author  slotosch 
Mon, 17 Feb 1997 10:57:11 +0100  
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child 3842  b55686a7b22c 
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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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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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 (symbols) 

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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 "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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(* 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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lub_def "lub S == (@x. S << x)" 
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end 
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