# HG changeset patch
# User krauss
# Date 1279015211 -7200
# Node ID ba0bc31b90d7503011080908314007142fdcc02c
# Parent  0d6b64060543f59bb9f44e336479c40fa8ca59f2
Heap_Monad uses Monad_Syntax

diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/Array.thy
--- a/src/HOL/Imperative_HOL/Array.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/Array.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -407,25 +407,25 @@
   by (simp add: upd'_def upd_return)
 
 lemma [code]:
-  "map_entry i f a = (do
+  "map_entry i f a = do {
      x \<leftarrow> nth a i;
      upd i (f x) a
-   done)"
+   }"
   by (rule Heap_eqI) (simp add: bind_def guard_def map_entry_def execute_simps)
 
 lemma [code]:
-  "swap i x a = (do
+  "swap i x a = do {
      y \<leftarrow> nth a i;
      upd i x a;
      return y
-   done)"
+   }"
   by (rule Heap_eqI) (simp add: bind_def guard_def swap_def execute_simps)
 
 lemma [code]:
-  "freeze a = (do
+  "freeze a = do {
      n \<leftarrow> len a;
      Heap_Monad.fold_map (\<lambda>i. nth a i) [0..<n]
-   done)"
+   }"
 proof (rule Heap_eqI)
   fix h
   have *: "List.map
@@ -440,15 +440,15 @@
     apply (simp_all add: nth_def guard_def *)
     apply (simp add: length_def map_nth)
     done
-  then have "execute (do
+  then have "execute (do {
       n \<leftarrow> len a;
       Heap_Monad.fold_map (Array.nth a) [0..<n]
-    done) h = Some (get_array a h, h)"
+    }) h = Some (get_array a h, h)"
     by (auto intro: execute_bind_eq_SomeI simp add: execute_simps)
-  then show "execute (freeze a) h = execute (do
+  then show "execute (freeze a) h = execute (do {
       n \<leftarrow> len a;
       Heap_Monad.fold_map (Array.nth a) [0..<n]
-    done) h" by (simp add: execute_simps)
+    }) h" by (simp add: execute_simps)
 qed
 
 hide_const (open) new' of_list' make' len' nth' upd'
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/Heap_Monad.thy
--- a/src/HOL/Imperative_HOL/Heap_Monad.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/Heap_Monad.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -5,7 +5,7 @@
 header {* A monad with a polymorphic heap and primitive reasoning infrastructure *}
 
 theory Heap_Monad
-imports Heap
+imports Heap Monad_Syntax
 begin
 
 subsection {* The monad *}
@@ -259,12 +259,16 @@
   obtains "False"
   using assms by (rule crelE) (simp add: success_def execute_simps)
 
-definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" (infixl ">>=" 54) where
-  [code del]: "f >>= g = Heap (\<lambda>h. case execute f h of
+definition bind :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" where
+  [code del]: "bind f g = Heap (\<lambda>h. case execute f h of
                   Some (x, h') \<Rightarrow> execute (g x) h'
                 | None \<Rightarrow> None)"
 
-notation bind (infixl "\<guillemotright>=" 54)
+setup {*
+  Adhoc_Overloading.add_variant 
+    @{const_name Monad_Syntax.bindM} @{const_name Heap_Monad.bind}
+*}
+
 
 lemma execute_bind [execute_simps]:
   "execute f h = Some (x, h') \<Longrightarrow> execute (f \<guillemotright>= g) h = execute (g x) h'"
@@ -314,92 +318,6 @@
 lemma raise_bind [simp]: "raise e \<guillemotright>= f = raise e"
   by (rule Heap_eqI) (simp add: execute_simps)
 
