diff -r ee97b6463cb4 -r b8da5f258b04 src/HOL/MiniML/MiniML.ML
--- a/src/HOL/MiniML/MiniML.ML	Mon Mar 01 13:51:21 2004 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,243 +0,0 @@
-(* Title:     HOL/MiniML/MiniML.ML
-   ID:        $Id$
-   Author:    Dieter Nazareth and Tobias Nipkow
-   Copyright  1995 TU Muenchen
-*)
-
-Addsimps has_type.intrs;
-Addsimps [Un_upper1,Un_upper2];
-
-Addsimps [is_bound_typ_instance_closed_subst];
-
-
-Goal "!!t::typ. $(%n. if n : (free_tv A) Un (free_tv t) then (S n) else (TVar n)) t = $S t";
-by (rtac typ_substitutions_only_on_free_variables 1);
-by (asm_full_simp_tac (simpset() addsimps [Ball_def]) 1);
-qed "s'_t_equals_s_t";
-
-Addsimps [s'_t_equals_s_t];
-
-Goal "!!A::type_scheme list. $(%n. if n : (free_tv A) Un (free_tv t) then (S n) else (TVar n)) A = $S A";
-by (rtac scheme_list_substitutions_only_on_free_variables 1);
-by (asm_full_simp_tac (simpset() addsimps [Ball_def]) 1);
-qed "s'_a_equals_s_a";
-
-Addsimps [s'_a_equals_s_a];
-
-Goal
- "$(%n. if n : (free_tv A) Un (free_tv t) then S n else TVar n) A |- \
-\    e :: $(%n. if n : (free_tv A) Un (free_tv t) then S n else TVar n) t \
-\ ==> $S A |- e :: $S t";
-
-by (res_inst_tac [("P","%A. A |- e :: $S t")] ssubst 1);
-by (rtac (s'_a_equals_s_a RS sym) 1);
-by (res_inst_tac [("P","%t. $ (%n. if n : free_tv A Un free_tv (?t1 S) then S n else TVar n) A |- e :: t")] ssubst 1);
-by (rtac (s'_t_equals_s_t RS sym) 1);
-by (Asm_full_simp_tac 1);
-qed "replace_s_by_s'";
-
-Goal "!!A::type_scheme list. $ (%x. TVar (if x : free_tv A then x else n + x)) A = $ id_subst A";
-by (rtac scheme_list_substitutions_only_on_free_variables 1);
-by (asm_full_simp_tac (simpset() addsimps [id_subst_def]) 1);
-qed "alpha_A'";
-
-Goal "!!A::type_scheme list. $ (%x. TVar (if x : free_tv A then x else n + x)) A = A";
-by (rtac (alpha_A' RS ssubst) 1);
-by (Asm_full_simp_tac 1);
-qed "alpha_A";
-
-Goal "$ (S o alpha) (t::typ) = $ S ($ (%x. TVar (alpha x)) t)";
-by (induct_tac "t" 1);
-by (ALLGOALS (Asm_full_simp_tac));
-qed "S_o_alpha_typ";
-
-Goal "$ (%u. (S o alpha) u) (t::typ) = $ S ($ (%x. TVar (alpha x)) t)";
-by (induct_tac "t" 1);
-by (ALLGOALS (Asm_full_simp_tac));
-val S_o_alpha_typ' = result ();
-
-Goal "$ (S o alpha) (sch::type_scheme) = $ S ($ (%x. TVar (alpha x)) sch)";
-by (induct_tac "sch" 1);
-by (ALLGOALS (Asm_full_simp_tac));
-qed "S_o_alpha_type_scheme";
-
-Goal "$ (S o alpha) (A::type_scheme list) = $ S ($ (%x. TVar (alpha x)) A)";
-by (induct_tac "A" 1);
-by (ALLGOALS (Asm_full_simp_tac));
-by (rtac (rewrite_rule [o_def] S_o_alpha_type_scheme) 1);
-qed "S_o_alpha_type_scheme_list";
-
-Goal "!!A::type_scheme list. \
-\     $ (%n. if n : free_tv A Un free_tv t then S n else TVar n) A = \
-\     $ ((%x. if x : free_tv A Un free_tv t then S x else TVar x) o \
-\        (%x. if x : free_tv A then x else n + x)) A";
