(* Title: HOL/Library/Code_Integer.thy
Author: Florian Haftmann, TU Muenchen
*)
header {* Pretty integer literals for code generation *}
theory Code_Integer
imports Main
begin
text {*
HOL numeral expressions are mapped to integer literals
in target languages, using predefined target language
operations for abstract integer operations.
*}
text {*
Preliminary: alternative representation of @{typ code_numeral}
for @{text Haskell} and @{text Scala}.
*}
code_include Haskell "Natural" {*
newtype Natural = Natural Integer deriving (Eq, Show, Read);
instance Num Natural where {
fromInteger k = Natural (if k >= 0 then k else 0);
Natural n + Natural m = Natural (n + m);
Natural n - Natural m = fromInteger (n - m);
Natural n * Natural m = Natural (n * m);
abs n = n;
signum _ = 1;
negate n = error "negate Natural";
};
instance Ord Natural where {
Natural n <= Natural m = n <= m;
Natural n < Natural m = n < m;
};
instance Real Natural where {
toRational (Natural n) = toRational n;
};
instance Enum Natural where {
toEnum k = fromInteger (toEnum k);
fromEnum (Natural n) = fromEnum n;
};
instance Integral Natural where {
toInteger (Natural n) = n;
divMod n m = quotRem n m;
quotRem (Natural n) (Natural m)
| (m == 0) = (0, Natural n)
| otherwise = (Natural k, Natural l) where (k, l) = quotRem n m;
};
*}
code_reserved Haskell Natural
code_include Scala "Natural" {*
import scala.Math
object Natural {
def apply(numeral: BigInt): Natural = new Natural(numeral max 0)
def apply(numeral: Int): Natural = Natural(BigInt(numeral))
def apply(numeral: String): Natural = Natural(BigInt(numeral))
}
class Natural private(private val value: BigInt) {
override def hashCode(): Int = this.value.hashCode()
override def equals(that: Any): Boolean = that match {
case that: Natural => this equals that
case _ => false
}
override def toString(): String = this.value.toString
def equals(that: Natural): Boolean = this.value == that.value
def as_BigInt: BigInt = this.value
def as_Int: Int = if (this.value >= Int.MinValue && this.value <= Int.MaxValue)
this.value.intValue
else this.value.intValue
def +(that: Natural): Natural = new Natural(this.value + that.value)
def -(that: Natural): Natural = Natural(this.value - that.value)
def *(that: Natural): Natural = new Natural(this.value * that.value)
def /%(that: Natural): (Natural, Natural) = if (that.value == 0) (new Natural(0), this)
else {
val (k, l) = this.value /% that.value
(new Natural(k), new Natural(l))
}
def <=(that: Natural): Boolean = this.value <= that.value
def <(that: Natural): Boolean = this.value < that.value
}
*}
code_reserved Scala Natural
code_type code_numeral
(Haskell "Natural.Natural")
(Scala "Natural")
setup {*
fold (Numeral.add_code @{const_name number_code_numeral_inst.number_of_code_numeral}
false Code_Printer.literal_alternative_numeral) ["Haskell", "Scala"]
*}
code_instance code_numeral :: eq
(Haskell -)
code_const "op + \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
(Haskell infixl 6 "+")
(Scala infixl 7 "+")
code_const "op - \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
(Haskell infixl 6 "-")
(Scala infixl 7 "-")
code_const "op * \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
(Haskell infixl 7 "*")
(Scala infixl 8 "*")
code_const div_mod_code_numeral
(Haskell "divMod")
(Scala infixl 8 "/%")
code_const "eq_class.eq \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
(Haskell infixl 4 "==")
(Scala infixl 5 "==")
code_const "op \<le> \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
(Haskell infix 4 "<=")
(Scala infixl 4 "<=")
code_const "op < \<Colon> code_numeral \<Rightarrow> code_numeral \<Rightarrow> bool"
(Haskell infix 4 "<")
(Scala infixl 4 "<")
text {*
Setup for @{typ int} proper.
