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(* Title: HOL/ex/insort.thy
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ID: $Id$
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Author: Tobias Nipkow
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Copyright 1994 TU Muenchen
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Insertion sort
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*)
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InSort = Sorting +
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consts
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ins :: "[['a,'a]=>bool, 'a, 'a list] => 'a list"
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insort :: "[['a,'a]=>bool, 'a list] => 'a list"
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rules
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ins_Nil "ins(f,x,[]) = [x]"
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ins_Cons "ins(f,x,Cons(y,ys)) = \
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\ if(f(x,y), Cons(x,Cons(y,ys)), Cons(y, ins(f,x,ys)))"
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insort_Nil "insort(f,[]) = []"
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insort_Cons "insort(f,Cons(x,xs)) = ins(f,x,insort(f,xs))"
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end
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