-abbreviation chain :: "'a Heap \<Rightarrow> 'b Heap \<Rightarrow> 'b Heap"  (infixl ">>" 54) where
-  "f >> g \<equiv> f >>= (\<lambda>_. g)"
-
-notation chain (infixl "\<guillemotright>" 54)
-
-
-subsubsection {* do-syntax *}
-
-text {*
-  We provide a convenient do-notation for monadic expressions
-  well-known from Haskell.  @{const Let} is printed
-  specially in do-expressions.
-*}
-
-nonterminals do_expr
-
-syntax
-  "_do" :: "do_expr \<Rightarrow> 'a"
-    ("(do (_)//done)" [12] 100)
-  "_bind" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
-    ("_ <- _;//_" [1000, 13, 12] 12)
-  "_chain" :: "'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
-    ("_;//_" [13, 12] 12)
-  "_let" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
-    ("let _ = _;//_" [1000, 13, 12] 12)
-  "_nil" :: "'a \<Rightarrow> do_expr"
-    ("_" [12] 12)
-
-syntax (xsymbols)
-  "_bind" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
-    ("_ \<leftarrow> _;//_" [1000, 13, 12] 12)
-
-translations
-  "_do f" => "f"
-  "_bind x f g" => "f \<guillemotright>= (\<lambda>x. g)"
-  "_chain f g" => "f \<guillemotright> g"
-  "_let x t f" => "CONST Let t (\<lambda>x. f)"
-  "_nil f" => "f"
-
-print_translation {*
-let
-  fun dest_abs_eta (Abs (abs as (_, ty, _))) =
-        let
-          val (v, t) = Syntax.variant_abs abs;
-        in (Free (v, ty), t) end
-    | dest_abs_eta t =
-        let
-          val (v, t) = Syntax.variant_abs ("", dummyT, t $ Bound 0);
-        in (Free (v, dummyT), t) end;
-  fun unfold_monad (Const (@{const_syntax bind}, _) $ f $ g) =
-        let
-          val (v, g') = dest_abs_eta g;
-          val vs = fold_aterms (fn Free (v, _) => insert (op =) v | _ => I) v [];
-          val v_used = fold_aterms
-            (fn Free (w, _) => (fn s => s orelse member (op =) vs w) | _ => I) g' false;
-        in if v_used then
-          Const (@{syntax_const "_bind"}, dummyT) $ v $ f $ unfold_monad g'
-        else
-          Const (@{syntax_const "_chain"}, dummyT) $ f $ unfold_monad g'
-        end
-    | unfold_monad (Const (@{const_syntax chain}, _) $ f $ g) =
-        Const (@{syntax_const "_chain"}, dummyT) $ f $ unfold_monad g
-    | unfold_monad (Const (@{const_syntax Let}, _) $ f $ g) =
-        let
-          val (v, g') = dest_abs_eta g;
-        in Const (@{syntax_const "_let"}, dummyT) $ v $ f $ unfold_monad g' end
-    | unfold_monad (Const (@{const_syntax Pair}, _) $ f) =
-        Const (@{const_syntax return}, dummyT) $ f
-    | unfold_monad f = f;
-  fun contains_bind (Const (@{const_syntax bind}, _) $ _ $ _) = true
-    | contains_bind (Const (@{const_syntax Let}, _) $ _ $ Abs (_, _, t)) =
-        contains_bind t;
-  fun bind_monad_tr' (f::g::ts) = list_comb
-    (Const (@{syntax_const "_do"}, dummyT) $
-      unfold_monad (Const (@{const_syntax bind}, dummyT) $ f $ g), ts);
-  fun Let_monad_tr' (f :: (g as Abs (_, _, g')) :: ts) =
-    if contains_bind g' then list_comb
-      (Const (@{syntax_const "_do"}, dummyT) $
-        unfold_monad (Const (@{const_syntax Let}, dummyT) $ f $ g), ts)
-    else raise Match;
-in
- [(@{const_syntax bind}, bind_monad_tr'),
-  (@{const_syntax Let}, Let_monad_tr')]
-end;
-*}
-
 
 subsection {* Generic combinators *}
 
@@ -451,11 +369,11 @@
 
 primrec fold_map :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap" where
   "fold_map f [] = return []"
-| "fold_map f (x # xs) = do
+| "fold_map f (x # xs) = do {
      y \<leftarrow> f x;
      ys \<leftarrow> fold_map f xs;
      return (y # ys)
-   done"
+   }"
 
 lemma fold_map_append:
   "fold_map f (xs @ ys) = fold_map f xs \<guillemotright>= (\<lambda>xs. fold_map f ys \<guillemotright>= (\<lambda>ys. return (xs @ ys)))"
@@ -611,7 +529,7 @@
 text {* Monad *}
 
 code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _")
-code_monad "op \<guillemotright>=" Haskell
+code_monad bind Haskell
 code_const return (Haskell "return")
 code_const Heap_Monad.raise' (Haskell "error/ _")
 
