src/HOL/Quickcheck_Exhaustive.thy
author wenzelm
Wed Aug 22 22:55:41 2012 +0200 (2012-08-22)
changeset 48891 c0eafbd55de3
parent 47203 ac625d8346b2
child 49948 744934b818c7
permissions -rw-r--r--
prefer ML_file over old uses;
bulwahn@40420
     1
(* Author: Lukas Bulwahn, TU Muenchen *)
bulwahn@40420
     2
bulwahn@41916
     3
header {* A simple counterexample generator performing exhaustive testing *}
bulwahn@40420
     4
bulwahn@41918
     5
theory Quickcheck_Exhaustive
bulwahn@40420
     6
imports Quickcheck
wenzelm@46950
     7
keywords "quickcheck_generator" :: thy_decl
bulwahn@40420
     8
begin
bulwahn@40420
     9
bulwahn@41916
    10
subsection {* basic operations for exhaustive generators *}
bulwahn@41105
    11
bulwahn@41105
    12
definition orelse :: "'a option => 'a option => 'a option" (infixr "orelse" 55)
bulwahn@41105
    13
where
bulwahn@41105
    14
  [code_unfold]: "x orelse y = (case x of Some x' => Some x' | None => y)"
bulwahn@40420
    15
bulwahn@41916
    16
subsection {* exhaustive generator type classes *}
bulwahn@40420
    17
bulwahn@41916
    18
class exhaustive = term_of +
bulwahn@45724
    19
  fixes exhaustive :: "('a \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
bulwahn@42310
    20
  
bulwahn@42310
    21
class full_exhaustive = term_of +
bulwahn@45722
    22
  fixes full_exhaustive :: "('a * (unit => term) \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
bulwahn@40420
    23
bulwahn@42310
    24
instantiation code_numeral :: full_exhaustive
bulwahn@40639
    25
begin
bulwahn@40639
    26
bulwahn@45722
    27
function full_exhaustive_code_numeral' :: "(code_numeral * (unit => term) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
bulwahn@42304
    28
  where "full_exhaustive_code_numeral' f d i =
bulwahn@42304
    29
    (if d < i then None
bulwahn@42304
    30
    else (f (i, %_. Code_Evaluation.term_of i)) orelse (full_exhaustive_code_numeral' f d (i + 1)))"
bulwahn@42304
    31
by pat_completeness auto
bulwahn@42304
    32
bulwahn@42304
    33
termination
bulwahn@42304
    34
  by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
bulwahn@42304
    35
bulwahn@42304
    36
definition "full_exhaustive f d = full_exhaustive_code_numeral' f d 0"
bulwahn@42304
    37
bulwahn@42310
    38
instance ..
bulwahn@42310
    39
bulwahn@42310
    40
end
bulwahn@42310
    41
bulwahn@42310
    42
instantiation code_numeral :: exhaustive
bulwahn@42310
    43
begin
bulwahn@42310
    44
bulwahn@45724
    45
function exhaustive_code_numeral' :: "(code_numeral => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
bulwahn@41916
    46
  where "exhaustive_code_numeral' f d i =
bulwahn@41916
    47
    (if d < i then None
bulwahn@42304
    48
    else (f i orelse exhaustive_code_numeral' f d (i + 1)))"
bulwahn@41231
    49
by pat_completeness auto
bulwahn@41231
    50
bulwahn@42304
    51
termination
bulwahn@41231
    52
  by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
bulwahn@41231
    53
bulwahn@41916
    54
definition "exhaustive f d = exhaustive_code_numeral' f d 0"
bulwahn@41231
    55
bulwahn@41231
    56
instance ..
bulwahn@41231
    57
bulwahn@41231
    58
end
bulwahn@41231
    59
bulwahn@41916
    60
instantiation nat :: exhaustive
bulwahn@41231
    61
begin
bulwahn@41231
    62
bulwahn@42304
    63
definition "exhaustive f d = exhaustive (%x. f (Code_Numeral.nat_of x)) d"
bulwahn@42304
    64
bulwahn@42310
    65
instance ..
bulwahn@42310
    66
bulwahn@42310
    67
end
bulwahn@42310
    68
bulwahn@42310
    69
instantiation nat :: full_exhaustive
bulwahn@42310
    70
begin
bulwahn@42310
    71
bulwahn@42304
    72
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"
bulwahn@41231
    73
bulwahn@41231
    74
instance ..
bulwahn@41231
    75
bulwahn@41231
    76
end
bulwahn@41231
    77
bulwahn@41916
    78
instantiation int :: exhaustive
bulwahn@40639
    79
begin
bulwahn@40639
    80
bulwahn@45724
    81
function exhaustive' :: "(int => (bool * term list) option) => int => int => (bool * term list) option"
bulwahn@42304
    82
  where "exhaustive' f d i = (if d < i then None else (f i orelse exhaustive' f d (i + 1)))"
bulwahn@40639
    83
by pat_completeness auto
bulwahn@40639
    84
bulwahn@40639
    85
termination 
bulwahn@40639
    86
  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
bulwahn@40639
    87
bulwahn@41916
    88
definition "exhaustive f d = exhaustive' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
bulwahn@40639
    89
bulwahn@42310
    90
instance ..
