--- a/src/ZF/ex/BinFn.ML Fri Sep 17 16:16:38 1993 +0200
+++ b/src/ZF/ex/BinFn.ML Fri Sep 17 16:52:10 1993 +0200
@@ -14,20 +14,19 @@
goal BinFn.thy "bin_rec(Plus,a,b,h) = a";
by (rtac (bin_rec_def RS def_Vrec RS trans) 1);
by (rewrite_goals_tac Bin.con_defs);
-by (SIMP_TAC rank_ss 1);
+by (simp_tac rank_ss 1);
val bin_rec_Plus = result();
goal BinFn.thy "bin_rec(Minus,a,b,h) = b";
by (rtac (bin_rec_def RS def_Vrec RS trans) 1);
by (rewrite_goals_tac Bin.con_defs);
-by (SIMP_TAC rank_ss 1);
+by (simp_tac rank_ss 1);
val bin_rec_Minus = result();
goal BinFn.thy "bin_rec(w$$x,a,b,h) = h(w, x, bin_rec(w,a,b,h))";
by (rtac (bin_rec_def RS def_Vrec RS trans) 1);
by (rewrite_goals_tac Bin.con_defs);
-by (SIMP_TAC (rank_ss addcongs
- (mk_typed_congs BinFn.thy [("h", "[i,i,i]=>i")])) 1);
+by (simp_tac rank_ss 1);
val bin_rec_Bcons = result();
(*Type checking*)
@@ -38,7 +37,7 @@
\ |] ==> bin_rec(w,a,b,h) : C(w)";
by (bin_ind_tac "w" prems 1);
by (ALLGOALS
- (ASM_SIMP_TAC (ZF_ss addrews (prems@[bin_rec_Plus,bin_rec_Minus,
+ (asm_simp_tac (ZF_ss addsimps (prems@[bin_rec_Plus,bin_rec_Minus,
bin_rec_Bcons]))));
val bin_rec_type = result();
@@ -106,13 +105,8 @@
[integ_of_bin_type, bin_succ_type, bin_pred_type,
bin_minus_type, bin_add_type, bin_mult_type];
-val bin_congs = mk_congs BinFn.thy
- ["bin_rec","op $$","integ_of_bin","bin_succ","bin_pred",
- "bin_minus","bin_add","bin_mult"];
-
val bin_ss = integ_ss
- addcongs (bin_congs@bool_congs)
- addrews([bool_1I, bool_0I,
+ addsimps([bool_1I, bool_0I,
bin_rec_Plus, bin_rec_Minus, bin_rec_Bcons] @
bin_recs integ_of_bin_def @ bool_rews @ bin_typechecks);
@@ -127,7 +121,7 @@
"!!z v. [| z $+ v = z' $+ v'; \
\ z: integ; z': integ; v: integ; v': integ; w: integ |] \
\ ==> z $+ (v $+ w) = z' $+ (v' $+ w)";
-by (ASM_SIMP_TAC (integ_ss addrews ([zadd_assoc RS sym])) 1);
+by (asm_simp_tac (integ_ss addsimps ([zadd_assoc RS sym])) 1);
val zadd_assoc_cong = result();
goal Integ.thy
@@ -136,7 +130,8 @@
by (REPEAT (ares_tac [zadd_commute RS zadd_assoc_cong] 1));
val zadd_assoc_swap = result();
-val [zadd_cong] = mk_congs Integ.thy ["op $+"];
+val zadd_cong =
+ read_instantiate_sg (sign_of Integ.thy) [("t","op $+")] subst_context2;
val zadd_kill = (refl RS zadd_cong);
val zadd_assoc_swap_kill = zadd_kill RSN (4, zadd_assoc_swap RS trans);
@@ -151,28 +146,28 @@
val zadd_swap_pairs = result();
-val carry_ss = bin_ss addrews
+val carry_ss = bin_ss addsimps
(bin_recs bin_succ_def @ bin_recs bin_pred_def);
goal BinFn.thy
"!!w. w: bin ==> integ_of_bin(bin_succ(w)) = $#1 $+ integ_of_bin(w)";
by (etac Bin.induct 1);
-by (SIMP_TAC (carry_ss addrews [zadd_0_right]) 1);
-by (SIMP_TAC (carry_ss addrews [zadd_zminus_inverse]) 1);
+by (simp_tac (carry_ss addsimps [zadd_0_right]) 1);
