(*****************************************************************************
 * Step 1: GRAPH GENERATION.                                                 *
 * The LNT specification "pots.lnt" is translated into a graph called        *
 * "pots.bcg", which is then reduced by BCG_MIN modulo strong equivalence.   *
 * Such strong minimization preserves the truth values of the requirements   *
 * to be checked later.                                                      *
 *****************************************************************************)

"pots.bcg" = strong reduction of generation of "pots.lnt";

-------------------------------------------------------------------------------

(*****************************************************************************
 * Step 2: VERIFICATION OF THE REQUIREMENTS                                  *
 * The 17 requirements characterizing the proper functioning of the POTS     *
 * are checked in turn. For each of these requirements, we give an informal  *
 * specification as expressed by P. Ernberg. Two techniques are used to      *
 * verify the requirements:                                                  *
 * - Equivalence checking consists in comparing "pots.bcg" to a reference    *
 *   specification using an equivalence relation. For each requirement       *
 *   we explain the approach and we give the SVL statement permitting to     *
 *   verify it using CADP.                                                   *
 * - Model checking consists in evaluating a temporal formula specified in   *
 *   the MCL language. For each requirement we give one or several (dataless *
 *   and/or value-passing) formulas, which are inlined in the SVL statements *
 *   used to verify them.                                                    *
 * The first 10 requirements are verified using both equivalence checking    *
 * and model checking, and the last 7 ones are verified using model checking *
 * only.                                                                     *
 *****************************************************************************)

% DEFAULT_MCL_LIBRARIES="standard.mcl"

(******************************* REQUIREMENT 1 *******************************)

property Requirement_1
    "There should be no deadlock in the specification."
is
    -- built-in deadlock detection
    "diag_1.seq" = deadlock of "pots.bcg";
    expected FALSE;

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [ true* ] < true > true;
    expected TRUE
end property

(******************************* REQUIREMENT 2 *******************************)

property Requirement_2_1 (Action, N, RESULT)
    "There should be no sink in the specification, i.e., for all states in"
    "the specification, it should be possible to eventually perform any action:"
    "checking action \"$Action\"."
is
    (*
     * We show that, for any state of the POTS specification graph, it is
     * possible to reach a state from which action "$Action" CAN BE performed.
     * Practicaly, we check that when only this action is considered as
     * visible, this graph is branching bisimilar to the following one:
     *
     *       des (0, 1, 1)
     *       (0, "$Action", 0)
     *)
    "diag_2_${N}.seq" = branching comparison
        (total hide all but "$Action" in "pots.bcg") == "r2_$N.aut";
    expected "$RESULT"
end property

-------------------------------------------------------------------------------

property Requirement_2_2 (Action, N, RESULT)
    "However, action \"$Action\" does not eventually happen because of"
    "potential livelocks."
is
    -- built-in livelock detection
    "diag_2_${N}.bcg" = livelock of
        total hide all but "$Action" in "pots.bcg";
    expected "$RESULT";

    -- model checking: dataless formula
    total hide all but "$Action" in "pots.bcg" |= with evaluator
        < true* > < "i" > @;
    expected "$RESULT";
end property

-------------------------------------------------------------------------------

property Requirement_2
    "There should be no sink in the specification, i.e., for all states in the"
    "specification, it should be possible to eventually perform any action."
    "Take tones here, environment is handled later."
is
    -- equivalence checking
    check Requirement_2_1 ("S !1 !DIALT !ON", 1, TRUE);
    check Requirement_2_1 ("S !1 !DIALT !OFF", 2, TRUE);
    check Requirement_2_1 ("S !1 !RINGT !ON", 3, TRUE);
    check Requirement_2_1 ("S !1 !RINGT !OFF", 4, TRUE);
    check Requirement_2_1 ("S !1 !RINGS !ON", 5, FALSE);
    check Requirement_2_1 ("S !1 !RINGS !OFF", 6, FALSE);
    check Requirement_2_1 ("S !1 !BUSYT !ON", 7, TRUE);
    check Requirement_2_1 ("S !1 !BUSYT !OFF", 8, TRUE);
    check Requirement_2_1 ("S !1 !ERRORT !ON", 9, TRUE);
    check Requirement_2_1 ("S !1 !ERRORT !OFF", 10, TRUE);
    check Requirement_2_2 ("S !1 !DIALT !ON", 11, TRUE);

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [ true* ] (
            (* potential (and fair) reachability of actions *)
            SOME (true* . "S !1 !DIALT !ON")		and
            SOME (true* . "S !1 !DIALT !OFF")		and
            SOME (true* . "S !1 !ERRORT !ON")		and
            SOME (true* . "S !1 !ERRORT !OFF")		and
            SOME (true* . "S !1 !RINGT !ON")		and
            SOME (true* . "S !1 !RINGT !OFF")		and
            SOME (true* . "S !1 !BUSYT !ON")		and
            SOME (true* . "S !1 !BUSYT !OFF")		and
            SOME (true* . "S !1 !SPEECHCONN !ON")	and
            SOME (true* . "S !1 !SPEECHCONN !OFF")	and

            SOME (true* . "S !2 !ERRORT !ON")		and
            SOME (true* . "S !2 !ERRORT !OFF")		and
            SOME (true* . "S !2 !RINGS !ON")		and
            SOME (true* . "S !2 !RINGS !OFF")		and
            SOME (true* . "S !2 !SPEECHCONN !ON")	and
            SOME (true* . "S !2 !SPEECHCONN !OFF")	and

