author wenzelm Fri Apr 16 21:28:09 2010 +0200 (2010-04-16) changeset 36176 3fe7e97ccca8 parent 36078 59f6773a7d1d child 37591 d3daea901123 permissions -rw-r--r--
replaced generic 'hide' command by more conventional 'hide_class', 'hide_type', 'hide_const', 'hide_fact' -- frees some popular keywords;
```     1 (*  Title:      HOL/Library/Heap_Monad.thy
```
```     2     Author:     John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen
```
```     3 *)
```
```     4
```
```     5 header {* A monad with a polymorphic heap *}
```
```     6
```
```     7 theory Heap_Monad
```
```     8 imports Heap
```
```     9 begin
```
```    10
```
```    11 subsection {* The monad *}
```
```    12
```
```    13 subsubsection {* Monad combinators *}
```
```    14
```
```    15 datatype exception = Exn
```
```    16
```
```    17 text {* Monadic heap actions either produce values
```
```    18   and transform the heap, or fail *}
```
```    19 datatype 'a Heap = Heap "heap \<Rightarrow> ('a + exception) \<times> heap"
```
```    20
```
```    21 primrec
```
```    22   execute :: "'a Heap \<Rightarrow> heap \<Rightarrow> ('a + exception) \<times> heap" where
```
```    23   "execute (Heap f) = f"
```
```    24 lemmas [code del] = execute.simps
```
```    25
```
```    26 lemma Heap_execute [simp]:
```
```    27   "Heap (execute f) = f" by (cases f) simp_all
```
```    28
```
```    29 lemma Heap_eqI:
```
```    30   "(\<And>h. execute f h = execute g h) \<Longrightarrow> f = g"
```
```    31     by (cases f, cases g) (auto simp: expand_fun_eq)
```
```    32
```
```    33 lemma Heap_eqI':
```
```    34   "(\<And>h. (\<lambda>x. execute (f x) h) = (\<lambda>y. execute (g y) h)) \<Longrightarrow> f = g"
```
```    35     by (auto simp: expand_fun_eq intro: Heap_eqI)
```
```    36
```
```    37 lemma Heap_strip: "(\<And>f. PROP P f) \<equiv> (\<And>g. PROP P (Heap g))"
```
```    38 proof
```
```    39   fix g :: "heap \<Rightarrow> ('a + exception) \<times> heap"
```
```    40   assume "\<And>f. PROP P f"
```
```    41   then show "PROP P (Heap g)" .
```
```    42 next
```
```    43   fix f :: "'a Heap"
```
```    44   assume assm: "\<And>g. PROP P (Heap g)"
```
```    45   then have "PROP P (Heap (execute f))" .
```
```    46   then show "PROP P f" by simp
```
```    47 qed
```
```    48
```
```    49 definition
```
```    50   heap :: "(heap \<Rightarrow> 'a \<times> heap) \<Rightarrow> 'a Heap" where
```
```    51   [code del]: "heap f = Heap (\<lambda>h. apfst Inl (f h))"
```
```    52
```
```    53 lemma execute_heap [simp]:
```
```    54   "execute (heap f) h = apfst Inl (f h)"
```
```    55   by (simp add: heap_def)
```
```    56
```
```    57 definition
```
```    58   bindM :: "'a Heap \<Rightarrow> ('a \<Rightarrow> 'b Heap) \<Rightarrow> 'b Heap" (infixl ">>=" 54) where
```
```    59   [code del]: "f >>= g = Heap (\<lambda>h. case execute f h of
```
```    60                   (Inl x, h') \<Rightarrow> execute (g x) h'
```
```    61                 | r \<Rightarrow> r)"
```
```    62
```
```    63 notation
```
```    64   bindM (infixl "\<guillemotright>=" 54)
```
```    65
```
```    66 abbreviation
```
```    67   chainM :: "'a Heap \<Rightarrow> 'b Heap \<Rightarrow> 'b Heap"  (infixl ">>" 54) where
```
```    68   "f >> g \<equiv> f >>= (\<lambda>_. g)"
```
```    69
```
```    70 notation
```
```    71   chainM (infixl "\<guillemotright>" 54)