-by (stac S_o_alpha_type_scheme_list 1);
-by (stac alpha_A 1);
-by (rtac refl 1);
-qed "S'_A_eq_S'_alpha_A";
-
-Goalw [free_tv_subst,dom_def]
- "dom (%n. if n : free_tv A Un free_tv t then S n else TVar n) <= \
-\ free_tv A Un free_tv t";
-by (Simp_tac 1);
-by (Fast_tac 1);
-qed "dom_S'";
-
-Goalw [free_tv_subst,cod_def,subset_def]
-  "!!(A::type_scheme list) (t::typ). \ 
-\  cod (%n. if n : free_tv A Un free_tv t then S n else TVar n) <= \
-\  free_tv ($ S A) Un free_tv ($ S t)";
-by (rtac ballI 1);
-by (etac UN_E 1);
-by (dtac (dom_S' RS subsetD) 1);
-by (Asm_full_simp_tac 1);
-by (fast_tac (claset() addDs [free_tv_of_substitutions_extend_to_scheme_lists] 
-                      addIs [free_tv_of_substitutions_extend_to_types RS subsetD]) 1);
-qed "cod_S'";
-
-Goalw [free_tv_subst]
- "!!(A::type_scheme list) (t::typ). \
-\ free_tv (%n. if n : free_tv A Un free_tv t then S n else TVar n) <= \
-\ free_tv A Un free_tv ($ S A) Un free_tv t Un free_tv ($ S t)";
-by (fast_tac (claset() addDs [dom_S' RS subsetD,cod_S' RS subsetD]) 1);
-qed "free_tv_S'";
-
-Goal "!!t1::typ. \
-\     (free_tv ($ (%x. TVar (if x : free_tv A then x else n + x)) t1) - free_tv A) <= \
-\         {x. ? y. x = n + y}";
-by (induct_tac "t1" 1);
-by (Simp_tac 1);
-by (Fast_tac 1);
-by (Simp_tac 1);
-by (Fast_tac 1);
-qed "free_tv_alpha";
-
-Goal "!!(k::nat). n <= n + k";
-by (induct_thm_tac nat_induct "k" 1);
-by (Simp_tac 1);
-by (Asm_simp_tac 1);
-val aux_plus = result();
-
-Addsimps [aux_plus];
-
-Goal "!!t::typ. new_tv n t ==> {x. ? y. x = n + y} Int free_tv t = {}";
-by Safe_tac;
-by (cut_facts_tac [aux_plus] 1);
-by (dtac new_tv_le 1);
-by (assume_tac 1);
-by (rotate_tac 1 1);
-by (dtac new_tv_not_free_tv 1);
-by (Fast_tac 1);
-val new_tv_Int_free_tv_empty_type = result ();
-
-Goal "!!sch::type_scheme. new_tv n sch ==> {x. ? y. x = n + y} Int free_tv sch = {}";
-by Safe_tac;
-by (cut_facts_tac [aux_plus] 1);
-by (dtac new_tv_le 1);
-by (assume_tac 1);
-by (rotate_tac 1 1);
-by (dtac new_tv_not_free_tv 1);
-by (Fast_tac 1);
-val new_tv_Int_free_tv_empty_scheme = result ();
-
-Goal "!A::type_scheme list. new_tv n A --> {x. ? y. x = n + y} Int free_tv A = {}";
-by (rtac allI 1);
-by (induct_tac "A" 1);
-by (Simp_tac 1);
-by (Simp_tac 1);
-by (fast_tac (claset() addDs [new_tv_Int_free_tv_empty_scheme ]) 1);
-val new_tv_Int_free_tv_empty_scheme_list = result ();
-
-Goalw [le_type_scheme_def,is_bound_typ_instance] 
-   "new_tv n A --> gen A t <= gen A ($ (%x. TVar (if x : free_tv A then x else n + x)) t)";
-by (strip_tac 1);
-by (etac exE 1);
-by (hyp_subst_tac 1);
-by (res_inst_tac [("x","(%x. S (if n <= x then x - n else x))")] exI 1);
-by (induct_tac "t" 1);
-by (Simp_tac 1);
-by (case_tac "nat : free_tv A" 1);
-by (Asm_simp_tac 1);
-by (subgoal_tac "n <= n + nat" 1);
-by (dtac new_tv_le 1);
