--- a/src/HOL/Int.thy Wed Apr 02 12:32:53 2008 +0200
+++ b/src/HOL/Int.thy Wed Apr 02 15:58:26 2008 +0200
@@ -1797,9 +1797,125 @@
subsection {* Configuration of the code generator *}
-instance int :: eq ..
+code_datatype Pls Min Bit0 Bit1 "number_of \<Colon> int \<Rightarrow> int"
+
+lemmas pred_succ_numeral_code [code func] =
+ pred_bin_simps succ_bin_simps
+
+lemmas plus_numeral_code [code func] =
+ add_bin_simps
+ arith_extra_simps(1) [where 'a = int]
+
+lemmas minus_numeral_code [code func] =
+ minus_bin_simps
+ arith_extra_simps(2) [where 'a = int]
+ arith_extra_simps(5) [where 'a = int]
+
+lemmas times_numeral_code [code func] =
+ mult_bin_simps
+ arith_extra_simps(4) [where 'a = int]
+
+instantiation int :: eq
+begin
+
+definition [code func del]: "eq k l \<longleftrightarrow> k - l = (0\<Colon>int)"
+
+instance by default (simp add: eq_int_def)
+
+end
+
+lemma eq_number_of_int_code [code func]:
+ "eq (number_of k \<Colon> int) (number_of l) \<longleftrightarrow> eq k l"
+ unfolding eq_int_def number_of_is_id ..
+
+lemma eq_int_code [code func]:
+ "eq Int.Pls Int.Pls \<longleftrightarrow> True"
+ "eq Int.Pls Int.Min \<longleftrightarrow> False"
+ "eq Int.Pls (Int.Bit0 k2) \<longleftrightarrow> eq Int.Pls k2"
+ "eq Int.Pls (Int.Bit1 k2) \<longleftrightarrow> False"
+ "eq Int.Min Int.Pls \<longleftrightarrow> False"
+ "eq Int.Min Int.Min \<longleftrightarrow> True"
+ "eq Int.Min (Int.Bit0 k2) \<longleftrightarrow> False"
+ "eq Int.Min (Int.Bit1 k2) \<longleftrightarrow> eq Int.Min k2"
+ "eq (Int.Bit0 k1) Int.Pls \<longleftrightarrow> eq Int.Pls k1"
+ "eq (Int.Bit1 k1) Int.Pls \<longleftrightarrow> False"
+ "eq (Int.Bit0 k1) Int.Min \<longleftrightarrow> False"
+ "eq (Int.Bit1 k1) Int.Min \<longleftrightarrow> eq Int.Min k1"
+ "eq (Int.Bit0 k1) (Int.Bit0 k2) \<longleftrightarrow> eq k1 k2"
+ "eq (Int.Bit0 k1) (Int.Bit1 k2) \<longleftrightarrow> False"
+ "eq (Int.Bit1 k1) (Int.Bit0 k2) \<longleftrightarrow> False"
+ "eq (Int.Bit1 k1) (Int.Bit1 k2) \<longleftrightarrow> eq k1 k2"
+ unfolding eq_number_of_int_code [symmetric, of Int.Pls]
+ eq_number_of_int_code [symmetric, of Int.Min]
+ eq_number_of_int_code [symmetric, of "Int.Bit0 k1"]
+ eq_number_of_int_code [symmetric, of "Int.Bit1 k1"]
+ eq_number_of_int_code [symmetric, of "Int.Bit0 k2"]
+ eq_number_of_int_code [symmetric, of "Int.Bit1 k2"]
+ by (simp_all add: eq Pls_def,
+ simp_all only: Min_def succ_def pred_def number_of_is_id)
+ (auto simp add: iszero_def)
-code_datatype Pls Min Bit0 Bit1 "number_of \<Colon> int \<Rightarrow> int"
+lemma less_eq_number_of_int_code [code func]:
+ "(number_of k \<Colon> int) \<le> number_of l \<longleftrightarrow> k \<le> l"
+ unfolding number_of_is_id ..
