src/HOL/Quickcheck_Narrowing.thy
author haftmann
Thu, 13 Apr 2017 10:10:06 +0200
changeset 65480 5407bc278c9a
parent 61799 4cf66f21b764
child 65481 b11b7ad22684
permissions -rw-r--r--
tuned
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
     1
(* Author: Lukas Bulwahn, TU Muenchen *)
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
     2
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
     3
section \<open>Counterexample generator performing narrowing-based testing\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
     4
41930
1e008cc4883a renaming lazysmallcheck ML file to Quickcheck_Narrowing
bulwahn
parents: 41929
diff changeset
     5
theory Quickcheck_Narrowing
56047
1f283d0a4966 make it possible to load Quickcheck exhaustive & narrowing in parallel
blanchet
parents: 55676
diff changeset
     6
imports Quickcheck_Random
46950
d0181abdbdac declare command keywords via theory header, including strict checking outside Pure;
wenzelm
parents: 46758
diff changeset
     7
keywords "find_unused_assms" :: diag
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
     8
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
     9
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    10
subsection \<open>Counterexample generator\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    11
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    12
subsubsection \<open>Code generation setup\<close>
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    13
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    14
setup \<open>Code_Target.add_derived_target ("Haskell_Quickcheck", [(Code_Haskell.target, I)])\<close>
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    15
52435
6646bb548c6b migration from code_(const|type|class|instance) to code_printing and from code_module to code_identifier
haftmann
parents: 51143
diff changeset
    16
code_printing
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    17
  code_module Typerep \<rightharpoonup> (Haskell_Quickcheck) \<open>
55676
fb46f1c379b5 avoid ad-hoc patching of generated code
haftmann
parents: 55147
diff changeset
    18
data Typerep = Typerep String [Typerep]
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    19
\<close>
55676
fb46f1c379b5 avoid ad-hoc patching of generated code
haftmann
parents: 55147
diff changeset
    20
| type_constructor typerep \<rightharpoonup> (Haskell_Quickcheck) "Typerep.Typerep"
fb46f1c379b5 avoid ad-hoc patching of generated code
haftmann
parents: 55147
diff changeset
    21
| constant Typerep.Typerep \<rightharpoonup> (Haskell_Quickcheck) "Typerep.Typerep"
52435
6646bb548c6b migration from code_(const|type|class|instance) to code_printing and from code_module to code_identifier
haftmann
parents: 51143
diff changeset
    22
| type_constructor integer \<rightharpoonup> (Haskell_Quickcheck) "Prelude.Int"
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
    23
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    24
code_reserved Haskell_Quickcheck Typerep
41909
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    25
58400
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    26
code_printing
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    27
  constant "0::integer" \<rightharpoonup>
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    28
    (Haskell_Quickcheck) "!(0/ ::/ Prelude.Int)"
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    29
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    30
setup \<open>
58400
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    31
  let
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    32
    val target = "Haskell_Quickcheck";
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    33
    fun print _ = Code_Haskell.print_numeral "Prelude.Int";
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    34
  in
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    35
    Numeral.add_code @{const_name Code_Numeral.Pos} I print target
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    36
    #> Numeral.add_code @{const_name Code_Numeral.Neg} (op ~) print target
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    37
  end
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    38
\<close>
58400
d0d3c30806b4 always annotate potentially polymorphic Haskell numerals
haftmann
parents: 58350
diff changeset
    39
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    40
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    41
subsubsection \<open>Narrowing's deep representation of types and terms\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    42
58350
919149921e46 added 'extraction' plugins -- this might help 'HOL-Proofs'
blanchet
parents: 58334
diff changeset
    43
datatype (plugins only: code extraction) narrowing_type =
58152
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    44
  Narrowing_sum_of_products "narrowing_type list list"
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    45
58350
919149921e46 added 'extraction' plugins -- this might help 'HOL-Proofs'
blanchet
parents: 58334
diff changeset
    46
datatype (plugins only: code extraction) narrowing_term =
58152
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    47
  Narrowing_variable "integer list" narrowing_type
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    48
| Narrowing_constructor integer "narrowing_term list"
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    49
58350
919149921e46 added 'extraction' plugins -- this might help 'HOL-Proofs'
blanchet
parents: 58334
diff changeset
    50
datatype (plugins only: code extraction) (dead 'a) narrowing_cons =
58152
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    51
  Narrowing_cons narrowing_type "(narrowing_term list \<Rightarrow> 'a) list"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    52
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
    53
primrec map_cons :: "('a => 'b) => 'a narrowing_cons => 'b narrowing_cons"
