src/Modal/S43.thy
changeset 0 a5a9c433f639
child 1150 66512c9e6bd6
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/Modal/S43.thy	Thu Sep 16 12:20:38 1993 +0200
     1.3 @@ -0,0 +1,79 @@
     1.4 +(*  Title: 	91/Modal/S43
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Martin Coen
     1.7 +    Copyright   1991  University of Cambridge
     1.8 +
     1.9 +This implements Rajeev Gore's sequent calculus for S43.
    1.10 +*)
    1.11 +
    1.12 +S43 = Modal0 +
    1.13 +
    1.14 +consts
    1.15 +  S43pi	:: "[sobj=>sobj, sobj=>sobj, sobj=>sobj,\
    1.16 +\	     sobj=>sobj, sobj=>sobj, sobj=>sobj] => prop"
    1.17 +  "@S43pi" :: "[sequence, sequence, sequence, sequence, sequence,\
    1.18 +\		sequence] => prop" ("S43pi((_);(_);(_);(_);(_);(_))" [] 5)
    1.19 +
    1.20 +rules
    1.21 +(* Definition of the star operation using a set of Horn clauses  *)
    1.22 +(* For system S43: gamma * == {[]P | []P : gamma}                *)
    1.23 +(*                 delta * == {<>P | <>P : delta}                *)
    1.24 +
    1.25 +  lstar0         "|L>"
    1.26 +  lstar1         "$G |L> $H ==> []P, $G |L> []P, $H"
    1.27 +  lstar2         "$G |L> $H ==>   P, $G |L>      $H"
    1.28 +  rstar0         "|R>"
    1.29 +  rstar1         "$G |R> $H ==> <>P, $G |R> <>P, $H"
    1.30 +  rstar2         "$G |R> $H ==>   P, $G |R>      $H"
    1.31 +
    1.32 +(* Set of Horn clauses to generate the antecedents for the S43 pi rule       *)
    1.33 +(* ie                                                                        *)
    1.34 +(*           S1...Sk,Sk+1...Sk+m                                             *)
    1.35 +(*     ----------------------------------                                    *)
    1.36 +(*     <>P1...<>Pk, $G |- $H, []Q1...[]Qm                                    *)
    1.37 +(*                                                                           *)
    1.38 +(*  where Si == <>P1...<>Pi-1,<>Pi+1,..<>Pk,Pi, $G * |- $H *, []Q1...[]Qm    *)
    1.39 +(*    and Sj == <>P1...<>Pk, $G * |- $H *, []Q1...[]Qj-1,[]Qj+1...[]Qm,Qj    *)
    1.40 +(*    and 1<=i<=k and k<j<=k+m                                               *)
    1.41 +
    1.42 +  S43pi0         "S43pi $L;; $R;; $Lbox; $Rdia"
    1.43 +  S43pi1
    1.44 +   "[| (S43pi <>P,$L';     $L;; $R; $Lbox;$Rdia);   $L',P,$L,$Lbox |- $R,$Rdia |] ==> \
    1.45 +\       S43pi     $L'; <>P,$L;; $R; $Lbox;$Rdia"
    1.46 +  S43pi2
    1.47 +   "[| (S43pi $L';; []P,$R';     $R; $Lbox;$Rdia);  $L',$Lbox |- $R',P,$R,$Rdia |] ==> \
    1.48 +\       S43pi $L';;     $R'; []P,$R; $Lbox;$Rdia"
    1.49 +
    1.50 +(* Rules for [] and <> for S43 *)
    1.51 +
    1.52 +  boxL           "$E, P, $F, []P |- $G ==> $E, []P, $F |- $G"
    1.53 +  diaR           "$E |- $F, P, $G, <>P ==> $E |- $F, <>P, $G"
    1.54 +  pi1
    1.55 +   "[| $L1,<>P,$L2 |L> $Lbox;  $L1,<>P,$L2 |R> $Ldia;  $R |L> $Rbox;  $R |R> $Rdia;  \
    1.56 +\      S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==> \
    1.57 +\   $L1, <>P, $L2 |- $R"
    1.58 +  pi2
    1.59 +   "[| $L |L> $Lbox;  $L |R> $Ldia;  $R1,[]P,$R2 |L> $Rbox;  $R1,[]P,$R2 |R> $Rdia;  \
    1.60 +\      S43pi ; $Ldia;; $Rbox; $Lbox; $Rdia |] ==> \
    1.61 +\   $L |- $R1, []P, $R2"
    1.62 +end
    1.63 +
    1.64 +ML
    1.65 +
    1.66 +local
    1.67 +
    1.68 +  val S43pi  = "S43pi";
    1.69 +  val SS43pi = "@S43pi";
    1.70 +
    1.71 +  val tr  = LK.seq_tr1;
    1.72 +  val tr' = LK.seq_tr1';
    1.73 +
    1.74 +  fun s43pi_tr[s1,s2,s3,s4,s5,s6]=
    1.75 +	Const(S43pi,dummyT)$tr s1$tr s2$tr s3$tr s4$tr s5$tr s6;
    1.76 +  fun s43pi_tr'[Abs(_,_,s1),Abs(_,_,s2),Abs(_,_,s3),
    1.77 +		Abs(_,_,s4),Abs(_,_,s5),Abs(_,_,s6)] =
    1.78 +        Const(SS43pi,dummyT)$tr' s1$tr' s2$tr' s3$tr' s4$tr' s5$tr' s6;
    1.79 +in
    1.80 +val parse_translation = [(SS43pi,s43pi_tr)];
    1.81 +val print_translation = [(S43pi,s43pi_tr')]
    1.82 +end