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Algebraic Example – OBJ3

Algebraic Example – OBJ3 . Tarang Garg Srikumar Nagaraj. OBJ3 - Revision. “ OBJ3 is a wide spectrum first order functional language that is rigorously based upon equational logic.” Based on order sorted equational logic

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Algebraic Example – OBJ3

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  1. Algebraic Example – OBJ3 Tarang Garg Srikumar Nagaraj cs599 - Formal Methods in Software Architecture

  2. OBJ3 - Revision “ OBJ3 is a wide spectrum first order functional language that is rigorously based upon equational logic.” • Based on order sorted equational logic • Provides notion of ‘Subsort’ that rigorously supports multiple inheritance • Exception handling and Overloading • It is a theorem prover • It gives powerful support for design and verification cs599 - Formal Methods in Software Architecture

  3. Cruise Control “ The objects are identified by the Nouns in the specification and the interaction between the objects are identified by the Verbs.” Objects : Vehicle (not a required object for specs) brake accelerator pedal CC(cruise control) button On /Off CC button Set/Accelerator CC button Resume/Decelerator cs599 - Formal Methods in Software Architecture

  4. Cruise Control Assumptions: *************************************************************************** 1. If cruise-speed = 0 then the car is not cruising and if cruise-speed <> 0 then the car is cruising. 2. cruise_state represents the button. 3. Max. allowed speed is 140 mph. 4. The car does not take any time to change speeds. **************************************************************************** th CAR-STATE is sort INT . protecting INT . protecting TRUTH-VALUE . op init1_ : INT  INT . op init2_ : TRUTH-VALUE  TRUTH-VALUE . vars curr_speed cruise_speed last_cruise_speed : INT . var cruise_state : TRUTH-VALUE . eq init1 curr_speed = 0 . eq init1 cruise_speed = 0 . eq init1 last_cruise_speed = 0 . eq init2 cruise_state = false . endth cs599 - Formal Methods in Software Architecture

  5. Cruise Control obj CC-ON-OFF[V-CAR-STATE :: CAR-STATE] . protecting TRUTH-VALUE . op cruise-press_ : TRUTH-VALUE  TRUTH-VALUE . var I : TRUTH-VALUE . cq cruise-press (cruise_state) = (I = false) *** This checks for the cruise control button if it is ON if cruise-state == true . eq cruise-state = I . cq cruise-press (cruise-state) = (I = false) and (last-cruise-speed = 0) *** This checks for the cruise control button if it is OFF if cruise-state == false . endo cs599 - Formal Methods in Software Architecture

  6. Cruise Control obj CC-SET-ACCELERATE[V-CAR-STATE :: CAR-STATE] . protecting INT . protecting TRUTH-VALUE . op button-press_ _ _ : INT INT TRUTH-VALUE  INT INT INT . op button-press_ _ : INT TRUTH-VALUE  INT INT . op time_ : INT  INT . vars X Y : INT . cq button-press (cruise-speed , curr-speed , cruise-state) = (cruise-speed = curr-speed) and (last-cruise-speed = cruise-speed) if (cruise-state == true) and (curr-speed > 30) and (curr-speed < 90) and (cruise-speed = 0) . cq button-press (cruise-speed , cruise-state) = (cruise-speed = cruise-speed + Y) and (last-cruise-speed = cruise-speed) if (cruise-state == true) and (cruise-speed > 30) and (cruise_speed < 90) . eq time X = Y . endo *** Assumption: Time is a function which takes time in seconds(X) for which SET is pressed & gives *** the speed factor(Y) to add to cruise-speed. cs599 - Formal Methods in Software Architecture

  7. Cruise Control obj CC-RESUME-DECELERATE[V-CAR-STATE :: CAR-STATE] . protecting INT . protecting TRUTH-VALUE . op button-press_ _ _ _ : INT INT INT TRUTH-VALUE  INT INT .. op button-press_ _ : INT TRUTH-VALUE  INT INT . op time_ : INT  INT . vars X Y : INT . cq button-press (cruise-speed , curr-speed , last-cruise-speed, cruise-state) = (cruise-speed = last-cruise-speed) if (cruise-state == true) and (curr-speed > 30) and (curr-speed < 90) and (cruise-speed == 0) and (last-cruise-speed =/= 0) . cq button-press (cruise-speed , cruise-state) = (cruise-speed = cruise-speed – Y ) and (last-cruise-speed = cruise-speed) if (cruise-state == true) and (cruise-speed =/= 0) . eq time X = Y . endo ***Assumption: Time is a function which takes time in seconds(X) for which RESUME is *** pressed and gives the speed factor(Y) to subtract to cruise-speed. cs599 - Formal Methods in Software Architecture

