author | nipkow |
Sun, 22 Dec 2002 10:43:43 +0100 | |
changeset 13763 | f94b569cd610 |
parent 12338 | de0f4a63baa5 |
child 14981 | e73f8140af78 |
permissions | -rw-r--r-- |
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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 => '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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