            (* subscriber 1 cannot be called *)
            NEVER ('S !1 !RINGS !O.*')			and

            (* subscriber 2 cannot call *)
            NEVER ('S !2 !DIALT !O.*')			and
            NEVER ('S !2 !RINGT !O.*')			and
            NEVER ('S !2 !BUSYT !O.*')			and

            (* loops forbidding inevitable reachability of actions *)
            < not (
                'S !1 !DIALT !O.*'	or
                'S !1 !ERRORT !O.*'	or
                'S !1 !RINGT !O.*'	or
                'S !1 !BUSYT !O.*'	or
                'S !1 !SPEECHCONN !O.*'
	      ) > @					and

            < not (
                'S !2 !ERRORT !O.*'	or
                'S !2 !RINGS !O.*'	or
                'S !2 !SPEECHCONN !O.*'
	      ) > @
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ] (
	    (* potential (and fair) reachability of actions *)
	    SOME (true* . SignalOn  (1, "DIALT"))	and
	    SOME (true* . SignalOff (1, "DIALT"))	and
	    SOME (true* . SignalOn  (1, "ERRORT"))	and
	    SOME (true* . SignalOff (1, "ERRORT"))	and
	    SOME (true* . SignalOn  (1, "RINGT"))	and
	    SOME (true* . SignalOff (1, "RINGT"))	and
	    SOME (true* . SignalOn  (1, "BUSYT"))	and
	    SOME (true* . SignalOff (1, "BUSYT"))	and
	    SOME (true* . SignalOn  (1, "SPEECHCONN"))	and
	    SOME (true* . SignalOff (1, "SPEECHCONN"))	and

	    SOME (true* . SignalOn  (2, "ERRORT"))	and
	    SOME (true* . SignalOff (2, "ERRORT"))	and
	    SOME (true* . SignalOn  (2, "RINGS"))	and
	    SOME (true* . SignalOff (2, "RINGS"))	and
	    SOME (true* . SignalOn  (2, "SPEECHCONN"))	and
	    SOME (true* . SignalOff (2, "SPEECHCONN"))	and

	    (* subscriber 1 cannot be called *)
	    NEVER (SignalAny (1, "RINGS"))		and

	    (* subscriber 2 cannot call *)
	    NEVER (SignalAny (2, "DIALT"))		and
	    NEVER (SignalAny (2, "RINGT"))		and
	    NEVER (SignalAny (2, "BUSYT"))		and

	    (* cycles forbidding inevitable reachability of actions *)
	    < not (
	        SignalAny (1, "DIALT")      or
	        SignalAny (1, "ERRORT")     or
	        SignalAny (1, "RINGT")      or
	        SignalAny (1, "BUSYT")      or
	        SignalAny (1, "SPEECHCONN")
	      ) > @					and

	    < not (
	        SignalAny (2, "ERRORT")     or
	        SignalAny (2, "RINGS")      or
	        SignalAny (2, "SPEECHCONN")
	      ) > @
	);
    expected TRUE
end property

(******************************* REQUIREMENT 3 *******************************)

property Requirement_3_Equivalence_Checking (Action, N)
    "It should always be possible for subscriber $N to dial a number:"
    "action \"$Action\" can always be performed."
is
    (*
     * We show that, from each state of the POTS specification graph, action
     * "$Action" can be performed. Practicaly, we rename all other actions
     * in OTHERS, and we check that this graph is strongly equivalent to the
     * following one:
     *
     *       des (0, 2, 1)
     *       (0, OTHERS, 0)
     *       (0, "$Action", 0)
     *)
    "diag_3_$N.seq" = strong comparison
        (
            total rename
                "$Action" -> "$Action",
                ".*" -> "OTHERS"
            in "pots.bcg"
        ) 
        == "r3_$N.aut";
    expected TRUE
end property

-------------------------------------------------------------------------------

property Requirement_3
    "It should always be possible for every subscriber to dial a number."
is
    -- equivalence checking
    check Requirement_3_Equivalence_Checking ("S !1 !DIAL !2", 1);
    check Requirement_3_Equivalence_Checking ("S !2 !DIAL !1", 2);

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [ true* ] (SOME ("S !1 !DIAL !2") and SOME ("S !2 !DIAL !1"));
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ] (SOME (Dial (1, 2)) and SOME (Dial (2, 1)));
    expected TRUE
end property

(******************************* REQUIREMENT 4 *******************************)

property Requirement_4_Equivalence_Checking (N, RESULT)
    "It should always be possible for subscriber $N to perform an offhook or"
    "an onhook: actions \"S !$N !OFFH !ASUBSC\", \"S !$N !OFFH !BSUBSC\""
    "and \"S !$N !ONH\" can always be performed." 
is
    (*
     * We show that, for each state of the POTS specification graph, at least
     * one of the following actions can always be executed:
     *     "S !$N !OFFH !ASUBSC",  "S !$N !OFFH !BSUBSC" or "S !$N !ONH".
     *
     * All these actions are renamed in ONHOOK_OFFHOOK, all other ones in
     * OTHERS, and we check that the resulting graph is strongly equivalent to
     * the following one:
     *
     *       des (0, 2, 1)
     *       (0, ONHOOK_OFFHOOK, 0)
     *       (0, OTHERS, 0)
     *
     * Performing a similar check for the 2nd subscriber shows that the
     * requirement happens to be false in this case. The diagnostic sequence
     * corresponds to an execution path leading to a state of the POTS
     * specification graph from which the ONHOOK_OFFHOOK action cannot be
     * executed.
     *)
    "diag_4_$N.seq" = strong comparison
        (
            total rename
                "S !$N !OFFH !ASUBSC" -> "ONHOOK_OFFHOOK", 
                "S !$N !OFFH !BSUBSC" -> "ONHOOK_OFFHOOK",
                "S !$N !ONH" -> "ONHOOK_OFFHOOK",
                ".*" -> "OTHERS"
            in "pots.bcg"
        )
        == "r4.aut";
    expected "$RESULT"
end property

