src/HOL/Product_Type.thy
author haftmann
Thu, 04 Oct 2007 19:54:44 +0200
changeset 24844 98c006a30218
parent 24699 c6674504103f
child 25511 54db9b5080b8
permissions -rw-r--r--
certificates for code generator case expressions
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
     1
(*  Title:      HOL/Product_Type.thy
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
     2
    ID:         $Id$
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
     4
    Copyright   1992  University of Cambridge
11777
wenzelm
parents: 11602
diff changeset
     5
*)
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
     6
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
     7
header {* Cartesian products *}
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
     8
15131
c69542757a4d New theory header syntax.
nipkow
parents: 14952
diff changeset
     9
theory Product_Type
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    10
imports Inductive
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    11
uses
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    12
  ("Tools/split_rule.ML")
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    13
  ("Tools/inductive_set_package.ML")
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    14
  ("Tools/inductive_realizer.ML")
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    15
  ("Tools/datatype_realizer.ML")
15131
c69542757a4d New theory header syntax.
nipkow
parents: 14952
diff changeset
    16
begin
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    17
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    18
subsection {* @{typ bool} is a datatype *}
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    19
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    20
rep_datatype bool
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    21
  distinct True_not_False False_not_True
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    22
  induction bool_induct
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    23
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    24
declare case_split [cases type: bool]
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    25
  -- "prefer plain propositional version"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    26
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    27
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    28
subsection {* Unit *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    29
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    30
typedef unit = "{True}"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    31
proof
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
    32
  show "True : ?unit" ..
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    33
qed
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    34
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    35
definition
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    36
  Unity :: unit    ("'(')")
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    37
where
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    38
  "() = Abs_unit True"
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    39
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
    40
lemma unit_eq [noatp]: "u = ()"
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    41
  by (induct u) (simp add: unit_def Unity_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    42
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    43
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    44
  Simplification procedure for @{thm [source] unit_eq}.  Cannot use
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    45
  this rule directly --- it loops!
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    46
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    47
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    48
ML_setup {*
13462
56610e2ba220 sane interface for simprocs;
wenzelm
parents: 12338
diff changeset
    49
  val unit_eq_proc =
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    50
    let val unit_meta_eq = mk_meta_eq @{thm unit_eq} in
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    51
      Simplifier.simproc @{theory} "unit_eq" ["x::unit"]
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15481
diff changeset
    52
      (fn _ => fn _ => fn t => if HOLogic.is_unit t then NONE else SOME unit_meta_eq)
13462
56610e2ba220 sane interface for simprocs;
wenzelm
parents: 12338
diff changeset
    53
    end;
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    54
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    55
  Addsimprocs [unit_eq_proc];
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    56
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    57
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    58
lemma unit_induct [noatp,induct type: unit]: "P () ==> P x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    59
  by simp
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    60
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    61
rep_datatype unit
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    62
  induction unit_induct
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
    63
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    64
lemma unit_all_eq1: "(!!x::unit. PROP P x) == PROP P ()"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    65
  by simp
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    66
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    67
lemma unit_all_eq2: "(!!x::unit. PROP P) == PROP P"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    68
  by (rule triv_forall_equality)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    69
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    70
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    71
  This rewrite counters the effect of @{text unit_eq_proc} on @{term
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    72
  [source] "%u::unit. f u"}, replacing it by @{term [source]
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    73
  f} rather than by @{term [source] "%u. f ()"}.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    74
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    75
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
    76
lemma unit_abs_eta_conv [simp,noatp]: "(%u::unit. f ()) = f"
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    77
  by (rule ext) simp
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    78
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    79
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
    80
subsection {* Pairs *}
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    81
11777
wenzelm
parents: 11602
diff changeset
    82
subsubsection {* Type definition *}
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    83
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    84
constdefs
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
    85
  Pair_Rep :: "['a, 'b] => ['a, 'b] => bool"
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
    86
  "Pair_Rep == (%a b. %x y. x=a & y=b)"
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    87
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    88
global
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    89
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    90
typedef (Prod)
22838
haftmann
parents: 22744
diff changeset
    91
  ('a, 'b) "*"    (infixr "*" 20)
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
    92
    = "{f. EX a b. f = Pair_Rep (a::'a) (b::'b)}"
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
    93
proof
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
    94
  fix a b show "Pair_Rep a b : ?Prod"
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
    95
    by blast
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
    96
qed
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
    97
12114
a8e860c86252 eliminated old "symbols" syntax, use "xsymbols" instead;
wenzelm
parents: 11966
diff changeset
    98
syntax (xsymbols)
15422
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
    99
  "*"      :: "[type, type] => type"         ("(_ \<times>/ _)" [21, 20] 20)
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   100
syntax (HTML output)
15422
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   101
  "*"      :: "[type, type] => type"         ("(_ \<times>/ _)" [21, 20] 20)
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   102
11777
wenzelm
parents: 11602
diff changeset
   103
local
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   104
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   105
subsubsection {* Definitions *}
11777
wenzelm
parents: 11602
diff changeset
   106
wenzelm
parents: 11602
diff changeset
   107
global
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   108
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   109
consts
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   110
  fst      :: "'a * 'b => 'a"
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   111
  snd      :: "'a * 'b => 'b"
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   112
  split    :: "[['a, 'b] => 'c, 'a * 'b] => 'c"
14189
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   113
  curry    :: "['a * 'b => 'c, 'a, 'b] => 'c"
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   114
  prod_fun :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd"
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   115
  Pair     :: "['a, 'b] => 'a * 'b"
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   116
  Sigma    :: "['a set, 'a => 'b set] => ('a * 'b) set"
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   117
11777
wenzelm
parents: 11602
diff changeset
   118
local
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   119
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   120
defs
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   121
  Pair_def:     "Pair a b == Abs_Prod (Pair_Rep a b)"
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   122
  fst_def:      "fst p == THE a. EX b. p = Pair a b"
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   123
  snd_def:      "snd p == THE b. EX a. p = Pair a b"
24162
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   124
  split_def:    "split == (%c p. c (fst p) (snd p))"
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   125
  curry_def:    "curry == (%c x y. c (Pair x y))"
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   126
  prod_fun_def: "prod_fun f g == split (%x y. Pair (f x) (g y))"
22744
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   127
  Sigma_def [code func]:    "Sigma A B == UN x:A. UN y:B x. {Pair x y}"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   128
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   129
abbreviation
21404
eb85850d3eb7 more robust syntax for definition/abbreviation/notation;
wenzelm
parents: 21331
diff changeset
   130
  Times :: "['a set, 'b set] => ('a * 'b) set"
eb85850d3eb7 more robust syntax for definition/abbreviation/notation;
wenzelm
parents: 21331
diff changeset
   131
    (infixr "<*>" 80) where
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   132
  "A <*> B == Sigma A (%_. B)"
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   133
21210
c17fd2df4e9e renamed 'const_syntax' to 'notation';
wenzelm
parents: 21195
diff changeset
   134
notation (xsymbols)
19656
09be06943252 tuned concrete syntax -- abbreviation/const_syntax;
wenzelm
parents: 19535
diff changeset
   135
  Times  (infixr "\<times>" 80)
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   136
21210
c17fd2df4e9e renamed 'const_syntax' to 'notation';
wenzelm
parents: 21195
diff changeset
   137
notation (HTML output)
19656
09be06943252 tuned concrete syntax -- abbreviation/const_syntax;
wenzelm
parents: 19535
diff changeset
   138
  Times  (infixr "\<times>" 80)
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   139
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   140
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   141
subsubsection {* Concrete syntax *}
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   142
11777
wenzelm
parents: 11602
diff changeset
   143
text {*
wenzelm
parents: 11602
diff changeset
   144
  Patterns -- extends pre-defined type @{typ pttrn} used in
wenzelm
parents: 11602
diff changeset
   145
  abstractions.
wenzelm
parents: 11602
diff changeset
   146
*}
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   147
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   148
nonterminals
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   149
  tuple_args patterns
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   150
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   151
syntax
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   152
  "_tuple"      :: "'a => tuple_args => 'a * 'b"        ("(1'(_,/ _'))")
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   153
  "_tuple_arg"  :: "'a => tuple_args"                   ("_")
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   154
  "_tuple_args" :: "'a => tuple_args => tuple_args"     ("_,/ _")
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   155
  "_pattern"    :: "[pttrn, patterns] => pttrn"         ("'(_,/ _')")
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   156
  ""            :: "pttrn => patterns"                  ("_")
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   157
  "_patterns"   :: "[pttrn, patterns] => patterns"      ("_,/ _")
22439
b709739c69e6 syntax: proper body priorty for derived binders;
wenzelm
parents: 22389
diff changeset
   158
  "@Sigma" ::"[pttrn, 'a set, 'b set] => ('a * 'b) set" ("(3SIGMA _:_./ _)" [0, 0, 10] 10)
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   159
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   160
translations
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   161
  "(x, y)"       == "Pair x y"
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   162
  "_tuple x (_tuple_args y z)" == "_tuple x (_tuple_arg (_tuple y z))"
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   163
  "%(x,y,zs).b"  == "split(%x (y,zs).b)"
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   164
  "%(x,y).b"     == "split(%x y. b)"
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   165
  "_abs (Pair x y) t" => "%(x,y).t"
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   166
  (* The last rule accommodates tuples in `case C ... (x,y) ... => ...'