  8. Cruise Control obj ACCELERATOR-PEDAL[V-CAR-STATE :: CAR-STATE] . protecting INT . op pedal-press_ _ : INT INT  INT . op time_ : INT  INT . op uphill _ _ : INT INT  INT . vars X Y : INT . cq pedal-press (curr-speed , cruise-speed) = (curr-speed = curr-speed + Y) if (cruise-speed == 0) and (curr-speed < 140) . eq time X = Y . cq uphill (curr-speed, cruise-speed) = ( curr-speed = curr-speed + Z) and (cruise-speed = curr-speed) if (cruise-speed =/= 0) and (current-speed < cruise-speed) . endo *** Assumption: Time is an operation which takes time in seconds(X) for which pedal is *** pressed and returns the factor(Y) by which the speed is to be increased. *** ‘Z’ is a factor which gives the drop in the speed when the car goes uphill cs599 - Formal Methods in Software Architecture

  9. Cruise Control obj BRAKE-PEDAL[V-CAR-STATE :: CAR-STATE] . protecting INT . op pedal-press_ _ : INT INT  INT . op pedal-press_ : INT  INT INT INT . op time_ : INT  INT . op downhill _ _ : INT INT  INT . vars X Y : INT . cq pedal-press (curr-speed , cruise-speed) = (curr-speed = curr-speed – X) if (cruise-speed == 0) and (curr-speed > 0) . cq pedal-press (cruise-speed) = (cruise-speed = 0) and (last-cruise-speed = 0) if (cruise-speed =/= 0) . eq time X = Y . eq downhill (curr-speed, cruise-speed) = ( curr-speed = curr-speed - Z) and (cruise-speed = curr-speed) if (cruise-speed =/= 0) and (current-speed > cruise-speed) . endo *** Assumption: Time is an operation which takes time for which the pedal is pressed and *** returns the factor by which the speed is decreased. *** ‘Z’ is the factor which gives the increase in the speed when the car goes downhill cs599 - Formal Methods in Software Architecture

  10. Gas Station Assumptions ************************************************************************ 1. When the customer goes to the cashier & pays cash, the cashier allots a pump no. & a password to the customer. 2. Pump has one nozzle and three buttons for premium, plus & regular. 3. type-of-gas has integer values viz. plus  1 $1.90 per gallon regular  2 $ 1.80 per gallon premium  3 $ 2.00 per gallon ************************************************************************ Objects: pump nozzle customer cashier car (unnecessary) Gas tank car tank (unnecessary) sensor meter on the pump (unnecessary) cs599 - Formal Methods in Software Architecture

  11. Gas Station th PASSWORD is sort INT . protecting INT . protecting TRUTH-VALUE . op init1_ : TRUTH-VALUE  TRUTH-VALUE . op init2_ : INT  INT . var enable-pump : TRUTH-VALUE . vars pump-password-value customer-password-value : INT . eq init1 enable-pump = false . eq init2 pump-password-value = 0 . eq init2 customer-password-value = 0 . endth th TANK-STATES is sort INT . protecting INT . op init1_ : INT  INT . vars amount-gas-car-tank amount-gas-station-tank : INT . eq init1 amount-gas-car-tank = 0 . eq init1 amount-gas-station-tank > threshold . endth *** Assumption: threshold is some integer value which is pre-defined for the tank. *** Initially we are assuming that the gas in the GAS STATION TANK is greater than threshold. cs599 - Formal Methods in Software Architecture