-------------------------------------------------------------------------------

property Requirement_4
    "It should always be possible for every subscriber to perform an offhook"
    "or an onhook. This property is false, because there exists a state of"
    "the POTS specification graph from which subscriber 2 cannot execute the"
    "ONHOOK_OFFHOOK action."
is
    -- equivalence checking
    check Requirement_4_Equivalence_Checking (1, TRUE);
    check Requirement_4_Equivalence_Checking (2, FALSE);

    -- model checking: dataless formula
    -- uncomment the following line to generate a diagnostic:
    -- "diag_4_dataless.bcg" =
    "pots.bcg" |= with evaluator
        [ true* ] (
            (* holds *)
            SOME ('S !1 !OFFH ![AB]SUBSC' or "S !1 !ONH") and
            (* fails *)
            SOME ('S !2 !OFFH ![AB]SUBSC' or "S !2 !ONH")
        );
    expected FALSE;

    -- model checking: value-passing formula
    -- uncomment the following line to obtain a diagnostic
    -- "diag_4_value_passing.bcg" =
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ] (
	    (* holds *)
	    SOME (OffHook (1) or OnHook (1)) and
	    (* fails *)
	    SOME (OffHook (2) or OnHook (2))
	);
    expected FALSE
end property

(************************** REQUIREMENT 5, 6 and 7 ***************************)

property Requirements_5_6_7_incorrect_Sub (N, R)
    "Subscriber 1: incorrect specification." 
is
    (*
     * These three requirements denote safety properties and they can be
     * verified in the same round. According to these requirements, the
     * expected behaviour of subscriber $N (N = 1, 2) with respect to
     * "S !$N !OFFH !ASUBSC", "S !$N !OFFH !BSUBSC" and "S !$N !ONH"
     * actions is expressed by the following graphs:
     *
     *       des (0, 3, 2)
     *       (0, "S !$N !OFFH !ASUBSC", 1)
     *       (0, "S !$N !OFFH !BSUBSC", 1)
     *       (1, "S !$N !ONH", 0)
     *
     * Requirements 5, 6 and 7 can then be simply verified by comparing these
     * graphs to the POTS specification one modulo safety equivalence.
     *
     * This requirement happens to be false for the 1st subscriber ($N = 1),
     * since "S !1 !OFFH !BSUBSC" action does not appear in the POTS
     * specification.
     *)
    "diag_5_${N}_KO.seq" = safety comparison
        (
            total hide all but
                "S !$N !OFFH !ASUBSC", 
                "S !$N !OFFH !BSUBSC",
                "S !$N !ONH"
            in "pots.bcg"
        )
        == "r5_${N}_KO.aut";
    result "$R" expected FALSE
end property

-------------------------------------------------------------------------------

property Requirements_5_6_7_correct_Sub (N, R)
    "Subscriber $N: correct specification."
is
    (*
     * For the 1st subscriber ($N = 1), a correct specification of the       
     * expected behaviour is the following one:
     *
     *       des (0, 2, 2)
     *       (0, "S !$N !OFFH !ASUBSC", 1)
     *       (1, "S !$N !ONH", 0)
     *)
    "diag_5_${N}_OK.seq" = safety comparison
        (
            total hide all but
                "S !$N !OFFH !ASUBSC", 
                "S !$N !OFFH !BSUBSC", 
                "S !$N !ONH"
            in "pots.bcg"
        )
        == "r5_${N}_OK.aut";
    result "$R" expected TRUE
end property

-------------------------------------------------------------------------------

property Requirement_5
    "Onhook and offhook for a subscriber are mutually exclusive, i.e., it is"
    "never possible for a subscriber to be able to perform both an offhook"
    "and an onhook at the same time."
is
    -- equivalence checking

    check Requirements_5_6_7_incorrect_Sub (1, RESULT_1_KO);
    -- result is stored in the shell variable $RESULT_1_KO
    -- for reuse in requirements 6 and 7

    check Requirements_5_6_7_correct_Sub (1, RESULT_1_OK);
    -- result is stored in the shell variable $RESULT_1_OK
    -- for reuse in requirements 6 and 7

    check Requirements_5_6_7_correct_Sub (2, RESULT_2_OK);
    -- result is stored in the shell variable $RESULT_2_OK
    -- for reuse in requirements 6 and 7

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [ true* ] (
            not (
                SOME ('S !1 !OFFH ![AB]SUBSC') and
                SOME ("S !1 !ONH !TRUE")
            )
            and
            not (
                SOME ('S !2 !OFFH ![AB]SUBSC') and
                SOME ("S !2 !ONH !TRUE")
            )
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ]
	    forall Subscriber:nat among { 1 ... 2 } .
		not (
		    SOME (OffHook (Subscriber)) and
		    SOME (OnHook (Subscriber))
		);
    expected TRUE
end property