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   167
     The (x,y) is parsed as `Pair x y' because it is logic, not pttrn *)
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   168
  "SIGMA x:A. B" == "Sigma A (%x. B)"
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   169
14359
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   170
(* reconstructs pattern from (nested) splits, avoiding eta-contraction of body*)
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   171
(* works best with enclosing "let", if "let" does not avoid eta-contraction   *)
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   172
print_translation {*
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   173
let fun split_tr' [Abs (x,T,t as (Abs abs))] =
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   174
      (* split (%x y. t) => %(x,y) t *)
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   175
      let val (y,t') = atomic_abs_tr' abs;
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   176
          val (x',t'') = atomic_abs_tr' (x,T,t');
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   177
    
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   178
      in Syntax.const "_abs" $ (Syntax.const "_pattern" $x'$y) $ t'' end
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   179
    | split_tr' [Abs (x,T,(s as Const ("split",_)$t))] =
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   180
       (* split (%x. (split (%y z. t))) => %(x,y,z). t *)
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   181
       let val (Const ("_abs",_)$(Const ("_pattern",_)$y$z)$t') = split_tr' [t];
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   182
           val (x',t'') = atomic_abs_tr' (x,T,t');
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   183
       in Syntax.const "_abs"$ 
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   184
           (Syntax.const "_pattern"$x'$(Syntax.const "_patterns"$y$z))$t'' end
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   185
    | split_tr' [Const ("split",_)$t] =
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   186
       (* split (split (%x y z. t)) => %((x,y),z). t *)   
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   187
       split_tr' [(split_tr' [t])] (* inner split_tr' creates next pattern *)
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   188
    | split_tr' [Const ("_abs",_)$x_y$(Abs abs)] =
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   189
       (* split (%pttrn z. t) => %(pttrn,z). t *)
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   190
       let val (z,t) = atomic_abs_tr' abs;
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   191
       in Syntax.const "_abs" $ (Syntax.const "_pattern" $x_y$z) $ t end
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   192
    | split_tr' _ =  raise Match;
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   193
in [("split", split_tr')]
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   194
end
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   195
*}
3d9948163018 Added print translation for pairs
schirmer
parents: 14337
diff changeset
   196
15422
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   197
(* print "split f" as "\<lambda>(x,y). f x y" and "split (\<lambda>x. f x)" as "\<lambda>(x,y). f x y" *) 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   198
typed_print_translation {*
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   199
let
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   200
  fun split_guess_names_tr' _ T [Abs (x,_,Abs _)] = raise Match
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   201
    | split_guess_names_tr' _ T  [Abs (x,xT,t)] =
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   202
        (case (head_of t) of
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   203
           Const ("split",_) => raise Match
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   204
         | _ => let 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   205
                  val (_::yT::_) = binder_types (domain_type T) handle Bind => raise Match;
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   206
                  val (y,t') = atomic_abs_tr' ("y",yT,(incr_boundvars 1 t)$Bound 0); 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   207
                  val (x',t'') = atomic_abs_tr' (x,xT,t');
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   208
                in Syntax.const "_abs" $ (Syntax.const "_pattern" $x'$y) $ t'' end)
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   209
    | split_guess_names_tr' _ T [t] =
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   210
       (case (head_of t) of
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   211
           Const ("split",_) => raise Match 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   212
         | _ => let 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   213
                  val (xT::yT::_) = binder_types (domain_type T) handle Bind => raise Match;
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   214
                  val (y,t') = 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   215
                        atomic_abs_tr' ("y",yT,(incr_boundvars 2 t)$Bound 1$Bound 0); 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   216
                  val (x',t'') = atomic_abs_tr' ("x",xT,t');
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   217
                in Syntax.const "_abs" $ (Syntax.const "_pattern" $x'$y) $ t'' end)
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   218
    | split_guess_names_tr' _ _ _ = raise Match;
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   219
in [("split", split_guess_names_tr')]
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   220
end 
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   221
*}
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   222
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   223
11966
wenzelm
parents: 11838
diff changeset
   224
subsubsection {* Lemmas and proof tool setup *}
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   225
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   226
lemma ProdI: "Pair_Rep a b : Prod"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   227
  unfolding Prod_def by blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   228
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   229
lemma Pair_Rep_inject: "Pair_Rep a b = Pair_Rep a' b' ==> a = a' & b = b'"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   230
  apply (unfold Pair_Rep_def)
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   231
  apply (drule fun_cong [THEN fun_cong], blast)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   232
  done
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   233
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   234
lemma inj_on_Abs_Prod: "inj_on Abs_Prod Prod"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   235
  apply (rule inj_on_inverseI)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   236
  apply (erule Abs_Prod_inverse)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   237
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   238
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   239
lemma Pair_inject:
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   240
  assumes "(a, b) = (a', b')"
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   241
    and "a = a' ==> b = b' ==> R"
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   242
  shows R
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   243
  apply (insert prems [unfolded Pair_def])
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   244
  apply (rule inj_on_Abs_Prod [THEN inj_onD, THEN Pair_Rep_inject, THEN conjE])
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   245
  apply (assumption | rule ProdI)+
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   246
  done
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   247
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   248
lemma Pair_eq [iff]: "((a, b) = (a', b')) = (a = a' & b = b')"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   249
  by (blast elim!: Pair_inject)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   250
22886
cdff6ef76009 moved recfun_codegen.ML to Code_Generator.thy
haftmann
parents: 22838
diff changeset
   251
lemma fst_conv [simp, code]: "fst (a, b) = a"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   252
  unfolding fst_def by blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   253
22886
cdff6ef76009 moved recfun_codegen.ML to Code_Generator.thy
haftmann
parents: 22838
diff changeset
   254
lemma snd_conv [simp, code]: "snd (a, b) = b"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   255
  unfolding snd_def by blast
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   256
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   257
lemma fst_eqD: "fst (x, y) = a ==> x = a"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   258
  by simp
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   259
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   260
lemma snd_eqD: "snd (x, y) = a ==> y = a"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   261
  by simp
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   262
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   263
lemma PairE_lemma: "EX x y. p = (x, y)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   264
  apply (unfold Pair_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   265
  apply (rule Rep_Prod [unfolded Prod_def, THEN CollectE])
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   266
  apply (erule exE, erule exE, rule exI, rule exI)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   267
  apply (rule Rep_Prod_inverse [symmetric, THEN trans])
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   268
  apply (erule arg_cong)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   269
  done
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   270
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   271
lemma PairE [cases type: *]: "(!!x y. p = (x, y) ==> Q) ==> Q"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   272
  using PairE_lemma [of p] by blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   273
16121
wenzelm
parents: 15570
diff changeset
   274
ML {*
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   275
  local val PairE = thm "PairE" in
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   276
    fun pair_tac s =
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   277
      EVERY' [res_inst_tac [("p", s)] PairE, hyp_subst_tac, K prune_params_tac];
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   278
  end;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   279
*}
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   280
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   281
lemma surjective_pairing: "p = (fst p, snd p)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   282
  -- {* Do not add as rewrite rule: invalidates some proofs in IMP *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   283
  by (cases p) simp
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   284
17085
5b57f995a179 more simprules now have names
paulson
parents: 17021
diff changeset
   285
lemmas pair_collapse = surjective_pairing [symmetric]
5b57f995a179 more simprules now have names
paulson
parents: 17021
diff changeset
   286
declare pair_collapse [simp]
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   287
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   288
lemma surj_pair [simp]: "EX x y. z = (x, y)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   289
  apply (rule exI)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   290
  apply (rule exI)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   291
  apply (rule surjective_pairing)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   292
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   293
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   294
lemma split_paired_all: "(!!x. PROP P x) == (!!a b. PROP P (a, b))"
11820
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   295
proof
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   296
  fix a b
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   297
  assume "!!x. PROP P x"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   298
  then show "PROP P (a, b)" .
