Sum.thy

   Sum      :: "(['a,'b,bool] => bool)set"
   Rep_Sum  :: "'a + 'b => (['a,'b,bool] => bool)"
   Abs_Sum  :: "(['a,'b,bool] => bool) => 'a+'b"
   Inl	   :: "'a => 'a+'b"
   Inr	   :: "'b => 'a+'b"
-  sum_case :: "['a+'b, 'a=>'c,'b=>'c] =>'c"
+  sum_case :: "['a=>'c,'b=>'c, 'a+'b] =>'c"
+  Part     :: "['a set, 'a=>'a] => 'a set"
+
+translations
+  "case p of Inl(x) => a | Inr(y) => b" == "sum_case(%x.a, %y.b, p)"
 
 rules
   Inl_Rep_def	"Inl_Rep == (%a. %x y p. x=a & p)"
   Inr_Rep_def	"Inr_Rep == (%b. %x y p. y=b & ~p)"
+
   Sum_def "Sum == {f. (? a. f = Inl_Rep(a)) | (? b. f = Inr_Rep(b))}"
     (*faking a type definition...*)
   Rep_Sum 		"Rep_Sum(s): Sum"
   Rep_Sum_inverse 	"Abs_Sum(Rep_Sum(s)) = s"
   Abs_Sum_inverse 	"f: Sum ==> Rep_Sum(Abs_Sum(f)) = f"
+
     (*defining the abstract constants*)
   Inl_def  		"Inl == (%a. Abs_Sum(Inl_Rep(a)))"
   Inr_def 		"Inr == (%b. Abs_Sum(Inr_Rep(b)))"
-  sum_case_def	"sum_case == (%p f g. @z.  (!x. p=Inl(x) --> z=f(x))\
-\                                        & (!y. p=Inr(y) --> z=g(y)))"
+  sum_case_def	"sum_case(f,g,p) == @z.  (!x. p=Inl(x) --> z=f(x))	\
+\                                      & (!y. p=Inr(y) --> z=g(y))"
+
+  (*for selecting out the components of a mutually recursive definition*)
+  Part_def	"Part(A,h) == A Int {x. ? z. x = h(z)}"
+
 end