+by (simp_tac (carry_ss addsimps [zadd_zminus_inverse]) 1);
by (etac boolE 1);
-by (ALLGOALS (ASM_SIMP_TAC (carry_ss addrews [zadd_assoc])));
+by (ALLGOALS (asm_simp_tac (carry_ss addsimps [zadd_assoc])));
by (REPEAT (ares_tac (zadd_swap_pairs::typechecks) 1));
val integ_of_bin_succ = result();
goal BinFn.thy
"!!w. w: bin ==> integ_of_bin(bin_pred(w)) = $~ ($#1) $+ integ_of_bin(w)";
by (etac Bin.induct 1);
-by (SIMP_TAC (carry_ss addrews [zadd_0_right]) 1);
-by (SIMP_TAC (carry_ss addrews [zadd_zminus_inverse]) 1);
+by (simp_tac (carry_ss addsimps [zadd_0_right]) 1);
+by (simp_tac (carry_ss addsimps [zadd_zminus_inverse]) 1);
by (etac boolE 1);
by (ALLGOALS
- (ASM_SIMP_TAC
- (carry_ss addrews [zadd_assoc RS sym,
+ (asm_simp_tac
+ (carry_ss addsimps [zadd_assoc RS sym,
zadd_zminus_inverse, zadd_zminus_inverse2])));
by (REPEAT (ares_tac ([zadd_commute, zadd_cong, refl]@typechecks) 1));
val integ_of_bin_pred = result();
@@ -183,68 +178,68 @@
(*** bin_minus: (unary!) negation of binary integers ***)
val bin_minus_ss =
- bin_ss addrews (bin_recs bin_minus_def @
+ bin_ss addsimps (bin_recs bin_minus_def @
[integ_of_bin_succ, integ_of_bin_pred]);
goal BinFn.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 addrews [zminus_0]) 1);
-by (SIMP_TAC (bin_minus_ss addrews [zadd_0_right]) 1);
+by (simp_tac (bin_minus_ss addsimps [zminus_0]) 1);
+by (simp_tac (bin_minus_ss addsimps [zadd_0_right]) 1);
by (etac boolE 1);
by (ALLGOALS
- (ASM_SIMP_TAC (bin_minus_ss addrews [zminus_zadd_distrib, zadd_assoc])));
+ (asm_simp_tac (bin_minus_ss addsimps [zminus_zadd_distrib, zadd_assoc])));
val integ_of_bin_minus = result();
(*** bin_add: binary addition ***)
goalw BinFn.thy [bin_add_def] "!!w. w: bin ==> bin_add(Plus,w) = w";
-by (ASM_SIMP_TAC bin_ss 1);
+by (asm_simp_tac bin_ss 1);
val bin_add_Plus = result();
goalw BinFn.thy [bin_add_def] "!!w. w: bin ==> bin_add(Minus,w) = bin_pred(w)";
-by (ASM_SIMP_TAC bin_ss 1);
+by (asm_simp_tac bin_ss 1);
val bin_add_Minus = result();
goalw BinFn.thy [bin_add_def] "bin_add(v$$x,Plus) = v$$x";
-by (SIMP_TAC bin_ss 1);
+by (simp_tac bin_ss 1);
val bin_add_Bcons_Plus = result();
goalw BinFn.thy [bin_add_def] "bin_add(v$$x,Minus) = bin_pred(v$$x)";
-by (SIMP_TAC bin_ss 1);
+by (simp_tac bin_ss 1);
val bin_add_Bcons_Minus = result();
goalw BinFn.thy [bin_add_def]
"!!w y. [| w: bin; y: bool |] ==> \
\ bin_add(v$$x, w$$y) = \
\ bin_add(v, cond(x and y, bin_succ(w), w)) $$ (x xor y)";
-by (ASM_SIMP_TAC bin_ss 1);
+by (asm_simp_tac bin_ss 1);
val bin_add_Bcons_Bcons = result();
val bin_add_rews = [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];
-val bin_add_ss = bin_ss addrews ([bool_subset_nat RS subsetD] @ bin_add_rews);