11820
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   299
next
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   300
  fix x
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   301
  assume "!!a b. PROP P (a, b)"
19535
e4fdeb32eadf replaced syntax/translations by abbreviation;
wenzelm
parents: 19179
diff changeset
   302
  from `PROP P (fst x, snd x)` show "PROP P x" by simp
11820
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   303
qed
015a82d4ee96 proper proof of split_paired_all (presently unused);
wenzelm
parents: 11777
diff changeset
   304
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   305
lemmas split_tupled_all = split_paired_all unit_all_eq2
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   306
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   307
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   308
  The rule @{thm [source] split_paired_all} does not work with the
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   309
  Simplifier because it also affects premises in congrence rules,
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   310
  where this can lead to premises of the form @{text "!!a b. ... =
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   311
  ?P(a, b)"} which cannot be solved by reflexivity.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   312
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   313
16121
wenzelm
parents: 15570
diff changeset
   314
ML_setup {*
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   315
  (* replace parameters of product type by individual component parameters *)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   316
  val safe_full_simp_tac = generic_simp_tac true (true, false, false);
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   317
  local (* filtering with exists_paired_all is an essential optimization *)
16121
wenzelm
parents: 15570
diff changeset
   318
    fun exists_paired_all (Const ("all", _) $ Abs (_, T, t)) =
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   319
          can HOLogic.dest_prodT T orelse exists_paired_all t
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   320
      | exists_paired_all (t $ u) = exists_paired_all t orelse exists_paired_all u
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   321
      | exists_paired_all (Abs (_, _, t)) = exists_paired_all t
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   322
      | exists_paired_all _ = false;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   323
    val ss = HOL_basic_ss
16121
wenzelm
parents: 15570
diff changeset
   324
      addsimps [thm "split_paired_all", thm "unit_all_eq2", thm "unit_abs_eta_conv"]
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   325
      addsimprocs [unit_eq_proc];
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   326
  in
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   327
    val split_all_tac = SUBGOAL (fn (t, i) =>
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   328
      if exists_paired_all t then safe_full_simp_tac ss i else no_tac);
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   329
    val unsafe_split_all_tac = SUBGOAL (fn (t, i) =>
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   330
      if exists_paired_all t then full_simp_tac ss i else no_tac);
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   331
    fun split_all th =
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   332
   if exists_paired_all (#prop (Thm.rep_thm th)) then full_simplify ss th else th;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   333
  end;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   334
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17782
diff changeset
   335
change_claset (fn cs => cs addSbefore ("split_all_tac", split_all_tac));
16121
wenzelm
parents: 15570
diff changeset
   336
*}
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   337
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   338
lemma split_paired_All [simp]: "(ALL x. P x) = (ALL a b. P (a, b))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   339
  -- {* @{text "[iff]"} is not a good idea because it makes @{text blast} loop *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   340
  by fast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   341
14189
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   342
lemma curry_split [simp]: "curry (split f) = f"
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   343
  by (simp add: curry_def split_def)
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   344
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   345
lemma split_curry [simp]: "split (curry f) = f"
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   346
  by (simp add: curry_def split_def)
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   347
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   348
lemma curryI [intro!]: "f (a,b) ==> curry f a b"
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   349
  by (simp add: curry_def)
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   350
14190
609c072edf90 Fixed blunder in the setup of the classical reasoner wrt. the constant
skalberg
parents: 14189
diff changeset
   351
lemma curryD [dest!]: "curry f a b ==> f (a,b)"
14189
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   352
  by (simp add: curry_def)
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   353
14190
609c072edf90 Fixed blunder in the setup of the classical reasoner wrt. the constant
skalberg
parents: 14189
diff changeset
   354
lemma curryE: "[| curry f a b ; f (a,b) ==> Q |] ==> Q"
14189
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   355
  by (simp add: curry_def)
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   356
24162
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   357
lemma curry_conv [simp, code func]: "curry f a b = f (a,b)"
14189
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   358
  by (simp add: curry_def)
de58f4d939e1 Added the constant "curry".
skalberg
parents: 14101
diff changeset
   359
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   360
lemma prod_induct [induct type: *]: "!!x. (!!a b. P (a, b)) ==> P x"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   361
  by fast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   362
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   363
rep_datatype prod
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   364
  inject Pair_eq
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   365
  induction prod_induct
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   366
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   367
lemma split_paired_Ex [simp]: "(EX x. P x) = (EX a b. P (a, b))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   368
  by fast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   369
24162
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   370
lemma split_conv [simp, code func]: "split c (a, b) = c a b"
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   371
  by (simp add: split_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   372
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   373
lemmas split = split_conv  -- {* for backwards compatibility *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   374
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   375
lemmas splitI = split_conv [THEN iffD2, standard]
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   376
lemmas splitD = split_conv [THEN iffD1, standard]
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   377
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   378
lemma split_Pair_apply: "split (%x y. f (x, y)) = f"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   379
  -- {* Subsumes the old @{text split_Pair} when @{term f} is the identity function. *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   380
  apply (rule ext)
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   381
  apply (tactic {* pair_tac "x" 1 *}, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   382
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   383
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   384
lemma split_paired_The: "(THE x. P x) = (THE (a, b). P (a, b))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   385
  -- {* Can't be added to simpset: loops! *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   386
  by (simp add: split_Pair_apply)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   387
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   388
lemma The_split: "The (split P) = (THE xy. P (fst xy) (snd xy))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   389
  by (simp add: split_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   390
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   391
lemma Pair_fst_snd_eq: "!!s t. (s = t) = (fst s = fst t & snd s = snd t)"
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   392
by (simp only: split_tupled_all, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   393
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   394
lemma prod_eqI [intro?]: "fst p = fst q ==> snd p = snd q ==> p = q"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   395
  by (simp add: Pair_fst_snd_eq)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   396
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   397
lemma split_weak_cong: "p = q ==> split c p = split c q"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   398
  -- {* Prevents simplification of @{term c}: much faster *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   399
  by (erule arg_cong)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   400
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   401
lemma split_eta: "(%(x, y). f (x, y)) = f"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   402
  apply (rule ext)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   403
  apply (simp only: split_tupled_all)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   404
  apply (rule split_conv)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   405
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   406
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   407
lemma cond_split_eta: "(!!x y. f x y = g (x, y)) ==> (%(x, y). f x y) = g"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   408
  by (simp add: split_eta)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   409
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   410
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   411
  Simplification procedure for @{thm [source] cond_split_eta}.  Using
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   412
  @{thm [source] split_eta} as a rewrite rule is not general enough,
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   413
  and using @{thm [source] cond_split_eta} directly would render some
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   414
  existing proofs very inefficient; similarly for @{text
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   415
  split_beta}. *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   416
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   417
ML_setup {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   418
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   419
local
18328
841261f303a1 simprocs: static evaluation of simpset;
wenzelm
parents: 18220
diff changeset
   420
  val cond_split_eta_ss = HOL_basic_ss addsimps [thm "cond_split_eta"]
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   421
  fun  Pair_pat k 0 (Bound m) = (m = k)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   422
  |    Pair_pat k i (Const ("Pair",  _) $ Bound m $ t) = i > 0 andalso
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   423
                        m = k+i andalso Pair_pat k (i-1) t
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   424
  |    Pair_pat _ _ _ = false;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   425
  fun no_args k i (Abs (_, _, t)) = no_args (k+1) i t
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   426
  |   no_args k i (t $ u) = no_args k i t andalso no_args k i u
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   427
  |   no_args k i (Bound m) = m < k orelse m > k+i
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   428
  |   no_args _ _ _ = true;
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15481
diff changeset
   429
  fun split_pat tp i (Abs  (_,_,t)) = if tp 0 i t then SOME (i,t) else NONE
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   430
  |   split_pat tp i (Const ("split", _) $ Abs (_, _, t)) = split_pat tp (i+1) t
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15481
diff changeset
   431
  |   split_pat tp i _ = NONE;
20044
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   432
  fun metaeq ss lhs rhs = mk_meta_eq (Goal.prove (Simplifier.the_context ss) [] []
13480
bb72bd43c6c3 use Tactic.prove instead of prove_goalw_cterm in internal proofs!
