--- a/Sum.thy Thu Aug 18 11:40:54 1994 +0200
+++ b/Sum.thy Thu Aug 18 11:43:40 1994 +0200
@@ -22,19 +22,29 @@
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