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

src/Sequents/T.thy

author | bulwahn |

Tue Aug 31 08:00:53 2010 +0200 (2010-08-31) | |

changeset 38950 | 62578950e748 |

parent 35762 | af3ff2ba4c54 |

child 39159 | 0dec18004e75 |

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

storing options for prolog code generation in the theory

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 axioms

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>"

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

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

18 rstar0: "|R>"

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

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

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"

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

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

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 =

46 {* Scan.succeed (K (SIMPLE_METHOD (T_Prover.solve_tac 2))) *} "T solver"

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

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

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

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

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

64 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) --> <>P | []Q" by T_solve

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

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

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

75 end