wenzelm
parents: 13462
diff changeset
   433
        (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs,rhs)))
18328
841261f303a1 simprocs: static evaluation of simpset;
wenzelm
parents: 18220
diff changeset
   434
        (K (simp_tac (Simplifier.inherit_context ss cond_split_eta_ss) 1)));
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   435
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   436
  fun beta_term_pat k i (Abs (_, _, t)) = beta_term_pat (k+1) i t
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   437
  |   beta_term_pat k i (t $ u) = Pair_pat k i (t $ u) orelse
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   438
                        (beta_term_pat k i t andalso beta_term_pat k i u)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   439
  |   beta_term_pat k i t = no_args k i t;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   440
  fun  eta_term_pat k i (f $ arg) = no_args k i f andalso Pair_pat k i arg
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   441
  |    eta_term_pat _ _ _ = false;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   442
  fun subst arg k i (Abs (x, T, t)) = Abs (x, T, subst arg (k+1) i t)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   443
  |   subst arg k i (t $ u) = if Pair_pat k i (t $ u) then incr_boundvars k arg
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   444
                              else (subst arg k i t $ subst arg k i u)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   445
  |   subst arg k i t = t;
20044
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   446
  fun beta_proc ss (s as Const ("split", _) $ Abs (_, _, t) $ arg) =
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   447
        (case split_pat beta_term_pat 1 t of
20044
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   448
        SOME (i,f) => SOME (metaeq ss s (subst arg 0 i f))
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15481
diff changeset
   449
        | NONE => NONE)
20044
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   450
  |   beta_proc _ _ = NONE;
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   451
  fun eta_proc ss (s as Const ("split", _) $ Abs (_, _, t)) =
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   452
        (case split_pat eta_term_pat 1 t of
20044
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   453
          SOME (_,ft) => SOME (metaeq ss s (let val (f $ arg) = ft in f end))
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15481
diff changeset
   454
        | NONE => NONE)
20044
92cc2f4c7335 simprocs: no theory argument -- use simpset context instead;
wenzelm
parents: 19656
diff changeset
   455
  |   eta_proc _ _ = NONE;
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   456
in
22577
1a08fce38565 ML antiquotes;
wenzelm
parents: 22439
diff changeset
   457
  val split_beta_proc = Simplifier.simproc @{theory} "split_beta" ["split f z"] (K beta_proc);
1a08fce38565 ML antiquotes;
wenzelm
parents: 22439
diff changeset
   458
  val split_eta_proc = Simplifier.simproc @{theory} "split_eta" ["split f"] (K eta_proc);
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   459
end;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   460
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   461
Addsimprocs [split_beta_proc, split_eta_proc];
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   462
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   463
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   464
lemma split_beta: "(%(x, y). P x y) z = P (fst z) (snd z)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   465
  by (subst surjective_pairing, rule split_conv)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   466
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
   467
lemma split_split [noatp]: "R(split c p) = (ALL x y. p = (x, y) --> R(c x y))"
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   468
  -- {* For use with @{text split} and the Simplifier. *}
15481
fc075ae929e4 the new subst tactic, by Lucas Dixon
paulson
parents: 15422
diff changeset
   469
  by (insert surj_pair [of p], clarify, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   470
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   471
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   472
  @{thm [source] split_split} could be declared as @{text "[split]"}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   473
  done after the Splitter has been speeded up significantly;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   474
  precompute the constants involved and don't do anything unless the
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   475
  current goal contains one of those constants.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   476
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   477
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
   478
lemma split_split_asm [noatp]: "R (split c p) = (~(EX x y. p = (x, y) & (~R (c x y))))"
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   479
by (subst split_split, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   480
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   481
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   482
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   483
  \medskip @{term split} used as a logical connective or set former.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   484
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   485
  \medskip These rules are for use with @{text blast}; could instead
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   486
  call @{text simp} using @{thm [source] split} as rewrite. *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   487
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   488
lemma splitI2: "!!p. [| !!a b. p = (a, b) ==> c a b |] ==> split c p"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   489
  apply (simp only: split_tupled_all)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   490
  apply (simp (no_asm_simp))
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   491
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   492
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   493
lemma splitI2': "!!p. [| !!a b. (a, b) = p ==> c a b x |] ==> split c p x"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   494
  apply (simp only: split_tupled_all)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   495
  apply (simp (no_asm_simp))
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   496
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   497
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   498
lemma splitE: "split c p ==> (!!x y. p = (x, y) ==> c x y ==> Q) ==> Q"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   499
  by (induct p) (auto simp add: split_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   500
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   501
lemma splitE': "split c p z ==> (!!x y. p = (x, y) ==> c x y z ==> Q) ==> Q"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   502
  by (induct p) (auto simp add: split_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   503
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   504
lemma splitE2:
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   505
  "[| Q (split P z);  !!x y. [|z = (x, y); Q (P x y)|] ==> R |] ==> R"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   506
proof -
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   507
  assume q: "Q (split P z)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   508
  assume r: "!!x y. [|z = (x, y); Q (P x y)|] ==> R"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   509
  show R
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   510
    apply (rule r surjective_pairing)+
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   511
    apply (rule split_beta [THEN subst], rule q)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   512
    done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   513
qed
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   514
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   515
lemma splitD': "split R (a,b) c ==> R a b c"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   516
  by simp
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   517
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   518
lemma mem_splitI: "z: c a b ==> z: split c (a, b)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   519
  by simp
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   520
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   521
lemma mem_splitI2: "!!p. [| !!a b. p = (a, b) ==> z: c a b |] ==> z: split c p"
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   522
by (simp only: split_tupled_all, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   523
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   524
lemma mem_splitE:
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   525
  assumes major: "z: split c p"
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   526
    and cases: "!!x y. [| p = (x,y); z: c x y |] ==> Q"
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   527
  shows Q
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   528
  by (rule major [unfolded split_def] cases surjective_pairing)+
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   529
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   530
declare mem_splitI2 [intro!] mem_splitI [intro!] splitI2' [intro!] splitI2 [intro!] splitI [intro!]
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   531
declare mem_splitE [elim!] splitE' [elim!] splitE [elim!]
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   532
16121
wenzelm
parents: 15570
diff changeset
   533
ML_setup {*
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   534
local (* filtering with exists_p_split is an essential optimization *)
16121
wenzelm
parents: 15570
diff changeset
   535
  fun exists_p_split (Const ("split",_) $ _ $ (Const ("Pair",_)$_$_)) = true
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   536
    | exists_p_split (t $ u) = exists_p_split t orelse exists_p_split u
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   537
    | exists_p_split (Abs (_, _, t)) = exists_p_split t
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   538
    | exists_p_split _ = false;
16121
wenzelm
parents: 15570
diff changeset
   539
  val ss = HOL_basic_ss addsimps [thm "split_conv"];
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   540
in
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   541
val split_conv_tac = SUBGOAL (fn (t, i) =>
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   542
    if exists_p_split t then safe_full_simp_tac ss i else no_tac);
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   543
end;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   544
(* This prevents applications of splitE for already splitted arguments leading
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   545
   to quite time-consuming computations (in particular for nested tuples) *)
17875
d81094515061 change_claset/simpset;
wenzelm
parents: 17782
diff changeset
   546
change_claset (fn cs => cs addSbefore ("split_conv_tac", split_conv_tac));
16121
wenzelm
parents: 15570
diff changeset
   547
*}
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   548
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
   549
lemma split_eta_SetCompr [simp,noatp]: "(%u. EX x y. u = (x, y) & P (x, y)) = P"
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   550
  by (rule ext) fast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   551
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
   552
lemma split_eta_SetCompr2 [simp,noatp]: "(%u. EX x y. u = (x, y) & P x y) = split P"
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   553
  by (rule ext) fast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   554
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   555
lemma split_part [simp]: "(%(a,b). P & Q a b) = (%ab. P & split Q ab)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   556
  -- {* Allows simplifications of nested splits in case of independent predicates. *}
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   557
  by (rule ext) blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   558
14337
e13731554e50 undid split_comp_eq[simp] because it leads to nontermination together with split_def!
nipkow
parents: 14208
diff changeset
   559
(* Do NOT make this a simp rule as it
e13731554e50 undid split_comp_eq[simp] because it leads to nontermination together with split_def!
nipkow
parents: 14208
diff changeset
   560
   a) only helps in special situations
e13731554e50 undid split_comp_eq[simp] because it leads to nontermination together with split_def!
