src/HOL/Library/Quickcheck_Narrowing.thy
author bulwahn
Thu, 09 Jun 2011 08:32:13 +0200
changeset 43308 fd6cc1378fec
parent 43237 8f5c3c6c2909
permissions -rw-r--r--
compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
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
41930
1e008cc4883a renaming lazysmallcheck ML file to Quickcheck_Narrowing
bulwahn
parents: 41929
diff changeset
     3
header {* Counterexample generator preforming narrowing-based testing *}
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
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
     6
imports Main "~~/src/HOL/Library/Code_Char"
41962
27a61a3266d8 correcting names in Narrowing_Engine and example theory for Quickcheck_Narrowing
bulwahn
parents: 41961
diff changeset
     7
uses
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
     8
  ("~~/src/HOL/Tools/Quickcheck/PNF_Narrowing_Engine.hs")
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
     9
  ("~~/src/HOL/Tools/Quickcheck/Narrowing_Engine.hs")
41962
27a61a3266d8 correcting names in Narrowing_Engine and example theory for Quickcheck_Narrowing
bulwahn
parents: 41961
diff changeset
    10
  ("~~/src/HOL/Tools/Quickcheck/narrowing_generators.ML")
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    11
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    12
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    13
subsection {* Counterexample generator *}
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
    14
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    15
text {* We create a new target for the necessary code generation setup. *}
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    16
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    17
setup {* Code_Target.extend_target ("Haskell_Quickcheck", (Code_Haskell.target, K I)) *}
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    18
41909
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    19
subsubsection {* Code generation setup *}
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    20
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    21
code_type typerep
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    22
  (Haskell_Quickcheck "Typerep")
41909
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    23
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    24
code_const Typerep.Typerep
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    25
  (Haskell_Quickcheck "Typerep")
41909
383bbdad1650 replacing strings in generated Code resolves the changing names of Typerep in lazysmallcheck prototype
bulwahn
parents: 41908
diff changeset
    26
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    27
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
    28
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
    29
subsubsection {* Type @{text "code_int"} for Haskell_Quickcheck's Int type *}
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
    30
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
    31
typedef (open) code_int = "UNIV \<Colon> int set"
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
    32
  morphisms int_of of_int by rule
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
    33
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    34
lemma of_int_int_of [simp]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    35
  "of_int (int_of k) = k"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    36
  by (rule int_of_inverse)
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    37
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    38
lemma int_of_of_int [simp]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    39
  "int_of (of_int n) = n"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    40
  by (rule of_int_inverse) (rule UNIV_I)
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    41
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    42
lemma code_int:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    43
  "(\<And>n\<Colon>code_int. PROP P n) \<equiv> (\<And>n\<Colon>int. PROP P (of_int n))"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    44
proof
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    45
  fix n :: int
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    46
  assume "\<And>n\<Colon>code_int. PROP P n"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    47
  then show "PROP P (of_int n)" .
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    48
next
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    49
  fix n :: code_int
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    50
  assume "\<And>n\<Colon>int. PROP P (of_int n)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    51
  then have "PROP P (of_int (int_of n))" .
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    52
  then show "PROP P n" by simp
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    53
qed
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    54
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    55
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
    56
lemma int_of_inject [simp]:
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
    57
  "int_of k = int_of l \<longleftrightarrow> k = l"
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
    58
  by (rule int_of_inject)
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
    59
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    60
lemma of_int_inject [simp]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    61
  "of_int n = of_int m \<longleftrightarrow> n = m"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    62
  by (rule of_int_inject) (rule UNIV_I)+
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    63
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    64
instantiation code_int :: equal
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    65
begin
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    66
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    67
definition
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    68
  "HOL.equal k l \<longleftrightarrow> HOL.equal (int_of k) (int_of l)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    69
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    70
instance proof
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    71
qed (auto simp add: equal_code_int_def equal_int_def eq_int_refl)
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    72
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    73
end
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    74
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    75
instantiation code_int :: number
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    76
begin
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    77
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    78
definition
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    79
  "number_of = of_int"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    80
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    81
instance ..
