(* 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 =
PP :: bool
MM :: int
NN :: int
UU :: bool
VV :: bool
constdefs
(** The program for process U **)
cmd0U :: "(state*state) set"
"cmd0U == {(s,s'). s' = s (|UU:=True, MM:=#1|) & MM s = #0}"
cmd1U :: "(state*state) set"
"cmd1U == {(s,s'). s' = s (|PP:= VV s, MM:=#2|) & MM s = #1}"
cmd2U :: "(state*state) set"
"cmd2U == {(s,s'). s' = s (|MM:=#3|) & ~ PP s & MM s = #2}"
cmd3U :: "(state*state) set"
"cmd3U == {(s,s'). s' = s (|UU:=False, MM:=#4|) & MM s = #3}"
cmd4U :: "(state*state) set"
"cmd4U == {(s,s'). s' = s (|PP:=True, MM:=#0|) & MM s = #4}"
(** The program for process V **)
cmd0V :: "(state*state) set"
"cmd0V == {(s,s'). s' = s (|VV:=True, NN:=#1|) & NN s = #0}"
cmd1V :: "(state*state) set"
"cmd1V == {(s,s'). s' = s (|PP:= ~ UU s, NN:=#2|) & NN s = #1}"
cmd2V :: "(state*state) set"
"cmd2V == {(s,s'). s' = s (|NN:=#3|) & PP s & NN s = #2}"
cmd3V :: "(state*state) set"
"cmd3V == {(s,s'). s' = s (|VV:=False, NN:=#4|) & NN s = #3}"
cmd4V :: "(state*state) set"
"cmd4V == {(s,s'). s' = s (|PP:=False, NN:=#0|) & NN s = #4}"
Mprg :: state program
"Mprg == mk_program ({s. ~ UU s & ~ VV s & MM s = #0 & NN s = #0},
{cmd0U, cmd1U, cmd2U, cmd3U, cmd4U,
cmd0V, cmd1V, cmd2V, cmd3V, cmd4V})"
(** The correct invariants **)
invariantU :: "state set"
"invariantU == {s. (UU s = (#1 <= MM s & MM s <= #3)) &
(MM s = #3 --> ~ PP s)}"
invariantV :: "state set"
"invariantV == {s. (VV s = (#1 <= NN s & NN s <= #3)) &
(NN s = #3 --> PP s)}"
(** The faulty invariant (for U alone) **)
bad_invariantU :: "state set"
"bad_invariantU == {s. (UU s = (#1 <= MM s & MM s <= #3)) &
(#3 <= MM s & MM s <= #4 --> ~ PP s)}"
end