--- a/src/Sequents/S43.thy Sun Sep 18 14:25:48 2005 +0200
+++ b/src/Sequents/S43.thy Sun Sep 18 15:20:08 2005 +0200
@@ -1,4 +1,4 @@
-(* Title: Modal/S43
+(* Title: Modal/S43.thy
ID: $Id$
Author: Martin Coen
Copyright 1991 University of Cambridge
@@ -6,7 +6,9 @@
This implements Rajeev Gore's sequent calculus for S43.
*)
-S43 = Modal0 +
+theory S43
+imports Modal0
+begin
consts
S43pi :: "[seq'=>seq', seq'=>seq', seq'=>seq',
@@ -15,17 +17,34 @@
"@S43pi" :: "[seq, seq, seq, seq, seq, seq] => prop"
("S43pi((_);(_);(_);(_);(_);(_))" [] 5)
-rules
+ML {*
+ val S43pi = "S43pi";
+ val SS43pi = "@S43pi";
+
+ val tr = seq_tr;
+ val tr' = seq_tr';
+
+ fun s43pi_tr[s1,s2,s3,s4,s5,s6]=
+ Const(S43pi,dummyT)$tr s1$tr s2$tr s3$tr s4$tr s5$tr s6;
+ fun s43pi_tr'[s1,s2,s3,s4,s5,s6] =
+ Const(SS43pi,dummyT)$tr' s1$tr' s2$tr' s3$tr' s4$tr' s5$tr' s6;
+
+*}
+
+parse_translation {* [(SS43pi,s43pi_tr)] *}
+print_translation {* [(S43pi,s43pi_tr')] *}
+
+axioms
(* Definition of the star operation using a set of Horn clauses *)
(* For system S43: gamma * == {[]P | []P : gamma} *)
(* delta * == {<>P | <>P : delta} *)
- lstar0 "|L>"
- lstar1 "$G |L> $H ==> []P, $G |L> []P, $H"
- lstar2 "$G |L> $H ==> P, $G |L> $H"
- rstar0 "|R>"
- rstar1 "$G |R> $H ==> <>P, $G |R> <>P, $H"
- rstar2 "$G |R> $H ==> P, $G |R> $H"
+ lstar0: "|L>"
+ lstar1: "$G |L> $H ==> []P, $G |L> []P, $H"
+ lstar2: "$G |L> $H ==> P, $G |L> $H"
+ rstar0: "|R>"
+ rstar1: "$G |R> $H ==> <>P, $G |R> <>P, $H"
+ rstar2: "$G |R> $H ==> P, $G |R> $H"
(* Set of Horn clauses to generate the antecedents for the S43 pi rule *)
(* ie *)
@@ -37,43 +56,27 @@
(* and Sj == <>P1...<>Pk, $G * |- $H *, []Q1...[]Qj-1,[]Qj+1...[]Qm,Qj *)
(* and 1<=i<=k and k<j<=k+m *)
- S43pi0 "S43pi $L;; $R;; $Lbox; $Rdia"
- S43pi1
- "[| (S43pi <>P,$L'; $L;; $R; $Lbox;$Rdia); $L',P,$L,$Lbox |- $R,$Rdia |] ==>
+ S43pi0: "S43pi $L;; $R;; $Lbox; $Rdia"
+ S43pi1:
+ "[| (S43pi <>P,$L'; $L;; $R; $Lbox;$Rdia); $L',P,$L,$Lbox |- $R,$Rdia |] ==>
S43pi $L'; <>P,$L;; $R; $Lbox;$Rdia"
- S43pi2
- "[| (S43pi $L';; []P,$R'; $R; $Lbox;$Rdia); $L',$Lbox |- $R',P,$R,$Rdia |] ==>
+ S43pi2:
+ "[| (S43pi $L';; []P,$R'; $R; $Lbox;$Rdia); $L',$Lbox |- $R',P,$R,$Rdia |] ==>
S43pi $L';; $R'; []P,$R; $Lbox;$Rdia"
(* Rules for [] and <> for S43 *)
- boxL "$E, P, $F, []P |- $G ==> $E, []P, $F |- $G"
- diaR "$E |- $F, P, $G, <>P ==> $E |- $F, <>P, $G"
- pi1
- "[| $L1,<>P,$L2 |L> $Lbox; $L1,<>P,$L2 |R> $Ldia; $R |L> $Rbox; $R |R> $Rdia;
- S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==>
+ boxL: "$E, P, $F, []P |- $G ==> $E, []P, $F |- $G"
+ diaR: "$E |- $F, P, $G, <>P ==> $E |- $F, <>P, $G"
+ pi1:
+ "[| $L1,<>P,$L2 |L> $Lbox; $L1,<>P,$L2 |R> $Ldia; $R |L> $Rbox; $R |R> $Rdia;
+ S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==>
$L1, <>P, $L2 |- $R"
- pi2
- "[| $L |L> $Lbox; $L |R> $Ldia; $R1,[]P,$R2 |L> $Rbox; $R1,[]P,$R2 |R> $Rdia;
- S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==>
+ pi2:
+ "[| $L |L> $Lbox; $L |R> $Ldia; $R1,[]P,$R2 |L> $Rbox; $R1,[]P,$R2 |R> $Rdia;
+ S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==>
$L |- $R1, []P, $R2"
-end
-
-ML
-local
-
- val S43pi = "S43pi";
- val SS43pi = "@S43pi";
-
- val tr = Sequents.seq_tr;
- val tr' = Sequents.seq_tr';
+ML {* use_legacy_bindings (the_context ()) *}
- fun s43pi_tr[s1,s2,s3,s4,s5,s6]=
- Const(S43pi,dummyT)$tr s1$tr s2$tr s3$tr s4$tr s5$tr s6;
- fun s43pi_tr'[s1,s2,s3,s4,s5,s6] =
- Const(SS43pi,dummyT)$tr' s1$tr' s2$tr' s3$tr' s4$tr' s5$tr' s6;
-in
-val parse_translation = [(SS43pi,s43pi_tr)];
-val print_translation = [(S43pi,s43pi_tr')]
end