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/Mrec.thy
--- a/src/HOL/Imperative_HOL/Mrec.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/Mrec.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -64,13 +64,12 @@
 
 lemma MREC_rule:
   "MREC x = 
-  (do y \<leftarrow> f x;
+  do { y \<leftarrow> f x;
                 (case y of 
                 Inl r \<Rightarrow> return r
               | Inr s \<Rightarrow> 
-                do z \<leftarrow> MREC s ;
-                   g x s z
-                done) done)"
+                do { z \<leftarrow> MREC s ;
+                     g x s z })}"
   unfolding MREC_def
   unfolding bind_def return_def
   apply simp
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/Ref.thy
--- a/src/HOL/Imperative_HOL/Ref.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/Ref.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -48,12 +48,12 @@
   [code del]: "update r v = Heap_Monad.heap (\<lambda>h. ((), set r v h))"
 
 definition change :: "('a\<Colon>heap \<Rightarrow> 'a) \<Rightarrow> 'a ref \<Rightarrow> 'a Heap" where
-  "change f r = (do
+  "change f r = do {
      x \<leftarrow> ! r;
      let y = f x;
      r := y;
      return y
-   done)"
+   }"
 
 
 subsection {* Properties *}
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy
--- a/src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/ex/Imperative_Quicksort.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -12,14 +12,14 @@
 
 definition swap :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap"
 where
-  "swap arr i j = (
-     do
+  "swap arr i j =
+     do {
        x \<leftarrow> nth arr i;
        y \<leftarrow> nth arr j;
        upd i y arr;
        upd j x arr;
        return ()
-     done)"
+     }"
 
 lemma crel_swapI [crel_intros]:
   assumes "i < Array.length a h" "j < Array.length a h"
@@ -40,12 +40,12 @@
 where
   "part1 a left right p = (
      if (right \<le> left) then return right
-     else (do
+     else do {
        v \<leftarrow> nth a left;
        (if (v \<le> p) then (part1 a (left + 1) right p)
-                    else (do swap a left right;
-  part1 a left (right - 1) p done))
-     done))"
+                    else (do { swap a left right;
+  part1 a left (right - 1) p }))
+     })"
 by pat_completeness auto
 
 termination
@@ -227,14 +227,14 @@
 
 fun partition :: "nat array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat Heap"
 where
-  "partition a left right = (do
+  "partition a left right = do {
      pivot \<leftarrow> nth a right;
      middle \<leftarrow> part1 a left (right - 1) pivot;
      v \<leftarrow> nth a middle;
      m \<leftarrow> return (if (v \<le> pivot) then (middle + 1) else middle);
      swap a m right;
      return m
-   done)"
+   }"
 
 declare partition.simps[simp del]
 
@@ -402,12 +402,12 @@
 where
   "quicksort arr left right =
      (if (right > left)  then
-        do
+        do {
           pivotNewIndex \<leftarrow> partition arr left right;
           pivotNewIndex \<leftarrow> assert (\<lambda>x. left \<le> x \<and> x \<le> right) pivotNewIndex;
           quicksort arr left (pivotNewIndex - 1);
           quicksort arr (pivotNewIndex + 1) right
-        done
+        }
      else return ())"
 by pat_completeness auto
 
@@ -645,11 +645,11 @@
 
 subsection {* Example *}
 
-definition "qsort a = do
+definition "qsort a = do {
     k \<leftarrow> len a;
     quicksort a 0 (k - 1);
     return a
-  done"
+  }"
 
 code_reserved SML upto
 
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/ex/Imperative_Reverse.thy
--- a/src/HOL/Imperative_HOL/ex/Imperative_Reverse.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/ex/Imperative_Reverse.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -11,19 +11,19 @@
 hide_const (open) swap rev
 
 fun swap :: "'a\<Colon>heap array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap" where
-  "swap a i j = (do
+  "swap a i j = do {
      x \<leftarrow> nth a i;
      y \<leftarrow> nth a j;
      upd i y a;
      upd j x a;
      return ()
-   done)"
+   }"
 
