src/HOL/Quickcheck_Exhaustive.thy
author bulwahn
Fri Jan 20 09:28:50 2012 +0100 (2012-01-20)
changeset 46305 8ea02e499d53
parent 46193 55a4769d0abe
child 46307 ec8f975c059b
permissions -rw-r--r--
adding check_all instance for sets; tuned
     1 (* Author: Lukas Bulwahn, TU Muenchen *)
     2 
     3 header {* A simple counterexample generator performing exhaustive testing *}
     4 
     5 theory Quickcheck_Exhaustive
     6 imports Quickcheck
     7 uses
     8   ("Tools/Quickcheck/exhaustive_generators.ML")
     9   ("Tools/Quickcheck/abstract_generators.ML")
    10 begin
    11 
    12 subsection {* basic operations for exhaustive generators *}
    13 
    14 definition orelse :: "'a option => 'a option => 'a option" (infixr "orelse" 55)
    15 where
    16   [code_unfold]: "x orelse y = (case x of Some x' => Some x' | None => y)"
    17 
    18 subsection {* exhaustive generator type classes *}
    19 
    20 class exhaustive = term_of +
    21   fixes exhaustive :: "('a \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
    22   
    23 class full_exhaustive = term_of +
    24   fixes full_exhaustive :: "('a * (unit => term) \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
    25 
    26 instantiation code_numeral :: full_exhaustive
    27 begin
    28 
    29 function full_exhaustive_code_numeral' :: "(code_numeral * (unit => term) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
    30   where "full_exhaustive_code_numeral' f d i =
    31     (if d < i then None
    32     else (f (i, %_. Code_Evaluation.term_of i)) orelse (full_exhaustive_code_numeral' f d (i + 1)))"
    33 by pat_completeness auto
    34 
    35 termination
    36   by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
    37 
    38 definition "full_exhaustive f d = full_exhaustive_code_numeral' f d 0"
    39 
    40 instance ..
    41 
    42 end
    43 
    44 instantiation code_numeral :: exhaustive
    45 begin
    46 
    47 function exhaustive_code_numeral' :: "(code_numeral => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
    48   where "exhaustive_code_numeral' f d i =
    49     (if d < i then None
    50     else (f i orelse exhaustive_code_numeral' f d (i + 1)))"
    51 by pat_completeness auto
    52 
    53 termination
    54   by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
    55 
    56 definition "exhaustive f d = exhaustive_code_numeral' f d 0"
    57 
    58 instance ..
    59 
    60 end
    61 
    62 instantiation nat :: exhaustive
    63 begin
    64 
    65 definition "exhaustive f d = exhaustive (%x. f (Code_Numeral.nat_of x)) d"
    66 
    67 instance ..
    68 
    69 end
    70 
    71 instantiation nat :: full_exhaustive
    72 begin
    73 
    74 definition "full_exhaustive f d = full_exhaustive (%(x, xt). f (Code_Numeral.nat_of x, %_. Code_Evaluation.term_of (Code_Numeral.nat_of x))) d"
    75 
    76 instance ..
    77 
    78 end
    79 
    80 instantiation int :: exhaustive
    81 begin
    82 
    83 function exhaustive' :: "(int => (bool * term list) option) => int => int => (bool * term list) option"
    84   where "exhaustive' f d i = (if d < i then None else (f i orelse exhaustive' f d (i + 1)))"
    85 by pat_completeness auto
    86 
    87 termination 
    88   by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
    89 
    90 definition "exhaustive f d = exhaustive' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
    91 
    92 instance ..
    93 
    94 end
    95 
    96 instantiation int :: full_exhaustive
    97 begin
    98 
    99 function full_exhaustive' :: "(int * (unit => term) => (bool * term list) option) => int => int => (bool * term list) option"
   100   where "full_exhaustive' f d i = (if d < i then None else (case f (i, %_. Code_Evaluation.term_of i) of Some t => Some t | None => full_exhaustive' f d (i + 1)))"
   101 by pat_completeness auto
   102 
   103 termination 
   104   by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
   105 
   106 definition "full_exhaustive f d = full_exhaustive' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
   107 
   108 instance ..
   109 
   110 end
   111 
   112 instantiation prod :: (exhaustive, exhaustive) exhaustive
   113 begin
   114 
   115 definition
   116   "exhaustive f d = exhaustive (%x. exhaustive (%y. f ((x, y))) d) d"
   117 
   118 instance ..