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
    54
where
58152
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    55
  "map_cons f (Narrowing_cons ty cs) = Narrowing_cons ty (map (\<lambda>c. f o c) cs)"
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
    56
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    57
subsubsection \<open>From narrowing's deep representation of terms to @{theory Code_Evaluation}'s terms\<close>
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
    58
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
    59
class partial_term_of = typerep +
43047
26774ccb1c74 automatic derivation of partial_term_of functions; renaming type and term to longer names narrowing_type and narrowing_term; hiding constant C; adding overlord option
bulwahn
parents: 42980
diff changeset
    60
  fixes partial_term_of :: "'a itself => narrowing_term => Code_Evaluation.term"
26774ccb1c74 automatic derivation of partial_term_of functions; renaming type and term to longer names narrowing_type and narrowing_term; hiding constant C; adding overlord option
bulwahn
parents: 42980
diff changeset
    61
26774ccb1c74 automatic derivation of partial_term_of functions; renaming type and term to longer names narrowing_type and narrowing_term; hiding constant C; adding overlord option
bulwahn
parents: 42980
diff changeset
    62
lemma partial_term_of_anything: "partial_term_of x nt \<equiv> t"
26774ccb1c74 automatic derivation of partial_term_of functions; renaming type and term to longer names narrowing_type and narrowing_term; hiding constant C; adding overlord option
bulwahn
parents: 42980
diff changeset
    63
  by (rule eq_reflection) (cases "partial_term_of x nt", cases t, simp)
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
    64
 
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    65
subsubsection \<open>Auxilary functions for Narrowing\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    66
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
    67
consts nth :: "'a list => integer => 'a"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    68
52435
6646bb548c6b migration from code_(const|type|class|instance) to code_printing and from code_module to code_identifier
haftmann
parents: 51143
diff changeset
    69
code_printing constant nth \<rightharpoonup> (Haskell_Quickcheck) infixl 9 "!!"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    70
41908
3bd9a21366d2 changing invocation of ghc from interactive mode to compilation increases the performance of lazysmallcheck by a factor of twenty; changing Integer type to Int reduces by another 50 percent
bulwahn
parents: 41905
diff changeset
    71
consts error :: "char list => 'a"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    72
52435
6646bb548c6b migration from code_(const|type|class|instance) to code_printing and from code_module to code_identifier
haftmann
parents: 51143
diff changeset
    73
code_printing constant error \<rightharpoonup> (Haskell_Quickcheck) "error"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    74
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
    75
consts toEnum :: "integer => char"
41908
3bd9a21366d2 changing invocation of ghc from interactive mode to compilation increases the performance of lazysmallcheck by a factor of twenty; changing Integer type to Int reduces by another 50 percent
bulwahn
parents: 41905
diff changeset
    76
52435
6646bb548c6b migration from code_(const|type|class|instance) to code_printing and from code_module to code_identifier
haftmann
parents: 51143
diff changeset
    77
code_printing constant toEnum \<rightharpoonup> (Haskell_Quickcheck) "Prelude.toEnum"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    78
43316
3e274608f06b removing char setup
bulwahn
parents: 43315
diff changeset
    79
consts marker :: "char"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    80
52435
6646bb548c6b migration from code_(const|type|class|instance) to code_printing and from code_module to code_identifier
haftmann
parents: 51143
diff changeset
    81
code_printing constant marker \<rightharpoonup> (Haskell_Quickcheck) "''\\0'"
43316
3e274608f06b removing char setup
bulwahn
parents: 43315
diff changeset
    82
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
    83
subsubsection \<open>Narrowing's basic operations\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    84
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
    85
type_synonym 'a narrowing = "integer => 'a narrowing_cons"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    86
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
    87
definition empty :: "'a narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    88
where
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
    89
  "empty d = Narrowing_cons (Narrowing_sum_of_products []) []"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    90
  
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
    91
definition cons :: "'a => 'a narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    92
where
58152
6fe60a9a5bad use 'datatype_new' in 'Main'
blanchet
parents: 56401
diff changeset
    93
  "cons a d = (Narrowing_cons (Narrowing_sum_of_products [[]]) [(\<lambda>_. a)])"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    94
43047
26774ccb1c74 automatic derivation of partial_term_of functions; renaming type and term to longer names narrowing_type and narrowing_term; hiding constant C; adding overlord option
bulwahn
parents: 42980
diff changeset
    95
fun conv :: "(narrowing_term list => 'a) list => narrowing_term => 'a"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    96
where
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
    97
  "conv cs (Narrowing_variable p _) = error (marker # map toEnum p)"
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
    98
| "conv cs (Narrowing_constructor i xs) = (nth cs i) xs"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    99
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   100