 fun rev :: "'a\<Colon>heap array \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> unit Heap" where
-  "rev a i j = (if (i < j) then (do
+  "rev a i j = (if (i < j) then do {
      swap a i j;
      rev a (i + 1) (j - 1)
-   done)
+   }
    else return ())"
 
 notation (output) swap ("swap")
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/ex/Linked_Lists.thy
--- a/src/HOL/Imperative_HOL/ex/Linked_Lists.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/ex/Linked_Lists.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -31,10 +31,10 @@
 primrec make_llist :: "'a\<Colon>heap list \<Rightarrow> 'a node Heap"
 where 
   [simp del]: "make_llist []     = return Empty"
-            | "make_llist (x#xs) = do tl   \<leftarrow> make_llist xs;
-                                      next \<leftarrow> ref tl;
-                                      return (Node x next)
-                                   done"
+            | "make_llist (x#xs) = do { tl \<leftarrow> make_llist xs;
+                                        next \<leftarrow> ref tl;
+                                        return (Node x next)
+                                   }"
 
 
 text {* define traverse using the MREC combinator *}
@@ -43,18 +43,18 @@
   traverse :: "'a\<Colon>heap node \<Rightarrow> 'a list Heap"
 where
 [code del]: "traverse = MREC (\<lambda>n. case n of Empty \<Rightarrow> return (Inl [])
-                                | Node x r \<Rightarrow> (do tl \<leftarrow> Ref.lookup r;
-                                                  return (Inr tl) done))
+                                | Node x r \<Rightarrow> do { tl \<leftarrow> Ref.lookup r;
+                                                  return (Inr tl) })
                    (\<lambda>n tl xs. case n of Empty \<Rightarrow> undefined
                                       | Node x r \<Rightarrow> return (x # xs))"
 
 
 lemma traverse_simps[code, simp]:
   "traverse Empty      = return []"
-  "traverse (Node x r) = do tl \<leftarrow> Ref.lookup r;
-                            xs \<leftarrow> traverse tl;
-                            return (x#xs)
-                         done"
+  "traverse (Node x r) = do { tl \<leftarrow> Ref.lookup r;
+                              xs \<leftarrow> traverse tl;
+                              return (x#xs)
+                         }"
 unfolding traverse_def
 by (auto simp: traverse_def MREC_rule)
 
@@ -529,25 +529,25 @@
 subsection {* Definition of in-place reversal *}
 
 definition rev' :: "(('a::heap) node ref \<times> 'a node ref) \<Rightarrow> 'a node ref Heap"
-where "rev' = MREC (\<lambda>(q, p). do v \<leftarrow> !p; (case v of Empty \<Rightarrow> (return (Inl q))
-                            | Node x next \<Rightarrow> do
+where "rev' = MREC (\<lambda>(q, p). do { v \<leftarrow> !p; (case v of Empty \<Rightarrow> (return (Inl q))
+                            | Node x next \<Rightarrow> do {
                                     p := Node x q;
                                     return (Inr (p, next))
-                                  done) done)
+                                  })})
              (\<lambda>x s z. return z)"
 
 lemma rev'_simps [code]:
   "rev' (q, p) =
-   do
+   do {
      v \<leftarrow> !p;
      (case v of
         Empty \<Rightarrow> return q
       | Node x next \<Rightarrow>
-        do
+        do {
           p := Node x q;
           rev' (p, next)
-        done)
-  done"
+        })
+  }"
   unfolding rev'_def MREC_rule[of _ _ "(q, p)"] unfolding rev'_def[symmetric]
 thm arg_cong2
   by (auto simp add: expand_fun_eq intro: arg_cong2[where f = "op \<guillemotright>="] split: node.split)
@@ -555,7 +555,7 @@
 primrec rev :: "('a:: heap) node \<Rightarrow> 'a node Heap" 
 where
   "rev Empty = return Empty"
-| "rev (Node x n) = (do q \<leftarrow> ref Empty; p \<leftarrow> ref (Node x n); v \<leftarrow> rev' (q, p); !v done)"
+| "rev (Node x n) = do { q \<leftarrow> ref Empty; p \<leftarrow> ref (Node x n); v \<leftarrow> rev' (q, p); !v }"
 
