-- ========================================================================
--	              QLOCK Simulation by Search
-- ========================================================================

-- ========================================================================
require qlock-sys

-- ========================================================================
mod SIMbySearch {pr(QLOCKsys)
-- Aid literals 
[AidLt < Aid]
-- an equation for literals of sort AidLt
eq (B1:AidLt = B2:AidLt) = (B1 == B2) .
-- arbitrary Aid literals
ops b1 b2 b3 b4 b5 b6 : -> AidLt .

-- mutual exclusion property: at most one agent is in the critical section
-- this is the goal predicate
pred mx_ : As .
eq (mx empS) = true .
eq (mx (A:Aid AS:As)) = (AS = empS) .
}

select SIMbySearch .

--> search all reachable states with one agent
red [empQ r b1 w empS c empS] =(*,*)=>* S:State .

#|

[ empQ r b1 w empS c empS ]
[ b1 r empS w b1 c empS ]
[ b1 r empS w empS c b1 ]

|#

--> search all reachable states with two agents
red [empQ r (b1 b2) w empS c empS] =(*,*)=>* S:State .

#|

[ empQ r (b1 b2) w empS c empS ]

[ b1 r b2 w b1 c empS ]
[ b2 r b1 w b2 c empS ]

[ b1 r b2 w empS c b1 ]
[ b2 r b1 w empS c b2 ]

[ (b1 | b2) r empS w (b2 b1) c empS ]
[ (b2 | b1) r empS w (b1 b2) c empS ]

[ (b1 | b2) r empS w b2 c b1 ]
[ (b2 | b1) r empS w b1 c b2 ]

|#


--> search all reachable states with three agents
red [empQ r (b1 b2 b3) w empS c empS] =(*,*)=>* S:State .

#|

[ empQ r (b1 b2 b3) w empS c empS ]

[ b1 r (b2 b3) w b1 c empS ]
[ b2 r (b1 b3) w b2 c empS ]
[ b3 r (b1 b2) w b3 c empS ]

[ b1 r (b2 b3) w empS c b1 ]
[ b2 r (b1 b3) w empS c b2 ]
[ b3 r (b1 b2) w empS c b3 ]

[ (b1 | b2) r b3 w (b2 b1) c empS ]
[ (b1 | b3) r b2 w (b3 b1) c empS ]
[ (b2 | b1) r b3 w (b1 b2) c empS ]
[ (b2 | b3) r b1 w (b3 b2) c empS ]
[ (b3 | b1) r b2 w (b1 b3) c empS ]
[ (b3 | b2) r b1 w (b2 b3) c empS ]

[ (b1 | b2) r b3 w b2 c b1 ]
[ (b1 | b3) r b2 w b3 c b1 ]
[ (b2 | b1) r b3 w b1 c b2 ]
[ (b2 | b3) r b1 w b3 c b2 ]
[ (b3 | b1) r b2 w b1 c b3 ]
[ (b3 | b2) r b1 w b2 c b3 ]

[ (b1 | b2 | b3) r empS w (b3 b2 b1) c empS ]
[ (b1 | b3 | b2) r empS w (b2 b3 b1) c empS ]
[ (b2 | b1 | b3) r empS w (b3 b1 b2) c empS ]
[ (b2 | b3 | b1) r empS w (b1 b3 b2) c empS ]
[ (b3 | b1 | b2) r empS w (b2 b1 b3) c empS ]
[ (b3 | b2 | b1) r empS w (b1 b2 b3) c empS ]

[ (b1 | b2 | b3) r empS w (b3 b2) c b1 ]
[ (b1 | b3 | b2) r empS w (b2 b3) c b1 ]
[ (b2 | b1 | b3) r empS w (b3 b1) c b2 ]
[ (b2 | b3 | b1) r empS w (b1 b3) c b2 ]
[ (b3 | b1 | b2) r empS w (b2 b1) c b3 ]
[ (b3 | b2 | b1) r empS w (b1 b2) c b3 ]

|#

--> check whether mutual exclusion property holds for 
--> all reachable states with 2 agents
red not([empQ r (b1 b2) w empS c empS]
        =(*,*)=>* 
       [AQ:Aq r ASr:As w ASw:As c ASc:As]
       suchThat (not(mx ASc))) .

--> check whether mutual exclusion property holds for 
--> all reachable states with 3 agents
red not([empQ r (b1 b2 b3) w empS c empS]
        =(*,*)=>* 
       [AQ:Aq r ASr:As w ASw:As c ASc:As]
       suchThat (not(mx ASc))) .

--> check whether mutual exclusion property holds for 
--> all reachable states with 4 agents
red not([empQ r (b1 b2 b3 b4) w empS c empS]
        =(*,*)=>* 
       [AQ:Aq r ASr:As w ASw:As c ASc:As]
       suchThat (not(mx ASc))) .

--> check whether mutual exclusion property holds for 
--> all reachable states with 5 agents
red not([empQ r (b1 b2 b3 b4 b5) w empS c empS]
        =(*,*)=>* 
       [AQ:Aq r ASr:As w ASw:As c ASc:As]
       suchThat (not(mx ASc))) .

--> check whether mutual exclusion property holds for 
--> all reachable states with 6 agents
red not([empQ r (b1 b2 b3 b4 b5 b6) w empS c empS]
        =(*,*)=>* 
       [AQ:Aq r ASr:As w ASw:As c ASc:As]
       suchThat (not(mx ASc))) .

-- ========================================================================
eof