   119 
   120 end
   121 
   122 instantiation prod :: (full_exhaustive, full_exhaustive) full_exhaustive
   123 begin
   124 
   125 definition
   126   "full_exhaustive f d = full_exhaustive (%(x, t1). full_exhaustive (%(y, t2). f ((x, y),
   127     %u. let T1 = (Typerep.typerep (TYPE('a)));
   128             T2 = (Typerep.typerep (TYPE('b)))
   129     in Code_Evaluation.App (Code_Evaluation.App (
   130       Code_Evaluation.Const (STR ''Product_Type.Pair'') 
   131       (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]]))
   132       (t1 ())) (t2 ()))) d) d"
   133 
   134 instance ..
   135 
   136 end
   137 
   138 instantiation set :: (exhaustive) exhaustive
   139 begin
   140 
   141 fun exhaustive_set
   142 where
   143   "exhaustive_set f i = (if i = 0 then None else (f {} orelse exhaustive_set (%A. f A orelse Quickcheck_Exhaustive.exhaustive (%x. if x \<in> A then None else f (insert x A)) (i - 1)) (i - 1)))"
   144 
   145 instance ..
   146 
   147 end
   148 
   149 definition (in term_syntax) [code_unfold]: "valterm_emptyset = Code_Evaluation.valtermify ({} :: ('a :: typerep) set)"
   150 definition (in term_syntax) [code_unfold]: "valtermify_insert x s = Code_Evaluation.valtermify insert {\<cdot>} (x :: ('a :: typerep * _)) {\<cdot>} s"
   151 
   152 instantiation set :: (full_exhaustive) full_exhaustive
   153 begin
   154 
   155 fun full_exhaustive_set 
   156 where
   157   "full_exhaustive_set f i = (if i = 0 then None else (f valterm_emptyset orelse full_exhaustive_set (%A. f A orelse Quickcheck_Exhaustive.full_exhaustive (%x. if fst x \<in> fst A then None else f (valtermify_insert x A)) (i - 1)) (i - 1)))"
   158 
   159 instance ..
   160 
   161 end
   162 
   163 instantiation "fun" :: ("{equal, exhaustive}", exhaustive) exhaustive
   164 begin
   165 
   166 fun exhaustive_fun' :: "(('a => 'b) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
   167 where
   168   "exhaustive_fun' f i d = (exhaustive (%b. f (%_. b)) d)
   169    orelse (if i > 1 then
   170      exhaustive_fun' (%g. exhaustive (%a. exhaustive (%b.
   171        f (g(a := b))) d) d) (i - 1) d else None)"
   172 
   173 definition exhaustive_fun :: "(('a => 'b) => (bool * term list) option) => code_numeral => (bool * term list) option"
   174 where
   175   "exhaustive_fun f d = exhaustive_fun' f d d" 
   176 
   177 instance ..
   178 
   179 end
   180 
   181 instantiation "fun" :: ("{equal, full_exhaustive}", full_exhaustive) full_exhaustive
   182 begin
   183 
   184 fun full_exhaustive_fun' :: "(('a => 'b) * (unit => term) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
   185 where
   186   "full_exhaustive_fun' f i d = (full_exhaustive (%(b, t). f (%_. b, %_. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a)) (t ()))) d)
   187    orelse (if i > 1 then
   188      full_exhaustive_fun' (%(g, gt). full_exhaustive (%(a, at). full_exhaustive (%(b, bt).
   189        f (g(a := b),
   190          (%_. let A = (Typerep.typerep (TYPE('a)));
   191                   B = (Typerep.typerep (TYPE('b)));
   192                   fun = (%T U. Typerep.Typerep (STR ''fun'') [T, U])
   193               in
   194                 Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
   195                   (Code_Evaluation.Const (STR ''Fun.fun_upd'') (fun (fun A B) (fun A (fun B (fun A B)))))
   196                 (gt ())) (at ())) (bt ())))) d) d) (i - 1) d else None)"
   197 
   198 definition full_exhaustive_fun :: "(('a => 'b) * (unit => term) => (bool * term list) option) => code_numeral => (bool * term list) option"
   199 where
   200   "full_exhaustive_fun f d = full_exhaustive_fun' f d d" 
   201 
   202 instance ..