 subsection {* Correctness Proof *}
 
@@ -680,7 +680,7 @@
 
 definition merge' :: "(('a::{heap, ord}) node ref * ('a::{heap, ord})) * ('a::{heap, ord}) node ref * ('a::{heap, ord}) node ref \<Rightarrow> ('a::{heap, ord}) node ref Heap"
 where
-"merge' = MREC (\<lambda>(_, p, q). (do v \<leftarrow> !p; w \<leftarrow> !q;
+"merge' = MREC (\<lambda>(_, p, q). do { v \<leftarrow> !p; w \<leftarrow> !q;
   (case v of Empty \<Rightarrow> return (Inl q)
           | Node valp np \<Rightarrow>
             (case w of Empty \<Rightarrow> return (Inl p)
@@ -688,8 +688,8 @@
                        if (valp \<le> valq) then
                          return (Inr ((p, valp), np, q))
                        else
-                         return (Inr ((q, valq), p, nq)))) done))
- (\<lambda> _ ((n, v), _, _) r. do n := Node v r; return n done)"
+                         return (Inr ((q, valq), p, nq)))) })
+ (\<lambda> _ ((n, v), _, _) r. do { n := Node v r; return n })"
 
 definition merge where "merge p q = merge' (undefined, p, q)"
 
@@ -713,21 +713,21 @@
 term "Ref.change"
 lemma merge_simps [code]:
 shows "merge p q =
-do v \<leftarrow> !p;
+do { v \<leftarrow> !p;
    w \<leftarrow> !q;
    (case v of node.Empty \<Rightarrow> return q
     | Node valp np \<Rightarrow>
         case w of node.Empty \<Rightarrow> return p
         | Node valq nq \<Rightarrow>
-            if valp \<le> valq then do r \<leftarrow> merge np q;
+            if valp \<le> valq then do { r \<leftarrow> merge np q;
                                    p := (Node valp r);
                                    return p
-                                done
-            else do r \<leftarrow> merge p nq;
+                                }
+            else do { r \<leftarrow> merge p nq;
                     q := (Node valq r);
                     return q
-                 done)
-done"
+                 })
+}"
 proof -
   {fix v x y
     have case_return: "(case v of Empty \<Rightarrow> return x | Node v n \<Rightarrow> return (y v n)) = return (case v of Empty \<Rightarrow> x | Node v n \<Rightarrow> y v n)" by (cases v) auto
@@ -997,11 +997,11 @@
 
 text {* A simple example program *}
 
-definition test_1 where "test_1 = (do ll_xs <- make_llist [1..(15::int)]; xs <- traverse ll_xs; return xs done)" 
-definition test_2 where "test_2 = (do ll_xs <- make_llist [1..(15::int)]; ll_ys <- rev ll_xs; ys <- traverse ll_ys; return ys done)"
+definition test_1 where "test_1 = (do { ll_xs <- make_llist [1..(15::int)]; xs <- traverse ll_xs; return xs })" 
+definition test_2 where "test_2 = (do { ll_xs <- make_llist [1..(15::int)]; ll_ys <- rev ll_xs; ys <- traverse ll_ys; return ys })"
 
 definition test_3 where "test_3 =
-  (do
+  (do {
     ll_xs \<leftarrow> make_llist (filter (%n. n mod 2 = 0) [2..8]);
     ll_ys \<leftarrow> make_llist (filter (%n. n mod 2 = 1) [5..11]);
     r \<leftarrow> ref ll_xs;
@@ -1010,7 +1010,7 @@
     ll_zs \<leftarrow> !p;
     zs \<leftarrow> traverse ll_zs;
     return zs
-  done)"
+  })"
 
 code_reserved SML upto
 
diff -r 0d6b64060543 -r ba0bc31b90d7 src/HOL/Imperative_HOL/ex/SatChecker.thy
--- a/src/HOL/Imperative_HOL/ex/SatChecker.thy	Tue Jul 13 11:50:22 2010 +0200
+++ b/src/HOL/Imperative_HOL/ex/SatChecker.thy	Tue Jul 13 12:00:11 2010 +0200
@@ -174,15 +174,15 @@
 primrec res_mem :: "Lit \<Rightarrow> Clause \<Rightarrow> Clause Heap"
 where
   "res_mem l [] = raise ''MiniSatChecked.res_thm: Cannot find literal''"
-| "res_mem l (x#xs) = (if (x = l) then return xs else (do v \<leftarrow> res_mem l xs; return (x # v) done))"
+| "res_mem l (x#xs) = (if (x = l) then return xs else do { v \<leftarrow> res_mem l xs; return (x # v) })"
 