nipkow
parents: 14208
diff changeset
   561
   b) can lead to nontermination in the presence of split_def
e13731554e50 undid split_comp_eq[simp] because it leads to nontermination together with split_def!
nipkow
parents: 14208
diff changeset
   562
*)
e13731554e50 undid split_comp_eq[simp] because it leads to nontermination together with split_def!
nipkow
parents: 14208
diff changeset
   563
lemma split_comp_eq: 
20415
e3d2d7b01279 explicit type variables prevent empty sorts
paulson
parents: 20380
diff changeset
   564
  fixes f :: "'a => 'b => 'c" and g :: "'d => 'a"
e3d2d7b01279 explicit type variables prevent empty sorts
paulson
parents: 20380
diff changeset
   565
  shows "(%u. f (g (fst u)) (snd u)) = (split (%x. f (g x)))"
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   566
  by (rule ext) auto
14101
d25c23e46173 added upd_fst, upd_snd, some thms
oheimb
parents: 13480
diff changeset
   567
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   568
lemma The_split_eq [simp]: "(THE (x',y'). x = x' & y = y') = (x, y)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   569
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   570
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   571
(*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   572
the following  would be slightly more general,
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   573
but cannot be used as rewrite rule:
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   574
### Cannot add premise as rewrite rule because it contains (type) unknowns:
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   575
### ?y = .x
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   576
Goal "[| P y; !!x. P x ==> x = y |] ==> (@(x',y). x = x' & P y) = (x,y)"
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   577
by (rtac some_equality 1)
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   578
by ( Simp_tac 1)
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   579
by (split_all_tac 1)
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   580
by (Asm_full_simp_tac 1)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   581
qed "The_split_eq";
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   582
*)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   583
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   584
lemma injective_fst_snd: "!!x y. [|fst x = fst y; snd x = snd y|] ==> x = y"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   585
  by auto
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   586
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   587
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   588
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   589
  \bigskip @{term prod_fun} --- action of the product functor upon
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   590
  functions.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   591
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   592
24162
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   593
lemma prod_fun [simp, code func]: "prod_fun f g (a, b) = (f a, g b)"
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   594
  by (simp add: prod_fun_def)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   595
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   596
lemma prod_fun_compose: "prod_fun (f1 o f2) (g1 o g2) = (prod_fun f1 g1 o prod_fun f2 g2)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   597
  apply (rule ext)
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   598
  apply (tactic {* pair_tac "x" 1 *}, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   599
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   600
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   601
lemma prod_fun_ident [simp]: "prod_fun (%x. x) (%y. y) = (%z. z)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   602
  apply (rule ext)
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   603
  apply (tactic {* pair_tac "z" 1 *}, simp)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   604
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   605
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   606
lemma prod_fun_imageI [intro]: "(a, b) : r ==> (f a, g b) : prod_fun f g ` r"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   607
  apply (rule image_eqI)
14208
144f45277d5a misc tidying
paulson
parents: 14190
diff changeset
   608
  apply (rule prod_fun [symmetric], assumption)
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   609
  done
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   610
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   611
lemma prod_fun_imageE [elim!]:
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   612
  assumes major: "c: (prod_fun f g)`r"
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   613
    and cases: "!!x y. [| c=(f(x),g(y));  (x,y):r |] ==> P"
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   614
  shows P
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   615
  apply (rule major [THEN imageE])
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   616
  apply (rule_tac p = x in PairE)
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   617
  apply (rule cases)
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   618
   apply (blast intro: prod_fun)
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   619
  apply blast
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   620
  done
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   621
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   622
22744
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   623
definition
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   624
  upd_fst :: "('a \<Rightarrow> 'c) \<Rightarrow> 'a \<times> 'b \<Rightarrow> 'c \<times> 'b"
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   625
where
22886
cdff6ef76009 moved recfun_codegen.ML to Code_Generator.thy
haftmann
parents: 22838
diff changeset
   626
  [code func del]: "upd_fst f = prod_fun f id"
14101
d25c23e46173 added upd_fst, upd_snd, some thms
oheimb
parents: 13480
diff changeset
   627
22744
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   628
definition
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   629
  upd_snd :: "('b \<Rightarrow> 'c) \<Rightarrow> 'a \<times> 'b \<Rightarrow> 'a \<times> 'c"
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   630
where
22886
cdff6ef76009 moved recfun_codegen.ML to Code_Generator.thy
haftmann
parents: 22838
diff changeset
   631
  [code func del]: "upd_snd f = prod_fun id f"
14101
d25c23e46173 added upd_fst, upd_snd, some thms
oheimb
parents: 13480
diff changeset
   632
22886
cdff6ef76009 moved recfun_codegen.ML to Code_Generator.thy
haftmann
parents: 22838
diff changeset
   633
lemma upd_fst_conv [simp, code]:
22744
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   634
  "upd_fst f (x, y) = (f x, y)" 
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   635
  by (simp add: upd_fst_def)
14101
d25c23e46173 added upd_fst, upd_snd, some thms
oheimb
parents: 13480
diff changeset
   636
22886
cdff6ef76009 moved recfun_codegen.ML to Code_Generator.thy
haftmann
parents: 22838
diff changeset
   637
lemma upd_snd_conv [simp, code]:
22744
5cbe966d67a2 Isar definitions are now added explicitly to code theorem table
haftmann
parents: 22577
diff changeset
   638
  "upd_snd f (x, y) = (x, f y)" 
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   639
  by (simp add: upd_snd_def)
14101
d25c23e46173 added upd_fst, upd_snd, some thms
oheimb
parents: 13480
diff changeset
   640
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   641
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   642
  \bigskip Disjoint union of a family of sets -- Sigma.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   643
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   644
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   645
lemma SigmaI [intro!]: "[| a:A;  b:B(a) |] ==> (a,b) : Sigma A B"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   646
  by (unfold Sigma_def) blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   647
14952
47455995693d removal of x-symbol syntax <Sigma> for dependent products
paulson
parents: 14565
diff changeset
   648
lemma SigmaE [elim!]:
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   649
    "[| c: Sigma A B;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   650
        !!x y.[| x:A;  y:B(x);  c=(x,y) |] ==> P
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   651
     |] ==> P"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   652
  -- {* The general elimination rule. *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   653
  by (unfold Sigma_def) blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   654
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   655
text {*
15422
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   656
  Elimination of @{term "(a, b) : A \<times> B"} -- introduces no
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   657
  eigenvariables.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   658
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   659
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   660
lemma SigmaD1: "(a, b) : Sigma A B ==> a : A"
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   661
  by blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   662
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   663
lemma SigmaD2: "(a, b) : Sigma A B ==> b : B a"
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   664
  by blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   665
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   666
lemma SigmaE2:
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   667
    "[| (a, b) : Sigma A B;
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   668
        [| a:A;  b:B(a) |] ==> P
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   669
     |] ==> P"
14952
47455995693d removal of x-symbol syntax <Sigma> for dependent products
paulson
parents: 14565
diff changeset
   670
  by blast
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   671
14952
47455995693d removal of x-symbol syntax <Sigma> for dependent products
paulson
parents: 14565
diff changeset
   672
lemma Sigma_cong:
15422
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   673
     "\<lbrakk>A = B; !!x. x \<in> B \<Longrightarrow> C x = D x\<rbrakk>
cbdddc0efadf added print translation for split: split f --> %(x,y). f x y
schirmer
parents: 15404
diff changeset
   674
      \<Longrightarrow> (SIGMA x: A. C x) = (SIGMA x: B. D x)"
18372
2bffdf62fe7f tuned proofs;
wenzelm
parents: 18334
diff changeset
   675
  by auto
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   676
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   677
lemma Sigma_mono: "[| A <= C; !!x. x:A ==> B x <= D x |] ==> Sigma A B <= Sigma C D"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   678
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   679
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   680
lemma Sigma_empty1 [simp]: "Sigma {} B = {}"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   681
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   682
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   683
lemma Sigma_empty2 [simp]: "A <*> {} = {}"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   684
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   685
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   686
lemma UNIV_Times_UNIV [simp]: "UNIV <*> UNIV = UNIV"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   687
  by auto
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   688
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   689
lemma Compl_Times_UNIV1 [simp]: "- (UNIV <*> A) = UNIV <*> (-A)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   690
  by auto
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   691
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   692
lemma Compl_Times_UNIV2 [simp]: "- (A <*> UNIV) = (-A) <*> UNIV"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   693
  by auto
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   694
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   695
lemma mem_Sigma_iff [iff]: "((a,b): Sigma A B) = (a:A & b:B(a))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   696
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   697
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   698
lemma Times_subset_cancel2: "x:C ==> (A <*> C <= B <*> C) = (A <= B)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   699
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   700
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   701
lemma Times_eq_cancel2: "x:C ==> (A <*> C = B <*> C) = (A = B)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   702
  by (blast elim: equalityE)
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   703
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   704
lemma SetCompr_Sigma_eq:
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   705
    "Collect (split (%x y. P x & Q x y)) = (SIGMA x:Collect P. Collect (Q x))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   706
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   707
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   708
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   709
  \bigskip Complex rules for Sigma.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   710
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   711
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   712
lemma Collect_split [simp]: "{(a,b). P a & Q b} = Collect P <*> Collect Q"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   713
