src/HOL/Library/Code_Integer.thy
author wenzelm
Wed Sep 12 13:42:28 2012 +0200 (2012-09-12)
changeset 49322 fbb320d02420
parent 48431 6efff142bb54
permissions -rw-r--r--
tuned headers;
haftmann@24999
     1
(*  Title:      HOL/Library/Code_Integer.thy
haftmann@24999
     2
    Author:     Florian Haftmann, TU Muenchen
haftmann@24999
     3
*)
haftmann@24999
     4
haftmann@24999
     5
header {* Pretty integer literals for code generation *}
haftmann@24999
     6
haftmann@24999
     7
theory Code_Integer
haftmann@37968
     8
imports Main Code_Natural
haftmann@24999
     9
begin
haftmann@24999
    10
haftmann@24999
    11
text {*
huffman@47108
    12
  Representation-ignorant code equations for conversions.
huffman@47108
    13
*}
huffman@47108
    14
huffman@47108
    15
lemma nat_code [code]:
huffman@47108
    16
  "nat k = (if k \<le> 0 then 0 else
huffman@47108
    17
     let
huffman@47108
    18
       (l, j) = divmod_int k 2;
huffman@47125
    19
       n = nat l;
huffman@47125
    20
       l' = n + n
huffman@47108
    21
     in if j = 0 then l' else Suc l')"
huffman@47108
    22
proof -
huffman@47108
    23
  have "2 = nat 2" by simp
huffman@47108
    24
  show ?thesis
huffman@47217
    25
    apply (subst mult_2 [symmetric])
huffman@47108
    26
    apply (auto simp add: Let_def divmod_int_mod_div not_le
huffman@47108
    27
     nat_div_distrib nat_mult_distrib mult_div_cancel mod_2_not_eq_zero_eq_one_int)
huffman@47108
    28
    apply (unfold `2 = nat 2`)
huffman@47108
    29
    apply (subst nat_mod_distrib [symmetric])
huffman@47108
    30
    apply simp_all
huffman@47108
    31
  done
huffman@47108
    32
qed
huffman@47108
    33
huffman@47108
    34
lemma (in ring_1) of_int_code:
huffman@47108
    35
  "of_int k = (if k = 0 then 0
huffman@47108
    36
     else if k < 0 then - of_int (- k)
huffman@47108
    37
     else let
huffman@47108
    38
       (l, j) = divmod_int k 2;
huffman@47108
    39
       l' = 2 * of_int l
huffman@47108
    40
     in if j = 0 then l' else l' + 1)"
huffman@47108
    41
proof -
huffman@47108
    42
  from mod_div_equality have *: "of_int k = of_int (k div 2 * 2 + k mod 2)" by simp
huffman@47108
    43
  show ?thesis
huffman@47108
    44
    by (simp add: Let_def divmod_int_mod_div mod_2_not_eq_zero_eq_one_int
huffman@47108
    45
      of_int_add [symmetric]) (simp add: * mult_commute)
huffman@47108
    46
qed
huffman@47108
    47
huffman@47108
    48
declare of_int_code [code]
huffman@47108
    49
huffman@47108
    50
text {*
haftmann@24999
    51
  HOL numeral expressions are mapped to integer literals
haftmann@24999
    52
  in target languages, using predefined target language
haftmann@24999
    53
  operations for abstract integer operations.
haftmann@24999
    54
*}
haftmann@24999
    55
haftmann@24999
    56
code_type int
haftmann@24999
    57
  (SML "IntInf.int")
haftmann@24999
    58
  (OCaml "Big'_int.big'_int")
haftmann@24999
    59
  (Haskell "Integer")
haftmann@34899
    60
  (Scala "BigInt")
haftmann@38053
    61
  (Eval "int")
haftmann@24999
    62
haftmann@38857
    63
code_instance int :: equal
haftmann@24999
    64
  (Haskell -)
haftmann@24999
    65
huffman@47108
    66
code_const "0::int"
huffman@47108
    67
  (SML "0")
huffman@47108
    68
  (OCaml "Big'_int.zero'_big'_int")
huffman@47108
    69
  (Haskell "0")
huffman@47108
    70
  (Scala "BigInt(0)")
huffman@47108
    71
haftmann@24999
    72
setup {*
huffman@47108
    73
  fold (Numeral.add_code @{const_name Int.Pos}
huffman@47108
    74
    false Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]
haftmann@24999
    75
*}
haftmann@24999
    76
huffman@47108
    77
setup {*
huffman@47108
    78
  fold (Numeral.add_code @{const_name Int.Neg}
huffman@47108
    79
    true Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]
huffman@47108
    80
*}
haftmann@24999
    81
haftmann@24999
    82
code_const "op + \<Colon> int \<Rightarrow> int \<Rightarrow> int"
