--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Code_Abstract_Char.thy Mon Jul 04 07:57:22 2022 +0000
@@ -0,0 +1,186 @@
+(* Title: HOL/Library/Code_Abstract_Char.thy
+ Author: Florian Haftmann, TU Muenchen
+ Author: René Thiemann, UIBK
+*)
+
+theory Code_Abstract_Char
+ imports
+ Main
+ "HOL-Library.Char_ord"
+begin
+
+definition Chr :: \<open>integer \<Rightarrow> char\<close>
+ where [simp]: \<open>Chr = char_of\<close>
+
+lemma char_of_integer_of_char [code abstype]:
+ \<open>Chr (integer_of_char c) = c\<close>
+ by (simp add: integer_of_char_def)
+
+lemma char_of_integer_code [code]:
+ \<open>integer_of_char (char_of_integer k) = take_bit 8 k\<close>
+ by (simp add: integer_of_char_def char_of_integer_def take_bit_eq_mod)
+
+context comm_semiring_1
+begin
+
+definition byte :: \<open>bool \<Rightarrow> bool \<Rightarrow> bool \<Rightarrow> bool \<Rightarrow> bool \<Rightarrow> bool \<Rightarrow> bool \<Rightarrow> bool \<Rightarrow> 'a\<close>
+ where [simp]: \<open>byte b0 b1 b2 b3 b4 b5 b6 b7 = horner_sum of_bool 2 [b0, b1, b2, b3, b4, b5, b6, b7]\<close>
+
+lemma byte_code [code]:
+ \<open>byte b0 b1 b2 b3 b4 b5 b6 b7 = (
+ let
+ s0 = if b0 then 1 else 0;
+ s1 = if b1 then s0 + 2 else s0;
+ s2 = if b2 then s1 + 4 else s1;
+ s3 = if b3 then s2 + 8 else s2;
+ s4 = if b4 then s3 + 16 else s3;
+ s5 = if b5 then s4 + 32 else s4;
+ s6 = if b6 then s5 + 64 else s5;
+ s7 = if b7 then s6 + 128 else s6
+ in s7)\<close>
+ by simp
+
+end
+
+lemma Char_code [code]:
+ \<open>integer_of_char (Char b0 b1 b2 b3 b4 b5 b6 b7) = byte b0 b1 b2 b3 b4 b5 b6 b7\<close>
+ by (simp add: integer_of_char_def)
+
+lemma digit_0_code [code]:
+ \<open>digit0 c \<longleftrightarrow> bit (integer_of_char c) 0\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_1_code [code]:
+ \<open>digit1 c \<longleftrightarrow> bit (integer_of_char c) 1\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_2_code [code]:
+ \<open>digit2 c \<longleftrightarrow> bit (integer_of_char c) 2\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_3_code [code]:
+ \<open>digit3 c \<longleftrightarrow> bit (integer_of_char c) 3\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_4_code [code]:
+ \<open>digit4 c \<longleftrightarrow> bit (integer_of_char c) 4\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_5_code [code]:
+ \<open>digit5 c \<longleftrightarrow> bit (integer_of_char c) 5\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_6_code [code]:
+ \<open>digit6 c \<longleftrightarrow> bit (integer_of_char c) 6\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma digit_7_code [code]:
+ \<open>digit7 c \<longleftrightarrow> bit (integer_of_char c) 7\<close>
+ by (cases c) (simp add: integer_of_char_def)
+
+lemma case_char_code [code]:
+ \<open>case_char f c = f (digit0 c) (digit1 c) (digit2 c) (digit3 c) (digit4 c) (digit5 c) (digit6 c) (digit7 c)\<close>
+ by (fact char.case_eq_if)
+
+lemma rec_char_code [code]:
+ \<open>rec_char f c = f (digit0 c) (digit1 c) (digit2 c) (digit3 c) (digit4 c) (digit5 c) (digit6 c) (digit7 c)\<close>
+ by (cases c) simp
+
+lemma char_of_code [code]:
+ \<open>integer_of_char (char_of a) =
+ byte (bit a 0) (bit a 1) (bit a 2) (bit a 3) (bit a 4) (bit a 5) (bit a 6) (bit a 7)\<close>
+ by (simp add: char_of_def integer_of_char_def)
+
+lemma ascii_of_code [code]:
+ \<open>integer_of_char (String.ascii_of c) = (let k = integer_of_char c in if k < 128 then k else k - 128)\<close>
+proof (cases \<open>of_char c < (128 :: integer)\<close>)
+ case True
+ moreover have \<open>(of_nat 0 :: integer) \<le> of_nat (of_char c)\<close>
+ by simp
+ then have \<open>(0 :: integer) \<le> of_char c\<close>
+ by (simp only: of_nat_0 of_nat_of_char)
+ ultimately show ?thesis
