src/HOLCF/porder.thy
author paulson
Mon Dec 07 18:26:25 1998 +0100 (1998-12-07)
changeset 6019 0e55c2fb2ebb
parent 297 5ef75ff3baeb
permissions -rw-r--r--
tidying
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(*  Title: 	HOLCF/porder.thy
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    ID:         $Id$
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    Author: 	Franz Regensburger
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    Copyright   1993 Technische Universitaet Muenchen
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Conservative extension of theory Porder0 by constant definitions 
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*)
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Porder = Porder0 +
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consts	
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	"<|"	::	"['a set,'a::po] => bool"	(infixl 55)
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	"<<|"	::	"['a set,'a::po] => bool"	(infixl 55)
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	lub	::	"'a set => 'a::po"
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	is_tord	::	"'a::po set => bool"
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	is_chain ::	"(nat=>'a::po) => bool"
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	max_in_chain :: "[nat,nat=>'a::po]=>bool"
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	finite_chain :: "(nat=>'a::po)=>bool"
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rules
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(* class definitions *)
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is_ub		"S  <| x == ! y.y:S --> y<<x"
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is_lub		"S <<| x == S <| x & (! u. S <| u  --> x << u)"
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lub		"lub(S) = (@x. S <<| x)"
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(* Arbitrary chains are total orders    *)                  
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is_tord		"is_tord(S) == ! x y. x:S & y:S --> (x<<y | y<<x)"
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(* Here we use countable chains and I prefer to code them as functions! *)
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is_chain	"is_chain(F) == (! i.F(i) << F(Suc(i)))"
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(* finite chains, needed for monotony of continouous functions *)
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max_in_chain_def "max_in_chain(i,C) == ! j. i <= j --> C(i) = C(j)" 
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finite_chain_def "finite_chain(C) == is_chain(C) & (? i. max_in_chain(i,C))"
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end