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    82
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    83
end
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    84
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    85
lemma int_of_number [simp]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    86
  "int_of (number_of k) = number_of k"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    87
  by (simp add: number_of_code_int_def number_of_is_id)
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    88
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    89
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
    90
definition nat_of :: "code_int => nat"
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
    91
where
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
    92
  "nat_of i = nat (int_of i)"
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
    93
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
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
code_datatype "number_of \<Colon> int \<Rightarrow> code_int"
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
    96
  
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
    97
  
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
    98
instantiation code_int :: "{minus, linordered_semidom, semiring_div, linorder}"
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
    99
begin
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
   100
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
   101
definition [simp, code del]:
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
   102
  "0 = of_int 0"
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
   103
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
   104
definition [simp, code del]:
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
   105
  "1 = of_int 1"
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
   106
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
   107
definition [simp, code del]:
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   108
  "n + m = of_int (int_of n + int_of m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   109
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   110
definition [simp, code del]:
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
   111
  "n - m = of_int (int_of n - int_of m)"
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
   112
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
   113
definition [simp, code del]:
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   114
  "n * m = of_int (int_of n * int_of m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   115
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   116
definition [simp, code del]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   117
  "n div m = of_int (int_of n div int_of m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   118
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   119
definition [simp, code del]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   120
  "n mod m = of_int (int_of n mod int_of m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   121
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   122
definition [simp, code del]:
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
   123
  "n \<le> m \<longleftrightarrow> int_of n \<le> int_of m"
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
   124
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
   125
definition [simp, code del]:
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
   126
  "n < m \<longleftrightarrow> int_of n < int_of m"
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
   127
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
   128
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   129
instance proof
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   130
qed (auto simp add: code_int left_distrib zmult_zless_mono2)
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
   131
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
   132
end
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   133
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
   134
lemma zero_code_int_code [code, code_unfold]:
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
   135
  "(0\<Colon>code_int) = Numeral0"
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   136
  by (simp add: number_of_code_int_def Pls_def)
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   137
lemma [code_post]: "Numeral0 = (0\<Colon>code_int)"
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   138
  using zero_code_int_code ..
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
   139
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   140
lemma one_code_int_code [code, code_unfold]:
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
   141
  "(1\<Colon>code_int) = Numeral1"
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   142
  by (simp add: number_of_code_int_def Pls_def Bit1_def)
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
   143
lemma [code_post]: "Numeral1 = (1\<Colon>code_int)"
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   144
  using one_code_int_code ..
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   145
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
   146
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   147
definition div_mod_code_int :: "code_int \<Rightarrow> code_int \<Rightarrow> code_int \<times> code_int" where
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   148
  [code del]: "div_mod_code_int n m = (n div m, n mod m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   149
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   150
lemma [code]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   151
  "div_mod_code_int n m = (if m = 0 then (0, n) else (n div m, n mod m))"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   152
  unfolding div_mod_code_int_def by auto
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   153
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   154
lemma [code]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   155
  "n div m = fst (div_mod_code_int n m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   156
  unfolding div_mod_code_int_def by simp
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   157
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   158
lemma [code]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   159
  "n mod m = snd (div_mod_code_int n m)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   160
  unfolding div_mod_code_int_def by simp
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   161
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   162
lemma int_of_code [code]:
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   163
  "int_of k = (if k = 0 then 0
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   164
    else (if k mod 2 = 0 then 2 * int_of (k div 2) else 2 * int_of (k div 2) + 1))"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   165
proof -
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   166
  have 1: "(int_of k div 2) * 2 + int_of k mod 2 = int_of k" 
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   167
    by (rule mod_div_equality)
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   168
  have "int_of k mod 2 = 0 \<or> int_of k mod 2 = 1" by auto
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   169
  from this show ?thesis
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   170
    apply auto
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   171
    apply (insert 1) by (auto simp add: mult_ac)
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   172
qed
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   173