-------------------------------------------------------------------------------

property Requirement_6
    "A subscriber can only onhook after he has performed an offhook."
is
    -- equivalence checking
    -- Requirement_6 is covered by verifications already done for Requirement_5
    % echo "$RESULT_1_KO"
	expected FALSE;
    % echo "$RESULT_1_OK"
	expected TRUE;
    % echo "$RESULT_2_OK"
	expected TRUE;

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        NEVER (
            ((nil | true*) . "S !1 !ONH" .
             (not 'S !1 !OFFH ![AB]SUBSC')* .
             "S !1 !ONH")
            |
            ((nil | true*) . "S !2 !ONH" .
             (not 'S !2 !OFFH ![AB]SUBSC')* .
             "S !2 !ONH")
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	forall Subscriber:nat among { 1 ... 2 } .
	    NEVER (
		(nil | (true* . OnHook (Subscriber))) .
		(not OffHook (Subscriber))* .
		OnHook (Subscriber)
	    );
    expected TRUE
end property

-------------------------------------------------------------------------------

property Requirement_7
    "Onhook and offhook alternate."
is
    -- equivalence checking
    -- Requirement_7 is covered by verifications already done for Requirement_5
    % echo "$RESULT_1_KO"
	expected FALSE;
    % echo "$RESULT_1_OK"
	expected TRUE;
    % echo "$RESULT_2_OK"
	expected TRUE;

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        nu ExpectOffHook . (
            NEVER ("S !1 !ONH")
            and
            [ 'S !1 !OFFH ![AB]SUBSC' ]
                nu Expect_OnHook . (
                    [ "S !1 !ONH" ] ExpectOffHook
                    and
                    NEVER ('S !1 !OFFH ![AB]SUBSC')
                    and
                    [ not ("S !1 !ONH" or 'S !1 !OFFH ![AB]SUBSC') ]
                        Expect_OnHook
                )
            and
            [ not ("S !1 !ONH" or 'S !1 !OFFH ![AB]SUBSC') ] ExpectOffHook
        )

        and

        nu ExpectOffHook . (
            NEVER ("S !2 !ONH")
            and
            [ 'S !2 !OFFH ![AB]SUBSC' ]
                nu Expect_OnHook . (
                    [ "S !2 !ONH" ] ExpectOffHook
                    and
                    NEVER ('S !2 !OFFH ![AB]SUBSC')
                    and
                    [ not ("S !2 !ONH" or 'S !2 !OFFH ![AB]SUBSC') ]
                        Expect_OnHook
                )
            and
            [ not ("S !2 !ONH" or 'S !2 !OFFH ![AB]SUBSC') ] ExpectOffHook
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	forall Subscriber:nat among { 1 ... 2 } .
	    nu Expect (off_or_on:bool := true) . (
	        [ OffHook (Subscriber) ]
	            (off_or_on and Expect (not off_or_on))
	        and
	        [ OnHook (Subscriber) ]
	            (not off_or_on and Expect (not off_or_on))
	        and
	        [ not (OnHook (Subscriber) or OffHook (Subscriber)) ]
		    Expect (off_or_on)
	    );
    expected TRUE
end property

(******************************* REQUIREMENT 8 *******************************)

property Requirement_8_Equivalence_Checking (X, Y1, Y2, Y3, Y4, Y5)
    "For a given subscriber, in order for a tone to be activated, the previous"
    "tone or signal has to be desactivated: $X signal."
is
    (*
     * The set of tone and signals is the following:
     *       Tone = DIALT, RINGT, RINGS, ERRORT, BUSYT, SPEECHCONN
     *
     * We show that for each ($X, $Y) in this set (with $X <> $Y),
     * "S !1 !$X !ON" action cannot be followed by a "S !1 !$Y !ON"
     * action, unless "S !1 !$X !OFF" occurred.
     *
     * Practicaly, if $X = DIALT :
     *
     *       "S !1 !DIALT !ON" is renamed in X_ON
     *       "S !1 !DIALT !OFF" is renamed in X_OFF
     *       "S !1 !$Y !ON" is renamed in Y, for all $Y in Tone different
     *       from $X (i.e., $Y1 to $Y5)
     *
     * Then, it remains to check that when only these actions are considered as
     * visible, the POTS specification graph is included (modulo the safety
     * preorder) into the following one:
     *
     *       des (0, 3, 2)
     *       (0, X_ON, 1)
     *       (1, X_OFF, 0)
     *       (0, Y, 0)
     *)
    "diag_8_$X.seq" = tau*.a comparison
        (
            total rename
                "S !1 !$X !ON" -> "X_ON",
                "S !1 !$Y1 !ON" -> "Y",
                "S !1 !$Y2 !ON" -> "Y",
                "S !1 !$Y3 !ON" -> "Y",
                "S !1 !$Y4 !ON" -> "Y",
                "S !1 !$Y5 !ON" -> "Y",
                "S !1 !$X !OFF" -> "X_OFF",
                "X_ON" -> "X_ON",
                "X_OFF" -> "X_OFF",
                "Y" -> "Y",
                ".*" -> "i" 
            in "pots.bcg"
        )
        <= "r8.aut";
    expected TRUE
end property

