src/Sequents/LK.thy
 changeset 7094 6f18ae72a90e parent 6456 23602e214ebf child 7117 37eccadf6b8a
```--- a/src/Sequents/LK.thy	Tue Jul 27 18:52:23 1999 +0200
+++ b/src/Sequents/LK.thy	Tue Jul 27 18:52:48 1999 +0200
@@ -1,89 +1,19 @@
-(*  Title:      LK/lk.thy
+(*  Title:      LK/LK
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

-Classical First-Order Sequent Calculus
+Axiom to express monotonicity (a variant of the deduction theorem).  Makes the
+link between |- and ==>, needed for instance to prove imp_cong.

-There may be printing problems if a seqent is in expanded normal form
-	(eta-expanded, beta-contracted)
+CANNOT be added to LK0.thy because modal logic is built upon it, and
+various modal rules would become inconsistent.
*)

-LK = Sequents +
-
-classes
-  term < logic
-
-default
-  term
-
-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)
+LK = LK0 +

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*)
+  monotonic  "(\$H |- P ==> \$H |- Q) ==> \$H, P |- Q"

-  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")];```