--- a/src/HOL/MiniML/W.ML Tue Jan 30 15:19:20 1996 +0100
+++ b/src/HOL/MiniML/W.ML Tue Jan 30 15:24:36 1996 +0100
@@ -11,7 +11,7 @@
(* stronger version of Suc_leD *)
goalw Nat.thy [le_def]
- "!!m. Suc m <= n ==> m < n";
+ "!!m. Suc m <= n ==> m < n";
by (Asm_full_simp_tac 1);
by (cut_facts_tac [less_linear] 1);
by (fast_tac HOL_cs 1);
@@ -20,7 +20,7 @@
(* correctness of W with respect to has_type *)
goal thy
- "!a s t m n . Ok (s,t,m) = W e a n --> ($ s a |- e :: t)";
+ "!a s t m n . Ok (s,t,m) = W e a n --> ($ s a |- e :: t)";
by (expr.induct_tac "e" 1);
(* case Var n *)
by (asm_simp_tac (!simpset setloop (split_tac [expand_if])) 1);
@@ -46,12 +46,12 @@
qed "W_correct";
val has_type_casesE = map(has_type.mk_cases expr.simps)
- [" s |- Var n :: t"," s |- Abs e :: t","s |- App e1 e2 ::t"];
+ [" s |- Var n :: t"," s |- Abs e :: t","s |- App e1 e2 ::t"];
(* the resulting type variable is always greater or equal than the given one *)
goal thy
- "!a n s t m. W e a n = Ok (s,t,m) --> n<=m";
+ "!a n s t m. W e a n = Ok (s,t,m) --> n<=m";
by (expr.induct_tac "e" 1);
(* case Var(n) *)
by (fast_tac (HOL_cs addss (!simpset setloop (split_tac [expand_if]))) 1);
@@ -83,7 +83,7 @@
Addsimps [W_var_ge];
goal thy
- "!! s. Ok (s,t,m) = W e a n ==> n<=m";
+ "!! s. Ok (s,t,m) = W e a n ==> n<=m";
by (asm_full_simp_tac (!simpset addsimps [eq_sym_conv]) 1);
qed "W_var_geD";
@@ -101,7 +101,7 @@
by (expr.induct_tac "e" 1);
(* case Var n *)
by (fast_tac (HOL_cs addss (!simpset
- addsimps [id_subst_def,list_all_nth,new_tv_list,new_tv_subst]
+ addsimps [id_subst_def,list_all_nth,new_tv_list,new_tv_subst]
setloop (split_tac [expand_if]))) 1);
(* case Abs e *)
@@ -111,7 +111,7 @@
by (eres_inst_tac [("x","Suc n")] allE 1);
by (eres_inst_tac [("x","(TVar n)#a")] allE 1);
by (fast_tac (HOL_cs addss (!simpset
- addsimps [new_tv_subst,new_tv_Suc_list])) 1);
+ addsimps [new_tv_subst,new_tv_Suc_list])) 1);
(* case App e1 e2 *)
by (simp_tac (!simpset setloop (split_tac [expand_bind])) 1);
@@ -139,15 +139,15 @@
by (fast_tac (HOL_cs addDs [W_var_geD] addIs
[new_tv_list_le,new_tv_subst_tel,lessI RS less_imp_le RS new_tv_subst_le])
1);
-be (sym RS mgu_new) 1;
+by (etac (sym RS mgu_new) 1);
by (fast_tac (HOL_cs addDs [W_var_geD] addIs [new_tv_subst_te,new_tv_list_le,
new_tv_subst_tel,lessI RS less_imp_le RS new_tv_le,lessI RS less_imp_le RS
new_tv_subst_le,new_tv_le]) 1);
by (fast_tac (HOL_cs addDs [W_var_geD] addIs
[new_tv_list_le,new_tv_subst_tel,new_tv_le]
- addss (!simpset)) 1);
-br (lessI RS new_tv_subst_var) 1;
-be (sym RS mgu_new) 1;
+ addss (!simpset)) 1);
+by (rtac (lessI RS new_tv_subst_var) 1);
+by (etac (sym RS mgu_new) 1);
by (fast_tac (HOL_cs addSIs [lessI RS less_imp_le RS new_tv_le,new_tv_subst_te]
addDs [W_var_geD] addIs
[new_tv_list_le,new_tv_subst_tel,lessI RS less_imp_le RS
@@ -159,7 +159,7 @@
goal thy
- "!n a s t m v. W e a n = Ok (s,t,m) --> \
+ "!n a s t m v. W e a n = Ok (s,t,m) --> \
\ (v:free_tv s | v:free_tv t) --> v<n --> v:free_tv a";