+val bin_add_ss = bin_ss addsimps ([bool_subset_nat RS subsetD] @ bin_add_rews);
goal BinFn.thy
"!!v. v: bin ==> \
\ ALL w: bin. integ_of_bin(bin_add(v,w)) = \
\ integ_of_bin(v) $+ integ_of_bin(w)";
by (etac Bin.induct 1);
-by (SIMP_TAC bin_add_ss 1);
-by (SIMP_TAC bin_add_ss 1);
+by (simp_tac bin_add_ss 1);
+by (simp_tac bin_add_ss 1);
by (rtac ballI 1);
by (bin_ind_tac "wa" [] 1);
-by (ASM_SIMP_TAC (bin_add_ss addrews [zadd_0_right]) 1);
-by (ASM_SIMP_TAC bin_add_ss 1);
+by (asm_simp_tac (bin_add_ss addsimps [zadd_0_right]) 1);
+by (asm_simp_tac bin_add_ss 1);
by (REPEAT (ares_tac (zadd_commute::typechecks) 1));
by (etac boolE 1);
-by (ASM_SIMP_TAC (bin_add_ss addrews [zadd_assoc, zadd_swap_pairs]) 2);
+by (asm_simp_tac (bin_add_ss addsimps [zadd_assoc, zadd_swap_pairs]) 2);
by (REPEAT (ares_tac ([refl, zadd_kill, zadd_assoc_swap_kill]@typechecks) 2));
by (etac boolE 1);
-by (ALLGOALS (ASM_SIMP_TAC (bin_add_ss addrews [zadd_assoc,zadd_swap_pairs])));
+by (ALLGOALS (asm_simp_tac (bin_add_ss addsimps [zadd_assoc,zadd_swap_pairs])));
by (REPEAT (ares_tac ([refl, zadd_kill, zadd_assoc_swap_kill RS sym]@
typechecks) 1));
val integ_of_bin_add_lemma = result();
@@ -255,7 +250,7 @@
(*** bin_add: binary multiplication ***)
val bin_mult_ss =
- bin_ss addrews (bin_recs bin_mult_def @
+ bin_ss addsimps (bin_recs bin_mult_def @
[integ_of_bin_minus, integ_of_bin_add]);
@@ -265,12 +260,12 @@
\ integ_of_bin(v) $* integ_of_bin(w)";
by (cut_facts_tac prems 1);
by (bin_ind_tac "v" [major] 1);
-by (SIMP_TAC (bin_mult_ss addrews [zmult_0]) 1);
-by (SIMP_TAC (bin_mult_ss addrews [zmult_1,zmult_zminus]) 1);
+by (asm_simp_tac (bin_mult_ss addsimps [zmult_0]) 1);
+by (asm_simp_tac (bin_mult_ss addsimps [zmult_1,zmult_zminus]) 1);
by (etac boolE 1);
-by (ASM_SIMP_TAC (bin_mult_ss addrews [zadd_zmult_distrib]) 2);
-by (ASM_SIMP_TAC
- (bin_mult_ss addrews [zadd_zmult_distrib, zmult_1, zadd_assoc]) 1);
+by (asm_simp_tac (bin_mult_ss addsimps [zadd_zmult_distrib]) 2);
+by (asm_simp_tac
+ (bin_mult_ss addsimps [zadd_zmult_distrib, zmult_1, zadd_assoc]) 1);
by (REPEAT (ares_tac ([zadd_commute, zadd_assoc_swap_kill RS sym]@
typechecks) 1));
val integ_of_bin_mult = result();
@@ -283,19 +278,19 @@
val [bin_pred_Plus, bin_pred_Minus, _] = bin_recs bin_pred_def;
goal BinFn.thy "bin_succ(w$$1) = bin_succ(w) $$ 0";
-by (SIMP_TAC carry_ss 1);
+by (simp_tac carry_ss 1);
val bin_succ_Bcons1 = result();
goal BinFn.thy "bin_succ(w$$0) = w$$1";
-by (SIMP_TAC carry_ss 1);
+by (simp_tac carry_ss 1);
val bin_succ_Bcons0 = result();
goal BinFn.thy "bin_pred(w$$1) = w$$0";
-by (SIMP_TAC carry_ss 1);
+by (simp_tac carry_ss 1);
val bin_pred_Bcons1 = result();
goal BinFn.thy "bin_pred(w$$0) = bin_pred(w) $$ 1";