   203 
   204 end
   205 
   206 subsubsection {* A smarter enumeration scheme for functions over finite datatypes *}
   207 
   208 class check_all = enum + term_of +
   209   fixes check_all :: "('a * (unit \<Rightarrow> term) \<Rightarrow> (bool * term list) option) \<Rightarrow> (bool * term list) option"
   210   fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list"
   211   
   212 fun check_all_n_lists :: "(('a :: check_all) list * (unit \<Rightarrow> term list) \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
   213 where
   214   "check_all_n_lists f n =
   215      (if n = 0 then f ([], (%_. [])) else check_all (%(x, xt). check_all_n_lists (%(xs, xst). f ((x # xs), (%_. (xt () # xst ())))) (n - 1)))"
   216 
   217 definition mk_map_term :: " (unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> unit \<Rightarrow> term"
   218 where
   219   "mk_map_term T1 T2 domm rng =
   220      (%_. let T1 = T1 ();
   221               T2 = T2 ();
   222               update_term = (%g (a, b).
   223                 Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
   224                  (Code_Evaluation.Const (STR ''Fun.fun_upd'')
   225                    (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
   226                       Typerep.Typerep (STR ''fun'') [T1,
   227                         Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
   228                         g) a) b)
   229           in
   230              List.foldl update_term (Code_Evaluation.Abs (STR ''x'') T1 (Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))"
   231 
   232 instantiation "fun" :: ("{equal, check_all}", check_all) check_all
   233 begin
   234 
   235 definition
   236   "check_all f =
   237     (let
   238       mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) (enum_term_of (TYPE('a)));
   239       enum = (Enum.enum :: 'a list)
   240     in check_all_n_lists (\<lambda>(ys, yst). f (the o map_of (zip enum ys), mk_term yst)) (Code_Numeral.of_nat (length enum)))"
   241 
   242 definition enum_term_of_fun :: "('a => 'b) itself => unit => term list"
   243 where
   244   "enum_term_of_fun = (%_ _. let
   245     enum_term_of_a = enum_term_of (TYPE('a));
   246     mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) enum_term_of_a
   247   in map (%ys. mk_term (%_. ys) ()) (Enum.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))"
   248  
   249 instance ..
   250 
   251 end
   252 
   253 fun (in term_syntax) check_all_subsets :: "(('a :: typerep) set * (unit => term) => (bool * term list) option) => ('a * (unit => term)) list => (bool * term list) option"
   254 where
   255   "check_all_subsets f [] = f valterm_emptyset"
   256 | "check_all_subsets f (x # xs) = check_all_subsets (%s. case f s of Some ts => Some ts | None => f (valtermify_insert x s)) xs"
   257 
   258 
   259 definition (in term_syntax) [code_unfold]: "term_emptyset = Code_Evaluation.termify ({} :: ('a :: typerep) set)"
   260 definition (in term_syntax) [code_unfold]: "termify_insert x s = Code_Evaluation.termify (insert :: ('a::typerep) => 'a set => 'a set)  <\<cdot>> x <\<cdot>> s"
   261 
   262 definition (in term_syntax) setify :: "('a::typerep) itself => term list => term"
   263 where
   264   "setify T ts = foldr (termify_insert T) ts (term_emptyset T)" 
   265 
   266 instantiation set :: (check_all) check_all
   267 begin
   268 
   269 definition
   270   "check_all_set f =
   271      check_all_subsets f (zip (Enum.enum :: 'a list) (map (%a. %u :: unit. a) (Quickcheck_Exhaustive.enum_term_of (TYPE ('a)) ())))"
   272 
   273 definition enum_term_of_set :: "'a set itself => unit => term list"
   274 where
   275   "enum_term_of_set _ _ = map (setify (TYPE('a))) (sublists (Quickcheck_Exhaustive.enum_term_of (TYPE('a)) ()))"
   276 
   277 instance ..
   278 
   279 end
   280 
   281 instantiation unit :: check_all
   282 begin
   283 
   284 definition
   285   "check_all f = f (Code_Evaluation.valtermify ())"
   286 
   287 definition enum_term_of_unit :: "unit itself => unit => term list"
   288 where
   289   "enum_term_of_unit = (%_ _. [Code_Evaluation.term_of ()])"
   290 
   291 instance ..
   292 
   293 end
   294 
   295 
   296 instantiation bool :: check_all
   297 begin
   298 
   299 definition
   300   "check_all f = (case f (Code_Evaluation.valtermify False) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify True))"
   301 
   302 definition enum_term_of_bool :: "bool itself => unit => term list"
   303 where
   304   "enum_term_of_bool = (%_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))"
   305 
   306 instance ..