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   714
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   715
lemma UN_Times_distrib:
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   716
  "(UN (a,b):(A <*> B). E a <*> F b) = (UNION A E) <*> (UNION B F)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   717
  -- {* Suggested by Pierre Chartier *}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   718
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   719
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
   720
lemma split_paired_Ball_Sigma [simp,noatp]:
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   721
    "(ALL z: Sigma A B. P z) = (ALL x:A. ALL y: B x. P(x,y))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   722
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   723
24286
7619080e49f0 ATP blacklisting is now in theory data, attribute noatp
paulson
parents: 24162
diff changeset
   724
lemma split_paired_Bex_Sigma [simp,noatp]:
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   725
    "(EX z: Sigma A B. P z) = (EX x:A. EX y: B x. P(x,y))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   726
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   727
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   728
lemma Sigma_Un_distrib1: "(SIGMA i:I Un J. C(i)) = (SIGMA i:I. C(i)) Un (SIGMA j:J. C(j))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   729
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   730
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   731
lemma Sigma_Un_distrib2: "(SIGMA i:I. A(i) Un B(i)) = (SIGMA i:I. A(i)) Un (SIGMA i:I. B(i))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   732
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   733
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   734
lemma Sigma_Int_distrib1: "(SIGMA i:I Int J. C(i)) = (SIGMA i:I. C(i)) Int (SIGMA j:J. C(j))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   735
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   736
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   737
lemma Sigma_Int_distrib2: "(SIGMA i:I. A(i) Int B(i)) = (SIGMA i:I. A(i)) Int (SIGMA i:I. B(i))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   738
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   739
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   740
lemma Sigma_Diff_distrib1: "(SIGMA i:I - J. C(i)) = (SIGMA i:I. C(i)) - (SIGMA j:J. C(j))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   741
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   742
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   743
lemma Sigma_Diff_distrib2: "(SIGMA i:I. A(i) - B(i)) = (SIGMA i:I. A(i)) - (SIGMA i:I. B(i))"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   744
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   745
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   746
lemma Sigma_Union: "Sigma (Union X) B = (UN A:X. Sigma A B)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   747
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   748
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   749
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   750
  Non-dependent versions are needed to avoid the need for higher-order
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   751
  matching, especially when the rules are re-oriented.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   752
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   753
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   754
lemma Times_Un_distrib1: "(A Un B) <*> C = (A <*> C) Un (B <*> C)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   755
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   756
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   757
lemma Times_Int_distrib1: "(A Int B) <*> C = (A <*> C) Int (B <*> C)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   758
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   759
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   760
lemma Times_Diff_distrib1: "(A - B) <*> C = (A <*> C) - (B <*> C)"
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   761
  by blast
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   762
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   763
11493
f3ff2549cdc8 added pair_imageI (also as intro rule)
oheimb
parents: 11451
diff changeset
   764
lemma pair_imageI [intro]: "(a, b) : A ==> f a b : (%(a, b). f a b) ` A"
11777
wenzelm
parents: 11602
diff changeset
   765
  apply (rule_tac x = "(a, b)" in image_eqI)
wenzelm
parents: 11602
diff changeset
   766
   apply auto
wenzelm
parents: 11602
diff changeset
   767
  done
wenzelm
parents: 11602
diff changeset
   768
11493
f3ff2549cdc8 added pair_imageI (also as intro rule)
oheimb
parents: 11451
diff changeset
   769
11838
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   770
text {*
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   771
  Setup of internal @{text split_rule}.
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   772
*}
02d75712061d got rid of ML proof scripts for Product_Type;
wenzelm
parents: 11820
diff changeset
   773
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   774
constdefs
11425
wenzelm
parents: 11032
diff changeset
   775
  internal_split :: "('a => 'b => 'c) => 'a * 'b => 'c"
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   776
  "internal_split == split"
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   777
24162
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   778
lemmas [code func del] = internal_split_def
8dfd5dd65d82 split off theory Option for benefit of code generator
haftmann
parents: 23247
diff changeset
   779
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   780
lemma internal_split_conv: "internal_split c (a, b) = c a b"
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   781
  by (simp only: internal_split_def split_conv)
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   782
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   783
hide const internal_split
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   784
11025
a70b796d9af8 converted to Isar therory, adding attributes complete_split and split_format
oheimb
parents: 10289
diff changeset
   785
use "Tools/split_rule.ML"
11032
83f723e86dac added hidden internal_split constant;
wenzelm
parents: 11025
diff changeset
   786
setup SplitRule.setup
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
   787
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   788
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   789
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   790
lemmas prod_caseI = prod.cases [THEN iffD2, standard]
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   791
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   792
lemma prod_caseI2: "!!p. [| !!a b. p = (a, b) ==> c a b |] ==> prod_case c p"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   793
  by auto
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   794
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   795
lemma prod_caseI2': "!!p. [| !!a b. (a, b) = p ==> c a b x |] ==> prod_case c p x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   796
  by (auto simp: split_tupled_all)
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   797
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   798
lemma prod_caseE: "prod_case c p ==> (!!x y. p = (x, y) ==> c x y ==> Q) ==> Q"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   799
  by (induct p) auto
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   800
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   801
lemma prod_caseE': "prod_case c p z ==> (!!x y. p = (x, y) ==> c x y z ==> Q) ==> Q"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   802
  by (induct p) auto
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   803
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   804
lemma prod_case_unfold: "prod_case = (%c p. c (fst p) (snd p))"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   805
  by (simp add: expand_fun_eq)
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   806
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   807
declare prod_caseI2' [intro!] prod_caseI2 [intro!] prod_caseI [intro!]
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   808
declare prod_caseE' [elim!] prod_caseE [elim!]
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   809
24844
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   810
lemma prod_case_split:
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   811
  "prod_case = split"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   812
  by (auto simp add: expand_fun_eq)
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   813
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   814
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   815
subsection {* Further cases/induct rules for tuples *}
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   816
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   817
lemma prod_cases3 [cases type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   818
  obtains (fields) a b c where "y = (a, b, c)"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   819
  by (cases y, case_tac b) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   820
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   821
lemma prod_induct3 [case_names fields, induct type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   822
    "(!!a b c. P (a, b, c)) ==> P x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   823
  by (cases x) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   824
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   825
lemma prod_cases4 [cases type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   826
  obtains (fields) a b c d where "y = (a, b, c, d)"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   827
  by (cases y, case_tac c) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   828
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   829
lemma prod_induct4 [case_names fields, induct type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   830
    "(!!a b c d. P (a, b, c, d)) ==> P x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   831
  by (cases x) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   832
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   833
lemma prod_cases5 [cases type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   834
  obtains (fields) a b c d e where "y = (a, b, c, d, e)"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   835
  by (cases y, case_tac d) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   836
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   837
lemma prod_induct5 [case_names fields, induct type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   838
    "(!!a b c d e. P (a, b, c, d, e)) ==> P x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   839
  by (cases x) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   840
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   841
lemma prod_cases6 [cases type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   842
  obtains (fields) a b c d e f where "y = (a, b, c, d, e, f)"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   843
  by (cases y, case_tac e) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   844
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   845
lemma prod_induct6 [case_names fields, induct type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   846
    "(!!a b c d e f. P (a, b, c, d, e, f)) ==> P x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   847
  by (cases x) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   848
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   849
lemma prod_cases7 [cases type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   850
  obtains (fields) a b c d e f g where "y = (a, b, c, d, e, f, g)"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   851
  by (cases y, case_tac f) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   852
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   853
lemma prod_induct7 [case_names fields, induct type]:
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   854
    "(!!a b c d e f g. P (a, b, c, d, e, f, g)) ==> P x"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   855
  by (cases x) blast
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   856
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
   857
21195
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   858
subsection {* Further lemmas *}
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   859
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   860
lemma
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   861
  split_Pair: "split Pair x = x"
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   862
  unfolding split_def by auto
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   863
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   864
lemma
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   865
  split_comp: "split (f \<circ> g) x = f (g (fst x)) (snd x)"
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   866
  by (cases x, simp)
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   867
0cca8d19557d two further lemmas on split
haftmann
parents: 21046
diff changeset
   868
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   869
subsection {* Code generator setup *}
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   870
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   871
instance unit :: eq ..