-------------------------------------------------------------------------------

property Requirement_8
    "For a given subscriber, only one tone or signal may be activated at a"
    "given time."
is
    -- equivalence checking
    check Requirement_8_Equivalence_Checking
              (DIALT, RINGT, RINGS, ERRORT, BUSYT, SPEECHCONN);
    check Requirement_8_Equivalence_Checking
              (RINGT, DIALT, RINGS, ERRORT, BUSYT, SPEECHCONN);
    check Requirement_8_Equivalence_Checking
              (RINGS, DIALT, RINGT, ERRORT, BUSYT, SPEECHCONN);
    check Requirement_8_Equivalence_Checking
              (ERRORT, DIALT, RINGT, RINGS, BUSYT, SPEECHCONN);
    check Requirement_8_Equivalence_Checking
              (BUSYT, DIALT, RINGT, RINGS, ERRORT, SPEECHCONN);
    check Requirement_8_Equivalence_Checking
              (SPEECHCONN, DIALT, RINGT, RINGS, ERRORT, BUSYT);

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [ true* ] (
            (* Subscriber 1 *)
            (
                SOME ("S !1 !DIALT !ON") implies
                NEVER ('S !1 .* !ON' and not "S !1 !DIALT !ON")
            ) and
            (
                SOME ("S !1 !RINGT !ON") implies
                NEVER ('S !1 .* !ON' and not "S !1 !RINGT !ON")
            ) and
            (
                SOME ("S !1 !RINGS !ON") implies
                NEVER ('S !1 .* !ON' and not "S !1 !RINGS !ON")
            ) and
            (
                SOME ("S !1 !ERRORT !ON") implies
                NEVER ('S !1 .* !ON' and not "S !1 !ERRORT !ON")
            ) and
            (
                SOME ("S !1 !BUSYT !ON") implies
                NEVER ('S !1 .* !ON' and not "S !1 !BUSYT !ON")
            ) and
            (
                SOME ("S !1 !SPEECHCONN !ON") implies
                NEVER ('S !1 .* !ON' and not "S !1 !SPEECHCONN !ON")
            ) and
            (* Subscriber 2 *)
            (
                SOME ("S !2 !DIALT !ON") implies
                NEVER ('S !2 .* !ON' and not "S !2 !DIALT !ON")
            ) and
            (
                SOME ("S !2 !RINGT !ON") implies
                NEVER ('S !2 .* !ON' and not "S !2 !RINGT !ON")
            ) and
            (
                SOME ("S !2 !RINGS !ON") implies
                NEVER ('S !2 .* !ON' and not "S !2 !RINGS !ON")
            ) and
            (
                SOME ("S !2 !ERRORT !ON") implies
                NEVER ('S !2 .* !ON' and not "S !2 !ERRORT !ON")
            ) and
            (
                SOME ("S !2 !BUSYT !ON") implies
                NEVER ('S !2 .* !ON' and not "S !2 !BUSYT !ON")
            ) and
            (
                SOME ("S !2 !SPEECHCONN !ON") implies
                NEVER ('S !2 .* !ON' and not "S !2 !SPEECHCONN !ON")
            )
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	macro Single_Tone (Subscriber, Tone) =
	    (
		SOME (SignalOn (Subscriber, Tone)) implies
		[ { S !(Subscriber) ?Signal:string !"ON" } ] (Signal = (Tone))
	    )
	end_macro
	[ true* ]
	    forall Subscriber:nat among { 1 ... 2 } . (
		Single_Tone (Subscriber, "DIALT")      and
		Single_Tone (Subscriber, "RINGT")      and
		Single_Tone (Subscriber, "RINGS")      and
		Single_Tone (Subscriber, "ERRORT")     and
		Single_Tone (Subscriber, "BUSYT")      and
		Single_Tone (Subscriber, "SPEECHCONN")
	    );
    expected TRUE
end property

(******************************* REQUIREMENT 9 *******************************)

property Requirement_9
    "For a given subscriber, once an onhook has been performed, no tone can"
    "be activated until offhook is performed."
is
    -- equivalence checking
    (*
     * We show that, after an occurrence of an "S !1 !ONH" action (i.e,
     * onhook), no "S !1 !$X !ON" action can be performed, for any $X
     * belonging to the set Tone, unless "S !1 !OFFH !ASUBSC" action occurs.
     *
     * Practicaly, "S !1 !X !ON" actions are renamed in TONE, and we check
     * that when only these actions are considered as visible the resulting
     * graph is included (modulo safety preorder) into the following one:
     *
     *       des (0, 4, 2)
     *       (0, "S !1 !ONH", 1)
     *       (1, "S !1 !OFFH !ASUBSC", 0)
     *       (0, "S !1 !OFFH !ASUBSC", 0)
     *       (0, TONE, 0)
     *)
    "diag_9.seq" = tau*.a comparison
        (
            total rename
                "S !1 !ONH" -> "S !1 !ONH",
                "S !1 !OFFH !ASUBSC" -> "S !1 !OFFH !ASUBSC",
                "S !1 !OFFH !BSUBSC" -> "S !1 !OFFH !BSUBSC",
                "S !1 !RINGT !ON" -> "TONE",
                "S !1 !ERRORT !ON" -> "TONE",
                "S !1 !BUSYT !ON" -> "TONE",
                "S !1 !SPEECHCONN !ON" -> "TONE",
                "S !1 !DIALT !ON" -> "TONE",
                ".*" -> "i"
            in "pots.bcg" 
        )
        <= "r9.aut";
    expected TRUE;

