src/HOL/Induct/PropLog.thy
author berghofe
Fri, 24 Jul 1998 13:19:38 +0200
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(*  Title:      HOL/ex/PropLog.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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Inductive definition of propositional logic.
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*)
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PropLog = Finite + Datatype +
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datatype
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    'a pl = false | var 'a ("#_" [1000]) | "->" ('a pl) ('a pl) (infixr 90)
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consts
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  thms :: 'a pl set => 'a pl set
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  "|-"  :: ['a pl set, 'a pl] => bool   (infixl 50)
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  "|="  :: ['a pl set, 'a pl] => bool   (infixl 50)
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  eval2 :: ['a pl, 'a set] => bool
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  eval  :: ['a set, 'a pl] => bool      ("_[_]" [100,0] 100)
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  hyps  :: ['a pl, 'a set] => 'a pl set
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translations
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  "H |- p" == "p : thms(H)"
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inductive "thms(H)"
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  intrs
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  H   "p:H ==> H |- p"
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  K   "H |- p->q->p"
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  S   "H |- (p->q->r) -> (p->q) -> p->r"
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  DN  "H |- ((p->false) -> false) -> p"
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  MP  "[| H |- p->q; H |- p |] ==> H |- q"
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defs
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  sat_def  "H |= p  ==  (!tt. (!q:H. tt[q]) --> tt[p])"
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  eval_def "tt[p] == eval2 p tt"
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primrec
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  "eval2(false) = (%x. False)"
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  "eval2(#v) = (%tt. v:tt)"
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  "eval2(p->q) = (%tt. eval2 p tt-->eval2 q tt)"
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primrec
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  "hyps(false) = (%tt.{})"
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  "hyps(#v) = (%tt.{if v:tt then #v else #v->false})"
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  "hyps(p->q) = (%tt. hyps p tt Un hyps q tt)"
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end
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