haftmann@24999
    83
  (SML "IntInf.+ ((_), (_))")
haftmann@24999
    84
  (OCaml "Big'_int.add'_big'_int")
haftmann@24999
    85
  (Haskell infixl 6 "+")
haftmann@34899
    86
  (Scala infixl 7 "+")
haftmann@37958
    87
  (Eval infixl 8 "+")
haftmann@24999
    88
haftmann@24999
    89
code_const "uminus \<Colon> int \<Rightarrow> int"
haftmann@24999
    90
  (SML "IntInf.~")
haftmann@24999
    91
  (OCaml "Big'_int.minus'_big'_int")
haftmann@24999
    92
  (Haskell "negate")
haftmann@34899
    93
  (Scala "!(- _)")
haftmann@37958
    94
  (Eval "~/ _")
haftmann@24999
    95
haftmann@24999
    96
code_const "op - \<Colon> int \<Rightarrow> int \<Rightarrow> int"
haftmann@24999
    97
  (SML "IntInf.- ((_), (_))")
haftmann@24999
    98
  (OCaml "Big'_int.sub'_big'_int")
haftmann@24999
    99
  (Haskell infixl 6 "-")
haftmann@34899
   100
  (Scala infixl 7 "-")
haftmann@37958
   101
  (Eval infixl 8 "-")
haftmann@24999
   102
huffman@47108
   103
code_const Int.dup
huffman@47108
   104
  (SML "IntInf.*/ (2,/ (_))")
huffman@47108
   105
  (OCaml "Big'_int.mult'_big'_int/ 2")
huffman@47108
   106
  (Haskell "!(2 * _)")
huffman@47108
   107
  (Scala "!(2 * _)")
huffman@47108
   108
  (Eval "!(2 * _)")
huffman@47108
   109
huffman@47108
   110
code_const Int.sub
huffman@47108
   111
  (SML "!(raise/ Fail/ \"sub\")")
huffman@47108
   112
  (OCaml "failwith/ \"sub\"")
huffman@47108
   113
  (Haskell "error/ \"sub\"")
haftmann@48073
   114
  (Scala "!sys.error(\"sub\")")
huffman@47108
   115
haftmann@24999
   116
code_const "op * \<Colon> int \<Rightarrow> int \<Rightarrow> int"
haftmann@24999
   117
  (SML "IntInf.* ((_), (_))")
haftmann@24999
   118
  (OCaml "Big'_int.mult'_big'_int")
haftmann@24999
   119
  (Haskell infixl 7 "*")
haftmann@34899
   120
  (Scala infixl 8 "*")
haftmann@37958
   121
  (Eval infixl 9 "*")
haftmann@24999
   122
haftmann@29936
   123
code_const pdivmod
haftmann@34899
   124
  (SML "IntInf.divMod/ (IntInf.abs _,/ IntInf.abs _)")
haftmann@34899
   125
  (OCaml "Big'_int.quomod'_big'_int/ (Big'_int.abs'_big'_int _)/ (Big'_int.abs'_big'_int _)")
haftmann@34944
   126
  (Haskell "divMod/ (abs _)/ (abs _)")
haftmann@37958
   127
  (Scala "!((k: BigInt) => (l: BigInt) =>/ if (l == 0)/ (BigInt(0), k) else/ (k.abs '/% l.abs))")
haftmann@37958
   128
  (Eval "Integer.div'_mod/ (abs _)/ (abs _)")
haftmann@29936
   129
haftmann@38857
   130
code_const "HOL.equal \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
haftmann@24999
   131
  (SML "!((_ : IntInf.int) = _)")
haftmann@24999
   132
  (OCaml "Big'_int.eq'_big'_int")
haftmann@39272
   133
  (Haskell infix 4 "==")
haftmann@34899
   134
  (Scala infixl 5 "==")
haftmann@37958
   135
  (Eval infixl 6 "=")
haftmann@24999
   136
haftmann@24999
   137
code_const "op \<le> \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
haftmann@24999
   138
  (SML "IntInf.<= ((_), (_))")
haftmann@24999
   139
  (OCaml "Big'_int.le'_big'_int")
haftmann@24999
   140
  (Haskell infix 4 "<=")
haftmann@34899
   141
  (Scala infixl 4 "<=")
haftmann@37958
   142
  (Eval infixl 6 "<=")
haftmann@24999
   143
haftmann@24999
   144
code_const "op < \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
haftmann@24999
   145
  (SML "IntInf.< ((_), (_))")
haftmann@24999
   146
  (OCaml "Big'_int.lt'_big'_int")
haftmann@24999
   147
  (Haskell infix 4 "<")
haftmann@37958
   148
  (Scala infixl 4 "<")
haftmann@37958
   149
  (Eval infixl 6 "<")
haftmann@24999
   150
haftmann@31205
   151
code_const Code_Numeral.int_of
haftmann@31192
   152
  (SML "IntInf.fromInt")
haftmann@31377
   153
  (OCaml "_")
haftmann@48431
   154
  (Haskell "Prelude.toInteger")
haftmann@37958
   155
  (Scala "!_.as'_BigInt")
haftmann@37958
   156
  (Eval "_")
haftmann@24999
   157
haftmann@32657
   158
code_const "Code_Evaluation.term_of \<Colon> int \<Rightarrow> term"
haftmann@31192
   159
  (Eval "HOLogic.mk'_number/ HOLogic.intT")
haftmann@28228
   160
huffman@47108
   161
end