src/HOL/Library/Code_Integer.thy
 author Christian Sternagel Thu Dec 13 13:11:38 2012 +0100 (2012-12-13) changeset 50516 ed6b40d15d1c parent 48431 6efff142bb54 permissions -rw-r--r--
renamed "emb" to "list_hembeq";
make "list_hembeq" reflexive independent of the base order;
renamed "sub" to "sublisteq";
dropped "transp_on" (state transitivity explicitly instead);
no need to hide "sub" after renaming;
replaced some ASCII symbols by proper Isabelle symbols;
NEWS
```     1 (*  Title:      HOL/Library/Code_Integer.thy
```
```     2     Author:     Florian Haftmann, TU Muenchen
```
```     3 *)
```
```     4
```
```     5 header {* Pretty integer literals for code generation *}
```
```     6
```
```     7 theory Code_Integer
```
```     8 imports Main Code_Natural
```
```     9 begin
```
```    10
```
```    11 text {*
```
```    12   Representation-ignorant code equations for conversions.
```
```    13 *}
```
```    14
```
```    15 lemma nat_code [code]:
```
```    16   "nat k = (if k \<le> 0 then 0 else
```
```    17      let
```
```    18        (l, j) = divmod_int k 2;
```
```    19        n = nat l;
```
```    20        l' = n + n
```
```    21      in if j = 0 then l' else Suc l')"
```
```    22 proof -
```
```    23   have "2 = nat 2" by simp
```
```    24   show ?thesis
```
```    25     apply (subst mult_2 [symmetric])
```
```    26     apply (auto simp add: Let_def divmod_int_mod_div not_le
```
```    27      nat_div_distrib nat_mult_distrib mult_div_cancel mod_2_not_eq_zero_eq_one_int)
```
```    28     apply (unfold `2 = nat 2`)
```
```    29     apply (subst nat_mod_distrib [symmetric])
```
```    30     apply simp_all
```
```    31   done
```
```    32 qed
```
```    33
```
```    34 lemma (in ring_1) of_int_code:
```
```    35   "of_int k = (if k = 0 then 0
```
```    36      else if k < 0 then - of_int (- k)
```
```    37      else let
```
```    38        (l, j) = divmod_int k 2;
```
```    39        l' = 2 * of_int l
```
```    40      in if j = 0 then l' else l' + 1)"
```
```    41 proof -
```
```    42   from mod_div_equality have *: "of_int k = of_int (k div 2 * 2 + k mod 2)" by simp
```
```    43   show ?thesis
```
```    44     by (simp add: Let_def divmod_int_mod_div mod_2_not_eq_zero_eq_one_int
```
```    45       of_int_add [symmetric]) (simp add: * mult_commute)
```
```    46 qed
```
```    47
```
```    48 declare of_int_code [code]
```
```    49
```
```    50 text {*
```
```    51   HOL numeral expressions are mapped to integer literals
```
```    52   in target languages, using predefined target language
```
```    53   operations for abstract integer operations.
