(* Title: HOL/UNITY/WFair
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
Weak Fairness versions of transient, ensures, leadsTo.
From Misra, "A Logic for Concurrent Programming", 1994
*)
WFair = Traces + Vimage +
constdefs
(*This definition specifies weak fairness. The rest of the theory
is generic to all forms of fairness.*)
transient :: "[('a * 'a)set set, 'a set] => bool"
"transient Acts A == EX act:Acts. A <= Domain act & act^^A <= Compl A"
ensures :: "[('a * 'a)set set, 'a set, 'a set] => bool"
"ensures Acts A B == constrains Acts (A-B) (A Un B) & transient Acts (A-B)"
(*(unless Acts A B) would be equivalent*)
consts leadsTo :: "[('a * 'a)set set, 'a set, 'a set] => bool"
leadsto :: "[('a * 'a)set set] => ('a set * 'a set) set"
translations
"leadsTo Acts A B" == "(A,B) : leadsto Acts"
inductive "leadsto Acts"
intrs
Basis "ensures Acts A B ==> leadsTo Acts A B"
Trans "[| leadsTo Acts A B; leadsTo Acts B C |]
==> leadsTo Acts A C"
(*Encoding using powerset of the desired axiom
(!!A. A : S ==> leadsTo Acts A B) ==> leadsTo Acts (Union S) B
*)
Union "(UN A:S. {(A,B)}) : Pow (leadsto Acts)
==> leadsTo Acts (Union S) B"
monos "[Pow_mono]"
(*wlt Acts B is the largest set that leads to B*)
constdefs wlt :: "[('a * 'a)set set, 'a set] => 'a set"
"wlt Acts B == Union {A. leadsTo Acts A B}"
end