
diff -r 8fe3e66abf0c -r c22b85994e17 src/HOLCF/porder.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/porder.thy	Wed Jan 19 17:35:01 1994 +0100
@@ -0,0 +1,71 @@
+(*  Title: 	HOLCF/porder.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Definition of class porder (partial order)
+
+The prototype theory for this class is void.thy 
+
+*)
+
+Porder = Void +
+
+(* Introduction of new class. The witness is type void. *)
+
+classes po < term
+
+(* default type is still term ! *)
+(* void is the prototype in po *)
+
+arities void :: po
+
+consts	"<<"	::	"['a,'a::po] => bool"	(infixl 55)
+
+	"<|"	::	"['a set,'a::po] => bool"	(infixl 55)
+	"<<|"	::	"['a set,'a::po] => bool"	(infixl 55)
+	lub	::	"'a set => 'a::po"
+	is_tord	::	"'a::po set => bool"
+	is_chain ::	"(nat=>'a::po) => bool"
+	max_in_chain :: "[nat,nat=>'a::po]=>bool"
+	finite_chain :: "(nat=>'a::po)=>bool"
+
+rules
+
+(* class axioms: justification is theory Void *)
+
+refl_less	"x << x"	
+				(* witness refl_less_void    *)
+
+antisym_less	"[|x<<y ; y<<x |] ==> x = y"	
+				(* witness antisym_less_void *)
+
+trans_less	"[|x<<y ; y<<z |] ==> x<<z"
+				(* witness trans_less_void   *)
+
+(* instance of << for the prototype void *)
+
+inst_void_po	"(op <<)::[void,void]=>bool = less_void"
+
+(* class definitions *)
+
+is_ub		"S  <| x == ! y.y:S --> y<<x"
+is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
+
+lub		"lub(S) = (@x. S <<| x)"
+
+(* Arbitrary chains are total orders    *)                  
+is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
+
+
+(* Here we use countable chains and I prefer to code them as functions! *)
+is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
+
+
+(* finite chains, needed for monotony of continouous functions *)
+
+max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)" 
+
+finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
+
+end 