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   872
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   873
lemma [code func]:
21454
a1937c51ed88 dropped eq const
haftmann
parents: 21404
diff changeset
   874
  "(u\<Colon>unit) = v \<longleftrightarrow> True" unfolding unit_eq [of u] unit_eq [of v] by rule+
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   875
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   876
code_type unit
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   877
  (SML "unit")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   878
  (OCaml "unit")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   879
  (Haskell "()")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   880
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   881
code_instance unit :: eq
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   882
  (Haskell -)
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   883
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   884
code_const "op = \<Colon> unit \<Rightarrow> unit \<Rightarrow> bool"
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   885
  (Haskell infixl 4 "==")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   886
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   887
code_const Unity
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   888
  (SML "()")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   889
  (OCaml "()")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   890
  (Haskell "()")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   891
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   892
code_reserved SML
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   893
  unit
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   894
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   895
code_reserved OCaml
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   896
  unit
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   897
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   898
instance * :: (eq, eq) eq ..
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   899
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   900
lemma [code func]:
21454
a1937c51ed88 dropped eq const
haftmann
parents: 21404
diff changeset
   901
  "(x1\<Colon>'a\<Colon>eq, y1\<Colon>'b\<Colon>eq) = (x2, y2) \<longleftrightarrow> x1 = x2 \<and> y1 = y2" by auto
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   902
24844
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   903
lemma split_case_cert:
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   904
  assumes "CASE \<equiv> split f"
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   905
  shows "CASE (a, b) \<equiv> f a b"
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   906
  using assms by simp
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   907
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   908
setup {*
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   909
  Code.add_case @{thm split_case_cert}
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   910
*}
98c006a30218 certificates for code generator case expressions
haftmann
parents: 24699
diff changeset
   911
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   912
code_type *
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   913
  (SML infix 2 "*")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   914
  (OCaml infix 2 "*")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   915
  (Haskell "!((_),/ (_))")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   916
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   917
code_instance * :: eq
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   918
  (Haskell -)
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   919
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   920
code_const "op = \<Colon> 'a\<Colon>eq \<times> 'b\<Colon>eq \<Rightarrow> 'a \<times> 'b \<Rightarrow> bool"
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   921
  (Haskell infixl 4 "==")
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   922
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   923
code_const Pair
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   924
  (SML "!((_),/ (_))")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   925
  (OCaml "!((_),/ (_))")
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   926
  (Haskell "!((_),/ (_))")
20588
c847c56edf0c added operational equality
haftmann
parents: 20415
diff changeset
   927
22389
bdf16741d039 using "fst" "snd" for Haskell code
haftmann
parents: 22349
diff changeset
   928
code_const fst and snd
bdf16741d039 using "fst" "snd" for Haskell code
haftmann
parents: 22349
diff changeset
   929
  (Haskell "fst" and "snd")
bdf16741d039 using "fst" "snd" for Haskell code
haftmann
parents: 22349
diff changeset
   930
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   931
types_code
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   932
  "*"     ("(_ */ _)")
16770
1f1b1fae30e4 Auxiliary functions to be used in generated code are now defined using "attach".
berghofe
parents: 16634
diff changeset
   933
attach (term_of) {*
1f1b1fae30e4 Auxiliary functions to be used in generated code are now defined using "attach".
berghofe
parents: 16634
diff changeset
   934
fun term_of_id_42 f T g U (x, y) = HOLogic.pair_const T U $ f x $ g y;
1f1b1fae30e4 Auxiliary functions to be used in generated code are now defined using "attach".
berghofe
parents: 16634
diff changeset
   935
*}
1f1b1fae30e4 Auxiliary functions to be used in generated code are now defined using "attach".
berghofe
parents: 16634
diff changeset
   936
attach (test) {*
1f1b1fae30e4 Auxiliary functions to be used in generated code are now defined using "attach".
berghofe
parents: 16634
diff changeset
   937
fun gen_id_42 aG bG i = (aG i, bG i);
1f1b1fae30e4 Auxiliary functions to be used in generated code are now defined using "attach".
berghofe
parents: 16634
diff changeset
   938
*}
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   939
18706
1e7562c7afe6 Re-inserted consts_code declaration accidentally deleted
berghofe
parents: 18702
diff changeset
   940
consts_code
1e7562c7afe6 Re-inserted consts_code declaration accidentally deleted
berghofe
parents: 18702
diff changeset
   941
  "Pair"    ("(_,/ _)")
1e7562c7afe6 Re-inserted consts_code declaration accidentally deleted
berghofe
parents: 18702
diff changeset
   942
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   943
setup {*
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   944
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
   945
let
18013
3f5d0acdfdba added extraction interface for code generator
haftmann
parents: 17956
diff changeset
   946
19039
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   947
fun strip_abs_split 0 t = ([], t)
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   948
  | strip_abs_split i (Abs (s, T, t)) =
18013
3f5d0acdfdba added extraction interface for code generator
haftmann
parents: 17956
diff changeset
   949
      let
3f5d0acdfdba added extraction interface for code generator
haftmann
parents: 17956
diff changeset
   950
        val s' = Codegen.new_name t s;
3f5d0acdfdba added extraction interface for code generator
haftmann
parents: 17956
diff changeset
   951
        val v = Free (s', T)
19039
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   952
      in apfst (cons v) (strip_abs_split (i-1) (subst_bound (v, t))) end
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   953
  | strip_abs_split i (u as Const ("split", _) $ t) = (case strip_abs_split (i+1) t of
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   954
        (v :: v' :: vs, u) => (HOLogic.mk_prod (v, v') :: vs, u)
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   955
      | _ => ([], u))
19039
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   956
  | strip_abs_split i t = ([], t);
18013
3f5d0acdfdba added extraction interface for code generator
haftmann
parents: 17956
diff changeset
   957
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   958
fun let_codegen thy defs gr dep thyname brack t = (case strip_comb t of
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   959
    (t1 as Const ("Let", _), t2 :: t3 :: ts) =>
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   960
    let
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   961
      fun dest_let (l as Const ("Let", _) $ t $ u) =
19039
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   962
          (case strip_abs_split 1 u of
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   963
             ([p], u') => apfst (cons (p, t)) (dest_let u')
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   964
           | _ => ([], l))
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   965
        | dest_let t = ([], t);
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   966
      fun mk_code (gr, (l, r)) =
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   967
        let
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   968
          val (gr1, pl) = Codegen.invoke_codegen thy defs dep thyname false (gr, l);
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   969
          val (gr2, pr) = Codegen.invoke_codegen thy defs dep thyname false (gr1, r);
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   970
        in (gr2, (pl, pr)) end
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   971
    in case dest_let (t1 $ t2 $ t3) of
15531
08c8dad8e399 Deleted Library.option type.
skalberg
parents: 15481
diff changeset
   972
        ([], _) => NONE
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   973
      | (ps, u) =>
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   974
          let
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   975
            val (gr1, qs) = foldl_map mk_code (gr, ps);
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   976
            val (gr2, pu) = Codegen.invoke_codegen thy defs dep thyname false (gr1, u);
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   977
            val (gr3, pargs) = foldl_map
17021
1c361a3de73d Fixed bug in code generator for let and split leading to ill-formed code.
berghofe
parents: 17002
diff changeset
   978
              (Codegen.invoke_codegen thy defs dep thyname true) (gr2, ts)
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   979
          in
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   980
            SOME (gr3, Codegen.mk_app brack
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   981
              (Pretty.blk (0, [Pretty.str "let ", Pretty.blk (0, List.concat
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   982
                  (separate [Pretty.str ";", Pretty.brk 1] (map (fn (pl, pr) =>
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   983
                    [Pretty.block [Pretty.str "val ", pl, Pretty.str " =",
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   984
                       Pretty.brk 1, pr]]) qs))),
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   985
                Pretty.brk 1, Pretty.str "in ", pu,
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   986
                Pretty.brk 1, Pretty.str "end"])) pargs)
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   987
          end
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   988
    end
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   989
  | _ => NONE);
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
   990
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   991
fun split_codegen thy defs gr dep thyname brack t = (case strip_comb t of
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   992
    (t1 as Const ("split", _), t2 :: ts) =>
19039
8eae46249628 added theory of executable rational numbers
haftmann
parents: 19008
diff changeset
   993
      (case strip_abs_split 1 (t1 $ t2) of
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   994
         ([p], u) =>
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   995
           let
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   996
             val (gr1, q) = Codegen.invoke_codegen thy defs dep thyname false (gr, p);
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   997
             val (gr2, pu) = Codegen.invoke_codegen thy defs dep thyname false (gr1, u);
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
   998
             val (gr3, pargs) = foldl_map
17021
1c361a3de73d Fixed bug in code generator for let and split leading to ill-formed code.
