
diff -r d8a5435732cf -r 8325414a370a Sum.thy
--- a/Sum.thy	Fri Nov 25 13:35:32 1994 +0100
+++ b/Sum.thy	Fri Nov 25 14:21:14 1994 +0100
@@ -1,55 +1,51 @@
-(*  Title: 	HOL/sum
+(*  Title:      HOL/Sum.thy
     ID:         $Id$
-    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1992  University of Cambridge
 
-The disjoint sum of two types
+The disjoint sum of two types.
 *)
 
 Sum = Prod +
 
-types
-  ('a,'b) "+"		      (infixr 10)
-
-arities
-  "+"      :: (term,term)term
+(* type definition *)
 
 consts
-  Inl_Rep  :: "['a,'a,'b,bool] => bool"
-  Inr_Rep  :: "['b,'a,'b,bool] => bool"
-  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=>'c,'b=>'c, 'a+'b] =>'c"
+  Inl_Rep       :: "['a, 'a, 'b, bool] => bool"
+  Inr_Rep       :: "['b, 'a, 'b, bool] => bool"
+
+defs
+  Inl_Rep_def   "Inl_Rep == (%a. %x y p. x=a & p)"
+  Inr_Rep_def   "Inr_Rep == (%b. %x y p. y=b & ~p)"
+
+subtype (Sum)
+  ('a, 'b) "+"          (infixr 10)
+    = "{f. (? a. f = Inl_Rep(a::'a)) | (? b. f = Inr_Rep(b::'b))}"
+
+
+(* abstract constants and syntax *)
+
+consts
+  Inl           :: "'a => 'a + 'b"
+  Inr           :: "'b => 'a + 'b"
+  sum_case      :: "['a => 'c, 'b => 'c, 'a + 'b] => 'c"
 
   (*disjoint sum for sets; the operator + is overloaded with wrong type!*)
-  "plus"   :: "['a set, 'b set] => ('a+'b)set"      	(infixr 65)
-  Part     :: "['a set, 'b=>'a] => 'a set"
+  "plus"        :: "['a set, 'b set] => ('a + 'b) set"        (infixr 65)
+  Part          :: "['a set, 'b => '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(f,g,p) == @z.  (!x. p=Inl(x) --> z=f(x))	\
-\                                      & (!y. p=Inr(y) --> z=g(y))"
+defs
+  Inl_def       "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
+  Inr_def       "Inr == (%b. Abs_Sum(Inr_Rep(b)))"
+  sum_case_def  "sum_case(f, g, p) == @z.  (!x. p=Inl(x) --> z=f(x))      \
+\                                        & (!y. p=Inr(y) --> z=g(y))"
 
   sum_def       "A plus B == (Inl``A) Un (Inr``B)"
 
   (*for selecting out the components of a mutually recursive definition*)
-  Part_def	"Part(A,h) == A Int {x. ? z. x = h(z)}"
+  Part_def      "Part(A, h) == A Int {x. ? z. x = h(z)}"
 
 end




