isabelle: src/Sequents/T.thy@87ac12bed1ab (annotated)

17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	1	(* Title: Modal/T.thy
2073 fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	2	ID: $Id$
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	3	Author: Martin Coen
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	4	Copyright 1991 University of Cambridge
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	5	*)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	6
17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	7	theory T
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	8	imports Modal0
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	9	begin
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	10
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	11	axioms
2073 fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	12	(* Definition of the star operation using a set of Horn clauses *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	13	(* For system T: gamma * == {P \| []P : gamma} *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	14	(* delta * == {P \| <>P : delta} *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	15
17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	16	lstar0: "\|L>"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	17	lstar1: "$G \|L> $H ==> []P, $G \|L> P, $H"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	18	lstar2: "$G \|L> $H ==> P, $G \|L> $H"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	19	rstar0: "\|R>"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	20	rstar1: "$G \|R> $H ==> <>P, $G \|R> P, $H"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	21	rstar2: "$G \|R> $H ==> P, $G \|R> $H"
2073 fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	22
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	23	(* Rules for [] and <> *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	24
17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	25	boxR:
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	26	"[\| $E \|L> $E'; $F \|R> $F'; $G \|R> $G';
2073 fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	27	$E' \|- $F', P, $G'\|] ==> $E \|- $F, []P, $G"
17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	28	boxL: "$E, P, $F \|- $G ==> $E, []P, $F \|- $G"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	29	diaR: "$E \|- $F, P, $G ==> $E \|- $F, <>P, $G"
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	30	diaL:
75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	31	"[\| $E \|L> $E'; $F \|L> $F'; $G \|R> $G';
2073 fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	32	$E', P, $F'\|- $G'\|] ==> $E, <>P, $F \|- $G"
17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	33
21426 87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	34	ML {*
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	35	structure T_Prover = Modal_ProverFun
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	36	(
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	37	val rewrite_rls = thms "rewrite_rls"
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	38	val safe_rls = thms "safe_rls"
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	39	val unsafe_rls = thms "unsafe_rls" @ [thm "boxR", thm "diaL"]
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	40	val bound_rls = thms "bound_rls" @ [thm "boxL", thm "diaR"]
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	41	val aside_rls = [thm "lstar0", thm "lstar1", thm "lstar2", thm "rstar0",
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	42	thm "rstar1", thm "rstar2"]
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	43	)
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	44	*}
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	45
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	46	method_setup T_solve =
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	47	{* Method.no_args (Method.SIMPLE_METHOD (T_Prover.solve_tac 2)) *} "T solver"
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	48
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	49
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	50	(* Theorems of system T from Hughes and Cresswell and Hailpern, LNCS 129 *)
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	51
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	52	lemma "\|- []P --> P" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	53	lemma "\|- [](P-->Q) --> ([]P-->[]Q)" by T_solve (* normality*)
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	54	lemma "\|- (P--<Q) --> []P --> []Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	55	lemma "\|- P --> <>P" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	56
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	57	lemma "\|- [](P & Q) <-> []P & []Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	58	lemma "\|- <>(P \| Q) <-> <>P \| <>Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	59	lemma "\|- [](P<->Q) <-> (P>-<Q)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	60	lemma "\|- <>(P-->Q) <-> ([]P--><>Q)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	61	lemma "\|- []P <-> ~<>(~P)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	62	lemma "\|- [](~P) <-> ~<>P" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	63	lemma "\|- ~[]P <-> <>(~P)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	64	lemma "\|- [][]P <-> ~<><>(~P)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	65	lemma "\|- ~<>(P \| Q) <-> ~<>P & ~<>Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	66
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	67	lemma "\|- []P \| []Q --> [](P \| Q)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	68	lemma "\|- <>(P & Q) --> <>P & <>Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	69	lemma "\|- [](P \| Q) --> []P \| <>Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	70	lemma "\|- <>P & []Q --> <>(P & Q)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	71	lemma "\|- [](P \| Q) --> <>P \| []Q" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	72	lemma "\|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	73	lemma "\|- (P--<Q) & (Q--<R) --> (P--<R)" by T_solve
87ac12bed1ab converted legacy ML scripts; wenzelm parents: 17481 diff changeset	74	lemma "\|- []P --> <>Q --> <>(P & Q)" by T_solve
17481 75166ebb619b converted to Isar theory format; wenzelm parents: 2073 diff changeset	75
2073 fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala paulson parents: diff changeset	76	end

author	wenzelm
	Mon, 20 Nov 2006 23:47:10 +0100
changeset 21426	87ac12bed1ab
parent 17481	75166ebb619b
child 21590	ef7278f553eb
permissions	-rw-r--r--