   307 
   308 end
   309 
   310 
   311 instantiation prod :: (check_all, check_all) check_all
   312 begin
   313 
   314 definition
   315   "check_all f = check_all (%(x, t1). check_all (%(y, t2). f ((x, y),
   316     %u. let T1 = (Typerep.typerep (TYPE('a)));
   317             T2 = (Typerep.typerep (TYPE('b)))
   318     in Code_Evaluation.App (Code_Evaluation.App (
   319       Code_Evaluation.Const (STR ''Product_Type.Pair'') 
   320       (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]]))
   321       (t1 ())) (t2 ()))))"
   322 
   323 definition enum_term_of_prod :: "('a * 'b) itself => unit => term list"
   324 where
   325   "enum_term_of_prod = (%_ _. map (%(x, y).
   326        let T1 = (Typerep.typerep (TYPE('a)));
   327            T2 = (Typerep.typerep (TYPE('b)))
   328        in Code_Evaluation.App (Code_Evaluation.App (
   329          Code_Evaluation.Const (STR ''Product_Type.Pair'') 
   330            (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]])) x) y)
   331      (Enum.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ())))  "
   332 
   333 instance ..
   334 
   335 end
   336 
   337 
   338 instantiation sum :: (check_all, check_all) check_all
   339 begin
   340 
   341 definition
   342   "check_all f = (case check_all (%(a, t). f (Inl a, %_. 
   343      let T1 = (Typerep.typerep (TYPE('a)));
   344          T2 = (Typerep.typerep (TYPE('b)))
   345        in Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'') 
   346            (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])) (t ()))) of Some x' => Some x'
   347              | None => check_all (%(b, t). f (Inr b, %_. let
   348                  T1 = (Typerep.typerep (TYPE('a)));
   349                  T2 = (Typerep.typerep (TYPE('b)))
   350                in Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'') 
   351                  (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])) (t ()))))"
   352 
   353 definition enum_term_of_sum :: "('a + 'b) itself => unit => term list"
   354 where
   355   "enum_term_of_sum = (%_ _.
   356      let
   357        T1 = (Typerep.typerep (TYPE('a)));
   358        T2 = (Typerep.typerep (TYPE('b)))
   359      in
   360        map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'') 
   361              (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
   362              (enum_term_of (TYPE('a)) ()) @
   363        map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'') 
   364              (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
   365              (enum_term_of (TYPE('b)) ()))"
   366 
   367 instance ..
   368 
   369 end
   370 
   371 instantiation nibble :: check_all
   372 begin
   373 
   374 definition
   375   "check_all f =
   376     f (Code_Evaluation.valtermify Nibble0) orelse
   377     f (Code_Evaluation.valtermify Nibble1) orelse
   378     f (Code_Evaluation.valtermify Nibble2) orelse
   379     f (Code_Evaluation.valtermify Nibble3) orelse
   380     f (Code_Evaluation.valtermify Nibble4) orelse
   381     f (Code_Evaluation.valtermify Nibble5) orelse
   382     f (Code_Evaluation.valtermify Nibble6) orelse
   383     f (Code_Evaluation.valtermify Nibble7) orelse
   384     f (Code_Evaluation.valtermify Nibble8) orelse
   385     f (Code_Evaluation.valtermify Nibble9) orelse
   386     f (Code_Evaluation.valtermify NibbleA) orelse
   387     f (Code_Evaluation.valtermify NibbleB) orelse
   388     f (Code_Evaluation.valtermify NibbleC) orelse
   389     f (Code_Evaluation.valtermify NibbleD) orelse
   390     f (Code_Evaluation.valtermify NibbleE) orelse
   391     f (Code_Evaluation.valtermify NibbleF)"
   392 
   393 definition enum_term_of_nibble :: "nibble itself => unit => term list"
   394 where
   395   "enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))"
   396 
   397 instance ..
   398 
   399 end
   400 
   401 
   402 instantiation char :: check_all
   403 begin
   404 
   405 definition
   406   "check_all f = check_all (%(x, t1). check_all (%(y, t2). f (Char x y, %_. Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.term_of Char) (t1 ())) (t2 ()))))"
   407 
   408 definition enum_term_of_char :: "char itself => unit => term list"
   409 where
   410   "enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))"
   411 
   412 instance ..