berghofe
parents: 17002
diff changeset
   999
               (Codegen.invoke_codegen thy defs dep thyname true) (gr2, ts)
16634
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1000
           in
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1001
             SOME (gr2, Codegen.mk_app brack
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1002
               (Pretty.block [Pretty.str "(fn ", q, Pretty.str " =>",
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1003
                 Pretty.brk 1, pu, Pretty.str ")"]) pargs)
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1004
           end
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1005
       | _ => NONE)
f19d58cfb47a Adapted to new interface of code generator.
berghofe
parents: 16417
diff changeset
  1006
  | _ => NONE);
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
  1007
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
  1008
in
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
  1009
20105
454f4be984b7 adaptions in codegen
haftmann
parents: 20044
diff changeset
  1010
  Codegen.add_codegen "let_codegen" let_codegen
454f4be984b7 adaptions in codegen
haftmann
parents: 20044
diff changeset
  1011
  #> Codegen.add_codegen "split_codegen" split_codegen
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
  1012
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
  1013
end
15394
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
  1014
*}
a2c34e6ca4f8 New code generator for let and split.
berghofe
parents: 15140
diff changeset
  1015
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1016
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1017
subsection {* Legacy bindings *}
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1018
21908
d02ba728cd56 moved code generator product setup here
haftmann
parents: 21454
diff changeset
  1019
ML {*
15404
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1020
val Collect_split = thm "Collect_split";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1021
val Compl_Times_UNIV1 = thm "Compl_Times_UNIV1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1022
val Compl_Times_UNIV2 = thm "Compl_Times_UNIV2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1023
val PairE = thm "PairE";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1024
val PairE_lemma = thm "PairE_lemma";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1025
val Pair_Rep_inject = thm "Pair_Rep_inject";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1026
val Pair_def = thm "Pair_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1027
val Pair_eq = thm "Pair_eq";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1028
val Pair_fst_snd_eq = thm "Pair_fst_snd_eq";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1029
val Pair_inject = thm "Pair_inject";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1030
val ProdI = thm "ProdI";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1031
val SetCompr_Sigma_eq = thm "SetCompr_Sigma_eq";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1032
val SigmaD1 = thm "SigmaD1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1033
val SigmaD2 = thm "SigmaD2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1034
val SigmaE = thm "SigmaE";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1035
val SigmaE2 = thm "SigmaE2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1036
val SigmaI = thm "SigmaI";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1037
val Sigma_Diff_distrib1 = thm "Sigma_Diff_distrib1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1038
val Sigma_Diff_distrib2 = thm "Sigma_Diff_distrib2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1039
val Sigma_Int_distrib1 = thm "Sigma_Int_distrib1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1040
val Sigma_Int_distrib2 = thm "Sigma_Int_distrib2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1041
val Sigma_Un_distrib1 = thm "Sigma_Un_distrib1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1042
val Sigma_Un_distrib2 = thm "Sigma_Un_distrib2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1043
val Sigma_Union = thm "Sigma_Union";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1044
val Sigma_def = thm "Sigma_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1045
val Sigma_empty1 = thm "Sigma_empty1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1046
val Sigma_empty2 = thm "Sigma_empty2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1047
val Sigma_mono = thm "Sigma_mono";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1048
val The_split = thm "The_split";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1049
val The_split_eq = thm "The_split_eq";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1050
val The_split_eq = thm "The_split_eq";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1051
val Times_Diff_distrib1 = thm "Times_Diff_distrib1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1052
val Times_Int_distrib1 = thm "Times_Int_distrib1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1053
val Times_Un_distrib1 = thm "Times_Un_distrib1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1054
val Times_eq_cancel2 = thm "Times_eq_cancel2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1055
val Times_subset_cancel2 = thm "Times_subset_cancel2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1056
val UNIV_Times_UNIV = thm "UNIV_Times_UNIV";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1057
val UN_Times_distrib = thm "UN_Times_distrib";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1058
val Unity_def = thm "Unity_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1059
val cond_split_eta = thm "cond_split_eta";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1060
val fst_conv = thm "fst_conv";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1061
val fst_def = thm "fst_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1062
val fst_eqD = thm "fst_eqD";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1063
val inj_on_Abs_Prod = thm "inj_on_Abs_Prod";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1064
val injective_fst_snd = thm "injective_fst_snd";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1065
val mem_Sigma_iff = thm "mem_Sigma_iff";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1066
val mem_splitE = thm "mem_splitE";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1067
val mem_splitI = thm "mem_splitI";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1068
val mem_splitI2 = thm "mem_splitI2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1069
val prod_eqI = thm "prod_eqI";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1070
val prod_fun = thm "prod_fun";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1071
val prod_fun_compose = thm "prod_fun_compose";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1072
val prod_fun_def = thm "prod_fun_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1073
val prod_fun_ident = thm "prod_fun_ident";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1074
val prod_fun_imageE = thm "prod_fun_imageE";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1075
val prod_fun_imageI = thm "prod_fun_imageI";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1076
val prod_induct = thm "prod_induct";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1077
val snd_conv = thm "snd_conv";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1078
val snd_def = thm "snd_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1079
val snd_eqD = thm "snd_eqD";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1080
val split = thm "split";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1081
val splitD = thm "splitD";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1082
val splitD' = thm "splitD'";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1083
val splitE = thm "splitE";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1084
val splitE' = thm "splitE'";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1085
val splitE2 = thm "splitE2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1086
val splitI = thm "splitI";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1087
val splitI2 = thm "splitI2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1088
val splitI2' = thm "splitI2'";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1089
val split_Pair_apply = thm "split_Pair_apply";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1090
val split_beta = thm "split_beta";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1091
val split_conv = thm "split_conv";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1092
val split_def = thm "split_def";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1093
val split_eta = thm "split_eta";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1094
val split_eta_SetCompr = thm "split_eta_SetCompr";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1095
val split_eta_SetCompr2 = thm "split_eta_SetCompr2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1096
val split_paired_All = thm "split_paired_All";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1097
val split_paired_Ball_Sigma = thm "split_paired_Ball_Sigma";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1098
val split_paired_Bex_Sigma = thm "split_paired_Bex_Sigma";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1099
val split_paired_Ex = thm "split_paired_Ex";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1100
val split_paired_The = thm "split_paired_The";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1101
val split_paired_all = thm "split_paired_all";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1102
val split_part = thm "split_part";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1103
val split_split = thm "split_split";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1104
val split_split_asm = thm "split_split_asm";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1105
val split_tupled_all = thms "split_tupled_all";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1106
val split_weak_cong = thm "split_weak_cong";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1107
val surj_pair = thm "surj_pair";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1108
val surjective_pairing = thm "surjective_pairing";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1109
val unit_abs_eta_conv = thm "unit_abs_eta_conv";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1110
val unit_all_eq1 = thm "unit_all_eq1";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1111
val unit_all_eq2 = thm "unit_all_eq2";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1112
val unit_eq = thm "unit_eq";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1113
val unit_induct = thm "unit_induct";
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1114
*}
a9a762f586b5 removal of NatArith.ML and Product_Type.ML
paulson
parents: 15394
diff changeset
  1115
24699
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1116
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1117
subsection {* Further inductive packages *}
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1118
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1119
use "Tools/inductive_realizer.ML"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1120
setup InductiveRealizer.setup
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1121
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1122
use "Tools/inductive_set_package.ML"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1123
setup InductiveSetPackage.setup
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1124
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1125
use "Tools/datatype_realizer.ML"
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1126
setup DatatypeRealizer.setup
c6674504103f datatype interpretators for size and datatype_realizer
haftmann
parents: 24286
diff changeset
  1127
10213
01c2744a3786 *** empty log message ***
nipkow
parents:
diff changeset
  1128
end