fun non_empty :: "narrowing_type => bool"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   101
where
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   102
  "non_empty (Narrowing_sum_of_products ps) = (\<not> (List.null ps))"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   103
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   104
definition "apply" :: "('a => 'b) narrowing => 'a narrowing => 'b narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   105
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   106
  "apply f a d =
65480
haftmann
parents: 61799
diff changeset
   107
     (case f d of Narrowing_cons (Narrowing_sum_of_products ps) cfs \<Rightarrow>
haftmann
parents: 61799
diff changeset
   108
       case a (d - 1) of Narrowing_cons ta cas \<Rightarrow>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   109
       let
65480
haftmann
parents: 61799
diff changeset
   110
         shallow = d > 0 \<and> non_empty ta;
haftmann
parents: 61799
diff changeset
   111
         cs = [(\<lambda>(x # xs) \<Rightarrow> cf xs (conv cas x)). shallow, cf \<leftarrow> cfs]
haftmann
parents: 61799
diff changeset
   112
       in Narrowing_cons (Narrowing_sum_of_products [ta # p. shallow, p \<leftarrow> ps]) cs)"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   113
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   114
definition sum :: "'a narrowing => 'a narrowing => 'a narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   115
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   116
  "sum a b d =
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   117
    (case a d of Narrowing_cons (Narrowing_sum_of_products ssa) ca => 
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   118
      case b d of Narrowing_cons (Narrowing_sum_of_products ssb) cb =>
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   119
      Narrowing_cons (Narrowing_sum_of_products (ssa @ ssb)) (ca @ cb))"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   120
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   121
lemma [fundef_cong]:
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   122
  assumes "a d = a' d" "b d = b' d" "d = d'"
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   123
  shows "sum a b d = sum a' b' d'"
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   124
using assms unfolding sum_def by (auto split: narrowing_cons.split narrowing_type.split)
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   125
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   126
lemma [fundef_cong]:
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   127
  assumes "f d = f' d" "(\<And>d'. 0 \<le> d' \<and> d' < d \<Longrightarrow> a d' = a' d')"
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   128
  assumes "d = d'"
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   129
  shows "apply f a d = apply f' a' d'"
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   130
proof -
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   131
  note assms
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   132
  moreover have "0 < d' \<Longrightarrow> 0 \<le> d' - 1"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   133
    by (simp add: less_integer_def less_eq_integer_def)
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   134
  ultimately show ?thesis
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   135
    by (auto simp add: apply_def Let_def
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   136
      split: narrowing_cons.split narrowing_type.split)
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   137
qed
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   138
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
   139
subsubsection \<open>Narrowing generator type class\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   140
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   141
class narrowing =
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   142
  fixes narrowing :: "integer => 'a narrowing_cons"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   143
58350
919149921e46 added 'extraction' plugins -- this might help 'HOL-Proofs'
blanchet
parents: 58334
diff changeset
   144
datatype (plugins only: code extraction) property =
58334
7553a1bcecb7 disable datatype 'plugins' for internal types
blanchet
parents: 58310
diff changeset
   145
  Universal narrowing_type "(narrowing_term => property)" "narrowing_term => Code_Evaluation.term"
7553a1bcecb7 disable datatype 'plugins' for internal types
blanchet
parents: 58310
diff changeset
   146
| Existential narrowing_type "(narrowing_term => property)" "narrowing_term => Code_Evaluation.term"
7553a1bcecb7 disable datatype 'plugins' for internal types
blanchet
parents: 58310
diff changeset
   147
| Property bool
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   148
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   149
(* FIXME: hard-wired maximal depth of 100 here *)
43315
893de45ac28d removing unneccessary manual instantiations and dead definitions; hiding more constants and facts
bulwahn
parents: 43314
diff changeset
   150
definition exists :: "('a :: {narrowing, partial_term_of} => property) => property"
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   151
where
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   152
  "exists f = (case narrowing (100 :: integer) of Narrowing_cons ty cs => Existential ty (\<lambda> t. f (conv cs t)) (partial_term_of (TYPE('a))))"
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   153
43315
893de45ac28d removing unneccessary manual instantiations and dead definitions; hiding more constants and facts
bulwahn
parents: 43314
diff changeset
   154
definition "all" :: "('a :: {narrowing, partial_term_of} => property) => property"
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   155
where
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   156