bulwahn@42310
    91
bulwahn@42310
    92
end
bulwahn@42310
    93
bulwahn@42310
    94
instantiation int :: full_exhaustive
bulwahn@42310
    95
begin
bulwahn@42310
    96
bulwahn@45722
    97
function full_exhaustive' :: "(int * (unit => term) => (bool * term list) option) => int => int => (bool * term list) option"
bulwahn@42304
    98
  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)))"
bulwahn@42304
    99
by pat_completeness auto
bulwahn@42304
   100
bulwahn@42304
   101
termination 
bulwahn@42304
   102
  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
bulwahn@42304
   103
bulwahn@42304
   104
definition "full_exhaustive f d = full_exhaustive' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
bulwahn@42304
   105
bulwahn@40639
   106
instance ..
bulwahn@40639
   107
bulwahn@40639
   108
end
bulwahn@40639
   109
bulwahn@41916
   110
instantiation prod :: (exhaustive, exhaustive) exhaustive
bulwahn@40639
   111
begin
bulwahn@40899
   112
bulwahn@40639
   113
definition
bulwahn@42304
   114
  "exhaustive f d = exhaustive (%x. exhaustive (%y. f ((x, y))) d) d"
bulwahn@42304
   115
bulwahn@42310
   116
instance ..
bulwahn@42310
   117
bulwahn@42310
   118
end
bulwahn@42310
   119
bulwahn@46307
   120
definition (in term_syntax) [code_unfold]: "valtermify_pair x y = Code_Evaluation.valtermify (Pair :: 'a :: typerep => 'b :: typerep => 'a * 'b) {\<cdot>} x {\<cdot>} y"
bulwahn@46307
   121
bulwahn@42310
   122
instantiation prod :: (full_exhaustive, full_exhaustive) full_exhaustive
bulwahn@42310
   123
begin
bulwahn@42310
   124
bulwahn@42304
   125
definition
bulwahn@46307
   126
  "full_exhaustive f d = full_exhaustive (%x. full_exhaustive (%y. f (valtermify_pair x y)) d) d"
bulwahn@40639
   127
bulwahn@40639
   128
instance ..
bulwahn@40639
   129
bulwahn@40639
   130
end
bulwahn@40639
   131
bulwahn@46193
   132
instantiation set :: (exhaustive) exhaustive
bulwahn@46193
   133
begin
bulwahn@46193
   134
bulwahn@46193
   135
fun exhaustive_set
bulwahn@46193
   136
where
bulwahn@46307
   137
  "exhaustive_set f i = (if i = 0 then None else (f {} orelse exhaustive_set (%A. f A orelse exhaustive (%x. if x \<in> A then None else f (insert x A)) (i - 1)) (i - 1)))"
bulwahn@46193
   138
bulwahn@46193
   139
instance ..
bulwahn@46193
   140
bulwahn@46193
   141
end
bulwahn@46193
   142
bulwahn@46193
   143
instantiation set :: (full_exhaustive) full_exhaustive
bulwahn@46193
   144
begin
bulwahn@46193
   145
bulwahn@46193
   146
fun full_exhaustive_set 
bulwahn@46193
   147
where
bulwahn@46193
   148
  "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)))"
bulwahn@46193
   149
bulwahn@46193
   150
instance ..
bulwahn@46193
   151
bulwahn@46193
   152
end
bulwahn@46193
   153
bulwahn@41916
   154
instantiation "fun" :: ("{equal, exhaustive}", exhaustive) exhaustive
bulwahn@40639
   155
begin
bulwahn@40639
   156
bulwahn@45724
   157
fun exhaustive_fun' :: "(('a => 'b) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
bulwahn@42304
   158
where
bulwahn@42304
   159
  "exhaustive_fun' f i d = (exhaustive (%b. f (%_. b)) d)
bulwahn@42304
   160
   orelse (if i > 1 then
bulwahn@42304
   161
     exhaustive_fun' (%g. exhaustive (%a. exhaustive (%b.
bulwahn@42304
   162
       f (g(a := b))) d) d) (i - 1) d else None)"
bulwahn@42304
   163
bulwahn@45724
   164
definition exhaustive_fun :: "(('a => 'b) => (bool * term list) option) => code_numeral => (bool * term list) option"
bulwahn@40639
   165
where
bulwahn@42304
   166
  "exhaustive_fun f d = exhaustive_fun' f d d" 
bulwahn@42304
   167
bulwahn@42310
   168
instance ..
