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")];