src/HOL/UNITY/WFair.thy
 author paulson Wed, 18 Nov 1998 15:10:46 +0100 changeset 5931 325300576da7 parent 5721 458a67fd5461 child 6536 281d44905cab permissions -rw-r--r--
Finally removing "Compl" from HOL
```
(*  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 = UNITY +

constdefs

(*This definition specifies weak fairness.  The rest of the theory
is generic to all forms of fairness.*)
transient :: "'a set => 'a program set"
"transient A == {F. EX act: Acts F. A <= Domain act & act^^A <= -A}"

ensures :: "['a set, 'a set] => 'a program set"
"ensures A B == constrains (A-B) (A Un B) Int transient (A-B)"

consts leadsto :: "'a program => ('a set * 'a set) set"

intrs

Basis  "F : ensures A B ==> (A,B) : leadsto F"

Trans  "[| (A,B) : leadsto F;  (B,C) : leadsto F |]
==> (A,C) : leadsto F"

(*Encoding using powerset of the desired axiom
(!!A. A : S ==> (A,B) : leadsto F) ==> (Union S, B) : leadsto F
*)
Union  "(UN A:S. {(A,B)}) : Pow (leadsto F) ==> (Union S, B) : leadsto F"

monos Pow_mono

constdefs (*visible version of the relation*)
leadsTo :: "['a set, 'a set] => 'a program set"
"leadsTo A B == {F. (A,B) : leadsto F}"

(*wlt F B is the largest set that leads to B*)
wlt :: "['a program, 'a set] => 'a set"
"wlt F B == Union {A. F: leadsTo A B}"

end
```