(* Title: HOL/UNITY/Comp.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
Composition
From Chandy and Sanders, "Reasoning About Program Composition"
*)
Comp = Union +
constdefs
(*Existential and Universal properties. I formalize the two-program
case, proving equivalence with Chandy and Sanders's n-ary definitions*)
ex_prop :: 'a program set => bool
"ex_prop X ==
ALL F G. (F:X | G: X) & States F = States G --> (F Join G) : X"
strict_ex_prop :: 'a program set => bool
"strict_ex_prop X ==
ALL F G. States F = States G --> (F:X | G: X) = (F Join G : X)"
uv_prop :: 'a program set => bool
"uv_prop X ==
SKIP UNIV : X &
(ALL F G. F:X & G: X & States F = States G --> (F Join G) : X)"
strict_uv_prop :: 'a program set => bool
"strict_uv_prop X ==
SKIP UNIV : X &
(ALL F G. States F = States G --> (F:X & G: X) = (F Join G : X))"
(*Ill-defined programs can arise through "Join"*)
welldef :: 'a program set
"welldef == {F. Init F ~= {}}"
component :: ['a program, 'a program] => bool
"component F H == EX G. F Join G = H & States F = States G"
guarantees :: ['a program set, 'a program set] => 'a program set (infixl 65)
"X guarantees Y == {F. ALL H. component F H --> H:X --> H:Y}"
refines :: ['a program, 'a program, 'a program set] => bool
("(3_ refines _ wrt _)" [10,10,10] 10)
"G refines F wrt X ==
States F = States G &
(ALL H. States F = States H & (F Join H) : welldef Int X
--> G Join H : welldef Int X)"
iso_refines :: ['a program, 'a program, 'a program set] => bool
("(3_ iso'_refines _ wrt _)" [10,10,10] 10)
"G iso_refines F wrt X ==
F : welldef Int X --> G : welldef Int X"
end