bulwahn@42310
   169
bulwahn@42310
   170
end
bulwahn@42310
   171
bulwahn@46307
   172
definition [code_unfold]: "valtermify_absdummy = (%(v, t). (%_::'a. v, %u::unit. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a::typerep)) (t ())))"
bulwahn@46307
   173
bulwahn@46307
   174
definition (in term_syntax) [code_unfold]: "valtermify_fun_upd g a b = Code_Evaluation.valtermify (fun_upd :: ('a :: typerep => 'b :: typerep) => 'a => 'b => 'a => 'b) {\<cdot>} g {\<cdot>} a {\<cdot>} b"
bulwahn@46307
   175
bulwahn@42310
   176
instantiation "fun" :: ("{equal, full_exhaustive}", full_exhaustive) full_exhaustive
bulwahn@42310
   177
begin
bulwahn@42304
   178
bulwahn@45722
   179
fun full_exhaustive_fun' :: "(('a => 'b) * (unit => term) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
bulwahn@42304
   180
where
bulwahn@46307
   181
  "full_exhaustive_fun' f i d = (full_exhaustive (%v. f (valtermify_absdummy v)) d)
bulwahn@42117
   182
   orelse (if i > 1 then
bulwahn@46307
   183
     full_exhaustive_fun' (%g. full_exhaustive (%a. full_exhaustive (%b.
bulwahn@46307
   184
       f (valtermify_fun_upd g a b)) d) d) (i - 1) d else None)"
bulwahn@40639
   185
bulwahn@45722
   186
definition full_exhaustive_fun :: "(('a => 'b) * (unit => term) => (bool * term list) option) => code_numeral => (bool * term list) option"
bulwahn@40639
   187
where
bulwahn@42304
   188
  "full_exhaustive_fun f d = full_exhaustive_fun' f d d" 
bulwahn@40639
   189
bulwahn@40639
   190
instance ..
bulwahn@40639
   191
bulwahn@40639
   192
end
bulwahn@40639
   193
bulwahn@41085
   194
subsubsection {* A smarter enumeration scheme for functions over finite datatypes *}
bulwahn@41085
   195
bulwahn@41085
   196
class check_all = enum + term_of +
bulwahn@45722
   197
  fixes check_all :: "('a * (unit \<Rightarrow> term) \<Rightarrow> (bool * term list) option) \<Rightarrow> (bool * term list) option"
bulwahn@41177
   198
  fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list"
bulwahn@41177
   199
  
bulwahn@45722
   200
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"
bulwahn@41085
   201
where
bulwahn@41085
   202
  "check_all_n_lists f n =
bulwahn@41085
   203
     (if n = 0 then f ([], (%_. [])) else check_all (%(x, xt). check_all_n_lists (%(xs, xst). f ((x # xs), (%_. (xt () # xst ())))) (n - 1)))"
bulwahn@41085
   204
bulwahn@46307
   205
definition (in term_syntax) [code_unfold]: "termify_fun_upd g a b = (Code_Evaluation.termify (fun_upd :: ('a :: typerep => 'b :: typerep) => 'a => 'b => 'a => 'b) <\<cdot>> g <\<cdot>> a <\<cdot>> b)"
bulwahn@46307
   206
bulwahn@41177
   207
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"
bulwahn@41085
   208
where
bulwahn@41177
   209
  "mk_map_term T1 T2 domm rng =
bulwahn@41177
   210
     (%_. let T1 = T1 ();
bulwahn@41085
   211
              T2 = T2 ();
bulwahn@41085
   212
              update_term = (%g (a, b).
bulwahn@41085
   213
                Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
bulwahn@41085
   214
                 (Code_Evaluation.Const (STR ''Fun.fun_upd'')
bulwahn@41085
   215
                   (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
bulwahn@41177
   216
                      Typerep.Typerep (STR ''fun'') [T1,
bulwahn@41177
   217
                        Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
bulwahn@41177
   218
                        g) a) b)
bulwahn@41085
   219
          in
bulwahn@41177
   220
             List.foldl update_term (Code_Evaluation.Abs (STR ''x'') T1 (Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))"
bulwahn@41177
   221
bulwahn@41177
   222
instantiation "fun" :: ("{equal, check_all}", check_all) check_all
bulwahn@41177
   223
begin
bulwahn@41085
   224
bulwahn@41085
   225
definition
bulwahn@41177
   226
  "check_all f =
bulwahn@41177
   227
    (let
bulwahn@41177
   228
      mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) (enum_term_of (TYPE('a)));
bulwahn@41177
   229
      enum = (Enum.enum :: 'a list)
bulwahn@41177
   230
    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)))"
bulwahn@41085
   231
bulwahn@41177
   232
definition enum_term_of_fun :: "('a => 'b) itself => unit => term list"
bulwahn@41177
   233
where
bulwahn@41177
   234
  "enum_term_of_fun = (%_ _. let
bulwahn@41177
   235
    enum_term_of_a = enum_term_of (TYPE('a));
bulwahn@41177
   236
    mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) enum_term_of_a
bulwahn@41177
   237
  in map (%ys. mk_term (%_. ys) ()) (Enum.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))"
bulwahn@41177
   238
 
bulwahn@41085
   239
instance ..