  12. Gas Station th GAS-STATE is sort INT . protecting INT . protecting FLOAT . protecting TRUTH-VALUE . op init1_ : TRUTH-VALUE  TRUTH-VALUE . op init2_ : INT  INT . vars nozzle-up lever-press : TRUTH-VALUE . var type-of-gas amount-gas-dispensed : INT . var amount-charged : FLOAT . eq init1 nozzle-up = false . eq init1 lever-press = false . eq init2 type-of-gas = 0 . eq init2 amount-gas-dispensed = 0 . eq init2 amount-charged = 0 . endth *** the gas is not selected right now cs599 - Formal Methods in Software Architecture

  13. Gas Station th CASH-STATE is sort INT . protecting INT . protecting TRUTH-VALUE . op init1_ : TRUTH-VALUE  TRUTH-VALUE . op init2_ : INT  INT . vars cash-given-by-customer pump-number : INT . var receipt : TRUTH-VALUE . eq init1 receipt = false . eq init2 cash-given-by-customer = 0 . eq init2 cash-received-as-change = 0 . eq init2 pump-number = 0 . endth *** initially there is no cash transaction cs599 - Formal Methods in Software Architecture

  14. Gas Station obj PUMP[V-PASSWORD :: PASSWORD , V-GAS-STATE :: GAS-STATE] . protecting INT . protecting FLOAT . protecting TRUTH-VALUE . op give-receipt_ _ : INT INT  FLOAT . op choose-gas-type_ _ : TRUTH-VALUE TRUTH-VALUE  INT . op calculate-rate_ : FLOAT  FLOAT . var X : FLOAT . var Y : INT . cq give-receipt (amount-gas-dispensed , type-of-gas) = (amount-charged = (amount-gas-dispensed * X)) if (type-of-gas =/= 0) and (amount-gas-dispensed =/= 0) . cq choose-gas-type (nozzle-up , lever-press) = (type-of-gas = Y) if (nozzle-up == true) and (lever-press == false) . eq calculate-rate (type-of-gas) = (X = 1.80) if (type-of-gas == 2). eq calculate-rate (type-of-gas) = (X = 1.90) if (type-of-gas == 1). eq calculate-rate (type-of-gas) = (X = 2.00) if (type-of-gas == 3). endo *** ‘Y’ is 1 when type of gas chosen is ‘PLUS’ *** ‘Y’ is 2 when type of gas chosen is ‘REGULAR’ *** ‘Y’ is 3 when type of gas chosen is ‘PREMIUM’ cs599 - Formal Methods in Software Architecture

  15. Gas Station obj NOZZLE[V-GAS-STATE :: GAS-STATE] . protecting INT . protecting TRUTH-VALUE . op dispense-gas_ _ _ : TRUTH-VALUE TRUTH-VALUE INT  INT INT . op lift-nozzle_ _ : INT INT  TRUTH-VALUE . op keep-nozzle-back_ _ : TRUTH-VALUE TRUTH-VALUE  INT TRUTH-VALUE . op lever-press_ _ : TRUTH-VALUE INT  TRUTH-VALUE . op cal_ : INT  INT . vars X Y : INT . cq dispense-gas (nozzle-up , lever-press , type-of-gas) = (amount-gas-car-tank = amount-gas-car-tank + Y) and (amount-gas-station-tank = amount-gas-station-tank – Y) if (nozzle-up == true) and (lever-press == true) and (type-of-gas =/= 0) . cq lift-nozzle (pump-password-value , customer-password-value) = (nozzle-up = true) if (pump-password-value == customer-password-value) . cq keep-nozzle-back (nozzle-up , lever-press) = (customer-password-value = 0) and (nozzle-up = false) if (nozzle-up == true) and (lever-press == false) . cq lever-press (nozzle-up , type-of-gas) = (lever-press = true) if (nozzle-up == true) and (type-of gas =/= 0) . eq cal X = Y . endo *** cal is a function which calculates the amount of gas dispensed taking the time for which the nozzle is *** pressed. The customer comes to the pump assigned and enters the password for enabling the pump cs599 - Formal Methods in Software Architecture

