--- 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
Copyright 1993 University of Cambridge
-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] 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")];