src/HOL/UNITY/Simple/Mutex.thy
author paulson
Mon Oct 22 11:54:22 2001 +0200 (2001-10-22)
changeset 11868 56db9f3a6b3e
parent 11704 3c50a2cd6f00
child 13785 e2fcd88be55d
permissions -rw-r--r--
Numerals now work for the integers: the binary numerals for 0 and 1 rewrite
to their abstract counterparts, while other binary numerals work correctly.
     1 (*  Title:      HOL/UNITY/Mutex.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1998  University of Cambridge
     5 
     6 Based on "A Family of 2-Process Mutual Exclusion Algorithms" by J Misra
     7 *)
     8 
     9 Mutex = SubstAx +
    10 
    11 record state =
    12   p :: bool
    13   m :: int
    14   n :: int
    15   u :: bool
    16   v :: bool
    17 
    18 types command = "(state*state) set"
    19 
    20 constdefs
    21   
    22   (** The program for process U **)
    23   
    24   U0 :: command
    25     "U0 == {(s,s'). s' = s (|u:=True, m:=1|) & m s = 0}"
    26 
    27   U1 :: command
    28     "U1 == {(s,s'). s' = s (|p:= v s, m:=2|) & m s = 1}"
    29 
    30   U2 :: command
    31     "U2 == {(s,s'). s' = s (|m:=3|) & ~ p s & m s = 2}"
    32 
    33   U3 :: command
    34     "U3 == {(s,s'). s' = s (|u:=False, m:=4|) & m s = 3}"
    35 
    36   U4 :: command
    37     "U4 == {(s,s'). s' = s (|p:=True, m:=0|) & m s = 4}"
    38 
    39   (** The program for process V **)
    40   
    41   V0 :: command
    42     "V0 == {(s,s'). s' = s (|v:=True, n:=1|) & n s = 0}"
    43 
    44   V1 :: command
    45     "V1 == {(s,s'). s' = s (|p:= ~ u s, n:=2|) & n s = 1}"
    46 
    47   V2 :: command
    48     "V2 == {(s,s'). s' = s (|n:=3|) & p s & n s = 2}"
    49 
    50   V3 :: command
    51     "V3 == {(s,s'). s' = s (|v:=False, n:=4|) & n s = 3}"
    52 
    53   V4 :: command
    54     "V4 == {(s,s'). s' = s (|p:=False, n:=0|) & n s = 4}"
    55 
    56   Mutex :: state program
    57     "Mutex == mk_program ({s. ~ u s & ~ v s & m s = 0 & n s = 0},
    58 		 	  {U0, U1, U2, U3, U4, V0, V1, V2, V3, V4},
    59 			  UNIV)"
    60 
    61 
    62   (** The correct invariants **)
    63 
    64   IU :: state set
    65     "IU == {s. (u s = (1 <= m s & m s <= 3)) & (m s = 3 --> ~ p s)}"
    66 
    67   IV :: state set
    68     "IV == {s. (v s = (1 <= n s & n s <= 3)) & (n s = 3 --> p s)}"
    69 
    70   (** The faulty invariant (for U alone) **)
    71 
    72   bad_IU :: state set
    73     "bad_IU == {s. (u s = (1 <= m s & m s <= 3)) &
    74 	           (3 <= m s & m s <= 4 --> ~ p s)}"
    75 
    76 end