  16. Gas Station obj CUSTOMER[V-CASH-STATE :: CASH-STATE] . protecting INT . protecting FLOAT . protecting TRUTH-VALUE . op gives-cash_ _ : INT INT  INT . op receives-balance_ _ _ : TRUTH-VALUE FLOAT FLOAT  TRUTH-VALUE FLOAT . op receives-receipt_ _ : TRUTH-VALUE INT  TRUTH-VALUE . var cash : FLOAT . cq gives-cash (customer-password-value , cash-given-by-customer) = (cash-given-by-customer = cash) if (customer-password-value == 0) and (cash-given-by-customer == 0) . cq receives-balance (nozzle-up, cash-given-by-customer, amount-charged) = (enable-pump = false) and (cash-received-as-change = cash-given-by-customer – amount-charged) and (customer-password-value = 0) if (nozzle-up == false) and (cash-given-by-customer =/= 0) and (cash-given-by-customer > amount-charged) . cq receives-receipt (nozzle , amount-gas-dispensed) = (receipt = true) if (nozzle-up == false) and (amount-gas-dispensed =/= 0) and (amount-charged =/= 0). endo *** cash is the amount of cash given by the customer to cashier for the gas.

  17. Gas Station obj CASHIER[V-CASH-STATE :: CASH-STATE] . protecting INT . protecting FLOAT . protecting TRUTH-VALUE . op receives-cash_ : INT  FLOAT INT INT TRUTH-VALUE . op gives-change_ _ _: TRUTH-VALUE INT FLOAT  TRUTH-VALUE INT INT INT . var cash : FLOAT . var pval : INT . cq receives-cash (cash-given-by-customer) = (cash-given-by-customer = cash ) and (pump-password-value = pval) and (customer-password-value = pval) and (enable-pump = true) if (cash-given-by-customer == 0) . cq gives-change (nozzle, amount-gas-dispensed, amount-charged) = (enable-pump = false) and (pump-password-value = 0 ) and (customer-password-value = 0) and (amount-gas-dispensed = 0) if (nozzle == false) and (amount-gas-dispensed =/= 0) and (amount-charged =/=0) . endo ***pval is a randomly generated number which is given as password to each customer. It *** never repeats. cs599 - Formal Methods in Software Architecture

  18. Gas Station obj GAS-TANK-PUMP[V-TANK-STATES :: TANK-STATES] . protected INT . op supply-gas-to-pump_ : INT  INT . var X : INT . cq supply-gas-to-pump (amount-gas-station-tank) = (amount-gas-station-tank = amount-gas-station-tank + X) if (amount-gas-station-tank < threshold) . endo *** Assumption: threshold is the pre-defined value for the tank. *** ‘X’ is the value of gas required to make the gas station tank full, it depends on the amount of gas already present in the tank. obj SENSOR[V-GAS-STATES :: GAS-STATES] . protecting INT . protecting TRUTH-VALUE. var max-tank-capacity : INT. op sense-gas-full_ : INT  TRUTH-VALUE . cq sense-gas-full (amount-gas-car-tank) = (lever-press = false) if (amount-gas-car-tank == max-tank-capacity) . endo *** max-tank-capacity is the maximum capacity of the gas car tank (dependent on the type of car), i.e. car specific. cs599 - Formal Methods in Software Architecture

  19. Inferences • It goes in a lot of details like the sorts and the subsorts • It is good in a place where accuracy is the prime issue and the details are the requirement while modeling the system. • Where lot of calculations are required. • It has got an Exceptional handling feature which can be very efficiently used to handle exceptions. • Very near to the implementation languages specially OOPS like C++ and Java, etc. • Would be liked by the coder.(directly lead to the code) • Not very good for state based problems, difficult to represent states. cs599 - Formal Methods in Software Architecture

  20. Our Approach • Dependent on OOPs • Chose the Objects (nouns of the specs) • Then chose the theories • Chose the operations for each object (interactions) • Then declared the objects with their operations. • Extensively used function overloading. • Made assumptions where ever required. cs599 - Formal Methods in Software Architecture

  21. Difficulties Faced • There is no form of diagrams here which explains the details of the problem. If the spec is very complicated then it is very difficult to understand. • It can be used in the intermediate stage of design and implementation, but not for design, if the specs are very complicated. • Did not understand the use of views. • Did not use any Exception handling feature of OBJ3. cs599 - Formal Methods in Software Architecture

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