bulwahn@41085
   240
bulwahn@41085
   241
end
bulwahn@41085
   242
bulwahn@46305
   243
fun (in term_syntax) check_all_subsets :: "(('a :: typerep) set * (unit => term) => (bool * term list) option) => ('a * (unit => term)) list => (bool * term list) option"
bulwahn@46305
   244
where
bulwahn@46305
   245
  "check_all_subsets f [] = f valterm_emptyset"
bulwahn@46305
   246
| "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"
bulwahn@46305
   247
bulwahn@46305
   248
bulwahn@46305
   249
definition (in term_syntax) [code_unfold]: "term_emptyset = Code_Evaluation.termify ({} :: ('a :: typerep) set)"
bulwahn@46305
   250
definition (in term_syntax) [code_unfold]: "termify_insert x s = Code_Evaluation.termify (insert :: ('a::typerep) => 'a set => 'a set)  <\<cdot>> x <\<cdot>> s"
bulwahn@46305
   251
bulwahn@46305
   252
definition (in term_syntax) setify :: "('a::typerep) itself => term list => term"
bulwahn@46305
   253
where
bulwahn@46305
   254
  "setify T ts = foldr (termify_insert T) ts (term_emptyset T)" 
bulwahn@46305
   255
bulwahn@46305
   256
instantiation set :: (check_all) check_all
bulwahn@46305
   257
begin
bulwahn@46305
   258
bulwahn@46305
   259
definition
bulwahn@46305
   260
  "check_all_set f =
bulwahn@46305
   261
     check_all_subsets f (zip (Enum.enum :: 'a list) (map (%a. %u :: unit. a) (Quickcheck_Exhaustive.enum_term_of (TYPE ('a)) ())))"
bulwahn@46305
   262
bulwahn@46305
   263
definition enum_term_of_set :: "'a set itself => unit => term list"
bulwahn@46305
   264
where
bulwahn@46305
   265
  "enum_term_of_set _ _ = map (setify (TYPE('a))) (sublists (Quickcheck_Exhaustive.enum_term_of (TYPE('a)) ()))"
bulwahn@46305
   266
bulwahn@46305
   267
instance ..
bulwahn@46305
   268
bulwahn@46305
   269
end
bulwahn@41105
   270
bulwahn@41105
   271
instantiation unit :: check_all
bulwahn@41105
   272
begin
bulwahn@41105
   273
bulwahn@41105
   274
definition
bulwahn@41105
   275
  "check_all f = f (Code_Evaluation.valtermify ())"
bulwahn@41105
   276
bulwahn@41177
   277
definition enum_term_of_unit :: "unit itself => unit => term list"
bulwahn@41177
   278
where
bulwahn@41177
   279
  "enum_term_of_unit = (%_ _. [Code_Evaluation.term_of ()])"
bulwahn@41177
   280
bulwahn@41105
   281
instance ..
bulwahn@41105
   282
bulwahn@41105
   283
end
bulwahn@41105
   284
bulwahn@41105
   285
bulwahn@41085
   286
instantiation bool :: check_all
bulwahn@41085
   287
begin
bulwahn@41085
   288
bulwahn@41085
   289
definition
bulwahn@41085
   290
  "check_all f = (case f (Code_Evaluation.valtermify False) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify True))"
bulwahn@41085
   291
bulwahn@41177
   292
definition enum_term_of_bool :: "bool itself => unit => term list"
bulwahn@41177
   293
where
bulwahn@41177
   294
  "enum_term_of_bool = (%_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))"
bulwahn@41177
   295
bulwahn@41085
   296
instance ..
bulwahn@41085
   297
bulwahn@41085
   298
end
bulwahn@41085
   299
bulwahn@46307
   300
definition (in term_syntax) [code_unfold]: "termify_pair x y = Code_Evaluation.termify (Pair :: 'a :: typerep => 'b :: typerep => 'a * 'b) <\<cdot>> x <\<cdot>> y"
bulwahn@41105
   301
bulwahn@41085
   302
instantiation prod :: (check_all, check_all) check_all
bulwahn@41085
   303
begin
bulwahn@41085
   304
bulwahn@41085
   305
definition
bulwahn@46307
   306
  "check_all f = check_all (%x. check_all (%y. f (valtermify_pair x y)))"
bulwahn@41085
   307
bulwahn@41177
   308
definition enum_term_of_prod :: "('a * 'b) itself => unit => term list"
bulwahn@41177
   309
where
bulwahn@46307
   310
  "enum_term_of_prod = (%_ _. map (%(x, y). termify_pair TYPE('a) TYPE('b) x y)
bulwahn@46307
   311
     (Enum.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ())))"
bulwahn@41177
   312
bulwahn@41085
   313
instance ..