-by (assume_tac 1);
-by (dtac new_tv_not_free_tv 1);
-by (dtac new_tv_not_free_tv 1);
-by (asm_simp_tac (simpset() addsimps [diff_add_inverse ]) 1);
-by (Simp_tac 1);
-by (Asm_simp_tac 1);
-qed_spec_mp "gen_t_le_gen_alpha_t";
-
-AddSIs has_type.intrs;
-
-Goal "A |- e::t ==> !B. A <= B -->  B |- e::t";
-by (etac has_type.induct 1);
-   by (simp_tac (simpset() addsimps [le_env_def]) 1);
-   by (fast_tac (claset() addEs [bound_typ_instance_trans] addss simpset()) 1);
-  by (Asm_full_simp_tac 1);
- by (Fast_tac 1);
-by (slow_tac (claset() addEs [le_env_free_tv RS free_tv_subset_gen_le]) 1);
-qed_spec_mp "has_type_le_env";
-
-(* has_type is closed w.r.t. substitution *)
-Goal "A |- e :: t ==> !S. $S A |- e :: $S t";
-by (etac has_type.induct 1);
-(* case VarI *)
-   by (rtac allI 1);
-   by (rtac has_type.VarI 1);
-    by (asm_full_simp_tac (simpset() addsimps [app_subst_list]) 1);
-   by (asm_simp_tac (simpset() addsimps [app_subst_list]) 1);
-  (* case AbsI *)
-  by (rtac allI 1);
-  by (Simp_tac 1);  
-  by (rtac has_type.AbsI 1);
-  by (Asm_full_simp_tac 1);
- (* case AppI *)
- by (rtac allI 1);
- by (rtac has_type.AppI 1);
-  by (Asm_full_simp_tac 1);
-  by (etac spec 1);
- by (etac spec 1);
-(* case LetI *)
-by (rtac allI 1);
-by (rtac replace_s_by_s' 1);
-by (cut_inst_tac [("A","$ S A"), 
-                  ("A'","A"),
-                  ("t","t"),
-                  ("t'","$ S t")] 
-                 ex_fresh_variable 1);
-by (etac exE 1);
-by (REPEAT (etac conjE 1));
-by (res_inst_tac [("t1.0","$((%x. if x : free_tv A Un free_tv t then S x else TVar x) o \
-\                            (%x. if x : free_tv A then x else n + x)) t1")] 
-                 has_type.LETI 1);
- by (dres_inst_tac [("x","(%x. if x : free_tv A Un free_tv t then S x else TVar x) o \
-\                         (%x. if x : free_tv A then x else n + x)")] spec 1);
- by (stac (S'_A_eq_S'_alpha_A) 1);
- by (assume_tac 1);
-by (stac S_o_alpha_typ 1);
-by (stac gen_subst_commutes 1);
- by (rtac subset_antisym 1);
-  by (rtac subsetI 1);
-  by (etac IntE 1);
-  by (dtac (free_tv_S' RS subsetD) 1);
-  by (dtac (free_tv_alpha RS subsetD) 1);
-  by (asm_full_simp_tac (simpset() delsimps [full_SetCompr_eq])  1);
-  by (etac exE 1);
-  by (hyp_subst_tac 1);
-  by (subgoal_tac "new_tv (n + y) ($ S A)" 1);
-   by (subgoal_tac "new_tv (n + y) ($ S t)" 1);
-    by (subgoal_tac "new_tv (n + y) A" 1);
-     by (subgoal_tac "new_tv (n + y) t" 1);
-      by (REPEAT (dtac new_tv_not_free_tv 1));
-      by (Fast_tac 1);
-     by (REPEAT ((rtac new_tv_le 1) THEN (assume_tac 2) THEN (Simp_tac 1)));
- by (Fast_tac 1);
-by (rtac has_type_le_env 1);
- by (dtac spec 1);
- by (dtac spec 1);
- by (assume_tac 1);
-by (rtac (app_subst_Cons RS subst) 1);
-by (rtac S_compatible_le_scheme_lists 1);
-by (Asm_simp_tac 1);
-qed "has_type_cl_sub";