```
```    72
```
```    73 definition
```
```    74   return :: "'a \<Rightarrow> 'a Heap" where
```
```    75   [code del]: "return x = heap (Pair x)"
```
```    76
```
```    77 lemma execute_return [simp]:
```
```    78   "execute (return x) h = apfst Inl (x, h)"
```
```    79   by (simp add: return_def)
```
```    80
```
```    81 definition
```
```    82   raise :: "string \<Rightarrow> 'a Heap" where -- {* the string is just decoration *}
```
```    83   [code del]: "raise s = Heap (Pair (Inr Exn))"
```
```    84
```
```    85 lemma execute_raise [simp]:
```
```    86   "execute (raise s) h = (Inr Exn, h)"
```
```    87   by (simp add: raise_def)
```
```    88
```
```    89
```
```    90 subsubsection {* do-syntax *}
```
```    91
```
```    92 text {*
```
```    93   We provide a convenient do-notation for monadic expressions
```
```    94   well-known from Haskell.  @{const Let} is printed
```
```    95   specially in do-expressions.
```
```    96 *}
```
```    97
```
```    98 nonterminals do_expr
```
```    99
```
```   100 syntax
```
```   101   "_do" :: "do_expr \<Rightarrow> 'a"
```
```   102     ("(do (_)//done)" [12] 100)
```
```   103   "_bindM" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
```
```   104     ("_ <- _;//_" [1000, 13, 12] 12)
```
```   105   "_chainM" :: "'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
```
```   106     ("_;//_" [13, 12] 12)
```
```   107   "_let" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
```
```   108     ("let _ = _;//_" [1000, 13, 12] 12)
```
```   109   "_nil" :: "'a \<Rightarrow> do_expr"
```
```   110     ("_" [12] 12)
```
```   111
```
```   112 syntax (xsymbols)
```
```   113   "_bindM" :: "pttrn \<Rightarrow> 'a \<Rightarrow> do_expr \<Rightarrow> do_expr"
```
```   114     ("_ \<leftarrow> _;//_" [1000, 13, 12] 12)
```
```   115
```
```   116 translations
```
```   117   "_do f" => "f"
```
```   118   "_bindM x f g" => "f \<guillemotright>= (\<lambda>x. g)"
```
```   119   "_chainM f g" => "f \<guillemotright> g"
```
```   120   "_let x t f" => "CONST Let t (\<lambda>x. f)"
```
```   121   "_nil f" => "f"
```
```   122
```
```   123 print_translation {*
```
```   124 let
```
```   125   fun dest_abs_eta (Abs (abs as (_, ty, _))) =
```
```   126         let
```
```   127           val (v, t) = Syntax.variant_abs abs;
```
```   128         in (Free (v, ty), t) end
```
```   129     | dest_abs_eta t =
```
```   130         let
```
```   131           val (v, t) = Syntax.variant_abs ("", dummyT, t \$ Bound 0);
```
```   132         in (Free (v, dummyT), t) end;
```
```   133   fun unfold_monad (Const (@{const_syntax bindM}, _) \$ f \$ g) =
```
```   134         let
```
```   135           val (v, g') = dest_abs_eta g;
```
```   136           val vs = fold_aterms (fn Free (v, _) => insert (op =) v | _ => I) v [];
```
```   137           val v_used = fold_aterms
```
```   138             (fn Free (w, _) => (fn s => s orelse member (op =) vs w) | _ => I) g' false;
```
```   139         in if v_used then
```
```   140           Const (@{syntax_const "_bindM"}, dummyT) \$ v \$ f \$ unfold_monad g'
```
```   141         else
```
```   142           Const (@{syntax_const "_chainM"}, dummyT) \$ f \$ unfold_monad g'
```
```   143         end
```
```   144     | unfold_monad (Const (@{const_syntax chainM}, _) \$ f \$ g) =
```
