author | regensbu |
Thu, 29 Jun 1995 16:28:40 +0200 | |
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parent 1150 | 66512c9e6bd6 |
child 1274 | ea0668a1c0ba |
permissions | -rw-r--r-- |
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(* Title: HOLCF/ssum0.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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Strict sum |
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*) |
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Ssum0 = Cfun3 + |
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(* new type for strict sum *) |
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types "++" 2 (infixr 10) |
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arities "++" :: (pcpo,pcpo)term |
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consts |
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Ssum :: "(['a,'b,bool]=>bool)set" |
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Sinl_Rep :: "['a,'a,'b,bool]=>bool" |
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Sinr_Rep :: "['b,'a,'b,bool]=>bool" |
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Rep_Ssum :: "('a ++ 'b) => (['a,'b,bool]=>bool)" |
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Abs_Ssum :: "(['a,'b,bool]=>bool) => ('a ++ 'b)" |
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Isinl :: "'a => ('a ++ 'b)" |
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Isinr :: "'b => ('a ++ 'b)" |
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Iwhen :: "('a->'c)=>('b->'c)=>('a ++ 'b)=> 'c" |
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defs |
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Sinl_Rep_def "Sinl_Rep == (%a.%x y p. |
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(a~=UU --> x=a & p))" |
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Sinr_Rep_def "Sinr_Rep == (%b.%x y p. |
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(b~=UU --> y=b & ~p))" |
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Ssum_def "Ssum =={f.(? a.f=Sinl_Rep(a))|(? b.f=Sinr_Rep(b))}" |
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rules |
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(*faking a type definition... *) |
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(* "++" is isomorphic to Ssum *) |
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Rep_Ssum "Rep_Ssum(p):Ssum" |
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Rep_Ssum_inverse "Abs_Ssum(Rep_Ssum(p)) = p" |
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Abs_Ssum_inverse "f:Ssum ==> Rep_Ssum(Abs_Ssum(f)) = f" |
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defs (*defining the abstract constants*) |
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Isinl_def "Isinl(a) == Abs_Ssum(Sinl_Rep(a))" |
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Isinr_def "Isinr(b) == Abs_Ssum(Sinr_Rep(b))" |
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Iwhen_def "Iwhen(f)(g)(s) == @z. |
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(s=Isinl(UU) --> z=UU) |
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&(!a. a~=UU & s=Isinl(a) --> z=f`a) |
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&(!b. b~=UU & s=Isinr(b) --> z=g`b)" |
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end |
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