src/ZF/ex/Bin.ML

-(*  Title: 	ZF/ex/Bin.ML
+(*  Title:      ZF/ex/Bin.ML
     ID:         $Id$
-    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1994  University of Cambridge
 
 For Bin.thy.  Arithmetic on binary integers.
 *)
 
 open Bin;
 
 (*Perform induction on l, then prove the major premise using prems. *)
 fun bin_ind_tac a prems i = 
     EVERY [res_inst_tac [("x",a)] bin.induct i,
-	   rename_last_tac a ["1"] (i+3),
-	   ares_tac prems i];
+           rename_last_tac a ["1"] (i+3),
+           ares_tac prems i];
 
 
 (** bin_rec -- by Vset recursion **)
 
 goal Bin.thy "bin_rec(Plus,a,b,h) = a";

 \       !!w x r. [| w: bin; x: bool; r: C(w) |] ==> h(w,x,r): C(Bcons(w,x))  \
 \    |] ==> bin_rec(w,a,b,h) : C(w)";
 by (bin_ind_tac "w" prems 1);
 by (ALLGOALS 
     (asm_simp_tac (ZF_ss addsimps (prems@[bin_rec_Plus, bin_rec_Minus,
-					  bin_rec_Bcons]))));
+                                          bin_rec_Bcons]))));
 qed "bin_rec_type";
 
 (** Versions for use with definitions **)
 
 val [rew] = goal Bin.thy

 by (rewtac rew);
 by (rtac bin_rec_Bcons 1);
 qed "def_bin_rec_Bcons";
 
 fun bin_recs def = map standard
-	([def] RL [def_bin_rec_Plus, def_bin_rec_Minus, def_bin_rec_Bcons]);
+        ([def] RL [def_bin_rec_Plus, def_bin_rec_Minus, def_bin_rec_Bcons]);
 
 goalw Bin.thy [norm_Bcons_def] "norm_Bcons(Plus,0) = Plus";
 by (asm_simp_tac (ZF_ss addsimps (bin.case_eqns @ bool_simps)) 1);
 qed "norm_Bcons_Plus_0";
 

     "norm_Bcons(Bcons(w,x),b) = Bcons(Bcons(w,x),b)";
 by (asm_simp_tac (ZF_ss addsimps bin.case_eqns) 1);
 qed "norm_Bcons_Bcons";
 
 val norm_Bcons_simps = [norm_Bcons_Plus_0, norm_Bcons_Plus_1, 
-			norm_Bcons_Minus_0, norm_Bcons_Minus_1,
-			norm_Bcons_Bcons];
+                        norm_Bcons_Minus_0, norm_Bcons_Minus_1,
+                        norm_Bcons_Bcons];
 
 (** Type checking **)
 
 val bin_typechecks0 = bin_rec_type :: bin.intrs;
 
 goalw Bin.thy [integ_of_bin_def]
     "!!w. w: bin ==> integ_of_bin(w) : integ";
 by (typechk_tac (bin_typechecks0@integ_typechecks@
-		 nat_typechecks@[bool_into_nat]));
+                 nat_typechecks@[bool_into_nat]));
 qed "integ_of_bin_type";
 
 goalw Bin.thy [norm_Bcons_def]
     "!!w. [| w: bin; b: bool |] ==> norm_Bcons(w,b) : bin";
 by (etac bin.elim 1);

 qed "bin_minus_type";
 
 goalw Bin.thy [bin_add_def]
     "!!v w. [| v: bin; w: bin |] ==> bin_add(v,w) : bin";
 by (typechk_tac ([norm_Bcons_type, bin_succ_type, bin_pred_type]@
-		 bin_typechecks0@ bool_typechecks@ZF_typechecks));
+                 bin_typechecks0@ bool_typechecks@ZF_typechecks));
 qed "bin_add_type";
 
 goalw Bin.thy [bin_mult_def]
     "!!v w. [| v: bin; w: bin |] ==> bin_mult(v,w) : bin";
 by (typechk_tac ([norm_Bcons_type, bin_minus_type, bin_add_type]@
-		 bin_typechecks0@ bool_typechecks));
+                 bin_typechecks0@ bool_typechecks));
 qed "bin_mult_type";
 
 val bin_typechecks = bin_typechecks0 @
     [integ_of_bin_type, norm_Bcons_type, bin_succ_type, bin_pred_type, 
      bin_minus_type, bin_add_type, bin_mult_type];
 
 val bin_ss = integ_ss 
     addsimps([bool_1I, bool_0I,
-	     bin_rec_Plus, bin_rec_Minus, bin_rec_Bcons] @ 
-	     bin_recs integ_of_bin_def @ bool_simps @ bin_typechecks);
+             bin_rec_Plus, bin_rec_Minus, bin_rec_Bcons] @ 
+             bin_recs integ_of_bin_def @ bool_simps @ bin_typechecks);
 
 val typechecks = bin_typechecks @ integ_typechecks @ nat_typechecks @
                  [bool_subset_nat RS subsetD];
 