```   145         Const (@{syntax_const "_chainM"}, dummyT) \$ f \$ unfold_monad g
```
```   146     | unfold_monad (Const (@{const_syntax Let}, _) \$ f \$ g) =
```
```   147         let
```
```   148           val (v, g') = dest_abs_eta g;
```
```   149         in Const (@{syntax_const "_let"}, dummyT) \$ v \$ f \$ unfold_monad g' end
```
```   150     | unfold_monad (Const (@{const_syntax Pair}, _) \$ f) =
```
```   151         Const (@{const_syntax return}, dummyT) \$ f
```
```   152     | unfold_monad f = f;
```
```   153   fun contains_bindM (Const (@{const_syntax bindM}, _) \$ _ \$ _) = true
```
```   154     | contains_bindM (Const (@{const_syntax Let}, _) \$ _ \$ Abs (_, _, t)) =
```
```   155         contains_bindM t;
```
```   156   fun bindM_monad_tr' (f::g::ts) = list_comb
```
```   157     (Const (@{syntax_const "_do"}, dummyT) \$
```
```   158       unfold_monad (Const (@{const_syntax bindM}, dummyT) \$ f \$ g), ts);
```
```   159   fun Let_monad_tr' (f :: (g as Abs (_, _, g')) :: ts) =
```
```   160     if contains_bindM g' then list_comb
```
```   161       (Const (@{syntax_const "_do"}, dummyT) \$
```
```   162         unfold_monad (Const (@{const_syntax Let}, dummyT) \$ f \$ g), ts)
```
```   163     else raise Match;
```
```   164 in
```
```   165  [(@{const_syntax bindM}, bindM_monad_tr'),
```
```   166   (@{const_syntax Let}, Let_monad_tr')]
```
```   167 end;
```
```   168 *}
```
```   169
```
```   170
```
```   171 subsection {* Monad properties *}
```
```   172
```
```   173 subsubsection {* Monad laws *}
```
```   174
```
```   175 lemma return_bind: "return x \<guillemotright>= f = f x"
```
```   176   by (simp add: bindM_def return_def)
```
```   177
```
```   178 lemma bind_return: "f \<guillemotright>= return = f"
```
```   179 proof (rule Heap_eqI)
```
```   180   fix h
```
```   181   show "execute (f \<guillemotright>= return) h = execute f h"
```
```   182     by (auto simp add: bindM_def return_def split: sum.splits prod.splits)
```
```   183 qed
```
```   184
```
```   185 lemma bind_bind: "(f \<guillemotright>= g) \<guillemotright>= h = f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= h)"
```
```   186   by (rule Heap_eqI) (auto simp add: bindM_def split: split: sum.splits prod.splits)
```
```   187
```
```   188 lemma bind_bind': "f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= h x) = f \<guillemotright>= (\<lambda>x. g x \<guillemotright>= (\<lambda>y. return (x, y))) \<guillemotright>= (\<lambda>(x, y). h x y)"
```
```   189   by (rule Heap_eqI) (auto simp add: bindM_def split: split: sum.splits prod.splits)
```
```   190
```
```   191 lemma raise_bind: "raise e \<guillemotright>= f = raise e"
```
```   192   by (simp add: raise_def bindM_def)
```
```   193
```
```   194
```
```   195 lemmas monad_simp = return_bind bind_return bind_bind raise_bind
```
```   196
```
```   197
```
```   198 subsection {* Generic combinators *}
```
```   199
```
```   200 definition
```
```   201   liftM :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b Heap"
```
```   202 where
```
```   203   "liftM f = return o f"
```
```   204
```
```   205 definition
```
```   206   compM :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> ('b \<Rightarrow> 'c Heap) \<Rightarrow> 'a \<Rightarrow> 'c Heap" (infixl ">>==" 54)
```
```   207 where
```
```   208   "(f >>== g) = (\<lambda>x. f x \<guillemotright>= g)"
