   by (auto intro: success_intros simp add: of_list_def)
 
 lemma effect_of_listI [effect_intros]:
   assumes "(a, h') = alloc xs h"
   shows "effect (of_list xs) h h' a"
   by (rule effectI) (simp add: assms execute_simps)
 
 lemma effect_of_listE [effect_elims]:
   assumes "effect (of_list xs) h h' r"
   obtains "r = fst (alloc xs h)" "h' = snd (alloc xs h)" 
     "get h' r = xs" "present h' r" "\<not> present h r"
   using assms by (rule effectE) (simp add: get_alloc execute_simps)
 
 lemma execute_make [execute_simps]:
   "execute (make n f) h = Some (alloc (map f [0 ..< n]) h)"
   by (simp add: make_def execute_simps)
 
 lemma success_makeI [success_intros]:
   "success (make n f) h"
   by (auto intro: success_intros simp add: make_def)
 
 lemma effect_makeI [effect_intros]:
   assumes "(a, h') = alloc (map f [0 ..< n]) h"
   shows "effect (make n f) h h' a"
   by (rule effectI) (simp add: assms execute_simps)
 
 lemma effect_makeE [effect_elims]:
   assumes "effect (make n f) h h' r"
   obtains "r = fst (alloc (map f [0 ..< n]) h)" "h' = snd (alloc (map f [0 ..< n]) h)" 
     "get h' r = map f [0 ..< n]" "present h' r" "\<not> present h r"
   using assms by (rule effectE) (simp add: get_alloc execute_simps)
 
 lemma execute_len [execute_simps]:
   "execute (len a) h = Some (length h a, h)"
   by (simp add: len_def execute_simps)
 
 lemma success_lenI [success_intros]:
   "success (len a) h"
   by (auto intro: success_intros simp add: len_def)
 
 lemma effect_lengthI [effect_intros]:
   assumes "h' = h" "r = length h a"
   shows "effect (len a) h h' r"
   by (rule effectI) (simp add: assms execute_simps)
 
 lemma effect_lengthE [effect_elims]:
   assumes "effect (len a) h h' r"
   obtains "r = length h' a" "h' = h" 
   using assms by (rule effectE) (simp add: execute_simps)
 
 lemma execute_nth [execute_simps]:
   "i < length h a \<Longrightarrow>
     execute (nth a i) h = Some (get h a ! i, h)"
   "i \<ge> length h a \<Longrightarrow> execute (nth a i) h = None"
   by (simp_all add: nth_def execute_simps)
 
 lemma success_nthI [success_intros]:
   "i < length h a \<Longrightarrow> success (nth a i) h"
   by (auto intro: success_intros simp add: nth_def)
 
 lemma effect_nthI [effect_intros]:
   assumes "i < length h a" "h' = h" "r = get h a ! i"
   shows "effect (nth a i) h h' r"
   by (rule effectI) (insert assms, simp add: execute_simps)
 
 lemma effect_nthE [effect_elims]:
   assumes "effect (nth a i) h h' r"
   obtains "i < length h a" "r = get h a ! i" "h' = h"
   using assms by (rule effectE) (cases "i < length h a", auto simp: execute_simps elim: successE)
 
 lemma execute_upd [execute_simps]:
   "i < length h a \<Longrightarrow>
     execute (upd i x a) h = Some (a, update a i x h)"
   "i \<ge> length h a \<Longrightarrow> execute (upd i x a) h = None"
   by (simp_all add: upd_def execute_simps)
 
 lemma success_updI [success_intros]:
   "i < length h a \<Longrightarrow> success (upd i x a) h"
   by (auto intro: success_intros simp add: upd_def)
 
 lemma effect_updI [effect_intros]:
   assumes "i < length h a" "h' = update a i v h"
   shows "effect (upd i v a) h h' a"
   by (rule effectI) (insert assms, simp add: execute_simps)
 
 lemma effect_updE [effect_elims]:
   assumes "effect (upd i v a) h h' r"
   obtains "r = a" "h' = update a i v h" "i < length h a"
   using assms by (rule effectE) (cases "i < length h a", auto simp: execute_simps elim: successE)
 