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        NEVER (
            true* .
            (
                (* Subscriber 1 *)
                (
                    (
                    ( "S !1 !DIALT !ON"      . (not "S !1 !DIALT !OFF")* )  |
                    ( "S !1 !RINGT !ON"      . (not "S !1 !RINGT !OFF")* )  |
                    ( "S !1 !RINGS !ON"      . (not "S !1 !RINGS !OFF")* )  |
                    ( "S !1 !ERRORT !ON"     . (not "S !1 !ERRORT !OFF")* ) |
                    ( "S !1 !BUSYT !ON"      . (not "S !1 !BUSYT !OFF")* )  |
                    ( "S !1 !SPEECHCONN !ON" . (not "S !1 !SPEECHCONN !OFF")* )
                    ) .
                    'S !1 .* !ON'
                ) |
                (* Subscriber 2 *)
                (
                    (
                    ( "S !2 !DIALT !ON"      . (not "S !2 !DIALT !OFF")* )  |
                    ( "S !2 !RINGT !ON"      . (not "S !2 !RINGT !OFF")* )  |
                    ( "S !2 !RINGS !ON"      . (not "S !2 !RINGS !OFF")* )  |
                    ( "S !2 !ERRORT !ON"     . (not "S !2 !ERRORT !OFF")* ) |
                    ( "S !2 !BUSYT !ON"      . (not "S !2 !BUSYT !OFF")* )  |
                    ( "S !2 !SPEECHCONN !ON" . (not "S !2 !SPEECHCONN !OFF")* )
                    ) .
                    'S !2 .* !ON'
                )
            )
        );
    expected TRUE;
    
    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ]
	    forall Subscriber:nat among { 1 ... 2 } .
		NEVER (
		    { S !Subscriber ?Signal:string !"ON" } .
		    (not SignalOff (Subscriber, Signal))* .
		    SignalOn (Subscriber)
		);
    expected TRUE
end property

(******************************* REQUIREMENT 10 ******************************)

property Requirement_10
    "For a given subscriber, once an offhook has been performed, no signal"
    "can be activated until offhook is performed."
is
    -- equivalence checking
    (*
     * We rather examine this requirement for the 2nd subscriber, since
     * "S !1 !RINGS !ON" action does not appear in the POTS specification.
     *
     * We show that, after any occurrence of "S !2 !OFFH !ASUBSC" or
     * "S !2 !OFFH !BSUBSC" action, "S !2 !RINGS !ON" action cannot be
     * performed unless "S !2 !ONH" action occurs. Practicaly, we check that
     * when only these actions are visible the resulting graph is included
     * (modulo safety preorder) into the following one:
     *
     *       des (0, 5, 2)
     *       (0, "S !2 !ONH", 0)
     *       (0, "S !2 !OFFH !ASUBSC", 1)
     *       (0, "S !2 !OFFH !BSUBSC", 1)
     *       (1, "S !2 !ONH", 0)
     *       (0, "S !2 !RINGS !ON", 0)
     *)
    "diag_10.seq" = tau*.a comparison
        (
            total hide all but
                "S !2 !ONH",
                "S !2 !OFFH !ASUBSC",
                "S !2 !RINGS !ON"
            in "pots.bcg"
        )
        <= "r10.aut";
    expected TRUE;

    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        NEVER (
            true* .
            (
            ("S !1 !ONH" . (not 'S !1 !OFFH ![AB]SUBSC')* . 'S !1 !.*T !ON')
            |
            ("S !2 !ONH" . (not 'S !2 !OFFH ![AB]SUBSC')* . 'S !2 !.*T !ON')
            )
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ]
	    forall Subscriber:nat among { 1 ... 2 } .
		NEVER (
		    OnHook (Subscriber) .
		    (not OffHook (Subscriber))* .
		    ToneOn (Subscriber)
		);
    expected TRUE
end property

(******************************* REQUIREMENT 11 ******************************)

property Requirement_11
    "For a given subscriber, once an offhook has been performed, no signal"
    "can be activated until onhook is performed."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        NEVER (
            true* .
            (
            ('S !1 !OFFH ![AB]SUBSC' . (not "S !1 !ONH")* . "S !1 !RINGS !ON")
            |
            ('S !2 !OFFH ![AB]SUBSC' . (not "S !2 !ONH")* . "S !2 !RINGS !ON")
            )
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* ]
	    forall Subscriber:nat among { 1 ... 2 } .
		NEVER (
		    OffHook (Subscriber) .
		    (not OnHook (Subscriber))* .
		    SignalOn (Subscriber, "RINGS")
		);
    expected TRUE
end property

(******************************* REQUIREMENT 12 ******************************)

property Requirement_12
    "If an S-subscriber performs offhook, there should be no possibility of"
    "activating any tone other than dialtone."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [ true* . 'S !1 !OFFH ![AB]SUBSC' ] (
            NEVER (
                (not 'S !1 !DIALT .*')* .
                "S !1 !RINGT !ON" or
                "S !1 !ERRORT !ON" or
                "S !1 !BUSYT !ON" or
                "S !1 !SPEECHCONN !ON"
            )
            and
            SOME (true* . "S !1 !DIALT !ON")
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* . OffHook (1) ] (
	    NEVER (
              (not SignalAny (1, "DIALT"))* .
	      SignalOn (1, "RINGT") or
	      SignalOn (1, "ERRORT") or
	      SignalOn (1, "BUSYT") or
	      SignalOn (1, "SPEECHCONN")
	    )
	    and
	    SOME (true* . SignalOn (1, "DIALT"))
	);
    expected TRUE
end property