 fun resolve1 :: "Lit \<Rightarrow> Clause \<Rightarrow> Clause \<Rightarrow> Clause Heap"
 where
   "resolve1 l (x#xs) (y#ys) =
   (if (x = l) then return (merge xs (y#ys))
-  else (if (x < y) then (do v \<leftarrow> resolve1 l xs (y#ys); return (x # v) done)
-  else (if (x > y) then (do v \<leftarrow> resolve1 l (x#xs) ys; return (y # v) done)
-  else (do v \<leftarrow> resolve1 l xs ys; return (x # v) done))))"
+  else (if (x < y) then do { v \<leftarrow> resolve1 l xs (y#ys); return (x # v) }
+  else (if (x > y) then do { v \<leftarrow> resolve1 l (x#xs) ys; return (y # v) }
+  else do { v \<leftarrow> resolve1 l xs ys; return (x # v) })))"
 | "resolve1 l [] ys = raise ''MiniSatChecked.res_thm: Cannot find literal''"
 | "resolve1 l xs [] = res_mem l xs"
 
@@ -190,9 +190,9 @@
 where
   "resolve2 l (x#xs) (y#ys) =
   (if (y = l) then return (merge (x#xs) ys)
-  else (if (x < y) then (do v \<leftarrow> resolve2 l xs (y#ys); return (x # v) done)
-  else (if (x > y) then (do v \<leftarrow> resolve2 l (x#xs) ys; return (y # v) done) 
-  else (do v \<leftarrow> resolve2 l xs ys; return (x # v) done))))"
+  else (if (x < y) then do { v \<leftarrow> resolve2 l xs (y#ys); return (x # v) }
+  else (if (x > y) then do { v \<leftarrow> resolve2 l (x#xs) ys; return (y # v) }
+  else do { v \<leftarrow> resolve2 l xs ys; return (x # v) })))"
   | "resolve2 l xs [] = raise ''MiniSatChecked.res_thm: Cannot find literal''"
   | "resolve2 l [] ys = res_mem l ys"
 
@@ -413,10 +413,10 @@
 definition get_clause :: "Clause option array \<Rightarrow> ClauseId \<Rightarrow> Clause Heap"
 where
   "get_clause a i = 
-       (do c \<leftarrow> nth a i;
+       do { c \<leftarrow> nth a i;
            (case c of None \<Rightarrow> raise (''Clause not found'')
                     | Some x \<Rightarrow> return x)
-        done)"
+       }"
 
 
 primrec res_thm2 :: "Clause option array \<Rightarrow> (Lit * ClauseId) \<Rightarrow> Clause \<Rightarrow> Clause Heap"
@@ -424,9 +424,9 @@
   "res_thm2 a (l, j) cli =
   ( if l = 0 then raise(''Illegal literal'')
     else
-     (do clj \<leftarrow> get_clause a j;
+     do { clj \<leftarrow> get_clause a j;
          res_thm' l cli clj
-      done))"
+     })"
 
 primrec
   foldM :: "('a \<Rightarrow> 'b \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b \<Rightarrow> 'b Heap"
@@ -437,27 +437,27 @@
 fun doProofStep2 :: "Clause option array \<Rightarrow> ProofStep \<Rightarrow> Clause list \<Rightarrow> Clause list Heap"
 where
   "doProofStep2 a (Conflict saveTo (i, rs)) rcs =
-  (do
+  do {
      cli \<leftarrow> get_clause a i;
      result \<leftarrow> foldM (res_thm2 a) rs cli;
      upd saveTo (Some result) a; 
      return rcs
-   done)"
-| "doProofStep2 a (Delete cid) rcs = (do upd cid None a; return rcs done)"
-| "doProofStep2 a (Root cid clause) rcs = (do upd cid (Some (remdups (sort clause))) a; return (clause # rcs) done)"
+  }"
+| "doProofStep2 a (Delete cid) rcs = do { upd cid None a; return rcs }"
+| "doProofStep2 a (Root cid clause) rcs = do { upd cid (Some (remdups (sort clause))) a; return (clause # rcs) }"
 | "doProofStep2 a (Xstep cid1 cid2) rcs = raise ''MiniSatChecked.doProofStep: Xstep constructor found.''"
 | "doProofStep2 a (ProofDone b) rcs = raise ''MiniSatChecked.doProofStep: ProofDone constructor found.''"
 