```
```   209
```
```   210 notation
```
```   211   compM (infixl "\<guillemotright>==" 54)
```
```   212
```
```   213 lemma liftM_collapse: "liftM f x = return (f x)"
```
```   214   by (simp add: liftM_def)
```
```   215
```
```   216 lemma liftM_compM: "liftM f \<guillemotright>== g = g o f"
```
```   217   by (auto intro: Heap_eqI' simp add: expand_fun_eq liftM_def compM_def bindM_def)
```
```   218
```
```   219 lemma compM_return: "f \<guillemotright>== return = f"
```
```   220   by (simp add: compM_def monad_simp)
```
```   221
```
```   222 lemma compM_compM: "(f \<guillemotright>== g) \<guillemotright>== h = f \<guillemotright>== (g \<guillemotright>== h)"
```
```   223   by (simp add: compM_def monad_simp)
```
```   224
```
```   225 lemma liftM_bind:
```
```   226   "(\<lambda>x. liftM f x \<guillemotright>= liftM g) = liftM (\<lambda>x. g (f x))"
```
```   227   by (rule Heap_eqI') (simp add: monad_simp liftM_def bindM_def)
```
```   228
```
```   229 lemma liftM_comp:
```
```   230   "liftM f o g = liftM (f o g)"
```
```   231   by (rule Heap_eqI') (simp add: liftM_def)
```
```   232
```
```   233 lemmas monad_simp' = monad_simp liftM_compM compM_return
```
```   234   compM_compM liftM_bind liftM_comp
```
```   235
```
```   236 primrec
```
```   237   mapM :: "('a \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b list Heap"
```
```   238 where
```
```   239   "mapM f [] = return []"
```
```   240   | "mapM f (x#xs) = do y \<leftarrow> f x;
```
```   241                         ys \<leftarrow> mapM f xs;
```
```   242                         return (y # ys)
```
```   243                      done"
```
```   244
```
```   245 primrec
```
```   246   foldM :: "('a \<Rightarrow> 'b \<Rightarrow> 'b Heap) \<Rightarrow> 'a list \<Rightarrow> 'b \<Rightarrow> 'b Heap"
```
```   247 where
```
```   248   "foldM f [] s = return s"
```
```   249   | "foldM f (x#xs) s = f x s \<guillemotright>= foldM f xs"
```
```   250
```
```   251 definition
```
```   252   assert :: "('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> 'a Heap"
```
```   253 where
```
```   254   "assert P x = (if P x then return x else raise (''assert''))"
```
```   255
```
```   256 lemma assert_cong [fundef_cong]:
```
```   257   assumes "P = P'"
```
```   258   assumes "\<And>x. P' x \<Longrightarrow> f x = f' x"
```
```   259   shows "(assert P x >>= f) = (assert P' x >>= f')"
```
```   260   using assms by (auto simp add: assert_def return_bind raise_bind)
```
```   261
```
```   262 subsubsection {* A monadic combinator for simple recursive functions *}
```
```   263
```
```   264 text {* Using a locale to fix arguments f and g of MREC *}
```
```   265
```
```   266 locale mrec =
```
```   267 fixes
```
```   268   f :: "'a => ('b + 'a) Heap"
```
```   269   and g :: "'a => 'a => 'b => 'b Heap"
```
```   270 begin
```
```   271
```
```   272 function (default "\<lambda>(x,h). (Inr Exn, undefined)")
```
```   273   mrec
```
```   274 where
```
```   275   "mrec x h =
```
```   276    (case Heap_Monad.execute (f x) h of
```
```   277      (Inl (Inl r), h') \<Rightarrow> (Inl r, h')
```
```   278    | (Inl (Inr s), h') \<Rightarrow>
```
```   279           (case mrec s h' of
```
```   280              (Inl z, h'') \<Rightarrow> Heap_Monad.execute (g x s z) h''
```
```   281            | (Inr e, h'') \<Rightarrow> (Inr e, h''))
```