 lemma execute_map_entry [execute_simps]:
   "i < length h a \<Longrightarrow>
    execute (map_entry i f a) h =
       Some (a, update a i (f (get h a ! i)) h)"
   "i \<ge> length h a \<Longrightarrow> execute (map_entry i f a) h = None"
   by (simp_all add: map_entry_def execute_simps)
 
 lemma success_map_entryI [success_intros]:
   "i < length h a \<Longrightarrow> success (map_entry i f a) h"
   by (auto intro: success_intros simp add: map_entry_def)
 
 lemma effect_map_entryI [effect_intros]:
   assumes "i < length h a" "h' = update a i (f (get h a ! i)) h" "r = a"
   shows "effect (map_entry i f a) h h' r"
   by (rule effectI) (insert assms, simp add: execute_simps)
 
 lemma effect_map_entryE [effect_elims]:
   assumes "effect (map_entry i f a) h h' r"
   obtains "r = a" "h' = update a i (f (get h a ! i)) h" "i < length h a"
   using assms by (rule effectE) (cases "i < length h a", auto simp: execute_simps elim: successE)
 
 lemma execute_swap [execute_simps]:
   "i < length h a \<Longrightarrow>
    execute (swap i x a) h =
       Some (get h a ! i, update a i x h)"
   "i \<ge> length h a \<Longrightarrow> execute (swap i x a) h = None"
   by (simp_all add: swap_def execute_simps)
 
 lemma success_swapI [success_intros]:
   "i < length h a \<Longrightarrow> success (swap i x a) h"
   by (auto intro: success_intros simp add: swap_def)
 
 lemma effect_swapI [effect_intros]:
   assumes "i < length h a" "h' = update a i x h" "r = get h a ! i"
   shows "effect (swap i x a) h h' r"
   by (rule effectI) (insert assms, simp add: execute_simps)
 
 lemma effect_swapE [effect_elims]:
   assumes "effect (swap i x a) h h' r"
   obtains "r = get h a ! i" "h' = update a i x h" "i < length h a"
   using assms by (rule effectE) (cases "i < length h a", auto simp: execute_simps elim: successE)
 
 lemma execute_freeze [execute_simps]:
   "execute (freeze a) h = Some (get h a, h)"
   by (simp add: freeze_def execute_simps)
 
 lemma success_freezeI [success_intros]:
   "success (freeze a) h"
   by (auto intro: success_intros simp add: freeze_def)
 
 lemma effect_freezeI [effect_intros]:
   assumes "h' = h" "r = get h a"
   shows "effect (freeze a) h h' r"
   by (rule effectI) (insert assms, simp add: execute_simps)
 
 lemma effect_freezeE [effect_elims]:
   assumes "effect (freeze a) h h' r"
   obtains "h' = h" "r = get h a"
   using assms by (rule effectE) (simp add: execute_simps)
 
 lemma upd_return:
   "upd i x a \<then> return a = upd i x a"
   by (rule Heap_eqI) (simp add: bind_def guard_def upd_def execute_simps)
 
 lemma array_make:
   "new n x = make n (\<lambda>_. x)"
   by (rule Heap_eqI) (simp add: map_replicate_trivial execute_simps)
 
 lemma array_of_list_make [code]:
   "of_list xs = make (List.length xs) (\<lambda>n. xs ! n)"
   by (rule Heap_eqI) (simp add: map_nth execute_simps)
 
 hide_const (open) present get set alloc length update noteq new of_list make len nth upd map_entry swap freeze
 
 
 subsection \<open>Code generator setup\<close>
 
 subsubsection \<open>Logical intermediate layer\<close>
 
 definition new' where
   [code del]: "new' = Array.new o nat_of_integer"
 
 lemma [code]:
   "Array.new = new' o of_nat"
   by (simp add: new'_def o_def)
 
 definition make' where
   [code del]: "make' i f = Array.make (nat_of_integer i) (f o of_nat)"
 
