--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/MicroJava/J/JBasis.ML Thu Nov 11 12:23:45 1999 +0100
@@ -0,0 +1,230 @@
+(* Title: HOL/MicroJava/J/JBasis.ML
+ ID: $Id$
+ Author: David von Oheimb
+ Copyright 1999 TU Muenchen
+*)
+
+val strip_tac1 = SELECT_GOAL (safe_tac (HOL_cs delrules [conjI, disjE, impCE]));
+
+Goalw [image_def]
+ "x \\<in> f``A \\<Longrightarrow> \\<exists>y. y \\<in> A \\<and> x = f y";
+by(Auto_tac);
+qed "image_rev";
+
+fun case_tac1 s i = EVERY [case_tac s i, rotate_tac ~1 i, rotate_tac ~1 (i+1)];
+
+val select_split = prove_goalw Prod.thy [split_def]
+ "(\\<epsilon>(x,y). P x y) = (\\<epsilon>xy. P (fst xy) (snd xy))" (K [rtac refl 1]);
+
+
+val split_beta = prove_goal Prod.thy "(\\<lambda>(x,y). P x y) z = P (fst z) (snd z)"
+ (fn _ => [stac surjective_pairing 1, stac split 1, rtac refl 1]);
+val split_beta2 = prove_goal Prod.thy "(\\<lambda>(x,y). P x y) (w,z) = P w z"
+ (fn _ => [Auto_tac]);
+val splitE2 = prove_goal Prod.thy "\\<lbrakk>Q (split P z); \\<And>x y. \\<lbrakk>z = (x, y); Q (P x y)\\<rbrakk> \\<Longrightarrow> R\\<rbrakk> \\<Longrightarrow> R" (fn prems => [
+ REPEAT (resolve_tac (prems@[surjective_pairing]) 1),
+ rtac (split_beta RS subst) 1,
+ rtac (hd prems) 1]);
+val splitE2' = prove_goal Prod.thy "\\<lbrakk>((\\<lambda>(x,y). P x y) z) w; \\<And>x y. \\<lbrakk>z = (x, y); (P x y) w\\<rbrakk> \\<Longrightarrow> R\\<rbrakk> \\<Longrightarrow> R" (fn prems => [
+ REPEAT (resolve_tac (prems@[surjective_pairing]) 1),
+ res_inst_tac [("P1","P")] (split_beta RS subst) 1,
+ rtac (hd prems) 1]);
+
+
+fun pair_tac s = res_inst_tac [("p",s)] PairE THEN' hyp_subst_tac;
+
+val BallE = prove_goal thy "\\<lbrakk>Ball A P; x \\<notin> A \\<Longrightarrow> Q; P x \\<Longrightarrow> Q \\<rbrakk> \\<Longrightarrow> Q"
+ (fn prems => [rtac ballE 1, resolve_tac prems 1,
+ eresolve_tac prems 1, eresolve_tac prems 1]);
+
+val set_cs2 = set_cs delrules [ballE] addSEs [BallE];
+
+Addsimps [Let_def];
+Addsimps [surjective_pairing RS sym];
+
+(* To HOL.ML *)
+
+val ex1_Eps_eq = prove_goal HOL.thy "\\<lbrakk> \\<exists>!x. P x; P y \\<rbrakk> \\<Longrightarrow> Eps P = y"
+ (fn prems => [
+ cut_facts_tac prems 1,
+ rtac select_equality 1,
+ atac 1,
+ etac ex1E 1,
+ etac all_dupE 1,
+ fast_tac HOL_cs 1]);
+
+
+val ball_insert = prove_goalw equalities.thy [Ball_def]
+ "Ball (insert x A) P = (P x \\<and> Ball A P)" (fn _ => [
+ fast_tac set_cs 1]);
+
+fun option_case_tac i = EVERY [
+ etac option_caseE i,
+ rotate_tac ~2 (i+1), asm_full_simp_tac HOL_basic_ss (i+1),
+ rotate_tac ~2 i , asm_full_simp_tac HOL_basic_ss i];
+
+val not_None_tac = EVERY' [dtac (not_None_eq RS iffD1),rotate_tac ~1,etac exE,
+ rotate_tac ~1,asm_full_simp_tac
+ (simpset() delsimps [split_paired_All,split_paired_Ex])];
+