```   282    | (Inr e, h') \<Rightarrow> (Inr e, h')
```
```   283    )"
```
```   284 by auto
```
```   285
```
```   286 lemma graph_implies_dom:
```
```   287   "mrec_graph x y \<Longrightarrow> mrec_dom x"
```
```   288 apply (induct rule:mrec_graph.induct)
```
```   289 apply (rule accpI)
```
```   290 apply (erule mrec_rel.cases)
```
```   291 by simp
```
```   292
```
```   293 lemma mrec_default: "\<not> mrec_dom (x, h) \<Longrightarrow> mrec x h = (Inr Exn, undefined)"
```
```   294   unfolding mrec_def
```
```   295   by (rule fundef_default_value[OF mrec_sumC_def graph_implies_dom, of _ _ "(x, h)", simplified])
```
```   296
```
```   297 lemma mrec_di_reverse:
```
```   298   assumes "\<not> mrec_dom (x, h)"
```
```   299   shows "
```
```   300    (case Heap_Monad.execute (f x) h of
```
```   301      (Inl (Inl r), h') \<Rightarrow> False
```
```   302    | (Inl (Inr s), h') \<Rightarrow> \<not> mrec_dom (s, h')
```
```   303    | (Inr e, h') \<Rightarrow> False
```
```   304    )"
```
```   305 using assms
```
```   306 by (auto split:prod.splits sum.splits)
```
```   307  (erule notE, rule accpI, elim mrec_rel.cases, simp)+
```
```   308
```
```   309
```
```   310 lemma mrec_rule:
```
```   311   "mrec x h =
```
```   312    (case Heap_Monad.execute (f x) h of
```
```   313      (Inl (Inl r), h') \<Rightarrow> (Inl r, h')
```
```   314    | (Inl (Inr s), h') \<Rightarrow>
```
```   315           (case mrec s h' of
```
```   316              (Inl z, h'') \<Rightarrow> Heap_Monad.execute (g x s z) h''
```
```   317            | (Inr e, h'') \<Rightarrow> (Inr e, h''))
```
```   318    | (Inr e, h') \<Rightarrow> (Inr e, h')
```
```   319    )"
```
```   320 apply (cases "mrec_dom (x,h)", simp)
```
```   321 apply (frule mrec_default)
```
```   322 apply (frule mrec_di_reverse, simp)
```
```   323 by (auto split: sum.split prod.split simp: mrec_default)
```
```   324
```
```   325
```
```   326 definition
```
```   327   "MREC x = Heap (mrec x)"
```
```   328
```
```   329 lemma MREC_rule:
```
```   330   "MREC x =
```
```   331   (do y \<leftarrow> f x;
```
```   332                 (case y of
```
```   333                 Inl r \<Rightarrow> return r
```
```   334               | Inr s \<Rightarrow>
```
```   335                 do z \<leftarrow> MREC s ;
```
```   336                    g x s z
```
```   337                 done) done)"
```
```   338   unfolding MREC_def
```
```   339   unfolding bindM_def return_def
```
```   340   apply simp
```
```   341   apply (rule ext)
```
```   342   apply (unfold mrec_rule[of x])
```
```   343   by (auto split:prod.splits sum.splits)
```
```   344
```
```   345
```
```   346 lemma MREC_pinduct:
```
```   347   assumes "Heap_Monad.execute (MREC x) h = (Inl r, h')"
```
```   348   assumes non_rec_case: "\<And> x h h' r. Heap_Monad.execute (f x) h = (Inl (Inl r), h') \<Longrightarrow> P x h h' r"
```
```   349   assumes rec_case: "\<And> x h h1 h2 h' s z r. Heap_Monad.execute (f x) h = (Inl (Inr s), h1) \<Longrightarrow> Heap_Monad.execute (MREC s) h1 = (Inl z, h2) \<Longrightarrow> P s h1 h2 z
```
```   350     \<Longrightarrow> Heap_Monad.execute (g x s z) h2 = (Inl r, h') \<Longrightarrow> P x h h' r"
```
```   351   shows "P x h h' r"
```
```   352 proof -
```
```   353   from assms(1) have mrec: "mrec x h = (Inl r, h')"
```
```   354     unfolding MREC_def execute.simps .
