src/HOLCF/Tr1.thy
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(*  Title:      HOLCF/tr1.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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Introduce the domain of truth values tr = one ++ one
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The type is axiomatized as the least solution of a domain equation.
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The functor term that specifies the domain equation is: 
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  FT = <++,K_{one},K_{one}>
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For details see chapter 5 of:
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[Franz Regensburger] HOLCF: Eine konservative Erweiterung von HOL um LCF,
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                     Dissertation, Technische Universit"at M"unchen, 1994
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*)
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Tr1 = One +
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types tr 0
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arities tr :: pcpo
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consts
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        abs_tr          :: "one ++ one -> tr"
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        rep_tr          :: "tr -> one ++ one"
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        TT              :: "tr"
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        FF              :: "tr"
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        tr_when         :: "'c -> 'c -> tr -> 'c"
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rules
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  abs_tr_iso    "abs_tr`(rep_tr`u) = u"
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  rep_tr_iso    "rep_tr`(abs_tr`x) = x"
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defs
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  TT_def        "TT == abs_tr`(sinl`one)"
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  FF_def        "FF == abs_tr`(sinr`one)"
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  tr_when_def "tr_when == 
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        (LAM e1 e2 t. sswhen`(LAM x.e1)`(LAM y.e2)`(rep_tr`t))"
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end