 lemma [code]:
   "Array.make n f = make' (of_nat n) (f o nat_of_integer)"
   by (simp add: make'_def o_def)
 
 definition len' where
   [code del]: "len' a = Array.len a \<bind> (\<lambda>n. return (of_nat n))"
 
 lemma [code]:
   "Array.len a = len' a \<bind> (\<lambda>i. return (nat_of_integer i))"
   by (simp add: len'_def)
 
 definition nth' where
   [code del]: "nth' a = Array.nth a o nat_of_integer"
 
 lemma [code]:
   "Array.nth a n = nth' a (of_nat n)"
   by (simp add: nth'_def)
 
 definition upd' where
   [code del]: "upd' a i x = Array.upd (nat_of_integer i) x a \<then> return ()"
 
 lemma [code]:
   "Array.upd i x a = upd' a (of_nat i) x \<then> return a"
   by (simp add: upd'_def upd_return)
 
 lemma [code]:
   "Array.map_entry i f a = do {
      x \<leftarrow> Array.nth a i;
      Array.upd i (f x) a
    }"
   by (rule Heap_eqI) (simp add: bind_def guard_def map_entry_def execute_simps)
 
 lemma [code]:
   "Array.swap i x a = do {
      y \<leftarrow> Array.nth a i;
      Array.upd i x a;
      return y
    }"
   by (rule Heap_eqI) (simp add: bind_def guard_def swap_def execute_simps)
 
 lemma [code]:
   "Array.freeze a = do {
      n \<leftarrow> Array.len a;
      Heap_Monad.fold_map (\<lambda>i. Array.nth a i) [0..<n]
    }"
 proof (rule Heap_eqI)
   fix h
   have *: "List.map
      (\<lambda>x. fst (the (if x < Array.length h a
                     then Some (Array.get h a ! x, h) else None)))
      [0..<Array.length h a] =
        List.map (List.nth (Array.get h a)) [0..<Array.length h a]"
     by simp
   have "execute (Heap_Monad.fold_map (Array.nth a) [0..<Array.length h a]) h =
     Some (Array.get h a, h)"
     apply (subst execute_fold_map_unchanged_heap)
     apply (simp_all add: nth_def guard_def *)
     apply (simp add: length_def map_nth)
     done
   then have "execute (do {
       n \<leftarrow> Array.len a;
       Heap_Monad.fold_map (Array.nth a) [0..<n]
     }) h = Some (Array.get h a, h)"
     by (auto intro: execute_bind_eq_SomeI simp add: execute_simps)
   then show "execute (Array.freeze a) h = execute (do {
       n \<leftarrow> Array.len a;
       Heap_Monad.fold_map (Array.nth a) [0..<n]
     }) h" by (simp add: execute_simps)
 qed
 
 hide_const (open) new' make' len' nth' upd'
 
 
 text \<open>SML\<close>
 
 code_printing type_constructor array \<rightharpoonup> (SML) "_/ array"
 code_printing constant Array \<rightharpoonup> (SML) "raise/ (Fail/ \"bare Array\")"
 code_printing constant Array.new' \<rightharpoonup> (SML) "(fn/ ()/ =>/ Array.array/ (IntInf.toInt _,/ (_)))"
 code_printing constant Array.of_list \<rightharpoonup> (SML) "(fn/ ()/ =>/ Array.fromList/ _)"
 code_printing constant Array.make' \<rightharpoonup> (SML) "(fn/ ()/ =>/ Array.tabulate/ (IntInf.toInt _,/ _ o IntInf.fromInt))"
 code_printing constant Array.len' \<rightharpoonup> (SML) "(fn/ ()/ =>/ IntInf.fromInt (Array.length/ _))"
 code_printing constant Array.nth' \<rightharpoonup> (SML) "(fn/ ()/ =>/ Array.sub/ ((_),/ IntInf.toInt _))"
 code_printing constant Array.upd' \<rightharpoonup> (SML) "(fn/ ()/ =>/ Array.update/ ((_),/ IntInf.toInt _,/ (_)))"
 code_printing constant "HOL.equal :: 'a array \<Rightarrow> 'a array \<Rightarrow> bool" \<rightharpoonup> (SML) infixl 6 "="
-  
+
 code_reserved SML Array
 