-by (SIMP_TAC carry_ss 1);
+by (simp_tac carry_ss 1);
val bin_pred_Bcons0 = result();
(** extra rules for bin_minus **)
@@ -303,28 +298,28 @@
val [bin_minus_Plus, bin_minus_Minus, _] = bin_recs bin_minus_def;
goal BinFn.thy "bin_minus(w$$1) = bin_pred(bin_minus(w) $$ 0)";
-by (SIMP_TAC bin_minus_ss 1);
+by (simp_tac bin_minus_ss 1);
val bin_minus_Bcons1 = result();
goal BinFn.thy "bin_minus(w$$0) = bin_minus(w) $$ 0";
-by (SIMP_TAC bin_minus_ss 1);
+by (simp_tac bin_minus_ss 1);
val bin_minus_Bcons0 = result();
(** extra rules for bin_add **)
goal BinFn.thy
"!!w. w: bin ==> bin_add(v$$1, w$$1) = bin_add(v, bin_succ(w)) $$ 0";
-by (ASM_SIMP_TAC bin_add_ss 1);
+by (asm_simp_tac bin_add_ss 1);
val bin_add_Bcons_Bcons11 = result();
goal BinFn.thy
"!!w. w: bin ==> bin_add(v$$1, w$$0) = bin_add(v,w) $$ 1";
-by (ASM_SIMP_TAC bin_add_ss 1);
+by (asm_simp_tac bin_add_ss 1);
val bin_add_Bcons_Bcons10 = result();
goal BinFn.thy
"!!w y.[| w: bin; y: bool |] ==> bin_add(v$$0, w$$y) = bin_add(v,w) $$ y";
-by (ASM_SIMP_TAC bin_add_ss 1);
+by (asm_simp_tac bin_add_ss 1);
val bin_add_Bcons_Bcons0 = result();
(** extra rules for bin_mult **)
@@ -332,24 +327,18 @@
val [bin_mult_Plus, bin_mult_Minus, _] = bin_recs bin_mult_def;
goal BinFn.thy "bin_mult(v$$1, w) = bin_add(bin_mult(v,w)$$0, w)";
-by (SIMP_TAC bin_mult_ss 1);
+by (simp_tac bin_mult_ss 1);
val bin_mult_Bcons1 = result();
goal BinFn.thy "bin_mult(v$$0, w) = bin_mult(v,w)$$0";
-by (SIMP_TAC bin_mult_ss 1);
+by (simp_tac bin_mult_ss 1);
val bin_mult_Bcons0 = result();
(*** The computation simpset ***)
-val bin_comp_ss = carry_ss addrews
- [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]
- setauto (type_auto_tac bin_typechecks0);
-
val bin_comp_ss = integ_ss
- addcongs bin_congs
- addrews [bin_succ_Plus, bin_succ_Minus,
+ addsimps [bin_succ_Plus, bin_succ_Minus,
bin_succ_Bcons1, bin_succ_Bcons0,
bin_pred_Plus, bin_pred_Minus,
bin_pred_Bcons1, bin_pred_Bcons0,
@@ -360,7 +349,7 @@
bin_add_Bcons_Bcons10, bin_add_Bcons_Bcons11,
bin_mult_Plus, bin_mult_Minus,
bin_mult_Bcons1, bin_mult_Bcons0]
- setauto (type_auto_tac ([bool_1I, bool_0I] @ bin_typechecks0));
+ setsolver (type_auto_tac ([bool_1I, bool_0I] @ bin_typechecks0));
(*** Examples of performing binary arithmetic by simplification ***)
@@ -370,7 +359,7 @@
(* 13+19 = 32 *)
goal BinFn.thy
"bin_add(Plus$$1$$1$$0$$1, Plus$$1$$0$$0$$1$$1) = Plus$$1$$0$$0$$0$$0$$0";
-by (SIMP_TAC bin_comp_ss 1); (*1.9 secs*)
+by (simp_tac bin_comp_ss 1); (*0.6 secs*)
result();
bin_add(binary_of_int 13, binary_of_int 19);
@@ -380,7 +369,7 @@
"bin_add(Plus$$1$$0$$0$$1$$1$$0$$1$$0$$0$$1$$0, \
\ Plus$$1$$0$$1$$1$$0$$0$$0$$1$$0$$1$$1$$1$$0) = \
\ Plus$$1$$1$$0$$1$$1$$0$$0$$0$$0$$0$$0$$0$$0";
