src/Sequents/LK.thy
 changeset 2073 fb0655539d05 child 3839 56544d061e1d
```--- /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)
+  "&"          :: [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")];```