```
```   355   from mrec have dom: "mrec_dom (x, h)"
```
```   356     apply -
```
```   357     apply (rule ccontr)
```
```   358     apply (drule mrec_default) by auto
```
```   359   from mrec have h'_r: "h' = (snd (mrec x h))" "r = (Sum_Type.Projl (fst (mrec x h)))"
```
```   360     by auto
```
```   361   from mrec have "P x h (snd (mrec x h)) (Sum_Type.Projl (fst (mrec x h)))"
```
```   362   proof (induct arbitrary: r h' rule: mrec.pinduct[OF dom])
```
```   363     case (1 x h)
```
```   364     obtain rr h' where "mrec x h = (rr, h')" by fastsimp
```
```   365     obtain fret h1 where exec_f: "Heap_Monad.execute (f x) h = (fret, h1)" by fastsimp
```
```   366     show ?case
```
```   367     proof (cases fret)
```
```   368       case (Inl a)
```
```   369       note Inl' = this
```
```   370       show ?thesis
```
```   371       proof (cases a)
```
```   372         case (Inl aa)
```
```   373         from this Inl' 1(1) exec_f mrec non_rec_case show ?thesis
```
```   374           by auto
```
```   375       next
```
```   376         case (Inr b)
```
```   377         note Inr' = this
```
```   378         obtain ret_mrec h2 where mrec_rec: "mrec b h1 = (ret_mrec, h2)" by fastsimp
```
```   379         from this Inl 1(1) exec_f mrec show ?thesis
```
```   380         proof (cases "ret_mrec")
```
```   381           case (Inl aaa)
```
```   382           from this mrec exec_f Inl' Inr' 1(1) mrec_rec 1(2)[OF exec_f Inl' Inr', of "aaa" "h2"] 1(3)
```
```   383             show ?thesis
```
```   384               apply auto
```
```   385               apply (rule rec_case)
```
```   386               unfolding MREC_def by auto
```
```   387         next
```
```   388           case (Inr b)
```
```   389           from this Inl 1(1) exec_f mrec Inr' mrec_rec 1(3) show ?thesis by auto
```
```   390         qed
```
```   391       qed
```
```   392     next
```
```   393       case (Inr b)
```
```   394       from this 1(1) mrec exec_f 1(3) show ?thesis by simp
```
```   395     qed
```
```   396   qed
```
```   397   from this h'_r show ?thesis by simp
```
```   398 qed
```
```   399
```
```   400 end
```
```   401
```
```   402 text {* Providing global versions of the constant and the theorems *}
```
```   403
```
```   404 abbreviation "MREC == mrec.MREC"
```
```   405 lemmas MREC_rule = mrec.MREC_rule
```
```   406 lemmas MREC_pinduct = mrec.MREC_pinduct
```
```   407
```
```   408 hide_const (open) heap execute
```
```   409
```
```   410
```
```   411 subsection {* Code generator setup *}
```
```   412
```
```   413 subsubsection {* Logical intermediate layer *}
```
```   414
```
```   415 definition
```
```   416   Fail :: "String.literal \<Rightarrow> exception"
```
```   417 where
```
```   418   [code del]: "Fail s = Exn"
```
```   419
```
```   420 definition
```
```   421   raise_exc :: "exception \<Rightarrow> 'a Heap"
```
```   422 where
```
```   423   [code del]: "raise_exc e = raise []"
```
```   424
```
```   425 lemma raise_raise_exc [code, code_unfold]:
```
```   426   "raise s = raise_exc (Fail (STR s))"
```
```   427   unfolding Fail_def raise_exc_def raise_def ..
