src/HOL/UNITY/Simple/Mutex.thy
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(*  Title:      HOL/UNITY/Mutex.thy
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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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Based on "A Family of 2-Process Mutual Exclusion Algorithms" by J Misra
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*)
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Mutex = SubstAx +
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record state =
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  p :: bool
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  m :: int
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  n :: int
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  u :: bool
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  v :: bool
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types command = "(state*state) set"
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constdefs
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  (** The program for process U **)
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  U0 :: command
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    "U0 == {(s,s'). s' = s (|u:=True, m:=Numeral1|) & m s = Numeral0}"
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  U1 :: command
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    "U1 == {(s,s'). s' = s (|p:= v s, m:=2|) & m s = Numeral1}"
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  U2 :: command
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    "U2 == {(s,s'). s' = s (|m:=3|) & ~ p s & m s = 2}"
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  U3 :: command
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    "U3 == {(s,s'). s' = s (|u:=False, m:=4|) & m s = 3}"
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  U4 :: command
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    "U4 == {(s,s'). s' = s (|p:=True, m:=Numeral0|) & m s = 4}"
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  (** The program for process V **)
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  V0 :: command
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    "V0 == {(s,s'). s' = s (|v:=True, n:=Numeral1|) & n s = Numeral0}"
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  V1 :: command
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    "V1 == {(s,s'). s' = s (|p:= ~ u s, n:=2|) & n s = Numeral1}"
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  V2 :: command
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    "V2 == {(s,s'). s' = s (|n:=3|) & p s & n s = 2}"
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  V3 :: command
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    "V3 == {(s,s'). s' = s (|v:=False, n:=4|) & n s = 3}"
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  V4 :: command
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    "V4 == {(s,s'). s' = s (|p:=False, n:=Numeral0|) & n s = 4}"
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  Mutex :: state program
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    "Mutex == mk_program ({s. ~ u s & ~ v s & m s = Numeral0 & n s = Numeral0},
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		 	  {U0, U1, U2, U3, U4, V0, V1, V2, V3, V4},
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			  UNIV)"
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  (** The correct invariants **)
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  IU :: state set
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    "IU == {s. (u s = (Numeral1 <= m s & m s <= 3)) & (m s = 3 --> ~ p s)}"
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  IV :: state set
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    "IV == {s. (v s = (Numeral1 <= n s & n s <= 3)) & (n s = 3 --> p s)}"
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  (** The faulty invariant (for U alone) **)
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  bad_IU :: state set
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    "bad_IU == {s. (u s = (Numeral1 <= m s & m s <= 3)) &
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	           (3 <= m s & m s <= 4 --> ~ p s)}"
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end