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   174
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   175
code_instance code_numeral :: equal
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   176
  (Haskell_Quickcheck -)
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   177
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   178
setup {* fold (Numeral.add_code @{const_name number_code_int_inst.number_of_code_int}
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   179
  false Code_Printer.literal_numeral) ["Haskell_Quickcheck"]  *}
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   180
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
   181
code_const "0 \<Colon> code_int"
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   182
  (Haskell_Quickcheck "0")
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
   183
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
   184
code_const "1 \<Colon> code_int"
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   185
  (Haskell_Quickcheck "1")
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
   186
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
   187
code_const "minus \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> code_int"
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   188
  (Haskell_Quickcheck "(_/ -/ _)")
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
   189
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   190
code_const div_mod_code_int
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   191
  (Haskell_Quickcheck "divMod")
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   192
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   193
code_const "HOL.equal \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> bool"
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   194
  (Haskell_Quickcheck infix 4 "==")
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   195
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
   196
code_const "op \<le> \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> bool"
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   197
  (Haskell_Quickcheck infix 4 "<=")
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
   198
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
   199
code_const "op < \<Colon> code_int \<Rightarrow> code_int \<Rightarrow> bool"
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   200
  (Haskell_Quickcheck infix 4 "<")
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
   201
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
   202
code_type code_int
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   203
  (Haskell_Quickcheck "Int")
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
   204
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   205
code_abort of_int
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   206
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   207
subsubsection {* Narrowing's deep representation of types and terms *}
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   208
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
   209
datatype narrowing_type = SumOfProd "narrowing_type list list"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   210
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
   211
datatype narrowing_term = Var "code_int list" narrowing_type | Ctr code_int "narrowing_term list"
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
   212
datatype 'a cons = C narrowing_type "(narrowing_term list => 'a) list"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   213
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   214
subsubsection {* From narrowing's deep representation of terms to Code_Evaluation's terms *}
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   215
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   216
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
   217
  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
   218
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
   219
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
   220
  by (rule eq_reflection) (cases "partial_term_of x nt", cases t, simp)
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
   221
42980
859fe9cc0838 improving code_int setup in Quickcheck_Narrowing; adding partial_term_of class in Quickcheck_Narrowing
bulwahn
parents: 42024
diff changeset
   222
41964
13904699c859 tuned subsubsection names in Quickcheck_Narrowing
bulwahn
parents: 41962
diff changeset
   223
subsubsection {* Auxilary functions for Narrowing *}
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   224
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
   225
consts nth :: "'a list => code_int => 'a"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   226
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   227
code_const nth (Haskell_Quickcheck infixl 9  "!!")
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   228
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
   229
consts error :: "char list => 'a"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   230
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   231
code_const error (Haskell_Quickcheck "error")
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   232
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
   233
consts toEnum :: "code_int => char"
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
   234
43308
fd6cc1378fec compilation of Haskell in its own target for Quickcheck; passing options by arguments in Narrowing_Generators
bulwahn
parents: 43237
diff changeset
   235
code_const toEnum (Haskell_Quickcheck "toEnum")
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   236
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
   237
consts map_index :: "(code_int * 'a => 'b) => 'a list => 'b list"  
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   238
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
   239
consts split_At :: "code_int => 'a list => 'a list * 'a list"
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
   240
 
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   241
subsubsection {* Narrowing's basic operations *}
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   242
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   243
type_synonym 'a narrowing = "code_int => 'a cons"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   244
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   245
definition empty :: "'a narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   246
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   247
  "empty d = C (SumOfProd []) []"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   248
  
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   249
definition cons :: "'a => 'a narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   250
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   251
  "cons a d = (C (SumOfProd [[]]) [(%_. a)])"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   252
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
   253
fun conv :: "(narrowing_term list => 'a) list => narrowing_term => 'a"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   254
where
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
   255
  "conv cs (Var p _) = error (Char Nibble0 Nibble0 # map toEnum p)"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   256
| "conv cs (Ctr i xs) = (nth cs i) xs"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   257
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
   258
fun nonEmpty :: "narrowing_type => bool"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   259
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   260
