src/HOLCF/Porder.thy
author wenzelm
Fri, 09 Nov 2001 00:09:47 +0100
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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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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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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        tord ::      "'a::po set => bool"
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        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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syntax
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  "@LUB"	:: "(('b::term) => 'a) => 'a"	(binder "LUB " 10)
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translations
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  "LUB x. t"	== "lub(range(%x. t))"
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syntax (xsymbols)
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  "LUB "	:: "[idts, 'a] => 'a"		("(3\\<Squnion>_./ _)"[0,10] 10)
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defs
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(* class definitions *)
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is_ub_def       "S  <| x == ! y. y:S --> y<<x"
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is_lub_def      "S <<| x == S <| x & (!u. S <| u  --> x << u)"
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(* Arbitrary chains are total orders    *)                  
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tord_def     "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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chain_def        "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 == chain(C) & (? i. max_in_chain i C)"
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lub_def          "lub S == (@x. S <<| x)"
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end 
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