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(* Title: HOL/Lex/MaxChop.thy
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ID: $Id$
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Author: Tobias Nipkow
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Copyright 1998 TUM
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*)
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6481
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MaxChop = MaxPrefix + Recdef +
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types 'a chopper = "'a list => 'a list list * 'a list"
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constdefs
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is_maxchopper :: ('a list => bool) => 'a chopper => bool
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"is_maxchopper P chopper ==
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!xs zs yss.
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(chopper(xs) = (yss,zs)) =
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(xs = concat yss @ zs & (!ys : set yss. ys ~= []) &
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(case yss of
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[] => is_maxpref P [] xs
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| us#uss => is_maxpref P us xs & chopper(concat(uss)@zs) = (uss,zs)))"
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constdefs
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reducing :: "'a splitter => bool"
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"reducing splitf ==
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!xs ys zs. splitf xs = (ys,zs) & ys ~= [] --> length zs < length xs"
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consts
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chopr :: "'a splitter * 'a list => 'a list list * 'a list"
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recdef chopr "measure (length o snd)"
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"chopr (splitf,xs) = (if reducing splitf
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then let pp = splitf xs
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in if fst(pp)=[] then ([],xs)
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else let qq = chopr (splitf,snd pp)
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in (fst pp # fst qq,snd qq)
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else arbitrary)"
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constdefs
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chop :: 'a splitter => 'a chopper
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"chop splitf xs == chopr(splitf,xs)"
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end
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