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")];