 (**** The carry/borrow functions, bin_succ and bin_pred ****)

                (bin_recs bin_succ_def @ bin_recs bin_pred_def);
 
 
 (*norm_Bcons preserves the integer value of its argument*)
 goal Bin.thy
-    "!!w. [| w: bin; b: bool |] ==>	\
+    "!!w. [| w: bin; b: bool |] ==>     \
 \         integ_of_bin(norm_Bcons(w,b)) = integ_of_bin(Bcons(w,b))";
 by (etac bin.elim 1);
 by (asm_simp_tac (ZF_ss addsimps norm_Bcons_simps) 3);
 by (ALLGOALS (etac boolE));
 by (ALLGOALS (asm_simp_tac (bin_ss addsimps (norm_Bcons_simps))));

 
 (*** bin_minus: (unary!) negation of binary integers ***)
 
 val bin_minus_ss =
     bin_ss addsimps (bin_recs bin_minus_def @
-		    [integ_of_bin_succ, integ_of_bin_pred]);
+                    [integ_of_bin_succ, integ_of_bin_pred]);
 
 goal Bin.thy
     "!!w. w: bin ==> integ_of_bin(bin_minus(w)) = $~ integ_of_bin(w)";
 by (etac bin.induct 1);
 by (simp_tac bin_minus_ss 1);

 \           norm_Bcons(bin_add(v, cond(x and y, bin_succ(w), w)), x xor y)";
 by (asm_simp_tac bin_ss 1);
 qed "bin_add_Bcons_Bcons";
 
 val bin_add_simps = [bin_add_Plus, bin_add_Minus, bin_add_Bcons_Plus,
-		     bin_add_Bcons_Minus, bin_add_Bcons_Bcons,
-		     integ_of_bin_succ, integ_of_bin_pred,
-		     integ_of_bin_norm_Bcons];
+                     bin_add_Bcons_Minus, bin_add_Bcons_Bcons,
+                     integ_of_bin_succ, integ_of_bin_pred,
+                     integ_of_bin_norm_Bcons];
 
 val bin_add_ss = 
     bin_ss addsimps ([bool_subset_nat RS subsetD] @ bin_add_simps);
 
 goal Bin.thy

 
 (*** bin_add: binary multiplication ***)
 
 val bin_mult_ss =
     bin_ss addsimps (bin_recs bin_mult_def @ 
-		       [integ_of_bin_minus, integ_of_bin_add,
-			integ_of_bin_norm_Bcons]);
+                       [integ_of_bin_minus, integ_of_bin_add,
+                        integ_of_bin_norm_Bcons]);
 
 val major::prems = goal Bin.thy
-    "[| v: bin; w: bin |] ==>	\
+    "[| v: bin; w: bin |] ==>   \
 \    integ_of_bin(bin_mult(v,w)) = \
 \    integ_of_bin(v) $* integ_of_bin(w)";
 by (cut_facts_tac prems 1);
 by (bin_ind_tac "v" [major] 1);
 by (asm_simp_tac bin_mult_ss 1);

 
 (*** The computation simpset ***)
 