   413 
   414 end
   415 
   416 
   417 instantiation option :: (check_all) check_all
   418 begin
   419 
   420 definition
   421   "check_all f = f (Code_Evaluation.valtermify (None :: 'a option)) orelse check_all (%(x, t). f (Some x, %_. Code_Evaluation.App
   422     (Code_Evaluation.Const (STR ''Option.option.Some'')
   423       (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))"
   424 
   425 definition enum_term_of_option :: "'a option itself => unit => term list"
   426 where
   427   "enum_term_of_option = (% _ _. (Code_Evaluation.term_of (None :: 'a option)) # (map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Option.option.Some'')
   428       (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]]))) (enum_term_of (TYPE('a)) ())))"
   429 
   430 instance ..
   431 
   432 end
   433 
   434 
   435 instantiation Enum.finite_1 :: check_all
   436 begin
   437 
   438 definition
   439   "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)"
   440 
   441 definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list"
   442 where
   443   "enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])"
   444 
   445 instance ..
   446 
   447 end
   448 
   449 instantiation Enum.finite_2 :: check_all
   450 begin
   451 
   452 definition
   453   "check_all f = (case f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>1) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>2))"
   454 
   455 definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list"
   456 where
   457   "enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))"
   458 
   459 instance ..
   460 
   461 end
   462 
   463 instantiation Enum.finite_3 :: check_all
   464 begin
   465 
   466 definition
   467   "check_all f = (case f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>1) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> (case f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>2) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>3)))"
   468 
   469 definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list"
   470 where
   471   "enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))"
   472 
   473 instance ..
   474 
   475 end
   476 
   477 subsection {* Bounded universal quantifiers *}
   478 
   479 class bounded_forall =
   480   fixes bounded_forall :: "('a \<Rightarrow> bool) \<Rightarrow> code_numeral \<Rightarrow> bool"
   481 
   482 subsection {* Fast exhaustive combinators *}
   483 
   484 class fast_exhaustive = term_of +
   485   fixes fast_exhaustive :: "('a \<Rightarrow> unit) \<Rightarrow> code_numeral \<Rightarrow> unit"
   486 
   487 axiomatization throw_Counterexample :: "term list => unit"
   488 axiomatization catch_Counterexample :: "unit => term list option"
   489 
   490 code_const throw_Counterexample
   491   (Quickcheck "raise (Exhaustive'_Generators.Counterexample _)")
   492 code_const catch_Counterexample
   493   (Quickcheck "(((_); NONE) handle Exhaustive'_Generators.Counterexample ts => SOME ts)")
   494 
   495 subsection {* Continuation passing style functions as plus monad *}
   496   
   497 type_synonym 'a cps = "('a => term list option) => term list option"
   498 
   499 definition cps_empty :: "'a cps"
   500 where
   501   "cps_empty = (%cont. None)"
   502 
   503 definition cps_single :: "'a => 'a cps"
   504 where
   505   "cps_single v = (%cont. cont v)"
   506 
   507 definition cps_bind :: "'a cps => ('a => 'b cps) => 'b cps" 
   508 where
   509   "cps_bind m f = (%cont. m (%a. (f a) cont))"
   510 
   511 definition cps_plus :: "'a cps => 'a cps => 'a cps"
   512 where
   513   "cps_plus a b = (%c. case a c of None => b c | Some x => Some x)"
   514 
   515 definition cps_if :: "bool => unit cps"
   516 where
   517   "cps_if b = (if b then cps_single () else cps_empty)"
   518 
   519 definition cps_not :: "unit cps => unit cps"
   520 where
   521   "cps_not n = (%c. case n (%u. Some []) of None => c () | Some _ => None)"
   522 
   523 type_synonym 'a pos_bound_cps = "('a => (bool * term list) option) => code_numeral => (bool * term list) option"
   524 
   525 definition pos_bound_cps_empty :: "'a pos_bound_cps"