  "all f = (case narrowing (100 :: integer) of Narrowing_cons ty cs => Universal ty (\<lambda>t. f (conv cs t)) (partial_term_of (TYPE('a))))"
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   157
61799
4cf66f21b764 isabelle update_cartouches -c -t;
wenzelm
parents: 60758
diff changeset
   158
subsubsection \<open>class \<open>is_testable\<close>\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   159
61799
4cf66f21b764 isabelle update_cartouches -c -t;
wenzelm
parents: 60758
diff changeset
   160
text \<open>The class \<open>is_testable\<close> ensures that all necessary type instances are generated.\<close>
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   161
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   162
class is_testable
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   163
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   164
instance bool :: is_testable ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   165
43047
26774ccb1c74 automatic derivation of partial_term_of functions; renaming type and term to longer names narrowing_type and narrowing_term; hiding constant C; adding overlord option
bulwahn
parents: 42980
diff changeset
   166
instance "fun" :: ("{term_of, narrowing, partial_term_of}", is_testable) is_testable ..
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   167
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   168
definition ensure_testable :: "'a :: is_testable => 'a :: is_testable"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   169
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   170
  "ensure_testable f = f"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   171
41910
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   172
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
   173
subsubsection \<open>Defining a simple datatype to represent functions in an incomplete and redundant way\<close>
42022
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   174
58350
919149921e46 added 'extraction' plugins -- this might help 'HOL-Proofs'
blanchet
parents: 58334
diff changeset
   175
datatype (plugins only: code quickcheck_narrowing extraction) (dead 'a, dead 'b) ffun =
58334
7553a1bcecb7 disable datatype 'plugins' for internal types
blanchet
parents: 58310
diff changeset
   176
  Constant 'b
7553a1bcecb7 disable datatype 'plugins' for internal types
blanchet
parents: 58310
diff changeset
   177
| Update 'a 'b "('a, 'b) ffun"
42022
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   178
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   179
primrec eval_ffun :: "('a, 'b) ffun => 'a => 'b"
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   180
where
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   181
  "eval_ffun (Constant c) x = c"
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   182
| "eval_ffun (Update x' y f) x = (if x = x' then y else eval_ffun f x)"
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   183
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   184
hide_type (open) ffun
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   185
hide_const (open) Constant Update eval_ffun
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   186
58350
919149921e46 added 'extraction' plugins -- this might help 'HOL-Proofs'
blanchet
parents: 58334
diff changeset
   187
datatype (plugins only: code quickcheck_narrowing extraction) (dead 'b) cfun = Constant 'b
42024
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   188
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   189
primrec eval_cfun :: "'b cfun => 'a => 'b"
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   190
where
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   191
  "eval_cfun (Constant c) y = c"
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   192
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   193
hide_type (open) cfun
45734
1024dd30da42 hide quickcheck constants Abs_cfun and Rep_cfun, to avoid clash with HOLCF
huffman
parents: 45001
diff changeset
   194
hide_const (open) Constant eval_cfun Abs_cfun Rep_cfun
42024
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   195
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
   196
subsubsection \<open>Setting up the counterexample generator\<close>
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   197
48891
c0eafbd55de3 prefer ML_file over old uses;
wenzelm
parents: 48565
diff changeset
   198
ML_file "Tools/Quickcheck/narrowing_generators.ML"
42024
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   199
45001
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   200
definition narrowing_dummy_partial_term_of :: "('a :: partial_term_of) itself => narrowing_term => term"
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   201
where
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   202
  "narrowing_dummy_partial_term_of = partial_term_of"
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   203
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   204
definition narrowing_dummy_narrowing :: "integer => ('a :: narrowing) narrowing_cons"
45001
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   205
where
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   206
  "narrowing_dummy_narrowing = narrowing"
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   207
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   208
lemma [code]:
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   209
  "ensure_testable f =
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   210
    (let
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   211
      x = narrowing_dummy_narrowing :: integer => bool narrowing_cons;
45001
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   212
      y = narrowing_dummy_partial_term_of :: bool itself => narrowing_term => term;
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   213
      z = (conv :: _ => _ => unit)  in f)"
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   214
unfolding Let_def ensure_testable_def ..
