src/HOL/Library/Code_Natural.thy
 author haftmann Thu Aug 26 12:19:50 2010 +0200 (2010-08-26 ago) changeset 38774 567b94f8bb6e parent 38771 f9cd27cbe8a4 child 38775 741ca0c98f6f permissions -rw-r--r--
tuned includes
```     1 (*  Title:      HOL/Library/Code_Natural.thy
```
```     2     Author:     Florian Haftmann, TU Muenchen
```
```     3 *)
```
```     4
```
```     5 theory Code_Natural
```
```     6 imports Main
```
```     7 begin
```
```     8
```
```     9 section {* Alternative representation of @{typ code_numeral} for @{text Haskell} and @{text Scala} *}
```
```    10
```
```    11 code_include Haskell "Natural"
```
```    12 {*newtype Natural = Natural Integer deriving (Eq, Show, Read);
```
```    13
```
```    14 instance Num Natural where {
```
```    15   fromInteger k = Natural (if k >= 0 then k else 0);
```
```    16   Natural n + Natural m = Natural (n + m);
```
```    17   Natural n - Natural m = fromInteger (n - m);
```
```    18   Natural n * Natural m = Natural (n * m);
```
```    19   abs n = n;
```
```    20   signum _ = 1;
```
```    21   negate n = error "negate Natural";
```
```    22 };
```
```    23
```
```    24 instance Ord Natural where {
```
```    25   Natural n <= Natural m = n <= m;
```
```    26   Natural n < Natural m = n < m;
```
```    27 };
```
```    28
```
```    29 instance Ix Natural where {
```
```    30   range (Natural n, Natural m) = map Natural (range (n, m));
```
```    31   index (Natural n, Natural m) (Natural q) = index (n, m) q;
```
```    32   inRange (Natural n, Natural m) (Natural q) = inRange (n, m) q;
```
```    33   rangeSize (Natural n, Natural m) = rangeSize (n, m);
```
```    34 };
```
```    35
```
```    36 instance Real Natural where {
```
```    37   toRational (Natural n) = toRational n;
```
```    38 };
```
```    39
```
```    40 instance Enum Natural where {
```
```    41   toEnum k = fromInteger (toEnum k);
```
```    42   fromEnum (Natural n) = fromEnum n;
```
```    43 };
```
```    44
```
```    45 instance Integral Natural where {
```
```    46   toInteger (Natural n) = n;
```
```    47   divMod n m = quotRem n m;
```
```    48   quotRem (Natural n) (Natural m)
```
```    49     | (m == 0) = (0, Natural n)
```
```    50     | otherwise = (Natural k, Natural l) where (k, l) = quotRem n m;
```
```    51 };*}
```
```    52
```
```    53 code_reserved Haskell Natural
```
```    54
```
```    55 code_include Scala "Natural"
```
```    56 {*import scala.Math
```
```    57
```
```    58 object Nat {
```
```    59
```
```    60   def apply(numeral: BigInt): Nat = new Nat(numeral max 0)
```
```    61   def apply(numeral: Int): Nat = Nat(BigInt(numeral))
```
```    62   def apply(numeral: String): Nat = Nat(BigInt(numeral))
```
```    63
```
```    64 }
```
```    65
```
```    66 class Nat private(private val value: BigInt) {
```
```    67
```
```    68   override def hashCode(): Int = this.value.hashCode()
```
```    69
```
```    70   override def equals(that: Any): Boolean = that match {
```
```    71     case that: Nat => this equals that
```
```    72     case _ => false
```
```    73   }
```
```    74
```
```    75   override def toString(): String = this.value.toString
```
```    76
```
```    77   def equals(that: Nat): Boolean = this.value == that.value
```
```    78
```
```    79   def as_BigInt: BigInt = this.value
```
```    80   def as_Int: Int = if (this.value >= Int.MinValue && this.value <= Int.MaxValue)
```
```    81       this.value.intValue
```
```    82     else error("Int value out of range: " + this.value.toString)
```
```    83
```
```    84   def +(that: Nat): Nat = new Nat(this.value + that.value)
```
```    85   def -(that: Nat): Nat = Nat(this.value - that.value)
```
```    86   def *(that: Nat): Nat = new Nat(this.value * that.value)
```
```    87
```
```    88   def /%(that: Nat): (Nat, Nat) = if (that.value == 0) (new Nat(0), this)
```
```    89     else {
```
```    90       val (k, l) = this.value /% that.value
```
```    91       (new Nat(k), new Nat(l))
```
```    92     }
```
```    93
```
```    94   def <=(that: Nat): Boolean = this.value <= that.value
```
```    95
```
```    96   def <(that: Nat): Boolean = this.value < that.value
```
```    97
```
```    98 }
```
```    99 *}
```
```   100
```
```   101 code_reserved Scala Natural
```
```   102
```
```   103 code_type code_numeral
```
```   104   (Haskell "Natural.Natural")
```
```   105   (Scala "Natural.Nat")
```
```   106
```
```   107 setup {*
```
```   108   fold (Numeral.add_code @{const_name number_code_numeral_inst.number_of_code_numeral}
```
```   109     false Code_Printer.literal_alternative_numeral) ["Haskell", "Scala"]
```
```   110 *}
```
```   111
```
```   112 code_instance code_numeral :: eq
```
```   113   (Haskell -)
```
```   114
```
```   115 code_const "op + \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
```
```   116   (Haskell infixl 6 "+")
```
```   117   (Scala infixl 7 "+")
```
```   118
```
```   119 code_const "op - \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
```
```   120   (Haskell infixl 6 "-")
```
```   121   (Scala infixl 7 "-")
```
```   122
```
```   123 code_const "op * \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
```
```   124   (Haskell infixl 7 "*")
```
```   125   (Scala infixl 8 "*")
```
```   126
```
```   127 code_const div_mod_code_numeral
```
```   128   (Haskell "divMod")
```
```   129   (Scala infixl 8 "/%")
```
```   130
```
```   131 code_const "eq_class.eq \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
```
```   132   (Haskell infixl 4 "==")
```
```   133   (Scala infixl 5 "==")
```
```   134
```
```   135 code_const "op \<le> \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
```
```   136   (Haskell infix 4 "<=")
```
```   137   (Scala infixl 4 "<=")
```
```   138
```
```   139 code_const "op < \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
```
```   140   (Haskell infix 4 "<")
```
```   141   (Scala infixl 4 "<")
```
```   142
```
```   143 end
```