by (expr.induct_tac "e" 1);
(* case Var n *)
@@ -198,8 +198,8 @@
by (eres_inst_tac [("x","v")] allE 1);
by (safe_tac (empty_cs addSIs [conjI,impI] addSEs [conjE]) );
by (asm_full_simp_tac (!simpset addsimps [rotate_Ok]) 1);
-bd W_var_geD 1;
-bd W_var_geD 1;
+by (dtac W_var_geD 1);
+by (dtac W_var_geD 1);
by ( (forward_tac [less_le_trans] 1) THEN (assume_tac 1) );
by (fast_tac (HOL_cs addDs [free_tv_comp_subst RS subsetD,sym RS mgu_free,
codD,free_tv_app_subst_te RS subsetD,free_tv_app_subst_tel RS subsetD,
@@ -207,8 +207,8 @@
addEs [UnE]
addss !simpset) 1);
by (Asm_full_simp_tac 1);
-bd (sym RS W_var_geD) 1;
-bd (sym RS W_var_geD) 1;
+by (dtac (sym RS W_var_geD) 1);
+by (dtac (sym RS W_var_geD) 1);
by ( (forward_tac [less_le_trans] 1) THEN (assume_tac 1) );
by (fast_tac (HOL_cs addDs [mgu_free, codD,free_tv_subst_var RS subsetD,
free_tv_app_subst_te RS subsetD,free_tv_app_subst_tel RS subsetD,
@@ -223,10 +223,10 @@
(* Completeness of W w.r.t. has_type *)
goal thy
- "!s' a t' n. ($ s' a |- e :: t') --> new_tv n a --> \
-\ (? s t. (? m. W e a n = Ok (s,t,m) ) & \
-\ (? r. $ s' a = $ r ($ s a) & \
-\ t' = $ r t ) )";
+ "!s' a t' n. ($ s' a |- e :: t') --> new_tv n a --> \
+\ (? s t. (? m. W e a n = Ok (s,t,m) ) & \
+\ (? r. $ s' a = $ r ($ s a) & \
+\ t' = $ r t ) )";
by (expr.induct_tac "e" 1);
(* case Var n *)
by (strip_tac 1);
@@ -262,14 +262,14 @@
by (eres_inst_tac [("x","$ s a")] allE 1);
by (eres_inst_tac [("x","t2")] allE 1);
by (eres_inst_tac [("x","m")] allE 1);
-bd asm_rl 1;
-bd asm_rl 1;
-bd asm_rl 1;
+by (dtac asm_rl 1);
+by (dtac asm_rl 1);
+by (dtac asm_rl 1);
by (Asm_full_simp_tac 1);
by (safe_tac HOL_cs);
by (fast_tac HOL_cs 1);
by (fast_tac (HOL_cs addIs [sym RS W_var_geD,new_tv_W RS
- conjunct1,new_tv_list_le,new_tv_subst_tel]) 1);
+ conjunct1,new_tv_list_le,new_tv_subst_tel]) 1);
by (subgoal_tac
"$ (%x.if x=ma then t' else (if x:(free_tv t - free_tv sa) then r x \
@@ -280,7 +280,7 @@
\ (if x:(free_tv t - free_tv sa) then r x else ra x)) ($ sa t)"),
("s","($ ra ta) -> t'")] ssubst 2);
by (asm_simp_tac (!simpset addsimps [subst_comp_te]) 2);
-br eq_free_eq_subst_te 2;
+by (rtac eq_free_eq_subst_te 2);
by (strip_tac 2);
by (subgoal_tac "na ~=ma" 2);
by (fast_tac (HOL_cs addDs [new_tv_W,sym RS W_var_geD,
@@ -291,7 +291,7 @@
setloop (split_tac [expand_if])) 3);
(* na : free_tv sa *)
by (dres_inst_tac [("ts1","$ s a")] (subst_comp_tel RSN (2,trans)) 2);
-bd eq_subst_tel_eq_free 2;
+by (dtac eq_subst_tel_eq_free 2);
by (fast_tac (HOL_cs addIs [free_tv_W,free_tv_le_new_tv] addDs [new_tv_W]) 2);
by (Asm_simp_tac 2);
by (case_tac "na:dom sa" 2);
@@ -299,12 +299,12 @@
by (asm_full_simp_tac (!simpset addsimps [dom_def]
setloop (split_tac [expand_if])) 3);
(* na : dom sa *)
-br eq_free_eq_subst_te 2;
+by (rtac eq_free_eq_subst_te 2);
by (strip_tac 2);
by (subgoal_tac "nb ~= ma" 2);
by ((forward_tac [new_tv_W] 3) THEN (atac 3));
-be conjE 3;
-bd new_tv_subst_tel 3;
+by (etac conjE 3);
