author | wenzelm |
Wed, 03 Feb 1999 17:28:02 +0100 | |
changeset 6208 | ea009b75b74e |
parent 3839 | 56544d061e1d |
child 6456 | 23602e214ebf |
permissions | -rw-r--r-- |
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New unified treatment of sequent calculi by Sara Kalvala
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(* Title: LK/lk.thy |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1993 University of Cambridge |
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Classical First-Order Sequent Calculus |
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There may be printing problems if a seqent is in expanded normal form |
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(eta-expanded, beta-contracted) |
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*) |
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LK = Sequents + |
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consts |
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Trueprop :: "two_seqi" |
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"@Trueprop" :: "two_seqe" ("((_)/ |- (_))" [6,6] 5) |
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True,False :: o |
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"=" :: ['a,'a] => o (infixl 50) |
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Not :: o => o ("~ _" [40] 40) |
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"&" :: [o,o] => o (infixr 35) |
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"|" :: [o,o] => o (infixr 30) |
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"-->","<->" :: [o,o] => o (infixr 25) |
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The :: ('a => o) => 'a (binder "THE " 10) |
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All :: ('a => o) => o (binder "ALL " 10) |
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Ex :: ('a => o) => o (binder "EX " 10) |
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rules |
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(*Structural rules*) |
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basic "$H, P, $G |- $E, P, $F" |
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thinR "$H |- $E, $F ==> $H |- $E, P, $F" |
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thinL "$H, $G |- $E ==> $H, P, $G |- $E" |
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cut "[| $H |- $E, P; $H, P |- $E |] ==> $H |- $E" |
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(*Propositional rules*) |
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conjR "[| $H|- $E, P, $F; $H|- $E, Q, $F |] ==> $H|- $E, P&Q, $F" |
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conjL "$H, P, Q, $G |- $E ==> $H, P & Q, $G |- $E" |
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disjR "$H |- $E, P, Q, $F ==> $H |- $E, P|Q, $F" |
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disjL "[| $H, P, $G |- $E; $H, Q, $G |- $E |] ==> $H, P|Q, $G |- $E" |
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impR "$H, P |- $E, Q, $F ==> $H |- $E, P-->Q, $F" |
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impL "[| $H,$G |- $E,P; $H, Q, $G |- $E |] ==> $H, P-->Q, $G |- $E" |
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notR "$H, P |- $E, $F ==> $H |- $E, ~P, $F" |
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notL "$H, $G |- $E, P ==> $H, ~P, $G |- $E" |
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FalseL "$H, False, $G |- $E" |
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True_def "True == False-->False" |
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iff_def "P<->Q == (P-->Q) & (Q-->P)" |
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(*Quantifiers*) |
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allR "(!!x.$H |- $E, P(x), $F) ==> $H |- $E, ALL x. P(x), $F" |
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allL "$H, P(x), $G, ALL x. P(x) |- $E ==> $H, ALL x. P(x), $G |- $E" |
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exR "$H |- $E, P(x), $F, EX x. P(x) ==> $H |- $E, EX x. P(x), $F" |
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exL "(!!x.$H, P(x), $G |- $E) ==> $H, EX x. P(x), $G |- $E" |
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(*Equality*) |
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refl "$H |- $E, a=a, $F" |
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sym "$H |- $E, a=b, $F ==> $H |- $E, b=a, $F" |
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trans "[| $H|- $E, a=b, $F; $H|- $E, b=c, $F |] ==> $H|- $E, a=c, $F" |
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(*Descriptions*) |
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The "[| $H |- $E, P(a), $F; !!x.$H, P(x) |- $E, x=a, $F |] ==> |
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$H |- $E, P(THE x. P(x)), $F" |
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end |
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ML |
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val parse_translation = [("@Trueprop",Sequents.two_seq_tr "Trueprop")]; |
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val print_translation = [("Trueprop",Sequents.two_seq_tr' "@Trueprop")]; |