added the, option_map, and case analysis theorems
authoroheimb
Tue, 04 Nov 1997 20:48:38 +0100
changeset 4133 0a08c2b9b1ed
parent 4132 daff3c9987cc
child 4134 5c6cb2a25816
added the, option_map, and case analysis theorems
src/HOL/Option.ML
src/HOL/Option.thy
--- a/src/HOL/Option.ML	Tue Nov 04 20:47:38 1997 +0100
+++ b/src/HOL/Option.ML	Tue Nov 04 20:48:38 1997 +0100
@@ -5,3 +5,55 @@
 
 Derived rules
 *)
+open Option;
+
+qed_goal "not_None_eq" thy "(x ~= None) = (? y. x = Some y)"
+	(K [option.induct_tac "x" 1, Auto_tac()]);
+
+section "case analysis in premises";
+
+val optionE = prove_goal thy 
+	"[| opt = None ==> P;  !!x. opt = Some x ==> P |] ==> P" (fn prems => [
+	case_tac "opt = None" 1,
+	 eresolve_tac prems 1,
+	dtac (not_None_eq RS iffD1) 1,
+	etac exE 1,
+	eresolve_tac prems 1]);
+fun optionE_tac s i = EVERY [
+	res_inst_tac [("opt",s)] optionE i,
+	 hyp_subst_tac (i+1),
+	hyp_subst_tac i];
+
+qed_goal "option_caseE" thy "[|case x of None => P | Some y => Q y; \
+\                  [|x = None;   P  |] ==> R; \
+\             !!y. [|x = Some y; Q y|] ==> R|] ==> R" (fn prems => [
+	cut_facts_tac prems 1,
+	res_inst_tac [("opt","x")] optionE 1,
+	 forward_tac prems 1,
+	  forward_tac prems 3, 
+	   Auto_tac()]);
+fun option_case_tac i = EVERY [
+	etac option_caseE i,
+	 hyp_subst_tac (i+1),
+	hyp_subst_tac i];
+
+
+section "the";
+
+qed_goalw "the_Some" thy [the_def]
+	"the (Some x) = x" (K [Simp_tac 1]);
+Addsimps [the_Some];
+
+
+section "option_map";
+
+qed_goalw "option_map_None" thy [option_map_def] 
+	"option_map f None = None" (K [Simp_tac 1]);
+qed_goalw "option_map_Some" thy [option_map_def] 
+	"option_map f (Some x) = Some (f x)" (K [Simp_tac 1]);
+Addsimps [option_map_None, option_map_Some];
+
+val option_map_SomeD = prove_goalw thy [option_map_def]
+	"!!x. option_map f x = Some y ==> ? z. x = Some z & f z = y" (K [
+	optionE_tac "x" 1,
+	 Auto_tac()]);
--- a/src/HOL/Option.thy	Tue Nov 04 20:47:38 1997 +0100
+++ b/src/HOL/Option.thy	Tue Nov 04 20:48:38 1997 +0100
@@ -7,5 +7,15 @@
 *)
 
 Option = Arith +
+
 datatype 'a option = None | Some 'a
+
+constdefs
+
+  the		:: "'a option => 'a"
+ "the  %y. case y of None => arbitrary | Some x => x"
+
+  option_map	:: "('a => 'b) => ('a option => 'b option)"
+ "option_map  %f y. case y of None => None | Some x => Some (f x)"
+
 end