src/Sequents/S43.thy
 changeset 17481 75166ebb619b parent 14765 bafb24c150c1 child 21426 87ac12bed1ab
```--- 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
@@ -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```