author  wenzelm 
Fri, 09 Nov 2001 00:09:47 +0100  
changeset 12114  a8e860c86252 
parent 12030  46d57d0290a2 
child 12338  de0f4a63baa5 
permissions  rwrr 
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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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