equal
deleted
inserted
replaced
15 (*This definition specifies weak fairness. The rest of the theory |
15 (*This definition specifies weak fairness. The rest of the theory |
16 is generic to all forms of fairness.*) |
16 is generic to all forms of fairness.*) |
17 transient :: "'a set => 'a program set" |
17 transient :: "'a set => 'a program set" |
18 "transient A == {F. EX act: Acts F. A <= Domain act & act^^A <= -A}" |
18 "transient A == {F. EX act: Acts F. A <= Domain act & act^^A <= -A}" |
19 |
19 |
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20 ensures :: "['a set, 'a set] => 'a program set" (infixl 60) |
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21 "A ensures B == (A-B co A Un B) Int transient (A-B)" |
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22 |
20 |
23 |
21 consts |
24 consts |
22 |
25 |
23 ensures :: "['a set, 'a set] => 'a program set" (infixl 60) |
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24 |
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25 (*LEADS-TO constant for the inductive definition*) |
26 (*LEADS-TO constant for the inductive definition*) |
26 leads :: "'a program => ('a set * 'a set) set" |
27 leads :: "'a program => ('a set * 'a set) set" |
27 |
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28 (*visible version of the LEADS-TO relation*) |
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29 leadsTo :: "['a set, 'a set] => 'a program set" (infixl 60) |
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30 |
28 |
31 |
29 |
32 inductive "leads F" |
30 inductive "leads F" |
33 intrs |
31 intrs |
34 |
32 |
42 Union "{(A,B) | A. A: S} : Pow (leads F) ==> (Union S, B) : leads F" |
40 Union "{(A,B) | A. A: S} : Pow (leads F) ==> (Union S, B) : leads F" |
43 |
41 |
44 monos Pow_mono |
42 monos Pow_mono |
45 |
43 |
46 |
44 |
47 |
45 constdefs |
48 defs |
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49 ensures_def "A ensures B == (A-B co A Un B) Int transient (A-B)" |
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50 |
46 |
51 leadsTo_def "A leadsTo B == {F. (A,B) : leads F}" |
47 (*visible version of the LEADS-TO relation*) |
52 |
48 leadsTo :: "['a set, 'a set] => 'a program set" (infixl 60) |
53 constdefs |
49 "A leadsTo B == {F. (A,B) : leads F}" |
54 |
50 |
55 (*wlt F B is the largest set that leads to B*) |
51 (*wlt F B is the largest set that leads to B*) |
56 wlt :: "['a program, 'a set] => 'a set" |
52 wlt :: "['a program, 'a set] => 'a set" |
57 "wlt F B == Union {A. F: A leadsTo B}" |
53 "wlt F B == Union {A. F: A leadsTo B}" |
58 |
54 |