```
```   428
```
```   429 hide_const (open) Fail raise_exc
```
```   430
```
```   431
```
```   432 subsubsection {* SML and OCaml *}
```
```   433
```
```   434 code_type Heap (SML "unit/ ->/ _")
```
```   435 code_const Heap (SML "raise/ (Fail/ \"bare Heap\")")
```
```   436 code_const "op \<guillemotright>=" (SML "!(fn/ f'_/ =>/ fn/ ()/ =>/ f'_/ (_/ ())/ ())")
```
```   437 code_const return (SML "!(fn/ ()/ =>/ _)")
```
```   438 code_const "Heap_Monad.Fail" (SML "Fail")
```
```   439 code_const "Heap_Monad.raise_exc" (SML "!(fn/ ()/ =>/ raise/ _)")
```
```   440
```
```   441 code_type Heap (OCaml "_")
```
```   442 code_const Heap (OCaml "failwith/ \"bare Heap\"")
```
```   443 code_const "op \<guillemotright>=" (OCaml "!(fun/ f'_/ ()/ ->/ f'_/ (_/ ())/ ())")
```
```   444 code_const return (OCaml "!(fun/ ()/ ->/ _)")
```
```   445 code_const "Heap_Monad.Fail" (OCaml "Failure")
```
```   446 code_const "Heap_Monad.raise_exc" (OCaml "!(fun/ ()/ ->/ raise/ _)")
```
```   447
```
```   448 setup {*
```
```   449
```
```   450 let
```
```   451
```
```   452 open Code_Thingol;
```
```   453
```
```   454 fun imp_program naming =
```
```   455
```
```   456   let
```
```   457     fun is_const c = case lookup_const naming c
```
```   458      of SOME c' => (fn c'' => c' = c'')
```
```   459       | NONE => K false;
```
```   460     val is_bindM = is_const @{const_name bindM};
```
```   461     val is_return = is_const @{const_name return};
```
```   462     val dummy_name = "";
```
```   463     val dummy_type = ITyVar dummy_name;
```
```   464     val dummy_case_term = IVar NONE;
```
```   465     (*assumption: dummy values are not relevant for serialization*)
```
```   466     val unitt = case lookup_const naming @{const_name Unity}
```
```   467      of SOME unit' => IConst (unit', (([], []), []))
```
```   468       | NONE => error ("Must include " ^ @{const_name Unity} ^ " in generated constants.");
```
```   469     fun dest_abs ((v, ty) `|=> t, _) = ((v, ty), t)
```
```   470       | dest_abs (t, ty) =
```
```   471           let
```
```   472             val vs = fold_varnames cons t [];
```
```   473             val v = Name.variant vs "x";
```
```   474             val ty' = (hd o fst o unfold_fun) ty;
```
```   475           in ((SOME v, ty'), t `\$ IVar (SOME v)) end;
```
```   476     fun force (t as IConst (c, _) `\$ t') = if is_return c
```
```   477           then t' else t `\$ unitt
```
```   478       | force t = t `\$ unitt;
```
```   479     fun tr_bind' [(t1, _), (t2, ty2)] =
```
```   480       let
```
```   481         val ((v, ty), t) = dest_abs (t2, ty2);
```
```   482       in ICase (((force t1, ty), [(IVar v, tr_bind'' t)]), dummy_case_term) end
```
```   483     and tr_bind'' t = case unfold_app t
```
```   484          of (IConst (c, (_, ty1 :: ty2 :: _)), [x1, x2]) => if is_bindM c
```
```   485               then tr_bind' [(x1, ty1), (x2, ty2)]
```
```   486               else force t
```
```   487           | _ => force t;
```
```   488     fun imp_monad_bind'' ts = (SOME dummy_name, dummy_type) `|=> ICase (((IVar (SOME dummy_name), dummy_type),
```
```   489       [(unitt, tr_bind' ts)]), dummy_case_term)
```
```   490     and imp_monad_bind' (const as (c, (_, tys))) ts = if is_bindM c then case (ts, tys)
```
