src/HOL/Option.ML
author oheimb
Wed, 09 Sep 1998 17:23:42 +0200
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permissions -rw-r--r--
AddIffs[not_None_eq]; made wrapper ospec really safe
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(*  Title:      Option.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow
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    Copyright   1996  TU Muenchen
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Derived rules
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*)
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open Option;
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qed_goal "not_None_eq" thy "(x ~= None) = (? y. x = Some y)"
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	(K [induct_tac "x" 1, Auto_tac]);
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AddIffs[not_None_eq];
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section "case analysis in premises";
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val optionE = prove_goal thy 
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	"[| opt = None ==> P;  !!x. opt = Some x ==> P |] ==> P" (fn prems => [
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	case_tac "opt = None" 1,
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	 eresolve_tac prems 1,
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	dtac (not_None_eq RS iffD1) 1,
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	etac exE 1,
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	eresolve_tac prems 1]);
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fun optionE_tac s = res_inst_tac [("opt",s)] optionE THEN_ALL_NEW hyp_subst_tac;
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qed_goal "option_caseE" thy "[|case x of None => P | Some y => Q y; \
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\                  [|x = None;   P  |] ==> R; \
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\             !!y. [|x = Some y; Q y|] ==> R|] ==> R" (fn prems => [
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	cut_facts_tac prems 1,
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	res_inst_tac [("opt","x")] optionE 1,
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	 forward_tac prems 1,
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	  forward_tac prems 3, 
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	   Auto_tac]);
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fun option_case_tac i = EVERY [
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	etac option_caseE i,
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	 hyp_subst_tac (i+1),
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	hyp_subst_tac i];
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section "the";
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qed_goalw "the_Some" thy [the_def]
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	"the (Some x) = x" (K [Simp_tac 1]);
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Addsimps [the_Some];
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section "option_map";
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qed_goalw "option_map_None" thy [option_map_def] 
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	"option_map f None = None" (K [Simp_tac 1]);
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qed_goalw "option_map_Some" thy [option_map_def] 
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	"option_map f (Some x) = Some (f x)" (K [Simp_tac 1]);
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Addsimps [option_map_None, option_map_Some];
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val option_map_eq_Some = prove_goalw thy [option_map_def]
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	"(option_map f xo = Some y) = (? z. xo = Some z & f z = y)" 
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 (K [asm_full_simp_tac (simpset() addsplits [option.split]) 1]);
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AddIffs[option_map_eq_Some];
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section "o2s";
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qed_goal "ospec" thy 
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	"!!x. [| !x:o2s A. P x; A = Some x |] ==> P x" (K [Auto_tac]);
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claset_ref() := claset() addSaltern ("ospec", 
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				dmatch_tac [ospec] THEN' eq_assume_tac);
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val elem_o2s = prove_goal thy "!!X. x : o2s xo = (xo = Some x)"
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 (K [optionE_tac "xo" 1, Auto_tac]);
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AddIffs [elem_o2s];
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val o2s_empty_eq = prove_goal thy "(o2s xo = {}) = (xo = None)"
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 (K [optionE_tac "xo" 1, Auto_tac]);
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Addsimps [o2s_empty_eq];
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