Improved error message.
(* Title: HOL/UNITY/Guar.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1999 University of Cambridge
Guarantees, etc.
From Chandy and Sanders, "Reasoning About Program Composition",
Technical Report 2000-003, University of Florida, 2000.
Revised by Sidi Ehmety on January 2001
Added: Compatibility, weakest guarantees, etc.
and Weakest existential property,
from Charpentier and Chandy "Theorems about Composition",
Fifth International Conference on Mathematics of Program, 2000.
*)
Guar = Comp +
instance program :: (term) order
(component_refl, component_trans, component_antisym,
program_less_le)
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 ok G -->F:X | G: X --> (F Join G) : X"
strict_ex_prop :: 'a program set => bool
"strict_ex_prop X == ALL F G. F ok G --> (F:X | G: X) = (F Join G : X)"
uv_prop :: 'a program set => bool
"uv_prop X == SKIP : X & (ALL F G. F ok G --> F:X & G: X --> (F Join G) : X)"
strict_uv_prop :: 'a program set => bool
"strict_uv_prop X == SKIP : X & (ALL F G. F ok G -->(F:X & G: X) = (F Join G : X))"
guar :: ['a program set, 'a program set] => 'a program set
(infixl "guarantees" 55) (*higher than membership, lower than Co*)
"X guarantees Y == {F. ALL G. F ok G --> F Join G : X --> F Join G : Y}"
(* Weakest guarantees *)
wg :: ['a program, 'a program set] => 'a program set
"wg F Y == Union({X. F:X guarantees Y})"
(* Weakest existential property stronger than X *)
wx :: "('a program) set => ('a program)set"
"wx X == Union({Y. Y<=X & ex_prop Y})"
(*Ill-defined programs can arise through "Join"*)
welldef :: 'a program set
"welldef == {F. Init F ~= {}}"
refines :: ['a program, 'a program, 'a program set] => bool
("(3_ refines _ wrt _)" [10,10,10] 10)
"G refines F wrt X ==
ALL H. (F ok H & G ok 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