New code generator setup (taken from Library/Executable_Real.thy,
also works for old code generator).
--- a/src/HOL/Real/RealDef.thy Thu Sep 06 11:38:10 2007 +0200
+++ b/src/HOL/Real/RealDef.thy Thu Sep 06 11:39:43 2007 +0200
@@ -549,8 +549,8 @@
real :: "'a => real"
defs (overloaded)
- real_of_nat_def [code unfold]: "real == real_of_nat"
- real_of_int_def [code unfold]: "real == real_of_int"
+ real_of_nat_def [code inline]: "real == real_of_nat"
+ real_of_int_def [code inline]: "real == real_of_int"
lemma real_eq_of_nat: "real = of_nat"
unfolding real_of_nat_def ..
@@ -926,38 +926,108 @@
lemma abs_sum_triangle_ineq: "abs ((x::real) + y + (-l + -m)) \<le> abs(x + -l) + abs(y + -m)"
by simp
-subsection{*Code generation using Isabelle's rats*}
+
+subsection {* Implementation of rational real numbers as pairs of integers *}
+
+definition
+ RealC :: "int \<times> int \<Rightarrow> real"
+where
+ "RealC = INum"
+
+code_datatype RealC
+
+lemma RealC_simp:
+ "RealC (k, l) = real_of_int k / real_of_int l"
+ unfolding RealC_def INum_def by simp
+
+lemma RealC_zero [simp]: "RealC 0\<^sub>N = 0"
+ by (simp add: RealC_simp)
+
+lemma RealC_lit [simp]: "RealC i\<^sub>N = real_of_int i"
+ by (simp add: RealC_simp)
+
+lemma zero_real_code [code, code unfold]:
+ "0 = RealC 0\<^sub>N" by simp
+
+lemma one_real_code [code, code unfold]:
+ "1 = RealC 1\<^sub>N" by simp
+
+instance real :: eq ..
+
+lemma real_eq_code [code]: "RealC x = RealC y \<longleftrightarrow> normNum x = normNum y"
+ unfolding RealC_def INum_normNum_iff ..
+
+lemma real_less_eq_code [code]: "RealC x \<le> RealC y \<longleftrightarrow> normNum x \<le>\<^sub>N normNum y"
+proof -
+ have "normNum x \<le>\<^sub>N normNum y \<longleftrightarrow> RealC (normNum x) \<le> RealC (normNum y)"
+ by (simp add: RealC_def del: normNum)
+ also have "\<dots> = (RealC x \<le> RealC y)" by (simp add: RealC_def)
+ finally show ?thesis by simp
+qed
+
+lemma real_less_code [code]: "RealC x < RealC y \<longleftrightarrow> normNum x <\<^sub>N normNum y"
+proof -
+ have "normNum x <\<^sub>N normNum y \<longleftrightarrow> RealC (normNum x) < RealC (normNum y)"
+ by (simp add: RealC_def del: normNum)
+ also have "\<dots> = (RealC x < RealC y)" by (simp add: RealC_def)
+ finally show ?thesis by simp
+qed
+
+lemma real_add_code [code]: "RealC x + RealC y = RealC (x +\<^sub>N y)"
+ unfolding RealC_def by simp
+
+lemma real_mul_code [code]: "RealC x * RealC y = RealC (x *\<^sub>N y)"
+ unfolding RealC_def by simp
+
+lemma real_neg_code [code]: "- RealC x = RealC (~\<^sub>N x)"
+ unfolding RealC_def by simp
+
+lemma real_sub_code [code]: "RealC x - RealC y = RealC (x -\<^sub>N y)"
+ unfolding RealC_def by simp
+
+lemma real_inv_code [code]: "inverse (RealC x) = RealC (Ninv x)"
+ unfolding RealC_def Ninv real_divide_def by simp
+
+lemma real_div_code [code]: "RealC x / RealC y = RealC (x \<div>\<^sub>N y)"
+ unfolding RealC_def by simp
+
+text {* Setup for old code generator *}
types_code
- real ("Rat.rat")
+ real ("(int */ int)")
attach (term_of) {*
-fun term_of_real x =
- let
- val rT = HOLogic.realT
- val (p, q) = Rat.quotient_of_rat x
- in if q = 1 then HOLogic.mk_number rT p
- else Const("HOL.divide",[rT,rT] ---> rT) $
- (HOLogic.mk_number rT p) $ (HOLogic.mk_number rT q)
-end;
+fun term_of_real (p, q) =
+ let val rT = HOLogic.realT
+ in
+ if q = 1 orelse p = 0 then HOLogic.mk_number rT p
+ else Const ("HOL.inverse_class.divide", [rT, rT] ---> rT) $
+ HOLogic.mk_number rT p $ HOLogic.mk_number rT q
+ end;
*}
attach (test) {*
fun gen_real i =
-let val p = random_range 0 i; val q = random_range 0 i;
- val r = if q=0 then Rat.rat_of_int i else Rat.rat_of_quotient(p,q)
-in if one_of [true,false] then r else Rat.neg r end;
+ let
+ val p = random_range 0 i;
+ val q = random_range 1 (i + 1);
+ val g = Integer.gcd p q;
+ val p' = Integer.div p g;
+ val q' = Integer.div q g;
+ in
+ (if one_of [true, false] then p' else ~ p',
+ if p' = 0 then 0 else q')
+ end;
*}
consts_code
- "0 :: real" ("Rat.zero")
- "1 :: real" ("Rat.one")
- "uminus :: real \<Rightarrow> real" ("Rat.neg")
- "op + :: real \<Rightarrow> real \<Rightarrow> real" ("Rat.add")
- "op * :: real \<Rightarrow> real \<Rightarrow> real" ("Rat.mult")
- "inverse :: real \<Rightarrow> real" ("Rat.inv")
- "op \<le> :: real \<Rightarrow> real \<Rightarrow> bool" ("Rat.le")
- "op < :: real \<Rightarrow> real \<Rightarrow> bool" ("Rat.lt")
- "op = :: real \<Rightarrow> real \<Rightarrow> bool" ("curry Rat.eq")
- "real :: int \<Rightarrow> real" ("Rat.rat'_of'_int")
- "real :: nat \<Rightarrow> real" ("(Rat.rat'_of'_int o {*int*})")
+ RealC ("(_)")
+
+consts_code
+ "of_int :: int \<Rightarrow> real" ("\<module>real'_of'_int")
+attach {*
+fun real_of_int 0 = (0, 0)
+ | real_of_int i = (i, 1);
+*}
+
+declare real_of_int_of_nat_eq [symmetric, code]
end