```   491        of ([t1, t2], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)]
```
```   492         | ([t1, t2, t3], ty1 :: ty2 :: _) => imp_monad_bind'' [(t1, ty1), (t2, ty2)] `\$ t3
```
```   493         | (ts, _) => imp_monad_bind (eta_expand 2 (const, ts))
```
```   494       else IConst const `\$\$ map imp_monad_bind ts
```
```   495     and imp_monad_bind (IConst const) = imp_monad_bind' const []
```
```   496       | imp_monad_bind (t as IVar _) = t
```
```   497       | imp_monad_bind (t as _ `\$ _) = (case unfold_app t
```
```   498          of (IConst const, ts) => imp_monad_bind' const ts
```
```   499           | (t, ts) => imp_monad_bind t `\$\$ map imp_monad_bind ts)
```
```   500       | imp_monad_bind (v_ty `|=> t) = v_ty `|=> imp_monad_bind t
```
```   501       | imp_monad_bind (ICase (((t, ty), pats), t0)) = ICase
```
```   502           (((imp_monad_bind t, ty),
```
```   503             (map o pairself) imp_monad_bind pats),
```
```   504               imp_monad_bind t0);
```
```   505
```
```   506   in (Graph.map_nodes o map_terms_stmt) imp_monad_bind end;
```
```   507
```
```   508 in
```
```   509
```
```   510 Code_Target.extend_target ("SML_imp", ("SML", imp_program))
```
```   511 #> Code_Target.extend_target ("OCaml_imp", ("OCaml", imp_program))
```
```   512
```
```   513 end
```
```   514
```
```   515 *}
```
```   516
```
```   517 code_reserved OCaml Failure raise
```
```   518
```
```   519
```
```   520 subsubsection {* Haskell *}
```
```   521
```
```   522 text {* Adaption layer *}
```
```   523
```
```   524 code_include Haskell "Heap"
```
```   525 {*import qualified Control.Monad;
```
```   526 import qualified Control.Monad.ST;
```
```   527 import qualified Data.STRef;
```
```   528 import qualified Data.Array.ST;
```
```   529
```
```   530 type RealWorld = Control.Monad.ST.RealWorld;
```
```   531 type ST s a = Control.Monad.ST.ST s a;
```
```   532 type STRef s a = Data.STRef.STRef s a;
```
```   533 type STArray s a = Data.Array.ST.STArray s Int a;
```
```   534
```
```   535 newSTRef = Data.STRef.newSTRef;
```
```   536 readSTRef = Data.STRef.readSTRef;
```
```   537 writeSTRef = Data.STRef.writeSTRef;
```
```   538
```
```   539 newArray :: (Int, Int) -> a -> ST s (STArray s a);
```
```   540 newArray = Data.Array.ST.newArray;
```
```   541
```
```   542 newListArray :: (Int, Int) -> [a] -> ST s (STArray s a);
```
```   543 newListArray = Data.Array.ST.newListArray;
```
```   544
```
```   545 lengthArray :: STArray s a -> ST s Int;
```
```   546 lengthArray a = Control.Monad.liftM snd (Data.Array.ST.getBounds a);
```
```   547
```
```   548 readArray :: STArray s a -> Int -> ST s a;
```
```   549 readArray = Data.Array.ST.readArray;
```
```   550
```
```   551 writeArray :: STArray s a -> Int -> a -> ST s ();
```
```   552 writeArray = Data.Array.ST.writeArray;*}
```
```   553
```
```   554 code_reserved Haskell Heap
```
```   555
```
```   556 text {* Monad *}
```
```   557
```
```   558 code_type Heap (Haskell "Heap.ST/ Heap.RealWorld/ _")
```
```   559 code_const Heap (Haskell "error/ \"bare Heap\"")
```
```   560 code_monad "op \<guillemotright>=" Haskell
```
```   561 code_const return (Haskell "return")
```
```   562 code_const "Heap_Monad.Fail" (Haskell "_")
```
```   563 code_const "Heap_Monad.raise_exc" (Haskell "error")
```
```   564
```
```   565 end
```