(******************************* REQUIREMENT 13 ******************************)

property Requirement_13
    "If A-subscriber dials B-subscriber while A's dialtone is active, then"
    "there should be a possibility of A's dialtone being deactivated."
    "If in addition B is onhooked, and B has no tones active, then:"
    " - There should be a possibility of B's ring tone being activated."
    " - There should be a possibility of deactivating A's dialtone and"
    "   activating A's ringtone (no other tones should be activated)."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        library macros_v3.mcl end_library
        [ true* . "S !1 !DIALT !ON" .
          (not "S !1 !DIALT !OFF")* . "S !1 !DIAL !2" ] 
            SOME ((not "S !1 !DIALT !OFF")* . "S !1 !DIALT !OFF")

        and
        NO_2_TONES_ACTIVE (
            [
                (not ('S !2 .*T !ON'))* .
                (
                    ("S !1 !DIALT !ON" .
                     (not ('S !2 .*T !ON' or "S !1 !DIALT !OFF"))* .
                     "S !2 !ONH") |
                    ("S !2 !ONH" .
                     (not ('S !2 .*T !ON' or "S !1 !DIALT !OFF"))* .
                     "S !1 !DIALT !ON")
                ) .
                (not ('S !2 .*T !ON' or "S !1 !DIALT !OFF"))* .
                "S !1 !DIAL !2"
            ] (
                SOME ((not 'S !2 .*T !ON' )* . "S !2 !RINGS !ON")
                and
                SOME ((not 'S !1 .*T !ON')* . "S !1 !DIALT !OFF" .
                  (not 'S !1 .*T !ON')* . "S !1 !RINGT !ON")
            )
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[ true* . SignalOn (1, "DIALT") .
	  (not SignalOff (1, "DIALT"))* . Dial (1, 2) ] 
	    SOME ((not SignalOff (1, "DIALT"))* . SignalOff (1, "DIALT"))
	and
	NO_2_TONES_ACTIVE (
	    [
	        (not ToneOn (2))* .
	        (
	            (SignalOn (1, "DIALT") .
	             (not (ToneOn (2) or SignalOff (1, "DIALT")))* .
	             OnHook (2)) |
	            (OnHook (2) .
	             (not (ToneOn (2) or SignalOff (1, "DIALT")))* .
	             SignalOn (1, "DIALT"))
	        ) .
	        (not (ToneOn (2) or SignalOff (1, "DIALT")))* .
	        Dial (1, 2)
	    ] (
	        SOME ((not ToneOn (2))* . SignalOn (2, "RINGS"))
	        and
	        SOME ((not ToneOn (1))* . SignalOff (1, "DIALT") .
	          (not ToneOn (1))* . SignalOn (1, "RINGT"))
	    )
	);
    expected TRUE
end property

(******************************* REQUIREMENT 14 ******************************)

property Requirement_14
    "If A-Subscriber dials B-subscriber and B-subscriber is offhooked,"
    "then there should be a possibility of activating A's busytone after"
    "deactivating dialtone (no other tones should be activated)."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [
            true* .
            (
                ("S !2 !OFFH !BSUBSC" . (not "S !2 !ONH")* . "S !1 !DIAL !2") |
                ("S !1 !DIAL !2" . (not "S !2 !ONH")* . "S !2 !OFFH !BSUBSC")
            )
        ]
        SOME (
            ('S !1 .* !ON' implies 'S !1 !DIALT !ON')* .
            "S !1 !DIALT !OFF" .
            (not 'S !1 .*T !ON')* .
            "S !1 !BUSYT !ON"
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[
	    true* .
	    (
	        (OffHook (2, "BSUBSC") . (not OnHook (2))* . Dial (1, 2)) |
	        (Dial (1, 2) . (not OnHook (2))* . OffHook (2, "BSUBSC"))
	    )
	]
	SOME (
	    (SignalOn (1) implies SignalOn (1, "DIALT"))* .
	    SignalOff (1, "DIALT") .
	    (not ToneOn (1))* .
	    SignalOn (1, "BUSYT")
	);
    expected TRUE
end property

(******************************* REQUIREMENT 15 ******************************)

property Requirement_15
    "If A subscriber dials B-subscriber when A has dialtone on, A is offhook,"
    "B is onhook, and has no tones active, then it is possible for B to"
    "perform offhook as a B-subscriber."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        library macros_v3.mcl end_library
        NO_2_TONES_ACTIVE (
            [
                (not ('S !2 .*T !ON'))* .
                "S !1 !DIALT !ON" .
                (not ('S !2 .*T !ON' or "S !1 !DIALT !OFF"))* .
                "S !1 !OFFH !ASUBSC" .
                (not ('S !2 .*T !ON' or "S !1 !DIALT !OFF" or "S !1 !ONH"))* .
                "S !2 !ONH" .
                (not ('S !2 .*T !ON' or "S !1 !DIALT !OFF" or "S !1 !ONH" or
                      'S !2 !OFFH .*'))* .
                "S !1 !DIAL !2"
            ]
            SOME ((not 'S !2 !OFFH .*')* . "S !2 !OFFH !BSUBSC")
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	NO_2_TONES_ACTIVE (
	    [
	        (not (ToneOn (2)))* .
	        SignalOn (1, "DIALT") .
	        (not (ToneOn (2) or SignalOff (1, "DIALT")))* .
	        OffHook (1, "ASUBSC") .
	        (not (ToneOn (2) or SignalOff (1, "DIALT") or OnHook (1)))* .
	        OnHook (2) .
	        (not (ToneOn (2) or SignalOff (1, "DIALT") or OnHook (1) or
	              OffHook (2)))* .
	        Dial (1, 2)
	    ]
	    SOME ((not OffHook (2))* . OffHook (2, "BSUBSC"))
	);
    expected TRUE
end property