+ by (simp add: Let_def integer_of_char_def take_bit_eq_mod unique_euclidean_semiring_numeral_class.mod_less)
+next
+ case False
+ then have \<open>(128 :: integer) \<le> of_char c\<close>
+ by simp
+ moreover have \<open>of_nat (of_char c) < (of_nat 256 :: integer)\<close>
+ by (simp only: of_nat_less_iff) simp
+ then have \<open>of_char c < (256 :: integer)\<close>
+ by (simp add: of_nat_of_char)
+ moreover define k :: integer where \<open>k = of_char c - 128\<close>
+ then have \<open>of_char c = k + 128\<close>
+ by simp
+ ultimately show ?thesis
+ by (simp add: Let_def integer_of_char_def take_bit_eq_mod unique_euclidean_semiring_numeral_class.mod_less)
+qed
+
+lemma equal_char_code [code]:
+ \<open>HOL.equal c d \<longleftrightarrow> integer_of_char c = integer_of_char d\<close>
+ by (simp add: integer_of_char_def equal)
+
+lemma less_eq_char_code [code]:
+ \<open>c \<le> d \<longleftrightarrow> integer_of_char c \<le> integer_of_char d\<close> (is \<open>?P \<longleftrightarrow> ?Q\<close>)
+proof -
+ have \<open>?P \<longleftrightarrow> of_nat (of_char c) \<le> (of_nat (of_char d) :: integer)\<close>
+ by (simp add: less_eq_char_def)
+ also have \<open>\<dots> \<longleftrightarrow> ?Q\<close>
+ by (simp add: of_nat_of_char integer_of_char_def)
+ finally show ?thesis .
+qed
+
+lemma less_char_code [code]:
+ \<open>c < d \<longleftrightarrow> integer_of_char c < integer_of_char d\<close> (is \<open>?P \<longleftrightarrow> ?Q\<close>)
+proof -
+ have \<open>?P \<longleftrightarrow> of_nat (of_char c) < (of_nat (of_char d) :: integer)\<close>
+ by (simp add: less_char_def)
+ also have \<open>\<dots> \<longleftrightarrow> ?Q\<close>
+ by (simp add: of_nat_of_char integer_of_char_def)
+ finally show ?thesis .
+qed
+
+lemma absdef_simps:
+ \<open>horner_sum of_bool 2 [] = (0 :: integer)\<close>
+ \<open>horner_sum of_bool 2 (False # bs) = (0 :: integer) \<longleftrightarrow> horner_sum of_bool 2 bs = (0 :: integer)\<close>
+ \<open>horner_sum of_bool 2 (True # bs) = (1 :: integer) \<longleftrightarrow> horner_sum of_bool 2 bs = (0 :: integer)\<close>
+ \<open>horner_sum of_bool 2 (False # bs) = (numeral (Num.Bit0 n) :: integer) \<longleftrightarrow> horner_sum of_bool 2 bs = (numeral n :: integer)\<close>
+ \<open>horner_sum of_bool 2 (True # bs) = (numeral (Num.Bit1 n) :: integer) \<longleftrightarrow> horner_sum of_bool 2 bs = (numeral n :: integer)\<close>
+ by auto (auto simp only: numeral_Bit0 [of n] numeral_Bit1 [of n] mult_2 [symmetric] add.commute [of _ 1] add.left_cancel mult_cancel_left)
+
+local_setup \<open>
+ let
+ val simps = @{thms absdef_simps integer_of_char_def of_char_Char numeral_One}
+ fun prove_eqn lthy n lhs def_eqn =
+ let
+ val eqn = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
+ (\<^term>\<open>integer_of_char\<close> $ lhs, HOLogic.mk_number \<^typ>\<open>integer\<close> n)
+ in
+ Goal.prove_future lthy [] [] eqn (fn {context = ctxt, ...} =>
+ unfold_tac ctxt (def_eqn :: simps))
+ end
+ fun define n =
+ let
+ val s = "Char_" ^ String_Syntax.hex n;
+ val b = Binding.name s;
+ val b_def = Thm.def_binding b;
+ val b_code = Binding.name (s ^ "_code");
+ in
+ Local_Theory.define ((b, Mixfix.NoSyn),
+ ((Binding.empty, []), HOLogic.mk_char n))
+ #-> (fn (lhs, (_, raw_def_eqn)) =>
+ Local_Theory.note ((b_def, @{attributes [code_abbrev]}), [HOLogic.mk_obj_eq raw_def_eqn])
+ #-> (fn (_, [def_eqn]) => `(fn lthy => prove_eqn lthy n lhs def_eqn))
+ #-> (fn raw_code_eqn => Local_Theory.note ((b_code, []), [raw_code_eqn]))
+ #-> (fn (_, [code_eqn]) => Code.declare_abstract_eqn code_eqn))
+ end
+ in
+ fold define (0 upto 255)
+ end
+\<close>
+
+code_identifier
+ code_module Code_Abstract_Char \<rightharpoonup>
+ (SML) Str and (OCaml) Str and (Haskell) Str and (Scala) Str
+
+end