src/HOL/UNITY/Union.thy
changeset 6012 1894bfc4aee9
parent 5804 8e0a4c4fd67b
child 6295 351b3c2b0d83
equal deleted inserted replaced
6011:c48050d6928d 6012:1894bfc4aee9
     9 *)
     9 *)
    10 
    10 
    11 Union = SubstAx + FP +
    11 Union = SubstAx + FP +
    12 
    12 
    13 constdefs
    13 constdefs
       
    14   eqStates :: ['a set, 'a => 'b program] => bool
       
    15     "eqStates I F == EX St. ALL i:I. States (F i) = St"
       
    16 
    14   JOIN  :: ['a set, 'a => 'b program] => 'b program
    17   JOIN  :: ['a set, 'a => 'b program] => 'b program
    15     "JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))"
    18     "JOIN I F == mk_program (INT i:I. States (F i),
       
    19 			     INT i:I. Init (F i),
       
    20 			     UN i:I. Acts (F i))"
    16 
    21 
    17   Join :: ['a program, 'a program] => 'a program      (infixl 65)
    22   Join :: ['a program, 'a program] => 'a program      (infixl 65)
    18     "F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)"
    23     "F Join G == mk_program (States F Int States G,
       
    24 			     Init F Int Init G,
       
    25 			     Acts F Un Acts G)"
    19 
    26 
    20   SKIP :: 'a program
    27   SKIP :: 'a set => 'a program
    21     "SKIP == mk_program (UNIV, {})"
    28     "SKIP states == mk_program (states, states, {})"
    22 
    29 
    23   Diff :: "['a program, ('a * 'a)set set] => 'a program"
    30   Diff :: "['a program, ('a * 'a)set set] => 'a program"
    24     "Diff F acts == mk_program (Init F, Acts F - acts)"
    31     "Diff F acts == mk_program (States F, Init F, Acts F - acts)"
    25 
    32 
    26   (*The set of systems that regard "v" as local to F*)
    33   (*The set of systems that regard "v" as local to F*)
    27   localTo :: ['a => 'b, 'a program] => 'a program set  (infixl 80)
    34   localTo :: ['a => 'b, 'a program] => 'a program set  (infixl 80)
    28     "v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}"
    35     "v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}"
    29 
    36 
    30   (*Two programs with disjoint actions, except for Id (idling)*)
    37   (*Two programs with disjoint actions, except for identity actions *)
    31   Disjoint :: ['a program, 'a program] => bool
    38   Disjoint :: ['a program, 'a program] => bool
    32     "Disjoint F G == Acts F Int Acts G <= {Id}"
    39     "Disjoint F G == States F = States G &
       
    40                      Acts F Int Acts G <= {diag (States G)}"
    33 
    41 
    34 syntax
    42 syntax
    35   "@JOIN"      :: [pttrn, 'a set, 'b set] => 'b set  ("(3JN _:_./ _)" 10)
    43   "@JOIN"      :: [pttrn, 'a set, 'b set] => 'b set  ("(3JN _:_./ _)" 10)
    36 
    44 
    37 translations
    45 translations