 
 text \<open>OCaml\<close>
 
 code_printing type_constructor array \<rightharpoonup> (OCaml) "_/ array"
 code_printing constant Array \<rightharpoonup> (OCaml) "failwith/ \"bare Array\""
 code_printing constant Array.new' \<rightharpoonup> (OCaml) "(fun/ ()/ ->/ Array.make/ (Z.to'_int/ _)/ _)"
 code_printing constant Array.of_list \<rightharpoonup> (OCaml) "(fun/ ()/ ->/ Array.of'_list/ _)"
 code_printing constant Array.make' \<rightharpoonup> (OCaml)
   "(fun/ ()/ ->/ Array.init/ (Z.to'_int/ _)/ (fun k'_ ->/ _/ (Z.of'_int/ k'_)))"
 code_printing constant Array.len' \<rightharpoonup> (OCaml) "(fun/ ()/ ->/ Z.of'_int/ (Array.length/ _))"
 code_printing constant Array.nth' \<rightharpoonup> (OCaml) "(fun/ ()/ ->/ Array.get/ _/ (Z.to'_int/ _))"
 code_printing constant Array.upd' \<rightharpoonup> (OCaml) "(fun/ ()/ ->/ Array.set/ _/ (Z.to'_int/ _)/ _)"
 code_printing constant "HOL.equal :: 'a array \<Rightarrow> 'a array \<Rightarrow> bool" \<rightharpoonup> (OCaml) infixl 4 "="
 
 code_reserved OCaml Array
 
 
 text \<open>Haskell\<close>
 
 code_printing type_constructor array \<rightharpoonup> (Haskell) "Heap.STArray/ Heap.RealWorld/ _"
 code_printing constant Array \<rightharpoonup> (Haskell) "error/ \"bare Array\""
 code_printing constant Array.new' \<rightharpoonup> (Haskell) "Heap.newArray"
 code_printing constant Array.of_list \<rightharpoonup> (Haskell) "Heap.newListArray"
 code_printing constant Array.make' \<rightharpoonup> (Haskell) "Heap.newFunArray"
 code_printing constant Array.len' \<rightharpoonup> (Haskell) "Heap.lengthArray"
 code_printing constant Array.nth' \<rightharpoonup> (Haskell) "Heap.readArray"
 code_printing constant Array.upd' \<rightharpoonup> (Haskell) "Heap.writeArray"
 code_printing constant "HOL.equal :: 'a array \<Rightarrow> 'a array \<Rightarrow> bool" \<rightharpoonup> (Haskell) infix 4 "=="
 code_printing class_instance array :: HOL.equal \<rightharpoonup> (Haskell) -
 
 
 text \<open>Scala\<close>
 
 code_printing type_constructor array \<rightharpoonup> (Scala) "!Array.T[_]"
 code_printing constant Array \<rightharpoonup> (Scala) "!sys.error(\"bare Array\")"
 code_printing constant Array.new' \<rightharpoonup> (Scala) "('_: Unit)/ => / Array.alloc((_))((_))"
 code_printing constant Array.make' \<rightharpoonup> (Scala) "('_: Unit)/ =>/ Array.make((_))((_))"
 code_printing constant Array.len' \<rightharpoonup> (Scala) "('_: Unit)/ =>/ Array.len((_))"
 code_printing constant Array.nth' \<rightharpoonup> (Scala) "('_: Unit)/ =>/ Array.nth((_), (_))"
 code_printing constant Array.upd' \<rightharpoonup> (Scala) "('_: Unit)/ =>/ Array.upd((_), (_), (_))"
 code_printing constant Array.freeze \<rightharpoonup> (Scala) "('_: Unit)/ =>/ Array.freeze((_))"
 code_printing constant "HOL.equal :: 'a array \<Rightarrow> 'a array \<Rightarrow> bool" \<rightharpoonup> (Scala) infixl 5 "=="
 
