--- a/src/Modal/s43.thy Sat Apr 05 16:24:20 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,79 +0,0 @@
-(* Title: 91/Modal/S43
- ID: $Id$
- Author: Martin Coen
- Copyright 1991 University of Cambridge
-
-This implements Rajeev Gore's sequent calculus for S43.
-*)
-
-S43 = Modal0 +
-
-consts
- S43pi :: "[sobj=>sobj, sobj=>sobj, sobj=>sobj,\
-\ sobj=>sobj, sobj=>sobj, sobj=>sobj] => prop"
- "@S43pi" :: "[sequence, sequence, sequence, sequence, sequence,\
-\ sequence] => prop" ("S43pi((_);(_);(_);(_);(_);(_))" [] 5)
-
-rules
-(* 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"
-
-(* Set of Horn clauses to generate the antecedents for the S43 pi rule *)
-(* ie *)
-(* S1...Sk,Sk+1...Sk+m *)
-(* ---------------------------------- *)
-(* <>P1...<>Pk, $G |- $H, []Q1...[]Qm *)
-(* *)
-(* where Si == <>P1...<>Pi-1,<>Pi+1,..<>Pk,Pi, $G * |- $H *, []Q1...[]Qm *)
-(* 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 |] ==> \
-\ S43pi $L'; <>P,$L;; $R; $Lbox;$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 |] ==> \
-\ $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 |] ==> \
-\ $L |- $R1, []P, $R2"
-end
-
-ML
-
-local
-
- val S43pi = "S43pi";
- val SS43pi = "@S43pi";
-
- val tr = LK.seq_tr1;
- val tr' = LK.seq_tr1';
-
- fun s43pi_tr[s1,s2,s3,s4,s5,s6]=
- Const(S43pi,dummyT)$tr s1$tr s2$tr s3$tr s4$tr s5$tr s6;
- fun s43pi_tr'[Abs(_,_,s1),Abs(_,_,s2),Abs(_,_,s3),
- Abs(_,_,s4),Abs(_,_,s5),Abs(_,_,s6)] =
- Const(SS43pi,dummyT)$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