*}
code_type int
(SML "IntInf.int")
(OCaml "Big'_int.big'_int")
(Haskell "Integer")
(Scala "BigInt")
code_instance int :: eq
(Haskell -)
setup {*
fold (Numeral.add_code @{const_name number_int_inst.number_of_int}
true Code_Printer.literal_numeral) ["SML", "OCaml", "Haskell", "Scala"]
*}
code_const "Int.Pls" and "Int.Min" and "Int.Bit0" and "Int.Bit1"
(SML "raise/ Fail/ \"Pls\""
and "raise/ Fail/ \"Min\""
and "!((_);/ raise/ Fail/ \"Bit0\")"
and "!((_);/ raise/ Fail/ \"Bit1\")")
(OCaml "failwith/ \"Pls\""
and "failwith/ \"Min\""
and "!((_);/ failwith/ \"Bit0\")"
and "!((_);/ failwith/ \"Bit1\")")
(Haskell "error/ \"Pls\""
and "error/ \"Min\""
and "error/ \"Bit0\""
and "error/ \"Bit1\"")
(Scala "!error(\"Pls\")"
and "!error(\"Min\")"
and "!error(\"Bit0\")"
and "!error(\"Bit1\")")
code_const Int.pred
(SML "IntInf.- ((_), 1)")
(OCaml "Big'_int.pred'_big'_int")
(Haskell "!(_/ -/ 1)")
(Scala "!(_/ -/ 1)")
(Eval "!(_/ -/ 1)")
code_const Int.succ
(SML "IntInf.+ ((_), 1)")
(OCaml "Big'_int.succ'_big'_int")
(Haskell "!(_/ +/ 1)")
(Scala "!(_/ +/ 1)")
(Eval "!(_/ +/ 1)")
code_const "op + \<Colon> int \<Rightarrow> int \<Rightarrow> int"
(SML "IntInf.+ ((_), (_))")
(OCaml "Big'_int.add'_big'_int")
(Haskell infixl 6 "+")
(Scala infixl 7 "+")
(Eval infixl 8 "+")
code_const "uminus \<Colon> int \<Rightarrow> int"
(SML "IntInf.~")
(OCaml "Big'_int.minus'_big'_int")
(Haskell "negate")
(Scala "!(- _)")
(Eval "~/ _")
code_const "op - \<Colon> int \<Rightarrow> int \<Rightarrow> int"
(SML "IntInf.- ((_), (_))")
(OCaml "Big'_int.sub'_big'_int")
(Haskell infixl 6 "-")
(Scala infixl 7 "-")
(Eval infixl 8 "-")
code_const "op * \<Colon> int \<Rightarrow> int \<Rightarrow> int"
(SML "IntInf.* ((_), (_))")
(OCaml "Big'_int.mult'_big'_int")
(Haskell infixl 7 "*")
(Scala infixl 8 "*")
(Eval infixl 9 "*")
code_const pdivmod
(SML "IntInf.divMod/ (IntInf.abs _,/ IntInf.abs _)")
(OCaml "Big'_int.quomod'_big'_int/ (Big'_int.abs'_big'_int _)/ (Big'_int.abs'_big'_int _)")
(Haskell "divMod/ (abs _)/ (abs _)")
(Scala "!((k: BigInt) => (l: BigInt) =>/ if (l == 0)/ (BigInt(0), k) else/ (k.abs '/% l.abs))")
(Eval "Integer.div'_mod/ (abs _)/ (abs _)")
code_const "eq_class.eq \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
(SML "!((_ : IntInf.int) = _)")
(OCaml "Big'_int.eq'_big'_int")
(Haskell infixl 4 "==")
(Scala infixl 5 "==")
(Eval infixl 6 "=")
code_const "op \<le> \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
(SML "IntInf.<= ((_), (_))")
(OCaml "Big'_int.le'_big'_int")
(Haskell infix 4 "<=")
(Scala infixl 4 "<=")
(Eval infixl 6 "<=")
code_const "op < \<Colon> int \<Rightarrow> int \<Rightarrow> bool"
(SML "IntInf.< ((_), (_))")
(OCaml "Big'_int.lt'_big'_int")
(Haskell infix 4 "<")
(Scala infixl 4 "<")
(Eval infixl 6 "<")
code_const Code_Numeral.int_of
(SML "IntInf.fromInt")
(OCaml "_")
(Haskell "toInteger")
(Scala "!_.as'_BigInt")
(Eval "_")
text {* Evaluation *}
code_const "Code_Evaluation.term_of \<Colon> int \<Rightarrow> term"
(Eval "HOLogic.mk'_number/ HOLogic.intT")
end