 end
diff --git a/src/HOL/Imperative_HOL/Heap.thy b/src/HOL/Imperative_HOL/Heap.thy
--- a/src/HOL/Imperative_HOL/Heap.thy
+++ b/src/HOL/Imperative_HOL/Heap.thy
@@ -1,96 +1,97 @@
 (*  Title:      HOL/Imperative_HOL/Heap.thy
     Author:     John Matthews, Galois Connections; Alexander Krauss, TU Muenchen
 *)
 
 section \<open>A polymorphic heap based on cantor encodings\<close>
 
 theory Heap
 imports Main "HOL-Library.Countable"
 begin
 
 subsection \<open>Representable types\<close>
 
 text \<open>The type class of representable types\<close>
 
 class heap = typerep + countable
 
 instance unit :: heap ..
 
 instance bool :: heap ..
 
 instance nat :: heap ..
 
 instance prod :: (heap, heap) heap ..
 
 instance sum :: (heap, heap) heap ..
 
 instance list :: (heap) heap ..
 
 instance option :: (heap) heap ..
 
 instance int :: heap ..
 
 instance String.literal :: heap ..
 
 instance char :: heap ..
 
 instance typerep :: heap ..
 
 
 subsection \<open>A polymorphic heap with dynamic arrays and references\<close>
 
 text \<open>
   References and arrays are developed in parallel,
   but keeping them separate makes some later proofs simpler.
 \<close>
 
 type_synonym addr = nat \<comment> \<open>untyped heap references\<close>
 type_synonym heap_rep = nat \<comment> \<open>representable values\<close>
 
 record heap =
   arrays :: "typerep \<Rightarrow> addr \<Rightarrow> heap_rep list"
   refs :: "typerep \<Rightarrow> addr \<Rightarrow> heap_rep"
   lim  :: addr
 
 definition empty :: heap where
   "empty = \<lparr>arrays = (\<lambda>_ _. []), refs = (\<lambda>_ _. 0), lim = 0\<rparr>"
 
 datatype 'a array = Array addr \<comment> \<open>note the phantom type 'a\<close>
 datatype 'a ref = Ref addr \<comment> \<open>note the phantom type 'a\<close>
 
 primrec addr_of_array :: "'a array \<Rightarrow> addr" where
   "addr_of_array (Array x) = x"
 
 primrec addr_of_ref :: "'a ref \<Rightarrow> addr" where
   "addr_of_ref (Ref x) = x"
 
 lemma addr_of_array_inj [simp]:
   "addr_of_array a = addr_of_array a' \<longleftrightarrow> a = a'"
   by (cases a, cases a') simp_all
 
 lemma addr_of_ref_inj [simp]:
   "addr_of_ref r = addr_of_ref r' \<longleftrightarrow> r = r'"
   by (cases r, cases r') simp_all
 
 instance array :: (type) countable
   by (rule countable_classI [of addr_of_array]) simp
 
 instance ref :: (type) countable
   by (rule countable_classI [of addr_of_ref]) simp
 
 instance array :: (type) heap ..
+
 instance ref :: (type) heap ..
-    
-    
+
+
 text \<open>Syntactic convenience\<close>
 
 setup \<open>
   Sign.add_const_constraint (\<^const_name>\<open>Array\<close>, SOME \<^typ>\<open>nat \<Rightarrow> 'a::heap array\<close>)
   #> Sign.add_const_constraint (\<^const_name>\<open>Ref\<close>, SOME \<^typ>\<open>nat \<Rightarrow> 'a::heap ref\<close>)
   #> Sign.add_const_constraint (\<^const_name>\<open>addr_of_array\<close>, SOME \<^typ>\<open>'a::heap array \<Rightarrow> nat\<close>)
   #> Sign.add_const_constraint (\<^const_name>\<open>addr_of_ref\<close>, SOME \<^typ>\<open>'a::heap ref \<Rightarrow> nat\<close>)
 \<close>
 
 hide_const (open) empty
 
 end