diff -r 6ac12b9478d5 -r fb0655539d05 src/Sequents/LK.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Sequents/LK.thy Wed Oct 09 13:32:33 1996 +0200 @@ -0,0 +1,84 @@ +(* Title: LK/lk.thy + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1993 University of Cambridge + +Classical First-Order Sequent Calculus + +There may be printing problems if a seqent is in expanded normal form + (eta-expanded, beta-contracted) +*) + +LK = Sequents + + + +consts + + Trueprop :: "two_seqi" + "@Trueprop" :: "two_seqe" ("((_)/ |- (_))" [6,6] 5) + + + True,False :: o + "=" :: ['a,'a] => o (infixl 50) + Not :: o => o ("~ _" [40] 40) + "&" :: [o,o] => o (infixr 35) + "|" :: [o,o] => o (infixr 30) + "-->","<->" :: [o,o] => o (infixr 25) + The :: ('a => o) => 'a (binder "THE " 10) + All :: ('a => o) => o (binder "ALL " 10) + Ex :: ('a => o) => o (binder "EX " 10) + +rules + (*Structural rules*) + + basic "$H, P, $G |- $E, P, $F" + + thinR "$H |- $E, $F ==> $H |- $E, P, $F" + thinL "$H, $G |- $E ==> $H, P, $G |- $E" + + cut "[| $H |- $E, P; $H, P |- $E |] ==> $H |- $E" + + (*Propositional rules*) + + conjR "[| $H|- $E, P, $F; $H|- $E, Q, $F |] ==> $H|- $E, P&Q, $F" + conjL "$H, P, Q, $G |- $E ==> $H, P & Q, $G |- $E" + + disjR "$H |- $E, P, Q, $F ==> $H |- $E, P|Q, $F" + disjL "[| $H, P, $G |- $E; $H, Q, $G |- $E |] ==> $H, P|Q, $G |- $E" + + impR "$H, P |- $E, Q, $F ==> $H |- $E, P-->Q, $F" + impL "[| $H,$G |- $E,P; $H, Q, $G |- $E |] ==> $H, P-->Q, $G |- $E" + + notR "$H, P |- $E, $F ==> $H |- $E, ~P, $F" + notL "$H, $G |- $E, P ==> $H, ~P, $G |- $E" + + FalseL "$H, False, $G |- $E" + + True_def "True == False-->False" + iff_def "P<->Q == (P-->Q) & (Q-->P)" + + (*Quantifiers*) + + allR "(!!x.$H |- $E, P(x), $F) ==> $H |- $E, ALL x.P(x), $F" + allL "$H, P(x), $G, ALL x.P(x) |- $E ==> $H, ALL x.P(x), $G |- $E" + + exR "$H |- $E, P(x), $F, EX x.P(x) ==> $H |- $E, EX x.P(x), $F" + exL "(!!x.$H, P(x), $G |- $E) ==> $H, EX x.P(x), $G |- $E" + + (*Equality*) + + refl "$H |- $E, a=a, $F" + sym "$H |- $E, a=b, $F ==> $H |- $E, b=a, $F" + trans "[| $H|- $E, a=b, $F; $H|- $E, b=c, $F |] ==> $H|- $E, a=c, $F" + + + (*Descriptions*) + + The "[| $H |- $E, P(a), $F; !!x.$H, P(x) |- $E, x=a, $F |] ==> + $H |- $E, P(THE x.P(x)), $F" +end + + ML + +val parse_translation = [("@Trueprop",Sequents.two_seq_tr "Trueprop")]; +val print_translation = [("Trueprop",Sequents.two_seq_tr' "@Trueprop")];