summary |
shortlog |
changelog |
graph |
tags |
branches |
files |
changeset |
file |
revisions |
annotate |
diff |
raw

src/Sequents/T.thy

author | wenzelm |

Sat Dec 14 17:28:05 2013 +0100 (2013-12-14) | |

changeset 54742 | 7a86358a3c0b |

parent 51309 | 473303ef6e34 |

child 60770 | 240563fbf41d |

permissions | -rw-r--r-- |

proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;

clarified tool context in some boundary cases;

clarified tool context in some boundary cases;

1 (* Title: Sequents/T.thy

2 Author: Martin Coen

3 Copyright 1991 University of Cambridge

4 *)

6 theory T

7 imports Modal0

8 begin

10 axiomatization where

11 (* Definition of the star operation using a set of Horn clauses *)

12 (* For system T: gamma * == {P | []P : gamma} *)

13 (* delta * == {P | <>P : delta} *)

15 lstar0: "|L>" and

16 lstar1: "$G |L> $H ==> []P, $G |L> P, $H" and

17 lstar2: "$G |L> $H ==> P, $G |L> $H" and

18 rstar0: "|R>" and

19 rstar1: "$G |R> $H ==> <>P, $G |R> P, $H" and

20 rstar2: "$G |R> $H ==> P, $G |R> $H" and

22 (* Rules for [] and <> *)

24 boxR:

25 "[| $E |L> $E'; $F |R> $F'; $G |R> $G';

26 $E' |- $F', P, $G'|] ==> $E |- $F, []P, $G" and

27 boxL: "$E, P, $F |- $G ==> $E, []P, $F |- $G" and

28 diaR: "$E |- $F, P, $G ==> $E |- $F, <>P, $G" and

29 diaL:

30 "[| $E |L> $E'; $F |L> $F'; $G |R> $G';

31 $E', P, $F'|- $G'|] ==> $E, <>P, $F |- $G"

33 ML {*

34 structure T_Prover = Modal_ProverFun

35 (

36 val rewrite_rls = @{thms rewrite_rls}

37 val safe_rls = @{thms safe_rls}

38 val unsafe_rls = @{thms unsafe_rls} @ [@{thm boxR}, @{thm diaL}]

39 val bound_rls = @{thms bound_rls} @ [@{thm boxL}, @{thm diaR}]

40 val aside_rls = [@{thm lstar0}, @{thm lstar1}, @{thm lstar2}, @{thm rstar0},

41 @{thm rstar1}, @{thm rstar2}]

42 )

43 *}

45 method_setup T_solve = {* Scan.succeed (fn ctxt => SIMPLE_METHOD (T_Prover.solve_tac ctxt 2)) *}

48 (* Theorems of system T from Hughes and Cresswell and Hailpern, LNCS 129 *)

50 lemma "|- []P --> P" by T_solve

51 lemma "|- [](P-->Q) --> ([]P-->[]Q)" by T_solve (* normality*)

52 lemma "|- (P--<Q) --> []P --> []Q" by T_solve

53 lemma "|- P --> <>P" by T_solve

55 lemma "|- [](P & Q) <-> []P & []Q" by T_solve

56 lemma "|- <>(P | Q) <-> <>P | <>Q" by T_solve

57 lemma "|- [](P<->Q) <-> (P>-<Q)" by T_solve

58 lemma "|- <>(P-->Q) <-> ([]P--><>Q)" by T_solve

59 lemma "|- []P <-> ~<>(~P)" by T_solve

60 lemma "|- [](~P) <-> ~<>P" by T_solve

61 lemma "|- ~[]P <-> <>(~P)" by T_solve

62 lemma "|- [][]P <-> ~<><>(~P)" by T_solve

63 lemma "|- ~<>(P | Q) <-> ~<>P & ~<>Q" by T_solve

65 lemma "|- []P | []Q --> [](P | Q)" by T_solve

66 lemma "|- <>(P & Q) --> <>P & <>Q" by T_solve

67 lemma "|- [](P | Q) --> []P | <>Q" by T_solve

68 lemma "|- <>P & []Q --> <>(P & Q)" by T_solve

69 lemma "|- [](P | Q) --> <>P | []Q" by T_solve

70 lemma "|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)" by T_solve

71 lemma "|- (P--<Q) & (Q--<R) --> (P--<R)" by T_solve

72 lemma "|- []P --> <>Q --> <>(P & Q)" by T_solve

74 end