 val bin_comp_ss = integ_ss 
     addsimps [integ_of_bin_add RS sym,   (*invoke bin_add*)
-	      integ_of_bin_minus RS sym, (*invoke bin_minus*)
-	      integ_of_bin_mult RS sym,	 (*invoke bin_mult*)
-	      bin_succ_Plus, bin_succ_Minus,
-	      bin_succ_Bcons1, bin_succ_Bcons0,
-	      bin_pred_Plus, bin_pred_Minus,
-	      bin_pred_Bcons1, bin_pred_Bcons0,
-	      bin_minus_Plus, bin_minus_Minus,
-	      bin_minus_Bcons1, bin_minus_Bcons0,
-	      bin_add_Plus, bin_add_Minus, bin_add_Bcons_Plus, 
-	      bin_add_Bcons_Minus, bin_add_Bcons_Bcons0, 
-	      bin_add_Bcons_Bcons10, bin_add_Bcons_Bcons11,
-	      bin_mult_Plus, bin_mult_Minus,
-	      bin_mult_Bcons1, bin_mult_Bcons0] @
+              integ_of_bin_minus RS sym, (*invoke bin_minus*)
+              integ_of_bin_mult RS sym,  (*invoke bin_mult*)
+              bin_succ_Plus, bin_succ_Minus,
+              bin_succ_Bcons1, bin_succ_Bcons0,
+              bin_pred_Plus, bin_pred_Minus,
+              bin_pred_Bcons1, bin_pred_Bcons0,
+              bin_minus_Plus, bin_minus_Minus,
+              bin_minus_Bcons1, bin_minus_Bcons0,
+              bin_add_Plus, bin_add_Minus, bin_add_Bcons_Plus, 
+              bin_add_Bcons_Minus, bin_add_Bcons_Bcons0, 
+              bin_add_Bcons_Bcons10, bin_add_Bcons_Bcons11,
+              bin_mult_Plus, bin_mult_Minus,
+              bin_mult_Bcons1, bin_mult_Bcons0] @
              norm_Bcons_simps
     setsolver (type_auto_tac ([bool_1I, bool_0I] @ bin_typechecks0));
 
 (*** Examples of performing binary arithmetic by simplification ***)
 
 proof_timing := true;
 (*All runtimes below are on a SPARCserver 10*)
 
 goal Bin.thy "#13  $+  #19 = #32";
-by (simp_tac bin_comp_ss 1);	(*0.4 secs*)
+by (simp_tac bin_comp_ss 1);    (*0.4 secs*)
 result();
 
 bin_add(binary_of_int 13, binary_of_int 19);
 
 goal Bin.thy "#1234  $+  #5678 = #6912";
-by (simp_tac bin_comp_ss 1);	(*1.3 secs*)
+by (simp_tac bin_comp_ss 1);    (*1.3 secs*)
 result();
 
 bin_add(binary_of_int 1234, binary_of_int 5678);
 
 goal Bin.thy "#1359  $+  #~2468 = #~1109";
-by (simp_tac bin_comp_ss 1);	(*1.2 secs*)
+by (simp_tac bin_comp_ss 1);    (*1.2 secs*)
 result();
 
 bin_add(binary_of_int 1359, binary_of_int ~2468);
 
 goal Bin.thy "#93746  $+  #~46375 = #47371";
-by (simp_tac bin_comp_ss 1);	(*1.9 secs*)
+by (simp_tac bin_comp_ss 1);    (*1.9 secs*)
 result();
 
 bin_add(binary_of_int 93746, binary_of_int ~46375);
 
 goal Bin.thy "$~ #65745 = #~65745";
-by (simp_tac bin_comp_ss 1);	(*0.4 secs*)
+by (simp_tac bin_comp_ss 1);    (*0.4 secs*)
 result();
 
 bin_minus(binary_of_int 65745);
 
 (* negation of ~54321 *)
 goal Bin.thy "$~ #~54321 = #54321";
-by (simp_tac bin_comp_ss 1);	(*0.5 secs*)
+by (simp_tac bin_comp_ss 1);    (*0.5 secs*)
 result();
 
 bin_minus(binary_of_int ~54321);
 
 goal Bin.thy "#13  $*  #19 = #247";
-by (simp_tac bin_comp_ss 1);	(*0.7 secs*)
+by (simp_tac bin_comp_ss 1);    (*0.7 secs*)
 result();
 
 bin_mult(binary_of_int 13, binary_of_int 19);
 
 goal Bin.thy "#~84  $*  #51 = #~4284";
-by (simp_tac bin_comp_ss 1);	(*1.3 secs*)
+by (simp_tac bin_comp_ss 1);    (*1.3 secs*)
 result();
 
 bin_mult(binary_of_int ~84, binary_of_int 51);
 
 (*The worst case for 8-bit operands *)
 goal Bin.thy "#255  $*  #255 = #65025";
-by (simp_tac bin_comp_ss 1);	(*4.3 secs*)
+by (simp_tac bin_comp_ss 1);    (*4.3 secs*)
 result();
 
 bin_mult(binary_of_int 255, binary_of_int 255);
 
 goal Bin.thy "#1359  $*  #~2468 = #~3354012";
-by (simp_tac bin_comp_ss 1);	(*6.1 secs*)
+by (simp_tac bin_comp_ss 1);    (*6.1 secs*)
 result();
 
 bin_mult(binary_of_int 1359, binary_of_int ~2468);