  "nonEmpty (SumOfProd ps) = (\<not> (List.null ps))"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   261
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   262
definition "apply" :: "('a => 'b) narrowing => 'a narrowing => 'b narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   263
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   264
  "apply f a d =
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   265
     (case f d of C (SumOfProd ps) cfs =>
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   266
       case a (d - 1) of C ta cas =>
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   267
       let
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   268
         shallow = (d > 0 \<and> nonEmpty ta);
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   269
         cs = [(%xs'. (case xs' of [] => undefined | x # xs => cf xs (conv cas x))). shallow, cf <- cfs]
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   270
       in C (SumOfProd [ta # p. shallow, p <- ps]) cs)"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   271
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   272
definition sum :: "'a narrowing => 'a narrowing => 'a narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   273
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   274
  "sum a b d =
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   275
    (case a d of C (SumOfProd ssa) ca => 
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   276
      case b d of C (SumOfProd ssb) cb =>
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   277
      C (SumOfProd (ssa @ ssb)) (ca @ cb))"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   278
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   279
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
   280
  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
   281
  shows "sum a b d = sum a' b' d'"
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
   282
using assms unfolding sum_def by (auto split: 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
   283
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   284
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
   285
  assumes "f d = f' d" "(\<And>d'. 0 <= d' & d' < d ==> a d' = 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
   286
  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
   287
  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
   288
proof -
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   289
  note assms moreover
41930
1e008cc4883a renaming lazysmallcheck ML file to Quickcheck_Narrowing
bulwahn
parents: 41929
diff changeset
   290
  have "int_of (of_int 0) < int_of d' ==> int_of (of_int 0) <= int_of (of_int (int_of d' - int_of (of_int 1)))"
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   291
    by (simp add: of_int_inverse)
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   292
  moreover
41930
1e008cc4883a renaming lazysmallcheck ML file to Quickcheck_Narrowing
bulwahn
parents: 41929
diff changeset
   293
  have "int_of (of_int (int_of d' - int_of (of_int 1))) < int_of 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
   294
    by (simp add: of_int_inverse)
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   295
  ultimately show ?thesis
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
   296
    unfolding apply_def by (auto split: cons.split narrowing_type.split simp add: Let_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
   297
qed
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   298
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
   299
type_synonym pos = "code_int list"
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   300
(*
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
   301
subsubsection {* Term refinement *}
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
   302
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
   303
definition new :: "pos => type list list => term list"
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
   304
where
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
   305
  "new p ps = map_index (%(c, ts). Ctr c (map_index (%(i, t). Var (p @ [i]) t) ts)) ps"
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
   306
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
   307
fun refine :: "term => pos => term list" and refineList :: "term list => pos => (term list) list"
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
   308
where
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
   309
  "refine (Var p (SumOfProd ss)) [] = new p ss"
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
   310
| "refine (Ctr c xs) p = map (Ctr c) (refineList xs p)"
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
   311
| "refineList xs (i # is) = (let (ls, xrs) = split_At i xs in (case xrs of x#rs => [ls @ y # rs. y <- refine x is]))"
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
   312
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
   313
text {* Find total instantiations of a partial value *}
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
   314
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
   315
function total :: "term => term list"
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
   316
where
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
   317
  "total (Ctr c xs) = [Ctr c ys. ys <- map total xs]"
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
   318
| "total (Var p (SumOfProd ss)) = [y. x <- new p ss, y <- total x]"
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
   319
by pat_completeness auto
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
   320
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
   321
termination sorry
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   322
*)
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   323
subsubsection {* Narrowing generator type class *}
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   324
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   325
class narrowing =
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   326
  fixes narrowing :: "code_int => 'a cons"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   327
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   328
definition cons1 :: "('a::narrowing => 'b) => 'b narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   329
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   330
  "cons1 f = apply (cons f) narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   331
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   332
definition cons2 :: "('a :: narrowing => 'b :: narrowing => 'c) => 'c narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   333
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   334
  "cons2 f = apply (apply (cons f) narrowing) narrowing"
42021
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   335
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   336
definition drawn_from :: "'a list => 'a cons"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   337
where "drawn_from xs = C (SumOfProd (map (%_. []) xs)) (map (%x y. x) xs)"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   338
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   339
instantiation int :: narrowing
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   340
begin
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   341
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   342
definition
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   343
  "narrowing_int d = (let i = Quickcheck_Narrowing.int_of d in drawn_from [-i .. i])"
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   344
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   345
instance ..