 definition checker :: "nat \<Rightarrow> ProofStep list \<Rightarrow> nat \<Rightarrow> Clause list Heap"
 where
   "checker n p i =
-  (do 
+  do {
      a \<leftarrow> Array.new n None;
      rcs \<leftarrow> foldM (doProofStep2 a) p [];
      ec \<leftarrow> Array.nth a i;
      (if ec = Some [] then return rcs 
                 else raise(''No empty clause''))
-   done)"
+  }"
 
 lemma crel_option_case:
   assumes "crel (case x of None \<Rightarrow> n | Some y \<Rightarrow> s y) h h' r"
@@ -651,10 +651,10 @@
   "ldoProofStep (Conflict saveTo (i, rs)) (xs, rcl) =
      (case (xs ! i) of
        None \<Rightarrow> raise (''MiniSatChecked.doProofStep: No starting clause in thms array for Conflict step.'')
-     | Some cli \<Rightarrow> (do
+     | Some cli \<Rightarrow> do {
                       result \<leftarrow> foldM (lres_thm xs) rs cli ;
                       return ((xs[saveTo:=Some result]), rcl)
-                    done))"
+                   })"
 | "ldoProofStep (Delete cid) (xs, rcl) = return (xs[cid:=None], rcl)"
 | "ldoProofStep (Root cid clause) (xs, rcl) = return (xs[cid:=Some (sort clause)], (remdups(sort clause)) # rcl)"
 | "ldoProofStep (Xstep cid1 cid2) (xs, rcl) = raise ''MiniSatChecked.doProofStep: Xstep constructor found.''"
@@ -663,11 +663,11 @@
 definition lchecker :: "nat \<Rightarrow> ProofStep list \<Rightarrow> nat \<Rightarrow> Clause list Heap"
 where
   "lchecker n p i =
-  (do 
+  do {
      rcs \<leftarrow> foldM (ldoProofStep) p ([], []);
      (if (fst rcs ! i) = Some [] then return (snd rcs) 
                 else raise(''No empty clause''))
-   done)"
+  }"
 
 
 section {* Functional version with RedBlackTrees *}
@@ -684,10 +684,10 @@
   "tdoProofStep (Conflict saveTo (i, rs)) (t, rcl) =
      (case (RBT_Impl.lookup t i) of
        None \<Rightarrow> raise (''MiniSatChecked.doProofStep: No starting clause in thms array for Conflict step.'')
-     | Some cli \<Rightarrow> (do
+     | Some cli \<Rightarrow> do {
                       result \<leftarrow> foldM (tres_thm t) rs cli;
                       return ((RBT_Impl.insert saveTo result t), rcl)
-                    done))"
+                   })"
 | "tdoProofStep (Delete cid) (t, rcl) = return ((RBT_Impl.delete cid t), rcl)"
 | "tdoProofStep (Root cid clause) (t, rcl) = return (RBT_Impl.insert cid (sort clause) t, (remdups(sort clause)) # rcl)"
 | "tdoProofStep (Xstep cid1 cid2) (t, rcl) = raise ''MiniSatChecked.doProofStep: Xstep constructor found.''"
@@ -696,11 +696,11 @@
 definition tchecker :: "nat \<Rightarrow> ProofStep list \<Rightarrow> nat \<Rightarrow> Clause list Heap"
 where
   "tchecker n p i =
-  (do 
+  do {
      rcs \<leftarrow> foldM (tdoProofStep) p (RBT_Impl.Empty, []);
      (if (RBT_Impl.lookup (fst rcs) i) = Some [] then return (snd rcs) 
                 else raise(''No empty clause''))
-   done)"
+  }"
 
 section {* Code generation setup *}