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(* Title: HOL/sum
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1992 University of Cambridge
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The disjoint sum of two types
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*)
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Sum = Prod +
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51
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types
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('a,'b) "+" (infixl 10)
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arities
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"+" :: (term,term)term
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consts
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Inl_Rep :: "['a,'a,'b,bool] => bool"
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Inr_Rep :: "['b,'a,'b,bool] => bool"
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Sum :: "(['a,'b,bool] => bool)set"
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Rep_Sum :: "'a + 'b => (['a,'b,bool] => bool)"
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Abs_Sum :: "(['a,'b,bool] => bool) => 'a+'b"
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Inl :: "'a => 'a+'b"
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Inr :: "'b => 'a+'b"
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sum_case :: "['a+'b, 'a=>'c,'b=>'c] =>'c"
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rules
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Inl_Rep_def "Inl_Rep == (%a. %x y p. x=a & p)"
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Inr_Rep_def "Inr_Rep == (%b. %x y p. y=b & ~p)"
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Sum_def "Sum == {f. (? a. f = Inl_Rep(a)) | (? b. f = Inr_Rep(b))}"
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(*faking a type definition...*)
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Rep_Sum "Rep_Sum(s): Sum"
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Rep_Sum_inverse "Abs_Sum(Rep_Sum(s)) = s"
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Abs_Sum_inverse "f: Sum ==> Rep_Sum(Abs_Sum(f)) = f"
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(*defining the abstract constants*)
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Inl_def "Inl == (%a. Abs_Sum(Inl_Rep(a)))"
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Inr_def "Inr == (%b. Abs_Sum(Inr_Rep(b)))"
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sum_case_def "sum_case == (%p f g. @z. (!x. p=Inl(x) --> z=f(x))\
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\ & (!y. p=Inr(y) --> z=g(y)))"
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end
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