author | paulson |
Thu, 13 Aug 1998 18:06:40 +0200 | |
changeset 5313 | 1861a564d7e2 |
parent 5277 | e4297d03e5d2 |
child 5340 | d75c03cf77b5 |
permissions | -rw-r--r-- |
4776 | 1 |
(* Title: HOL/UNITY/WFair |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1998 University of Cambridge |
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Weak Fairness versions of transient, ensures, leadsTo. |
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From Misra, "A Logic for Concurrent Programming", 1994 |
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*) |
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A higher-level treatment of LeadsTo, minimizing use of "reachable"
paulson
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WFair = UNITY + |
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constdefs |
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(*This definition specifies weak fairness. The rest of the theory |
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is generic to all forms of fairness.*) |
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transient :: "[('a * 'a)set set, 'a set] => bool" |
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"transient acts A == EX act:acts. A <= Domain act & act^^A <= Compl A" |
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ensures :: "[('a * 'a)set set, 'a set, 'a set] => bool" |
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"ensures acts A B == constrains acts (A-B) (A Un B) & transient acts (A-B)" |
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(*(unless acts A B) would be equivalent*) |
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consts leadsTo :: "[('a * 'a)set set, 'a set, 'a set] => bool" |
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leadsto :: "[('a * 'a)set set] => ('a set * 'a set) set" |
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translations |
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"leadsTo acts A B" == "(A,B) : leadsto acts" |
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inductive "leadsto acts" |
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intrs |
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Basis "ensures acts A B ==> leadsTo acts A B" |
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Trans "[| leadsTo acts A B; leadsTo acts B C |] |
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==> leadsTo acts A C" |
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(*Encoding using powerset of the desired axiom |
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(!!A. A : S ==> leadsTo acts A B) ==> leadsTo acts (Union S) B |
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*) |
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Union "(UN A:S. {(A,B)}) : Pow (leadsto acts) |
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==> leadsTo acts (Union S) B" |
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monos "[Pow_mono]" |
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(*wlt acts B is the largest set that leads to B*) |
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constdefs wlt :: "[('a * 'a)set set, 'a set] => 'a set" |
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"wlt acts B == Union {A. leadsTo acts A B}" |
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end |