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   346
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   347
end
52551c0a3374 extending code_int type more; adding narrowing instance for type int; added test case for int instance
bulwahn
parents: 41965
diff changeset
   348
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   349
instantiation unit :: narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   350
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   351
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   352
definition
41965
328371f4f927 removing definition of cons0; hiding constants in Quickcheck_Narrowing
bulwahn
parents: 41964
diff changeset
   353
  "narrowing = cons ()"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   354
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   355
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   356
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   357
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   358
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   359
instantiation bool :: narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   360
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   361
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   362
definition
41965
328371f4f927 removing definition of cons0; hiding constants in Quickcheck_Narrowing
bulwahn
parents: 41964
diff changeset
   363
  "narrowing = sum (cons True) (cons False)" 
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   364
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   365
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   366
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   367
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   368
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   369
instantiation option :: (narrowing) narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   370
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   371
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   372
definition
41965
328371f4f927 removing definition of cons0; hiding constants in Quickcheck_Narrowing
bulwahn
parents: 41964
diff changeset
   373
  "narrowing = sum (cons None) (cons1 Some)"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   374
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   375
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   376
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   377
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   378
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   379
instantiation sum :: (narrowing, narrowing) narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   380
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   381
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   382
definition
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   383
  "narrowing = sum (cons1 Inl) (cons1 Inr)"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   384
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   385
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   386
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   387
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   388
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   389
instantiation list :: (narrowing) narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   390
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   391
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   392
function narrowing_list :: "'a list narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   393
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   394
  "narrowing_list d = sum (cons []) (apply (apply (cons Cons) narrowing) narrowing_list) d"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   395
by pat_completeness auto
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   396
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   397
termination proof (relation "measure nat_of")
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   398
qed (auto simp add: of_int_inverse nat_of_def)
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   399
    
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   400
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   401
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   402
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   403
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   404
instantiation nat :: narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   405
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   406
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   407
function narrowing_nat :: "nat narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   408
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   409
  "narrowing_nat d = sum (cons 0) (apply (cons Suc) narrowing_nat) d"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   410
by pat_completeness auto
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   411
41912
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   412
termination proof (relation "measure nat_of")
1848775589e5 adding termination proofs to series functions in LSC; commenting out momentarily unused term refinement functions in LSC
bulwahn
parents: 41910
diff changeset
   413
qed (auto simp add: of_int_inverse nat_of_def)
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   414
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   415
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   416
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   417
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   418
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   419
instantiation Enum.finite_1 :: narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   420
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   421
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   422
definition narrowing_finite_1 :: "Enum.finite_1 narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   423
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   424
  "narrowing_finite_1 = cons (Enum.finite_1.a\<^isub>1 :: Enum.finite_1)"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   425
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   426
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   427
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   428
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   429
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   430
instantiation Enum.finite_2 :: narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   431
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   432
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   433
definition narrowing_finite_2 :: "Enum.finite_2 narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   434
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   435
  "narrowing_finite_2 = sum (cons (Enum.finite_2.a\<^isub>1 :: Enum.finite_2)) (cons (Enum.finite_2.a\<^isub>2 :: Enum.finite_2))"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   436
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   437
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   438
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   439
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   440
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   441
instantiation Enum.finite_3 :: narrowing
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   442
begin
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   443
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   444
definition narrowing_finite_3 :: "Enum.finite_3 narrowing"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   445
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   446
  "narrowing_finite_3 = sum (cons (Enum.finite_3.a\<^isub>1 :: Enum.finite_3)) (sum (cons (Enum.finite_3.a\<^isub>2 :: Enum.finite_3)) (cons (Enum.finite_3.a\<^isub>3 :: Enum.finite_3)))"
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   447
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   448
instance ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   449
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   450
end
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   451
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   452
instantiation Enum.finite_4 :: narrowing
41910
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   453
begin
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   454
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   455
definition narrowing_finite_4 :: "Enum.finite_4 narrowing"
41910
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   456
where
41961
fdd37cfcd4a3 renaming series and serial to narrowing in Quickcheck_Narrowing
bulwahn
parents: 41943
diff changeset
   457
  "narrowing_finite_4 = sum (cons Enum.finite_4.a\<^isub>1) (sum (cons Enum.finite_4.a\<^isub>2) (sum (cons Enum.finite_4.a\<^isub>3) (cons Enum.finite_4.a\<^isub>4)))"
41910
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   458
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   459
instance ..