bulwahn@41085
   314
bulwahn@41085
   315
end
bulwahn@41085
   316
bulwahn@46307
   317
definition (in term_syntax) [code_unfold]: "valtermify_Inl x = Code_Evaluation.valtermify (Inl :: 'a :: typerep => 'a + 'b :: typerep) {\<cdot>} x"
bulwahn@46307
   318
definition (in term_syntax) [code_unfold]: "valtermify_Inr x = Code_Evaluation.valtermify (Inr :: 'b :: typerep => 'a ::typerep + 'b) {\<cdot>} x"
bulwahn@41105
   319
bulwahn@41105
   320
instantiation sum :: (check_all, check_all) check_all
bulwahn@41105
   321
begin
bulwahn@41105
   322
bulwahn@41105
   323
definition
bulwahn@46307
   324
  "check_all f = check_all (%a. f (valtermify_Inl a)) orelse check_all (%b. f (valtermify_Inr b))"
bulwahn@41105
   325
bulwahn@41177
   326
definition enum_term_of_sum :: "('a + 'b) itself => unit => term list"
bulwahn@41177
   327
where
bulwahn@41722
   328
  "enum_term_of_sum = (%_ _.
bulwahn@41722
   329
     let
bulwahn@41722
   330
       T1 = (Typerep.typerep (TYPE('a)));
bulwahn@41722
   331
       T2 = (Typerep.typerep (TYPE('b)))
bulwahn@41722
   332
     in
bulwahn@41722
   333
       map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'') 
bulwahn@41722
   334
             (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
bulwahn@41722
   335
             (enum_term_of (TYPE('a)) ()) @
bulwahn@41722
   336
       map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'') 
bulwahn@41722
   337
             (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
bulwahn@41722
   338
             (enum_term_of (TYPE('b)) ()))"
bulwahn@41177
   339
bulwahn@41105
   340
instance ..
bulwahn@41105
   341
bulwahn@41105
   342
end
bulwahn@41105
   343
bulwahn@41105
   344
instantiation nibble :: check_all
bulwahn@41105
   345
begin
bulwahn@41105
   346
bulwahn@41105
   347
definition
bulwahn@41105
   348
  "check_all f =
bulwahn@41105
   349
    f (Code_Evaluation.valtermify Nibble0) orelse
bulwahn@41105
   350
    f (Code_Evaluation.valtermify Nibble1) orelse
bulwahn@41105
   351
    f (Code_Evaluation.valtermify Nibble2) orelse
bulwahn@41105
   352
    f (Code_Evaluation.valtermify Nibble3) orelse
bulwahn@41105
   353
    f (Code_Evaluation.valtermify Nibble4) orelse
bulwahn@41105
   354
    f (Code_Evaluation.valtermify Nibble5) orelse
bulwahn@41105
   355
    f (Code_Evaluation.valtermify Nibble6) orelse
bulwahn@41105
   356
    f (Code_Evaluation.valtermify Nibble7) orelse
bulwahn@41105
   357
    f (Code_Evaluation.valtermify Nibble8) orelse
bulwahn@41105
   358
    f (Code_Evaluation.valtermify Nibble9) orelse
bulwahn@41105
   359
    f (Code_Evaluation.valtermify NibbleA) orelse
bulwahn@41105
   360
    f (Code_Evaluation.valtermify NibbleB) orelse
bulwahn@41105
   361
    f (Code_Evaluation.valtermify NibbleC) orelse
bulwahn@41105
   362
    f (Code_Evaluation.valtermify NibbleD) orelse
bulwahn@41105
   363
    f (Code_Evaluation.valtermify NibbleE) orelse
bulwahn@41105
   364
    f (Code_Evaluation.valtermify NibbleF)"
bulwahn@41105
   365
bulwahn@41177
   366
definition enum_term_of_nibble :: "nibble itself => unit => term list"
bulwahn@41177
   367
where
bulwahn@41177
   368
  "enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))"
bulwahn@41177
   369
bulwahn@41105
   370
instance ..
bulwahn@41105
   371
bulwahn@41105
   372
end
bulwahn@41105
   373
bulwahn@41105
   374
bulwahn@41105
   375
instantiation char :: check_all
bulwahn@41105
   376
begin
bulwahn@41105
   377
bulwahn@41105
   378
definition
bulwahn@41105
   379
  "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 ()))))"
bulwahn@41105
   380
bulwahn@41177
   381
definition enum_term_of_char :: "char itself => unit => term list"
bulwahn@41177
   382
where
bulwahn@41177
   383
  "enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))"
bulwahn@41177
   384
bulwahn@41105
   385
instance ..
