(* Title: HOL/UNITY/Mutex.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
Based on "A Family of 2-Process Mutual Exclusion Algorithms" by J Misra
*)
Mutex = SubstAx +
record state =
p :: bool
m :: int
n :: int
u :: bool
v :: bool
types command = "(state*state) set"
constdefs
(** The program for process U **)
U0 :: command
"U0 == {(s,s'). s' = s (|u:=True, m:=#1|) & m s = #0}"
U1 :: command
"U1 == {(s,s'). s' = s (|p:= v s, m:=#2|) & m s = #1}"
U2 :: command
"U2 == {(s,s'). s' = s (|m:=#3|) & ~ p s & m s = #2}"
U3 :: command
"U3 == {(s,s'). s' = s (|u:=False, m:=#4|) & m s = #3}"
U4 :: command
"U4 == {(s,s'). s' = s (|p:=True, m:=#0|) & m s = #4}"
(** The program for process V **)
V0 :: command
"V0 == {(s,s'). s' = s (|v:=True, n:=#1|) & n s = #0}"
V1 :: command
"V1 == {(s,s'). s' = s (|p:= ~ u s, n:=#2|) & n s = #1}"
V2 :: command
"V2 == {(s,s'). s' = s (|n:=#3|) & p s & n s = #2}"
V3 :: command
"V3 == {(s,s'). s' = s (|v:=False, n:=#4|) & n s = #3}"
V4 :: command
"V4 == {(s,s'). s' = s (|p:=False, n:=#0|) & n s = #4}"
Mutex :: state program
"Mutex == mk_program ({s. ~ u s & ~ v s & m s = #0 & n s = #0},
{U0, U1, U2, U3, U4, V0, V1, V2, V3, V4},
UNIV)"
(** The correct invariants **)
IU :: state set
"IU == {s. (u s = (#1 <= m s & m s <= #3)) & (m s = #3 --> ~ p s)}"
IV :: state set
"IV == {s. (v s = (#1 <= n s & n s <= #3)) & (n s = #3 --> p s)}"
(** The faulty invariant (for U alone) **)
bad_IU :: state set
"bad_IU == {s. (u s = (#1 <= m s & m s <= #3)) &
(#3 <= m s & m s <= #4 --> ~ p s)}"
end