src/HOLCF/Porder.thy
 author regensbu Thu, 29 Jun 1995 16:28:40 +0200 changeset 1168 74be52691d62 parent 297 5ef75ff3baeb child 1274 ea0668a1c0ba permissions -rw-r--r--
The curried version of HOLCF is now just called HOLCF. The old uncurried version is no longer supported

(*  Title: 	HOLCF/porder.thy
ID:         \$Id\$
Author: 	Franz Regensburger

Conservative extension of theory Porder0 by constant definitions

*)

Porder = Porder0 +

consts
"<|"	::	"['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"

defs

(* class definitions *)

is_ub		"S  <| x == ! y.y:S --> y<<x"
is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"

(* 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)"

rules

lub		"lub(S) = (@x. S <<| x)"

end