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   460
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   461
end
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   462
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   463
datatype property = Universal narrowing_type "(narrowing_term => property)" "narrowing_term => Code_Evaluation.term" | Existential narrowing_type "(narrowing_term => property)" "narrowing_term => Code_Evaluation.term" | Property bool
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   464
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   465
(* FIXME: hard-wired maximal depth of 100 here *)
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   466
fun exists :: "('a :: {narrowing, partial_term_of} => property) => property"
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   467
where
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   468
  "exists f = (case narrowing (100 :: code_int) of C ty cs => Existential ty (\<lambda> t. f (conv cs t)) (partial_term_of (TYPE('a))))"
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   469
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   470
fun "all" :: "('a :: {narrowing, partial_term_of} => property) => property"
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   471
where
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   472
  "all f = (case narrowing (100 :: code_int) of C ty cs => Universal ty (\<lambda>t. f (conv cs t)) (partial_term_of (TYPE('a))))"
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   473
41943
12f24ad566ea fixed document;
wenzelm
parents: 41930
diff changeset
   474
subsubsection {* class @{text is_testable} *}
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   475
41943
12f24ad566ea fixed document;
wenzelm
parents: 41930
diff changeset
   476
text {* The class @{text is_testable} ensures that all necessary type instances are generated. *}
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   477
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   478
class is_testable
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   479
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   480
instance bool :: is_testable ..
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   481
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
   482
instance "fun" :: ("{term_of, narrowing, partial_term_of}", is_testable) is_testable ..
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   483
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   484
definition ensure_testable :: "'a :: is_testable => 'a :: is_testable"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   485
where
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   486
  "ensure_testable f = f"
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   487
41910
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   488
declare simp_thms(17,19)[code del]
709c04e7b703 adding serial instance of finite_4 in lazysmallcheck; changing code equations for implies
bulwahn
parents: 41909
diff changeset
   489
42022
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   490
subsubsection {* Defining a simple datatype to represent functions in an incomplete and redundant way *}
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   491
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   492
datatype ('a, 'b) ffun = Constant 'b | Update 'a 'b "('a, 'b) ffun"
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   493
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   494
primrec eval_ffun :: "('a, 'b) ffun => 'a => 'b"
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   495
where
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   496
  "eval_ffun (Constant c) x = c"
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   497
| "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
   498
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   499
hide_type (open) ffun
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   500
hide_const (open) Constant Update eval_ffun
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   501
42024
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   502
datatype 'b cfun = Constant 'b
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   503
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   504
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
   505
where
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   506
  "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
   507
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   508
hide_type (open) cfun
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   509
hide_const (open) Constant eval_cfun
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   510
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   511
subsubsection {* Setting up the counterexample generator *}
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   512
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   513
setup {* Thy_Load.provide_file (Path.explode ("~~/src/HOL/Tools/Quickcheck/PNF_Narrowing_Engine.hs")) *}
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   514
setup {* Thy_Load.provide_file (Path.explode ("~~/src/HOL/Tools/Quickcheck/Narrowing_Engine.hs")) *}
42024
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   515
use "~~/src/HOL/Tools/Quickcheck/narrowing_generators.ML"
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   516
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   517
setup {* Narrowing_Generators.setup *}
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   518
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
   519
hide_type (open) code_int narrowing_type narrowing_term cons
42024
51df23535105 handling a quite restricted set of functions in Quickcheck_Narrowing by an easy transformation
bulwahn
parents: 42022
diff changeset
   520
hide_const (open) int_of of_int nth error toEnum map_index split_At empty
43237
8f5c3c6c2909 adding compilation that allows existentials in Quickcheck_Narrowing
bulwahn
parents: 43047
diff changeset
   521
  C cons conv nonEmpty "apply" sum cons1 cons2 ensure_testable all exists
42022
101ce92333f4 adding a simple datatype for representing functions in Quickcheck_Narrowing
bulwahn
parents: 42021
diff changeset
   522
41905
e2611bc96022 adding files for prototype of lazysmallcheck
bulwahn
parents:
diff changeset
   523
end