   526 where
   527   "pos_bound_cps_empty = (%cont i. None)"
   528 
   529 definition pos_bound_cps_single :: "'a => 'a pos_bound_cps"
   530 where
   531   "pos_bound_cps_single v = (%cont i. cont v)"
   532 
   533 definition pos_bound_cps_bind :: "'a pos_bound_cps => ('a => 'b pos_bound_cps) => 'b pos_bound_cps" 
   534 where
   535   "pos_bound_cps_bind m f = (%cont i. if i = 0 then None else (m (%a. (f a) cont i) (i - 1)))"
   536 
   537 definition pos_bound_cps_plus :: "'a pos_bound_cps => 'a pos_bound_cps => 'a pos_bound_cps"
   538 where
   539   "pos_bound_cps_plus a b = (%c i. case a c i of None => b c i | Some x => Some x)"
   540 
   541 definition pos_bound_cps_if :: "bool => unit pos_bound_cps"
   542 where
   543   "pos_bound_cps_if b = (if b then pos_bound_cps_single () else pos_bound_cps_empty)"
   544 
   545 datatype 'a unknown = Unknown | Known 'a
   546 datatype 'a three_valued = Unknown_value | Value 'a | No_value
   547 
   548 type_synonym 'a neg_bound_cps = "('a unknown => term list three_valued) => code_numeral => term list three_valued"
   549 
   550 definition neg_bound_cps_empty :: "'a neg_bound_cps"
   551 where
   552   "neg_bound_cps_empty = (%cont i. No_value)"
   553 
   554 definition neg_bound_cps_single :: "'a => 'a neg_bound_cps"
   555 where
   556   "neg_bound_cps_single v = (%cont i. cont (Known v))"
   557 
   558 definition neg_bound_cps_bind :: "'a neg_bound_cps => ('a => 'b neg_bound_cps) => 'b neg_bound_cps" 
   559 where
   560   "neg_bound_cps_bind m f = (%cont i. if i = 0 then cont Unknown else m (%a. case a of Unknown => cont Unknown | Known a' => f a' cont i) (i - 1))"
   561 
   562 definition neg_bound_cps_plus :: "'a neg_bound_cps => 'a neg_bound_cps => 'a neg_bound_cps"
   563 where
   564   "neg_bound_cps_plus a b = (%c i. case a c i of No_value => b c i | Value x => Value x | Unknown_value => (case b c i of No_value => Unknown_value | Value x => Value x | Unknown_value => Unknown_value))"
   565 
   566 definition neg_bound_cps_if :: "bool => unit neg_bound_cps"
   567 where
   568   "neg_bound_cps_if b = (if b then neg_bound_cps_single () else neg_bound_cps_empty)"
   569 
   570 definition neg_bound_cps_not :: "unit pos_bound_cps => unit neg_bound_cps"
   571 where
   572   "neg_bound_cps_not n = (%c i. case n (%u. Some (True, [])) i of None => c (Known ()) | Some _ => No_value)"
   573 
   574 definition pos_bound_cps_not :: "unit neg_bound_cps => unit pos_bound_cps"
   575 where
   576   "pos_bound_cps_not n = (%c i. case n (%u. Value []) i of No_value => c () | Value _ => None | Unknown_value => None)"
   577 
   578 subsection {* Defining generators for any first-order data type *}
   579 
   580 axiomatization unknown :: 'a
   581 
   582 notation (output) unknown  ("?")
   583  
   584 use "Tools/Quickcheck/exhaustive_generators.ML"
   585 
   586 setup {* Exhaustive_Generators.setup *}
   587 
   588 declare [[quickcheck_batch_tester = exhaustive]]
   589 
   590 subsection {* Defining generators for abstract types *}
   591 
   592 use "Tools/Quickcheck/abstract_generators.ML"
   593 
   594 hide_fact orelse_def
   595 no_notation orelse (infixr "orelse" 55)
   596 
   597 hide_fact
   598   exhaustive'_def
   599   exhaustive_code_numeral'_def
   600 
   601 hide_const valterm_emptyset valtermify_insert term_emptyset termify_insert setify
   602 
   603 hide_const (open)
   604   exhaustive full_exhaustive exhaustive' exhaustive_code_numeral' full_exhaustive_code_numeral'
   605   throw_Counterexample catch_Counterexample
   606   check_all enum_term_of
   607   orelse unknown mk_map_term check_all_n_lists check_all_subsets
   608 
   609 hide_type (open) cps pos_bound_cps neg_bound_cps unknown three_valued
   610 hide_const (open) cps_empty cps_single cps_bind cps_plus cps_if cps_not
   611   pos_bound_cps_empty pos_bound_cps_single pos_bound_cps_bind pos_bound_cps_plus pos_bound_cps_if pos_bound_cps_not
   612   neg_bound_cps_empty neg_bound_cps_single neg_bound_cps_bind neg_bound_cps_plus neg_bound_cps_if neg_bound_cps_not
   613   Unknown Known Unknown_value Value No_value
   614 
   615 end