bulwahn@41105
   386
bulwahn@41105
   387
end
bulwahn@41105
   388
bulwahn@41105
   389
bulwahn@41105
   390
instantiation option :: (check_all) check_all
bulwahn@41105
   391
begin
bulwahn@41105
   392
bulwahn@41105
   393
definition
bulwahn@41178
   394
  "check_all f = f (Code_Evaluation.valtermify (None :: 'a option)) orelse check_all (%(x, t). f (Some x, %_. Code_Evaluation.App
bulwahn@41178
   395
    (Code_Evaluation.Const (STR ''Option.option.Some'')
bulwahn@41178
   396
      (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))"
bulwahn@41105
   397
bulwahn@41177
   398
definition enum_term_of_option :: "'a option itself => unit => term list"
bulwahn@41177
   399
where
bulwahn@41722
   400
  "enum_term_of_option = (% _ _. (Code_Evaluation.term_of (None :: 'a option)) # (map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Option.option.Some'')
bulwahn@41722
   401
      (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]]))) (enum_term_of (TYPE('a)) ())))"
bulwahn@41177
   402
bulwahn@41105
   403
instance ..
bulwahn@41105
   404
bulwahn@41105
   405
end
bulwahn@41105
   406
bulwahn@41105
   407
bulwahn@41085
   408
instantiation Enum.finite_1 :: check_all
bulwahn@41085
   409
begin
bulwahn@41085
   410
bulwahn@41085
   411
definition
bulwahn@41085
   412
  "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)"
bulwahn@41085
   413
bulwahn@41177
   414
definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list"
bulwahn@41177
   415
where
bulwahn@41177
   416
  "enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])"
bulwahn@41177
   417
bulwahn@41085
   418
instance ..
bulwahn@41085
   419
bulwahn@41085
   420
end
bulwahn@41085
   421
bulwahn@41085
   422
instantiation Enum.finite_2 :: check_all
bulwahn@41085
   423
begin
bulwahn@41085
   424
bulwahn@41085
   425
definition
bulwahn@46417
   426
  "check_all f = (f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>1)
bulwahn@46417
   427
    orelse f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>2))"
bulwahn@41085
   428
bulwahn@41177
   429
definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list"
bulwahn@41177
   430
where
bulwahn@41177
   431
  "enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))"
bulwahn@41177
   432
bulwahn@41085
   433
instance ..
bulwahn@41085
   434
bulwahn@41085
   435
end
bulwahn@41085
   436
bulwahn@41085
   437
instantiation Enum.finite_3 :: check_all
bulwahn@41085
   438
begin
bulwahn@41085
   439
bulwahn@41085
   440
definition
bulwahn@46417
   441
  "check_all f = (f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>1)
bulwahn@46417
   442
    orelse f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>2)
bulwahn@46417
   443
    orelse f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>3))"
bulwahn@41085
   444
bulwahn@41177
   445
definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list"
bulwahn@41177
   446
where
bulwahn@41177
   447
  "enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))"
bulwahn@41177
   448
bulwahn@41085
   449
instance ..
bulwahn@41085
   450
bulwahn@41085
   451
end
bulwahn@41085
   452
bulwahn@46417
   453
instantiation Enum.finite_4 :: check_all
bulwahn@46417
   454
begin
bulwahn@46417
   455
bulwahn@46417
   456
definition
bulwahn@46417
   457
  "check_all f = (f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>1)
bulwahn@46417
   458
    orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>2)
bulwahn@46417
   459
    orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>3)
bulwahn@46417
   460
    orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>4))"
bulwahn@46417
   461
bulwahn@46417
   462
definition enum_term_of_finite_4 :: "Enum.finite_4 itself => unit => term list"
bulwahn@46417
   463
where
bulwahn@46417
   464
  "enum_term_of_finite_4 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_4 list))"
bulwahn@46417
   465
bulwahn@46417
   466
instance ..
