src/HOLCF/Porder.thy
author slotosch
Mon, 17 Feb 1997 10:57:11 +0100
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Changes of HOLCF from Oscar Slotosch: 1. axclass instead of class * less instead of less_fun, less_cfun, less_sprod, less_cprod, less_ssum, less_up, less_lift * @x.!y.x<<y instead of UUU instead of UU_fun, UU_cfun, ... * no witness type void needed (eliminated Void.thy.Void.ML) * inst_<typ>_<class> derived as theorems 2. improved some proves on less_sprod and less_cprod * eliminated the following theorems Sprod1.ML: less_sprod1a Sprod1.ML: less_sprod1b Sprod1.ML: less_sprod2a Sprod1.ML: less_sprod2b Sprod1.ML: less_sprod2c Sprod2.ML: less_sprod3a Sprod2.ML: less_sprod3b Sprod2.ML: less_sprod4b Sprod2.ML: less_sprod4c Sprod3.ML: less_sprod5b Sprod3.ML: less_sprod5c Cprod1.ML: less_cprod1b Cprod1.ML: less_cprod2a Cprod1.ML: less_cprod2b Cprod1.ML: less_cprod2c Cprod2.ML: less_cprod3a Cprod2.ML: less_cprod3b 3. new classes: * cpo<po, * chfin<pcpo, * flat<pcpo, * derived: flat<chfin to do: show instances for lift 4. Data Type One * Used lift for the definition: one = unit lift * Changed the constant one into ONE 5. Data Type Tr * Used lift for the definition: tr = bool lift * adopted definitions of if,andalso,orelse,neg * only one theory Tr.thy,Tr.ML instead of Tr1.thy,Tr1.ML, Tr2.thy,Tr2.ML * reintroduced ceils for =TT,=FF 6. typedef * Using typedef instead of faking type definitions to do: change fapp, fabs from Cfun1 to Rep_Cfun, Abs_Cfun 7. adopted examples and domain construct to theses changes These changes eliminated all rules and arities from HOLCF
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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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