+fun ex_ftac thm = EVERY' [forward_tac [thm], REPEAT o (etac exE), rotate_tac ~1,
+ asm_full_simp_tac (simpset() delsimps [split_paired_All,split_paired_Ex])];
+
+val optionE = prove_goal thy
+ "\\<lbrakk> opt = None \\<Longrightarrow> P; \\<And>x. opt = Some x \\<Longrightarrow> P \\<rbrakk> \\<Longrightarrow> P"
+ (fn prems => [
+ case_tac "opt = None" 1,
+ eresolve_tac prems 1,
+ not_None_tac 1,
+ eresolve_tac prems 1]);
+
+fun option_case_tac2 s i = EVERY [
+ exhaust_tac s i,
+ rotate_tac ~1 (i+1), asm_full_simp_tac HOL_basic_ss (i+1),
+ rotate_tac ~1 i , asm_full_simp_tac HOL_basic_ss i];
+
+val option_map_SomeD = prove_goalw thy [option_map_def]
+ "\\<And>x. option_map f x = Some y \\<Longrightarrow> \\<exists>z. x = Some z \\<and> f z = y" (K [
+ option_case_tac2 "x" 1,
+ Auto_tac]);
+
+
+section "unique";
+
+Goal "(x, y) : set l --> x : fst `` set l";
+by (induct_tac "l" 1);
+by Auto_tac;
+qed_spec_mp "fst_in_set_lemma";
+
+Goalw [unique_def] "unique []";
+by (Simp_tac 1);
+qed "unique_Nil";
+
+Goalw [unique_def] "unique ((x,y)#l) = (unique l \\<and> (!y. (x,y) ~: set l))";
+by (auto_tac (claset() addDs [fst_in_set_lemma],simpset()));
+qed "unique_Cons";
+
+Addsimps [unique_Nil,unique_Cons];
+
+Goal "unique l' ==> unique l --> \
+\ (!(x,y):set l. !(x',y'):set l'. x' ~= x) --> unique (l @ l')";
+by (induct_tac "l" 1);
+by (auto_tac (claset() addDs [fst_in_set_lemma],simpset()));
+qed_spec_mp "unique_append";
+
+Goal "unique l --> inj f --> unique (map (%(k,x). (f k, g k x)) l)";
+by (induct_tac "l" 1);
+by (auto_tac (claset() addDs [fst_in_set_lemma],simpset()));
+qed_spec_mp "unique_map_inj";
+
+Goal "\\<And>l. unique l \\<Longrightarrow> unique (map (split (\\<lambda>k. Pair (k, C))) l)";
+by(etac unique_map_inj 1);
+by(rtac injI 1);
+by Auto_tac;
+qed "unique_map_Pair";
+
+Goal "\\<lbrakk>M = N; \\<And>x. x\\<in>N \\<Longrightarrow> f x = g x\\<rbrakk> \\<Longrightarrow> f``M = g``N";
+by(rtac set_ext 1);
+by(simp_tac (simpset() addsimps image_def::premises()) 1);
+qed "image_cong";
+
+val split_Pair_eq = prove_goal Prod.thy
+"\\<And>X. ((x, y), z) \\<in> split (\\<lambda>x. Pair (x, Y)) `` A \\<Longrightarrow> y = Y" (K [
+ etac imageE 1,
+ split_all_tac 1,
+ auto_tac(claset_of Prod.thy,simpset_of Prod.thy)]);
+
+
+section "list_all2";
+
+val list_all2_lengthD = prove_goalw thy [list_all2_def]
+ "\\<And>X. list_all2 P as bs \\<Longrightarrow> length as = length bs" (K [Auto_tac]);
+
+val list_all2_Nil = prove_goalw thy [list_all2_def]
+ "list_all2 P [] []" (K [Auto_tac]);
+Addsimps[list_all2_Nil];
+AddSIs[list_all2_Nil];
+
+val list_all2_Cons = prove_goalw thy [list_all2_def]
+ "\\<And>X. list_all2 P (a#as) (b#bs) = (P a b \\<and> list_all2 P as bs)" (K [Auto_tac]);
+AddIffs[list_all2_Cons];
+
+
+(* More about Maps *)
+