bulwahn@46417
   467
bulwahn@46417
   468
end
bulwahn@46417
   469
bulwahn@42195
   470
subsection {* Bounded universal quantifiers *}
bulwahn@41085
   471
bulwahn@42195
   472
class bounded_forall =
bulwahn@42195
   473
  fixes bounded_forall :: "('a \<Rightarrow> bool) \<Rightarrow> code_numeral \<Rightarrow> bool"
bulwahn@42195
   474
bulwahn@42305
   475
subsection {* Fast exhaustive combinators *}
bulwahn@42305
   476
bulwahn@42305
   477
class fast_exhaustive = term_of +
bulwahn@42305
   478
  fixes fast_exhaustive :: "('a \<Rightarrow> unit) \<Rightarrow> code_numeral \<Rightarrow> unit"
bulwahn@42305
   479
bulwahn@45818
   480
axiomatization throw_Counterexample :: "term list => unit"
bulwahn@45818
   481
axiomatization catch_Counterexample :: "unit => term list option"
bulwahn@42305
   482
bulwahn@42305
   483
code_const throw_Counterexample
bulwahn@42305
   484
  (Quickcheck "raise (Exhaustive'_Generators.Counterexample _)")
bulwahn@42305
   485
code_const catch_Counterexample
bulwahn@42305
   486
  (Quickcheck "(((_); NONE) handle Exhaustive'_Generators.Counterexample ts => SOME ts)")
bulwahn@42305
   487
bulwahn@45450
   488
subsection {* Continuation passing style functions as plus monad *}
bulwahn@45450
   489
  
bulwahn@45450
   490
type_synonym 'a cps = "('a => term list option) => term list option"
bulwahn@45450
   491
bulwahn@45450
   492
definition cps_empty :: "'a cps"
bulwahn@45450
   493
where
bulwahn@45450
   494
  "cps_empty = (%cont. None)"
bulwahn@45450
   495
bulwahn@45450
   496
definition cps_single :: "'a => 'a cps"
bulwahn@45450
   497
where
bulwahn@45450
   498
  "cps_single v = (%cont. cont v)"
bulwahn@45450
   499
bulwahn@45450
   500
definition cps_bind :: "'a cps => ('a => 'b cps) => 'b cps" 
bulwahn@45450
   501
where
bulwahn@45450
   502
  "cps_bind m f = (%cont. m (%a. (f a) cont))"
bulwahn@45450
   503
bulwahn@45450
   504
definition cps_plus :: "'a cps => 'a cps => 'a cps"
bulwahn@45450
   505
where
bulwahn@45450
   506
  "cps_plus a b = (%c. case a c of None => b c | Some x => Some x)"
bulwahn@45450
   507
bulwahn@45450
   508
definition cps_if :: "bool => unit cps"
bulwahn@45450
   509
where
bulwahn@45450
   510
  "cps_if b = (if b then cps_single () else cps_empty)"
bulwahn@45450
   511
bulwahn@45450
   512
definition cps_not :: "unit cps => unit cps"
bulwahn@45450
   513
where
bulwahn@45450
   514
  "cps_not n = (%c. case n (%u. Some []) of None => c () | Some _ => None)"
bulwahn@45450
   515
bulwahn@45750
   516
type_synonym 'a pos_bound_cps = "('a => (bool * term list) option) => code_numeral => (bool * term list) option"
bulwahn@45450
   517
bulwahn@45450
   518
definition pos_bound_cps_empty :: "'a pos_bound_cps"
bulwahn@45450
   519
where
bulwahn@45450
   520
  "pos_bound_cps_empty = (%cont i. None)"
bulwahn@45450
   521
bulwahn@45450
   522
definition pos_bound_cps_single :: "'a => 'a pos_bound_cps"
bulwahn@45450
   523
where
bulwahn@45450
   524
  "pos_bound_cps_single v = (%cont i. cont v)"
bulwahn@45450
   525
bulwahn@45450
   526
definition pos_bound_cps_bind :: "'a pos_bound_cps => ('a => 'b pos_bound_cps) => 'b pos_bound_cps" 
bulwahn@45450
   527
where
bulwahn@45450
   528
  "pos_bound_cps_bind m f = (%cont i. if i = 0 then None else (m (%a. (f a) cont i) (i - 1)))"
bulwahn@45450
   529
bulwahn@45450
   530
definition pos_bound_cps_plus :: "'a pos_bound_cps => 'a pos_bound_cps => 'a pos_bound_cps"
bulwahn@45450
   531
where
bulwahn@45450
   532
  "pos_bound_cps_plus a b = (%c i. case a c i of None => b c i | Some x => Some x)"
bulwahn@45450
   533
bulwahn@45450
   534
definition pos_bound_cps_if :: "bool => unit pos_bound_cps"
bulwahn@45450
   535
where
bulwahn@45450
   536
  "pos_bound_cps_if b = (if b then pos_bound_cps_single () else pos_bound_cps_empty)"
bulwahn@45450
   537
bulwahn@45450
   538
datatype 'a unknown = Unknown | Known 'a
bulwahn@45450
   539
datatype 'a three_valued = Unknown_value | Value 'a | No_value
bulwahn@45450
   540
bulwahn@45450
   541