```
```    54 *}
```
```    55
```
```    56 code_type int
```
```    57   (SML "IntInf.int")
```
```    58   (OCaml "Big'_int.big'_int")
```
```    59   (Haskell "Integer")
```
```    60   (Scala "BigInt")
```
```    61   (Eval "int")
```
```    62
```
```    63 code_instance int :: equal
```
```    64   (Haskell -)
```
```    65
```
```    66 code_const "0::int"
```
```    67   (SML "0")
```
```    68   (OCaml "Big'_int.zero'_big'_int")
```
```    69   (Haskell "0")
```
```    70   (Scala "BigInt(0)")
```
```    71
```
```    72 setup {*
```
```    73   fold (Numeral.add_code @{const_name Int.Pos}
```
```    74     false Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]
```
```    75 *}
```
```    76
```
```    77 setup {*
```
```    78   fold (Numeral.add_code @{const_name Int.Neg}
```
```    79     true Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]
```
```    80 *}
```
```    81
```
```    82 code_const "op + \<Colon> int \<Rightarrow> int \<Rightarrow> int"
```
```    83   (SML "IntInf.+ ((_), (_))")
```
```    84   (OCaml "Big'_int.add'_big'_int")
```
```    85   (Haskell infixl 6 "+")
```
```    86   (Scala infixl 7 "+")
```
```    87   (Eval infixl 8 "+")
```
```    88
```
```    89 code_const "uminus \<Colon> int \<Rightarrow> int"
```
```    90   (SML "IntInf.~")
```
```    91   (OCaml "Big'_int.minus'_big'_int")
```
```    92   (Haskell "negate")
```
```    93   (Scala "!(- _)")
```
```    94   (Eval "~/ _")
```
```    95
```
```    96 code_const "op - \<Colon> int \<Rightarrow> int \<Rightarrow> int"
```
```    97   (SML "IntInf.- ((_), (_))")
```
```    98   (OCaml "Big'_int.sub'_big'_int")
```
```    99   (Haskell infixl 6 "-")
```
```   100   (Scala infixl 7 "-")
```
```   101   (Eval infixl 8 "-")
```
```   102
```
```   103 code_const Int.dup
```
```   104   (SML "IntInf.*/ (2,/ (_))")
```
```   105   (OCaml "Big'_int.mult'_big'_int/ 2")
```
```   106   (Haskell "!(2 * _)")
```
```   107   (Scala "!(2 * _)")
```
```   108   (Eval "!(2 * _)")
```
```   109
```
```   110 code_const Int.sub
```
```   111   (SML "!(raise/ Fail/ \"sub\")")
```
```   112   (OCaml "failwith/ \"sub\"")
```
```   113   (Haskell "error/ \"sub\"")
```
```   114   (Scala "!sys.error(\"sub\")")
```
```   115
```
```   116 code_const "op * \<Colon> int \<Rightarrow> int \<Rightarrow> int"
```
```   117   (SML "IntInf.* ((_), (_))")
```
```   118   (OCaml "Big'_int.mult'_big'_int")
```
```   119   (Haskell infixl 7 "*")
```
```   120   (Scala infixl 8 "*")
```
```   121   (Eval infixl 9 "*")
```
```   122
```
```   123 code_const pdivmod
```
```   124   (SML "IntInf.divMod/ (IntInf.abs _,/ IntInf.abs _)")
```
```   125   (OCaml "Big'_int.quomod'_big'_int/ (Big'_int.abs'_big'_int _)/ (Big'_int.abs'_big'_int _)")
```
```   126   (Haskell "divMod/ (abs _)/ (abs _)")
```
```   127   (Scala "!((k: BigInt) => (l: BigInt) =>/ if (l == 0)/ (BigInt(0), k) else/ (k.abs '/% l.abs))")
```
```   128   (Eval "Integer.div'_mod/ (abs _)/ (abs _)")
```
```   129
```
```   130 code_const "HOL.equal \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
```
```   131   (SML "!((_ : IntInf.int) = _)")
```
```   132   (OCaml "Big'_int.eq'_big'_int")
```
```   133   (Haskell infix 4 "==")
```
```   134   (Scala infixl 5 "==")
```
```   135   (Eval infixl 6 "=")
```
```   136
```
```   137 code_const "op \<le> \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
```
```   138   (SML "IntInf.<= ((_), (_))")
```
```   139   (OCaml "Big'_int.le'_big'_int")
```
```   140   (Haskell infix 4 "<=")
```
```   141   (Scala infixl 4 "<=")
```
```   142   (Eval infixl 6 "<=")
```
```   143
```
```   144 code_const "op < \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
```
```   145   (SML "IntInf.< ((_), (_))")
```
```   146   (OCaml "Big'_int.lt'_big'_int")
```
```   147   (Haskell infix 4 "<")
```
```   148   (Scala infixl 4 "<")
```
```   149   (Eval infixl 6 "<")
```
```   150
```
```   151 code_const Code_Numeral.int_of
```
```   152   (SML "IntInf.fromInt")
```
```   153   (OCaml "_")
```
```   154   (Haskell "Prelude.toInteger")
```
```   155   (Scala "!_.as'_BigInt")
```
```   156   (Eval "_")
```
```   157
```
```   158 code_const "Code_Evaluation.term_of \<Colon> int \<Rightarrow> term"
```
```   159   (Eval "HOLogic.mk'_number/ HOLogic.intT")
```
```   160
```
```   161 end
```