+val override_SomeD = prove_goalw thy [override_def] "(s \\<oplus> t) k = Some x \\<Longrightarrow> \
+\ t k = Some x | t k = None \\<and> s k = Some x" (fn prems => [
+ cut_facts_tac prems 1,
+ case_tac "\\<exists>x. t k = Some x" 1,
+ etac exE 1,
+ rotate_tac ~1 1,
+ Asm_full_simp_tac 1,
+ asm_full_simp_tac (HOL_ss addsimps [not_None_eq RS sym]) 1,
+ rotate_tac ~1 1,
+ Asm_full_simp_tac 1]);
+
+Addsimps [fun_upd_same, fun_upd_other];
+
+Goal "unique xys \\<longrightarrow> (map_of xys x = Some y) = ((x,y) \\<in> set xys)";
+by(induct_tac "xys" 1);
+ by(Simp_tac 1);
+by(force_tac (claset(), simpset() addsimps [unique_Cons]) 1);
+qed_spec_mp "unique_map_of_Some_conv";
+
+val in_set_get = unique_map_of_Some_conv RS iffD2;
+val get_in_set = unique_map_of_Some_conv RS iffD1;
+
+Goal "(\\<forall>(x,y)\\<in>set l. P x y) \\<longrightarrow> (\\<forall>x. \\<forall>y. map_of l x = Some y \\<longrightarrow> P x y)";
+by(induct_tac "l" 1);
+by(ALLGOALS Simp_tac);
+by Safe_tac;
+by Auto_tac;
+bind_thm("Ball_set_table",result() RS mp);
+
+val table_mono = prove_goal thy
+"unique l' \\<longrightarrow> (\\<forall>xy. (xy)\\<in>set l \\<longrightarrow> (xy)\\<in>set l') \\<longrightarrow>\
+\ (\\<forall>k y. map_of l k = Some y \\<longrightarrow> map_of l' k = Some y)" (fn _ => [
+ induct_tac "l" 1,
+ Auto_tac,
+ fast_tac (HOL_cs addSIs [in_set_get]) 1])
+ RS mp RS mp RS spec RS spec RS mp;
+
+val table_map_Some' = prove_goal thy "map_of t k = Some (k', x) \\<longrightarrow> \
+\ map_of (map (\\<lambda>u. ((fst u, fst (snd u)), snd (snd u))) t) (k, k') = Some x" (K [
+ induct_tac "t" 1,
+ ALLGOALS Simp_tac,
+ case_tac1 "k = fst a" 1,
+ Auto_tac]) RS mp;
+val table_map_Some = prove_goal thy
+"map_of (map (\\<lambda>((k,k'),x). (k,(k',x))) t) k = Some (k',x) \\<longrightarrow> \
+\map_of t (k, k') = Some x" (K [
+ induct_tac "t" 1,
+ Auto_tac]) RS mp;
+
+
+val table_mapf_Some = prove_goal thy "\\<And>f. \\<forall>x y. f x = f y \\<longrightarrow> x = y \\<Longrightarrow> \
+\ map_of (map (\\<lambda>(k,x). (k,f x)) t) k = Some (f x) \\<longrightarrow> map_of t k = Some x" (K [
+ induct_tac "t" 1,
+ Auto_tac]) RS mp;
+val table_mapf_SomeD = prove_goal thy
+"map_of (map (\\<lambda>(k,x). (k, f x)) t) k = Some z \\<longrightarrow> (\\<exists>y. (k,y)\\<in>set t \\<and> z = f y)"(K [
+ induct_tac "t" 1,
+ Auto_tac]) RS mp;
+
+val table_mapf_Some2 = prove_goal thy
+"\\<And>k. map_of (map (\\<lambda>(k,x). (k,C,x)) t) k = Some (D,x) \\<Longrightarrow> C = D \\<and> map_of t k = Some x" (K [
+ forward_tac [table_mapf_SomeD] 1,
+ Auto_tac,
+ rtac table_mapf_Some 1,
+ atac 2,
+ Fast_tac 1]);
+
+val finite_map_of = rewrite_rule [dom_def] finite_dom_map_of;
+
+Goal
+"map_of (map (\\<lambda>(a,b). (a,f b)) xs) x = option_map f (map_of xs x)";
+by (induct_tac "xs" 1);
+auto();
+qed "map_of_map";
+
+