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   215
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
   216
subsection \<open>Narrowing for sets\<close>
46308
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   217
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   218
instantiation set :: (narrowing) narrowing
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   219
begin
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   220
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   221
definition "narrowing_set = Quickcheck_Narrowing.apply (Quickcheck_Narrowing.cons set) narrowing"
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   222
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   223
instance ..
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   224
e5abbec2697a adding narrowing instance for sets
bulwahn
parents: 46032
diff changeset
   225
end
45001
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   226
  
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
   227
subsection \<open>Narrowing for integers\<close>
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   228
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   229
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   230
definition drawn_from :: "'a list \<Rightarrow> 'a narrowing_cons"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   231
where
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   232
  "drawn_from xs =
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   233
    Narrowing_cons (Narrowing_sum_of_products (map (\<lambda>_. []) xs)) (map (\<lambda>x _. x) xs)"
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   234
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   235
function around_zero :: "int \<Rightarrow> int list"
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   236
where
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   237
  "around_zero i = (if i < 0 then [] else (if i = 0 then [0] else around_zero (i - 1) @ [i, -i]))"
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   238
  by pat_completeness auto
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   239
termination by (relation "measure nat") auto
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   240
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   241
declare around_zero.simps [simp del]
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   242
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   243
lemma length_around_zero:
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   244
  assumes "i >= 0" 
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   245
  shows "length (around_zero i) = 2 * nat i + 1"
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   246
proof (induct rule: int_ge_induct [OF assms])
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   247
  case 1
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   248
  from 1 show ?case by (simp add: around_zero.simps)
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   249
next
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   250
  case (2 i)
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   251
  from 2 show ?case
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   252
    by (simp add: around_zero.simps [of "i + 1"])
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   253
qed
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   254
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   255
instantiation int :: narrowing
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   256
begin
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   257
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   258
definition
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   259
  "narrowing_int d = (let (u :: _ \<Rightarrow> _ \<Rightarrow> unit) = conv; i = int_of_integer d
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   260
    in drawn_from (around_zero i))"
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   261
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   262
instance ..
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   263
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   264
end
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   265
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   266
lemma [code, code del]: "partial_term_of (ty :: int itself) t \<equiv> undefined"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   267
  by (rule partial_term_of_anything)+
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   268
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   269
lemma [code]:
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   270
  "partial_term_of (ty :: int itself) (Narrowing_variable p t) \<equiv>
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   271
    Code_Evaluation.Free (STR ''_'') (Typerep.Typerep (STR ''Int.int'') [])"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   272
  "partial_term_of (ty :: int itself) (Narrowing_constructor i []) \<equiv>
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   273
    (if i mod 2 = 0
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   274
     then Code_Evaluation.term_of (- (int_of_integer i) div 2)
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   275
     else Code_Evaluation.term_of ((int_of_integer i + 1) div 2))"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   276
  by (rule partial_term_of_anything)+
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   277
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   278
instantiation integer :: narrowing
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   279
begin
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   280
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   281
definition
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   282
  "narrowing_integer d = (let (u :: _ \<Rightarrow> _ \<Rightarrow> unit) = conv; i = int_of_integer d
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   283
    in drawn_from (map integer_of_int (around_zero i)))"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   284
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   285
instance ..