+
+lemma less_eq_int_code [code func]:
+ "Int.Pls \<le> Int.Pls \<longleftrightarrow> True"
+ "Int.Pls \<le> Int.Min \<longleftrightarrow> False"
+ "Int.Pls \<le> Int.Bit0 k \<longleftrightarrow> Int.Pls \<le> k"
+ "Int.Pls \<le> Int.Bit1 k \<longleftrightarrow> Int.Pls \<le> k"
+ "Int.Min \<le> Int.Pls \<longleftrightarrow> True"
+ "Int.Min \<le> Int.Min \<longleftrightarrow> True"
+ "Int.Min \<le> Int.Bit0 k \<longleftrightarrow> Int.Min < k"
+ "Int.Min \<le> Int.Bit1 k \<longleftrightarrow> Int.Min \<le> k"
+ "Int.Bit0 k \<le> Int.Pls \<longleftrightarrow> k \<le> Int.Pls"
+ "Int.Bit1 k \<le> Int.Pls \<longleftrightarrow> k < Int.Pls"
+ "Int.Bit0 k \<le> Int.Min \<longleftrightarrow> k \<le> Int.Min"
+ "Int.Bit1 k \<le> Int.Min \<longleftrightarrow> k \<le> Int.Min"
+ "Int.Bit0 k1 \<le> Int.Bit0 k2 \<longleftrightarrow> k1 \<le> k2"
+ "Int.Bit0 k1 \<le> Int.Bit1 k2 \<longleftrightarrow> k1 \<le> k2"
+ "Int.Bit1 k1 \<le> Int.Bit0 k2 \<longleftrightarrow> k1 < k2"
+ "Int.Bit1 k1 \<le> Int.Bit1 k2 \<longleftrightarrow> k1 \<le> k2"
+ unfolding less_eq_number_of_int_code [symmetric, of Int.Pls]
+ less_eq_number_of_int_code [symmetric, of Int.Min]
+ less_eq_number_of_int_code [symmetric, of "Int.Bit0 k1"]
+ less_eq_number_of_int_code [symmetric, of "Int.Bit1 k1"]
+ less_eq_number_of_int_code [symmetric, of "Int.Bit0 k2"]
+ less_eq_number_of_int_code [symmetric, of "Int.Bit1 k2"]
+ by (simp_all add: Pls_def, simp_all only: Min_def succ_def pred_def number_of_is_id)
+ (auto simp add: neg_def linorder_not_less group_simps
+ zle_add1_eq_le [symmetric] del: iffI , auto simp only: Bit0_def Bit1_def)
+
+lemma less_number_of_int_code [code func]:
+ "(number_of k \<Colon> int) < number_of l \<longleftrightarrow> k < l"
+ unfolding number_of_is_id ..
+
+lemma less_int_code [code func]:
+ "Int.Pls < Int.Pls \<longleftrightarrow> False"
+ "Int.Pls < Int.Min \<longleftrightarrow> False"
+ "Int.Pls < Int.Bit0 k \<longleftrightarrow> Int.Pls < k"
+ "Int.Pls < Int.Bit1 k \<longleftrightarrow> Int.Pls \<le> k"
+ "Int.Min < Int.Pls \<longleftrightarrow> True"
+ "Int.Min < Int.Min \<longleftrightarrow> False"
+ "Int.Min < Int.Bit0 k \<longleftrightarrow> Int.Min < k"
+ "Int.Min < Int.Bit1 k \<longleftrightarrow> Int.Min < k"
+ "Int.Bit0 k < Int.Pls \<longleftrightarrow> k < Int.Pls"
+ "Int.Bit1 k < Int.Pls \<longleftrightarrow> k < Int.Pls"
+ "Int.Bit0 k < Int.Min \<longleftrightarrow> k \<le> Int.Min"
+ "Int.Bit1 k < Int.Min \<longleftrightarrow> k < Int.Min"
+ "Int.Bit0 k1 < Int.Bit0 k2 \<longleftrightarrow> k1 < k2"
+ "Int.Bit0 k1 < Int.Bit1 k2 \<longleftrightarrow> k1 \<le> k2"
+ "Int.Bit1 k1 < Int.Bit0 k2 \<longleftrightarrow> k1 < k2"
+ "Int.Bit1 k1 < Int.Bit1 k2 \<longleftrightarrow> k1 < k2"
+ unfolding less_number_of_int_code [symmetric, of Int.Pls]
+ less_number_of_int_code [symmetric, of Int.Min]
+ less_number_of_int_code [symmetric, of "Int.Bit0 k1"]
+ less_number_of_int_code [symmetric, of "Int.Bit1 k1"]
+ less_number_of_int_code [symmetric, of "Int.Bit0 k2"]
+ less_number_of_int_code [symmetric, of "Int.Bit1 k2"]
+ by (simp_all add: Pls_def, simp_all only: Min_def succ_def pred_def number_of_is_id)
+ (auto simp add: neg_def group_simps zle_add1_eq_le [symmetric] del: iffI,
+ auto simp only: Bit0_def Bit1_def)
definition
int_aux :: "nat \<Rightarrow> int \<Rightarrow> int" where