author | paulson |
Thu, 11 Nov 1999 10:25:17 +0100 | |
changeset 8005 | b64d86018785 |
parent 7961 | 422ac6888c7f |
child 8160 | 837a6b515005 |
permissions | -rw-r--r-- |
3981 | 1 |
(* Title: HOL/Map.ML |
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ID: $Id$ |
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Author: Tobias Nipkow |
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Copyright 1997 TU Muenchen |
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Map lemmas |
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*) |
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section "empty"; |
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Goalw [empty_def] "empty k = None"; |
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by (Simp_tac 1); |
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qed "empty_def2"; |
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Addsimps [empty_def2]; |
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section "map_upd"; |
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qed_goal "map_upd_triv" thy "!!X. t k = Some x ==> t(k|->x) = t" |
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(K [rtac ext 1, Asm_simp_tac 1]); |
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(*Addsimps [map_upd_triv];*) |
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section "map_upds"; |
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Goal "a ~: set as --> (!m bs. (m(a|->b)(as[|->]bs)) = (m(as[|->]bs)(a|->b)))"; |
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by (induct_tac "as" 1); |
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by (auto_tac (claset(), simpset() delsimps[fun_upd_apply])); |
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by (REPEAT(dtac spec 1)); |
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by (rotate_tac ~1 1); |
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by (etac subst 1); |
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by (etac (fun_upd_twist RS subst) 1); |
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by (rtac refl 1); |
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qed_spec_mp "map_upds_twist"; |
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Addsimps [map_upds_twist]; |
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section "chg_map"; |
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qed_goalw "chg_map_new" thy [chg_map_def] |
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"!!s. m a = None ==> chg_map f a m = m" (K [Auto_tac]); |
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qed_goalw "chg_map_upd" thy [chg_map_def] |
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"!!s. m a = Some b ==> chg_map f a m = m(a|->f b)" (K [Auto_tac]); |
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Addsimps[chg_map_new, chg_map_upd]; |
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4526
6be35399125a
added update_same, update_other, update_triv, and map_of_SomeD
oheimb
parents:
4423
diff
changeset
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section "map_of"; |
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Goal "map_of xs k = Some y --> (k,y):set xs"; |
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by (induct_tac "xs" 1); |
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by (Simp_tac 1); |
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by (split_all_tac 1); |
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by (Asm_simp_tac 1); |
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qed_spec_mp "map_of_SomeD"; |
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Goal "[| map_of xs k = Some z; P z |] ==> map_of [(k,z):xs . P z] k = Some z"; |
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by (rtac mp 1); |
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by (assume_tac 2); |
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by (etac thin_rl 1); |
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by (induct_tac "xs" 1); |
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by Auto_tac; |
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qed "map_of_filter_in"; |
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section "option_map related"; |
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qed_goal "option_map_o_empty" thy |
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"option_map f o empty = empty" (K [rtac ext 1, Simp_tac 1]); |
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qed_goal "option_map_o_map_upd" thy |
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"option_map f o m(a|->b) = (option_map f o m)(a|->f b)" |
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(K [rtac ext 1, Simp_tac 1]); |
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Addsimps[option_map_o_empty, option_map_o_map_upd]; |
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section "++"; |
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Goalw [override_def] "m ++ empty = m"; |
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by (Simp_tac 1); |
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qed "override_empty"; |
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Addsimps [override_empty]; |
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Goalw [override_def] "empty ++ m = m"; |
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by (Simp_tac 1); |
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by (rtac ext 1); |
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by (split_tac [option.split] 1); |
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by (Simp_tac 1); |
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qed "empty_override"; |
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Addsimps [empty_override]; |
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Goalw [override_def] |
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"((m ++ n) k = Some x) = (n k = Some x | n k = None & m k = Some x)"; |
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by (simp_tac (simpset() addsplits [option.split]) 1); |
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qed_spec_mp "override_Some_iff"; |
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bind_thm ("override_SomeD", standard(override_Some_iff RS iffD1)); |
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AddSDs[override_SomeD]; |
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Goal "!!xx. n k = Some xx ==> (m ++ n) k = Some xx"; |
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by (stac override_Some_iff 1); |
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by (Fast_tac 1); |
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qed "override_find_right"; |
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Addsimps[override_find_right]; |
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Goalw [override_def] "((m ++ n) k = None) = (n k = None & m k = None)"; |
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by (simp_tac (simpset() addsplits [option.split]) 1); |
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qed "override_None"; |
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AddIffs [override_None]; |
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Goalw [override_def] "map_of ys ++ map_of xs = map_of (xs@ys)"; |
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by (rtac sym 1); |
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by (induct_tac "xs" 1); |
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by (Simp_tac 1); |
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by (rtac ext 1); |
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by (asm_simp_tac (simpset() addsplits [option.split]) 1); |
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qed "map_of_override"; |
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Addsimps [map_of_override]; |
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section "dom"; |
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Goalw [dom_def] "dom empty = {}"; |
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by (Simp_tac 1); |
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qed "dom_empty"; |
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Addsimps [dom_empty]; |
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Goalw [dom_def] "dom(m(a|->b)) = insert a (dom m)"; |
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by (Simp_tac 1); |
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by (Blast_tac 1); |
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qed "dom_map_upd"; |
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Addsimps [dom_map_upd]; |
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qed_goalw "finite_dom_map_of" Map.thy [dom_def] "finite (dom (map_of l))" (K[ |
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induct_tac "l" 1, |
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ALLGOALS Simp_tac, |
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stac (insert_Collect RS sym) 1, |
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Asm_full_simp_tac 1]); |
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Goalw [dom_def] "dom(m++n) = dom n Un dom m"; |
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by (Simp_tac 1); |
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by (Blast_tac 1); |
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qed "dom_override"; |
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Addsimps [dom_override]; |
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section "ran"; |
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Goalw [ran_def] "ran empty = {}"; |
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by (Simp_tac 1); |
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qed "ran_empty"; |
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Addsimps [ran_empty]; |
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Goalw [ran_def] "m a = None ==> ran(m(a|->b)) = insert b (ran m)"; |
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by Auto_tac; |
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by (subgoal_tac "~(aa = a)" 1); |
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by Auto_tac; |
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qed "ran_map_upd"; |
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Addsimps [ran_map_upd]; |