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   286
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   287
end
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   288
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   289
lemma [code, code del]: "partial_term_of (ty :: integer itself) t \<equiv> undefined"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   290
  by (rule partial_term_of_anything)+
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   291
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   292
lemma [code]:
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   293
  "partial_term_of (ty :: integer itself) (Narrowing_variable p t) \<equiv>
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   294
    Code_Evaluation.Free (STR ''_'') (Typerep.Typerep (STR ''Code_Numeral.integer'') [])"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   295
  "partial_term_of (ty :: integer itself) (Narrowing_constructor i []) \<equiv>
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   296
    (if i mod 2 = 0
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   297
     then Code_Evaluation.term_of (- i div 2)
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   298
     else Code_Evaluation.term_of ((i + 1) div 2))"
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   299
  by (rule partial_term_of_anything)+
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   300
56401
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   301
code_printing constant "Code_Evaluation.term_of :: integer \<Rightarrow> term" \<rightharpoonup> (Haskell_Quickcheck) 
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   302
  "(let { t = Typerep.Typerep \"Code'_Numeral.integer\" [];
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   303
     mkFunT s t = Typerep.Typerep \"fun\" [s, t];
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   304
     numT = Typerep.Typerep \"Num.num\" [];
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   305
     mkBit 0 = Generated'_Code.Const \"Num.num.Bit0\" (mkFunT numT numT);
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   306
     mkBit 1 = Generated'_Code.Const \"Num.num.Bit1\" (mkFunT numT numT);
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   307
     mkNumeral 1 = Generated'_Code.Const \"Num.num.One\" numT;
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   308
     mkNumeral i = let { q = i `Prelude.div` 2; r = i `Prelude.mod` 2 }
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   309
       in Generated'_Code.App (mkBit r) (mkNumeral q);
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   310
     mkNumber 0 = Generated'_Code.Const \"Groups.zero'_class.zero\" t;
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   311
     mkNumber 1 = Generated'_Code.Const \"Groups.one'_class.one\" t;
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   312
     mkNumber i = if i > 0 then
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   313
         Generated'_Code.App
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   314
           (Generated'_Code.Const \"Num.numeral'_class.numeral\"
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   315
              (mkFunT numT t))
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   316
           (mkNumeral i)
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   317
       else
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   318
         Generated'_Code.App
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   319
           (Generated'_Code.Const \"Groups.uminus'_class.uminus\" (mkFunT t t))
3b2db6132bfd add missing adaptation for narrowing to work with variables of type integer => integer
Andreas Lochbihler
parents: 56047
diff changeset
   320
           (mkNumber (- i)); } in mkNumber)"
43356
2dee03f192b7 adding another narrowing strategy for integers
bulwahn
parents: 43341
diff changeset
   321
61799
4cf66f21b764 isabelle update_cartouches -c -t;
wenzelm
parents: 60758
diff changeset
   322
subsection \<open>The \<open>find_unused_assms\<close> command\<close>
46589
689311986778 adding new command "find_unused_assms"
bulwahn
parents: 46308
diff changeset
   323
48891
c0eafbd55de3 prefer ML_file over old uses;
wenzelm
parents: 48565
diff changeset
   324
ML_file "Tools/Quickcheck/find_unused_assms.ML"
46589
689311986778 adding new command "find_unused_assms"
bulwahn
parents: 46308
diff changeset
   325
60758
d8d85a8172b5 isabelle update_cartouches;
wenzelm
parents: 59104
diff changeset
   326
subsection \<open>Closing up\<close>
46589
689311986778 adding new command "find_unused_assms"
bulwahn
parents: 46308
diff changeset
   327
51143
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   328
hide_type narrowing_type narrowing_term narrowing_cons property
0a2371e7ced3 two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
parents: 50046
diff changeset
   329
hide_const map_cons nth error toEnum marker empty Narrowing_cons conv non_empty ensure_testable all exists drawn_from around_zero
46758
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   330
hide_const (open) Narrowing_variable Narrowing_constructor "apply" sum cons
4106258260b3 choosing longer constant names in Quickcheck_Narrowing to reduce the chances of name clashes in Quickcheck-Narrowing
bulwahn
parents: 46589
diff changeset
   331
hide_fact empty_def cons_def conv.simps non_empty.simps apply_def sum_def ensure_testable_def all_def exists_def
42022
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   332
45001
5c8d7d6db682 ensuring that some constants are generated in the source code by adding calls in ensure_testable
bulwahn
parents: 43887
diff changeset
   333
end