type_synonym 'a neg_bound_cps = "('a unknown => term list three_valued) => code_numeral => term list three_valued"
bulwahn@45450
   542
bulwahn@45450
   543
definition neg_bound_cps_empty :: "'a neg_bound_cps"
bulwahn@45450
   544
where
bulwahn@45450
   545
  "neg_bound_cps_empty = (%cont i. No_value)"
bulwahn@45450
   546
bulwahn@45450
   547
definition neg_bound_cps_single :: "'a => 'a neg_bound_cps"
bulwahn@45450
   548
where
bulwahn@45450
   549
  "neg_bound_cps_single v = (%cont i. cont (Known v))"
bulwahn@45450
   550
bulwahn@45450
   551
definition neg_bound_cps_bind :: "'a neg_bound_cps => ('a => 'b neg_bound_cps) => 'b neg_bound_cps" 
bulwahn@45450
   552
where
bulwahn@45450
   553
  "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))"
bulwahn@45450
   554
bulwahn@45450
   555
definition neg_bound_cps_plus :: "'a neg_bound_cps => 'a neg_bound_cps => 'a neg_bound_cps"
bulwahn@45450
   556
where
bulwahn@45450
   557
  "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))"
bulwahn@45450
   558
bulwahn@45450
   559
definition neg_bound_cps_if :: "bool => unit neg_bound_cps"
bulwahn@45450
   560
where
bulwahn@45450
   561
  "neg_bound_cps_if b = (if b then neg_bound_cps_single () else neg_bound_cps_empty)"
bulwahn@45450
   562
bulwahn@45450
   563
definition neg_bound_cps_not :: "unit pos_bound_cps => unit neg_bound_cps"
bulwahn@45450
   564
where
bulwahn@45750
   565
  "neg_bound_cps_not n = (%c i. case n (%u. Some (True, [])) i of None => c (Known ()) | Some _ => No_value)"
bulwahn@45450
   566
bulwahn@45450
   567
definition pos_bound_cps_not :: "unit neg_bound_cps => unit pos_bound_cps"
bulwahn@45450
   568
where
bulwahn@45450
   569
  "pos_bound_cps_not n = (%c i. case n (%u. Value []) i of No_value => c () | Value _ => None | Unknown_value => None)"
bulwahn@45450
   570
bulwahn@45925
   571
subsection {* Defining generators for any first-order data type *}
bulwahn@40420
   572
bulwahn@45697
   573
axiomatization unknown :: 'a
bulwahn@45697
   574
bulwahn@45697
   575
notation (output) unknown  ("?")
bulwahn@45684
   576
 
wenzelm@48891
   577
ML_file "Tools/Quickcheck/exhaustive_generators.ML"
bulwahn@40420
   578
bulwahn@41918
   579
setup {* Exhaustive_Generators.setup *}
bulwahn@40420
   580
bulwahn@43882
   581
declare [[quickcheck_batch_tester = exhaustive]]
bulwahn@40915
   582
bulwahn@45925
   583
subsection {* Defining generators for abstract types *}
bulwahn@45925
   584
wenzelm@48891
   585
ML_file "Tools/Quickcheck/abstract_generators.ML"
bulwahn@45925
   586
bulwahn@47203
   587
hide_fact (open) orelse_def
bulwahn@41105
   588
no_notation orelse (infixr "orelse" 55)
bulwahn@45818
   589
bulwahn@45818
   590
hide_fact
bulwahn@45818
   591
  exhaustive'_def
bulwahn@45818
   592
  exhaustive_code_numeral'_def
bulwahn@45818
   593
bulwahn@46307
   594
hide_const valtermify_absdummy valtermify_fun_upd valterm_emptyset valtermify_insert valtermify_pair
bulwahn@46307
   595
  valtermify_Inl valtermify_Inr
bulwahn@46307
   596
  termify_fun_upd term_emptyset termify_insert termify_pair setify
bulwahn@46305
   597
bulwahn@45818
   598
hide_const (open)
bulwahn@45818
   599
  exhaustive full_exhaustive exhaustive' exhaustive_code_numeral' full_exhaustive_code_numeral'
bulwahn@45818
   600
  throw_Counterexample catch_Counterexample
bulwahn@45818
   601
  check_all enum_term_of
bulwahn@46305
   602
  orelse unknown mk_map_term check_all_n_lists check_all_subsets
bulwahn@40420
   603
bulwahn@45450
   604
hide_type (open) cps pos_bound_cps neg_bound_cps unknown three_valued
bulwahn@45450
   605
hide_const (open) cps_empty cps_single cps_bind cps_plus cps_if cps_not
bulwahn@45450
   606
  pos_bound_cps_empty pos_bound_cps_single pos_bound_cps_bind pos_bound_cps_plus pos_bound_cps_if pos_bound_cps_not
bulwahn@45450
   607
  neg_bound_cps_empty neg_bound_cps_single neg_bound_cps_bind neg_bound_cps_plus neg_bound_cps_if neg_bound_cps_not
bulwahn@45450
   608
  Unknown Known Unknown_value Value No_value
bulwahn@45450
   609
bulwahn@45450
   610
end