-by (SIMP_TAC bin_comp_ss 1); (*8.9 secs*)
+by (simp_tac bin_comp_ss 1); (*2.6 secs*)
result();
bin_add(binary_of_int 1234, binary_of_int 5678);
@@ -390,7 +379,7 @@
"bin_add(Plus$$1$$0$$1$$0$$1$$0$$0$$1$$1$$1$$1, \
\ Minus$$0$$1$$1$$0$$0$$1$$0$$1$$1$$1$$0$$0) = \
\ Minus$$1$$0$$1$$1$$1$$0$$1$$0$$1$$0$$1$$1";
-by (SIMP_TAC bin_comp_ss 1); (*7.4 secs*)
+by (simp_tac bin_comp_ss 1); (*2.3 secs*)
result();
bin_add(binary_of_int 1359, binary_of_int ~2468);
@@ -400,7 +389,7 @@
"bin_add(Plus$$1$$0$$1$$1$$0$$1$$1$$1$$0$$0$$0$$1$$1$$0$$0$$1$$0, \
\ Minus$$0$$1$$0$$0$$1$$0$$1$$0$$1$$1$$0$$1$$1$$0$$0$$1) = \
\ Plus$$0$$1$$0$$1$$1$$1$$0$$0$$1$$0$$0$$0$$0$$1$$0$$1$$1";
-by (SIMP_TAC bin_comp_ss 1); (*13.7 secs*)
+by (simp_tac bin_comp_ss 1); (*3.9 secs*)
result();
bin_add(binary_of_int 93746, binary_of_int ~46375);
@@ -409,7 +398,7 @@
goal BinFn.thy
"bin_minus(Plus$$1$$0$$0$$0$$0$$0$$0$$0$$0$$1$$1$$0$$1$$0$$0$$0$$1) = \
\ Minus$$0$$1$$1$$1$$1$$1$$1$$1$$1$$0$$0$$1$$0$$1$$1$$1$$1";
-by (SIMP_TAC bin_comp_ss 1); (*2.8 secs*)
+by (simp_tac bin_comp_ss 1); (*0.6 secs*)
result();
bin_minus(binary_of_int 65745);
@@ -418,7 +407,7 @@
goal BinFn.thy
"bin_minus(Minus$$0$$0$$1$$0$$1$$0$$1$$1$$1$$1$$0$$0$$1$$1$$1$$1) = \
\ Plus$$0$$1$$1$$0$$1$$0$$1$$0$$0$$0$$0$$1$$1$$0$$0$$0$$1";
-by (SIMP_TAC bin_comp_ss 1); (*3.3 secs*)
+by (simp_tac bin_comp_ss 1); (*0.7 secs*)
result();
bin_minus(binary_of_int ~54321);
@@ -426,7 +415,7 @@
(* 13*19 = 247 *)
goal BinFn.thy "bin_mult(Plus$$1$$1$$0$$1, Plus$$1$$0$$0$$1$$1) = \
\ Plus$$1$$1$$1$$1$$0$$1$$1$$1";
-by (SIMP_TAC bin_comp_ss 1); (*4.4 secs*)
+by (simp_tac bin_comp_ss 1); (*1.5 secs*)
result();
bin_mult(binary_of_int 13, binary_of_int 19);
@@ -435,7 +424,7 @@
goal BinFn.thy
"bin_mult(Minus$$0$$1$$0$$1$$1$$0$$0, Plus$$1$$1$$0$$0$$1$$1) = \
\ Minus$$0$$1$$1$$1$$1$$0$$1$$0$$0$$0$$1$$0$$0";
-by (SIMP_TAC bin_comp_ss 1); (*9.2 secs*)
+by (simp_tac bin_comp_ss 1); (*2.6 secs*)
result();
bin_mult(binary_of_int ~84, binary_of_int 51);
@@ -445,19 +434,17 @@
"bin_mult(Plus$$1$$1$$1$$1$$1$$1$$1$$1, \
\ Plus$$1$$1$$1$$1$$1$$1$$1$$1) = \
\ Plus$$1$$1$$1$$1$$1$$1$$1$$0$$0$$0$$0$$0$$0$$0$$0$$1";
-by (SIMP_TAC bin_comp_ss 1); (*38.4 secs*)
+by (simp_tac bin_comp_ss 1); (*9.8 secs*)
result();
bin_mult(binary_of_int 255, binary_of_int 255);
-(***************** TOO SLOW TO INCLUDE IN TEST RUNS
(* 1359 * ~2468 = ~3354012 *)
goal BinFn.thy
"bin_mult(Plus$$1$$0$$1$$0$$1$$0$$0$$1$$1$$1$$1, \
\ Minus$$0$$1$$1$$0$$0$$1$$0$$1$$1$$1$$0$$0) = \
\ Minus$$0$$0$$1$$1$$0$$0$$1$$1$$0$$1$$0$$0$$1$$0$$0$$1$$1$$0$$0$$1$$0$$0";
-by (SIMP_TAC bin_comp_ss 1); (*54.8 secs*)
+by (simp_tac bin_comp_ss 1); (*13.7 secs*)
result();
-****************)
bin_mult(binary_of_int 1359, binary_of_int ~2468);