+by (dtac new_tv_subst_tel 3);
by (fast_tac (HOL_cs addIs [new_tv_list_le] addDs [sym RS W_var_geD]) 3);
by (fast_tac (set_cs addDs [new_tv_W,new_tv_not_free_tv] addss
(!simpset addsimps [cod_def,free_tv_subst])) 3);
@@ -312,12 +312,12 @@
setloop (split_tac [expand_if]))) 2);
by (Simp_tac 2);
-br eq_free_eq_subst_te 2;
+by (rtac eq_free_eq_subst_te 2);
by (strip_tac 2 );
by (subgoal_tac "na ~= ma" 2);
by ((forward_tac [new_tv_W] 3) THEN (atac 3));
-be conjE 3;
-bd (sym RS W_var_geD) 3;
+by (etac conjE 3);
+by (dtac (sym RS W_var_geD) 3);
by (fast_tac (HOL_cs addDs [new_tv_list_le,new_tv_subst_tel,new_tv_W,new_tv_not_free_tv]) 3);
by (case_tac "na: free_tv t - free_tv sa" 2);
(* case na ~: free_tv t - free_tv sa *)
@@ -325,37 +325,37 @@
(* case na : free_tv t - free_tv sa *)
by( asm_full_simp_tac (!simpset setloop (split_tac [expand_if])) 2);
by (dres_inst_tac [("ts1","$ s a")] (subst_comp_tel RSN (2,trans)) 2);
-bd eq_subst_tel_eq_free 2;
+by (dtac eq_subst_tel_eq_free 2);
by (fast_tac (HOL_cs addIs [free_tv_W,free_tv_le_new_tv] addDs [new_tv_W]) 2);
by (asm_full_simp_tac (!simpset addsimps [free_tv_subst,dom_def,not_disj]) 2);
by (asm_simp_tac (!simpset setloop (split_tac [expand_bind])) 1);
by (safe_tac HOL_cs );
-bd mgu_Ok 1;
+by (dtac mgu_Ok 1);
by( fast_tac (HOL_cs addss !simpset) 1);
by (REPEAT (resolve_tac [exI,conjI] 1));
by (fast_tac HOL_cs 1);
by (fast_tac HOL_cs 1);
by ((dtac mgu_mg 1) THEN (atac 1));
-be exE 1;
+by (etac exE 1);
by (res_inst_tac [("x","rb")] exI 1);
-br conjI 1;
+by (rtac conjI 1);
by (dres_inst_tac [("x","ma")] fun_cong 2);
by( asm_full_simp_tac (!simpset addsimps [eq_sym_conv]) 2);
by (simp_tac (!simpset addsimps [subst_comp_tel RS sym]) 1);
by (res_inst_tac [("ts2","($ sa ($ s a))")] ((subst_comp_tel RS sym) RSN
(2,trans)) 1);
by( asm_full_simp_tac (!simpset addsimps [o_def,eq_sym_conv]) 1);
-br eq_free_eq_subst_tel 1;
+by (rtac eq_free_eq_subst_tel 1);
by( safe_tac HOL_cs );
by (subgoal_tac "ma ~= na" 1);
by ((forward_tac [new_tv_W] 2) THEN (atac 2));
-be conjE 2;
-bd new_tv_subst_tel 2;
+by (etac conjE 2);
+by (dtac new_tv_subst_tel 2);
by (fast_tac (HOL_cs addIs [new_tv_list_le] addDs [sym RS W_var_geD]) 2);
by (( forw_inst_tac [("xd","m")] (sym RSN (2,new_tv_W)) 2) THEN (atac 2));
-be conjE 2;
-bd (free_tv_app_subst_tel RS subsetD) 2;
+by (etac conjE 2);
+by (dtac (free_tv_app_subst_tel RS subsetD) 2);
by (fast_tac (set_cs addDs [W_var_geD,new_tv_list_le,codD,
new_tv_not_free_tv]) 2);
by (case_tac "na: free_tv t - free_tv sa" 1);
@@ -363,7 +363,7 @@
by (asm_full_simp_tac (!simpset setloop (split_tac [expand_if])) 2);
(* case na : free_tv t - free_tv sa *)
by (asm_full_simp_tac (!simpset setloop (split_tac [expand_if])) 1);
-bd (free_tv_app_subst_tel RS subsetD) 1;
+by (dtac (free_tv_app_subst_tel RS subsetD) 1);
by (fast_tac (set_cs addDs [codD,subst_comp_tel RSN (2,trans),
eq_subst_tel_eq_free] addss ((!simpset addsimps
[not_disj,free_tv_subst,dom_def]))) 1);