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1 (* Title: HOL/UNITY/WFair.thy |
1 (* Title: HOL/UNITY/WFair.thy |
2 ID: $Id$ |
|
3 Author: Sidi Ehmety, Computer Laboratory |
2 Author: Sidi Ehmety, Computer Laboratory |
4 Copyright 1998 University of Cambridge |
3 Copyright 1998 University of Cambridge |
5 *) |
4 *) |
6 |
5 |
7 header{*Progress under Weak Fairness*} |
6 header{*Progress under Weak Fairness*} |
17 definition |
16 definition |
18 (* This definition specifies weak fairness. The rest of the theory |
17 (* This definition specifies weak fairness. The rest of the theory |
19 is generic to all forms of fairness.*) |
18 is generic to all forms of fairness.*) |
20 transient :: "i=>i" where |
19 transient :: "i=>i" where |
21 "transient(A) =={F:program. (EX act: Acts(F). A<=domain(act) & |
20 "transient(A) =={F:program. (EX act: Acts(F). A<=domain(act) & |
22 act``A <= state-A) & st_set(A)}" |
21 act``A <= state-A) & st_set(A)}" |
23 |
22 |
24 definition |
23 definition |
25 ensures :: "[i,i] => i" (infixl "ensures" 60) where |
24 ensures :: "[i,i] => i" (infixl "ensures" 60) where |
26 "A ensures B == ((A-B) co (A Un B)) Int transient(A-B)" |
25 "A ensures B == ((A-B) co (A Un B)) Int transient(A-B)" |
27 |
26 |
35 "leads(D, F)" <= "Pow(D)*Pow(D)" |
34 "leads(D, F)" <= "Pow(D)*Pow(D)" |
36 intros |
35 intros |
37 Basis: "[| F:A ensures B; A:Pow(D); B:Pow(D) |] ==> <A,B>:leads(D, F)" |
36 Basis: "[| F:A ensures B; A:Pow(D); B:Pow(D) |] ==> <A,B>:leads(D, F)" |
38 Trans: "[| <A,B> : leads(D, F); <B,C> : leads(D, F) |] ==> <A,C>:leads(D, F)" |
37 Trans: "[| <A,B> : leads(D, F); <B,C> : leads(D, F) |] ==> <A,C>:leads(D, F)" |
39 Union: "[| S:Pow({A:S. <A, B>:leads(D, F)}); B:Pow(D); S:Pow(Pow(D)) |] ==> |
38 Union: "[| S:Pow({A:S. <A, B>:leads(D, F)}); B:Pow(D); S:Pow(Pow(D)) |] ==> |
40 <Union(S),B>:leads(D, F)" |
39 <Union(S),B>:leads(D, F)" |
41 |
40 |
42 monos Pow_mono |
41 monos Pow_mono |
43 type_intros Union_Pow_iff [THEN iffD2] UnionI PowI |
42 type_intros Union_Pow_iff [THEN iffD2] UnionI PowI |
44 |
43 |
45 definition |
44 definition |