(******************************* REQUIREMENT 16 ******************************)

property Requirement_16
    "If B-subscriber has ringsignal activated and B performs offhook while A"
    "remains onhooked then:"
    " - There should be a possibility of A's ring tone being deactivated."
    " - There should be a possibility of B's ring signal being deactivated."
    " - If A's ring tone is deactivated, there should be a possibility of"
    "   A's speech connection being activated."
    " - If B's ring signal is deactivated, there should be a possibility of"
    "   B's speech connection being activated."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [
            true* .
            "S !1 !ONH" .
            (not "S !1 !OFFH !ASUBSC")* .
            "S !2 !RINGS !ON" .
            (not "S !1 !OFFH !ASUBSC")* .
            "S !2 !OFFH !BSUBSC"
        ] (
            SOME(true* . "S !1 !RINGT !OFF")
            and
            SOME (true* . "S !2 !RINGS !OFF")
            and
            [ (not "S !1 !OFFH !ASUBSC")* . "S !1 !RINGT !OFF" ]
                SOME(true* . "S !1 !SPEECHCONN !ON")
            and
            [ (not "S !1 !OFFH !ASUBSC")* . "S !2 !RINGS !OFF" ]
                SOME (true* . "S !2 !SPEECHCONN !ON")
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[
	    true* .
	    OnHook (1) .
	    (not OffHook (1, "ASUBSC"))* .
	    SignalOn (2, "RINGS") .
	    (not OffHook (1, "ASUBSC"))* .
	    OffHook (2, "BSUBSC")
	] (
	    SOME (true* . SignalOff (1, "RINGT"))
	    and
	    SOME (true* . SignalOff (2, "RINGS"))
	    and
	    [ (not OffHook (1, "ASUBSC"))* . SignalOff (1, "RINGT") ]
	        SOME (true* . SignalOn (1, "SPEECHCONN"))
	    and
	    [ (not OffHook (1, "ASUBSC"))* . SignalOff (2, "RINGS") ]
	        SOME (true* . SignalOn (2, "SPEECHCONN"))
	);
    expected TRUE
end property

(******************************* REQUIREMENT 17 ******************************)

property Requirement_17
    "If A-subscriber and B-subscriber have speech connection activated and"
    "B-subscriber performs onhook then:"
    " - There should be a possibility of the speech connection being"
    "   deactivated."
    " - Once speech connection is deactivated, A's error tone is activated."
is
    -- model checking: dataless formula
    "pots.bcg" |= with evaluator
        [
            true* .
            "S !1 !SPEECHCONN !ON" .
            (not 'S ![12] !SPEECHCONN !OFF')* .
            "S !2 !SPEECHCONN !ON" .
            (not 'S ![12] !SPEECHCONN !OFF')* .
            "S !2 !ONH"
        ] (
            SOME (true* . 'S ![12] !SPEECHCONN !OFF')
            and
            (* fair (but not inevitable) reachability *)
            [ true* . 'S ![12] !SPEECHCONN !OFF' . (not "S !1 !ERRORT !ON")* ]
                SOME((not "S !1 !ERRORT !ON")* . "S !1 !ERRORT !ON")
        );
    expected TRUE;

    -- model checking: value-passing formula
    "pots.bcg" |= with evaluator
        library macros_v4.mcl end_library
	[
	    true* .
	    SignalOn (1, "SPEECHCONN") .
	    (not (SignalOff (1, "SPEECHCONN") or
		  SignalOff (2, "SPEECHCONN")))* .
	    SignalOn (2, "SPEECHCONN") .
	    (not (SignalOff (1, "SPEECHCONN") or
		  SignalOff (2, "SPEECHCONN")))* .
	    OnHook (2)
	] (
	    SOME (true* . SignalOff (1, "SPEECHCONN") or
		      SignalOff (2, "SPEECHCONN"))
	    and
	    (* fair (but not inevitable) reachability *)
	    [ true* . SignalOff (1, "SPEECHCONN") or
		      SignalOff (2, "SPEECHCONN") .
	      (not SignalOn (1, "ERRORT"))* ]
	        SOME ((not SignalOn (1, "ERRORT"))* . SignalOn (1, "ERRORT"))
	);
    expected TRUE
end property

-------------------------------------------------------------------------------

(*****************************************************************************
 * Step 3: LNT vs LOTOS COMPARISON.                                          *
 * The original LOTOS specification is translated into a graph, which is     *
 * compared against the graph generated from the LNT specification. Both     *
 * graphs are expected to be strongly equivalent.                            *
 *****************************************************************************)

(* generation of the original LOTOS specification *)

% (cd LOTOS ; echo "" ; svl)

(* comparison of the graphs generated from LOTOS and LNT *)

"diag.bcg" = strong comparison "pots.bcg" == "LOTOS/pots.bcg";

(* cleanup *)

% SVL_COMMAND_FOR_CLEAN "(cd LOTOS ; svl -clean)"