Theory: parallel

Parents

• process_ty
• CSP_base

Type constants

Term constants

• PAR:process -> process -> process {fixity = Infix 450}

Axioms

Definitions

PAR

|- !P Q.
     (ALPHA (P PAR Q) = ALPHA P UNION ALPHA Q) /\
     (TRACES (P PAR Q) =
      {s |
        s IN STAR (ALPHA P UNION ALPHA Q) /\
        RESTRICT s (ALPHA P) IN TRACES P /\
        RESTRICT s (ALPHA Q) IN TRACES Q})

Theorems

IS_PROCESS_PAR

|- !P Q.
     IS_PROCESS
       (ALPHA P UNION ALPHA Q,
        {s |
          s IN STAR (ALPHA P UNION ALPHA Q) /\
          RESTRICT s (ALPHA P) IN TRACES P /\
          RESTRICT s (ALPHA Q) IN TRACES Q})

ALPHA_PAR

|- !Q P. ALPHA (P PAR Q) = ALPHA P UNION ALPHA Q

TRACES_PAR

|- !Q P.
     TRACES (P PAR Q) =
     {s |
       s IN STAR (ALPHA P UNION ALPHA Q) /\
       RESTRICT s (ALPHA P) IN TRACES P /\
       RESTRICT s (ALPHA Q) IN TRACES Q}