test-1-mock

represents function of type Int -> Int True/False j. Evaluate the expression 1 # 2 will return 4 . True/False Question 2 (15 point) Write down your answer in the space provided. a. (9 point) Define the following library functions by recursion: > product :: [Int] -> Int > length :: [a] -> Int > reverse :: [a] -> [a] b. (6 point) Let h be the function which has the following type: > h :: Char -> Int -> Char -> Int State the types of Expression i , ii and iii in the space provided: Expression Type i . [(False, 0 ), (True, 1 )] ii . ([False,True], [ 0 , 1 ]) iii . h a 3

Question 6 (20 point) (Kripke’s structure) Let M 1 = ( W 1 , I 1 , J 1 ) be a Kripke structure defined as follows: • W 1 = { w 0 , w 1 , w 2 } • I 1 : PropVar → P ( W 1 ) (the interpretation function) I 1 ( q ) = { w 0 , w 2 } , I 1 ( r ) = { w 1 } , I 1 ( s ) = { w 1 , w 2 } . • J 1 : PName → P ( W 1 × W 1 ) be defined as: J 1 ( Alice ) = { ( w 0 , w 0 ) , ( w 1 , w 1 ) , ( w 2 , w 2 ) } , J 1 ( Bob ) = { ( w 0 , w 0 ) , ( w 0 , w 1 ) , ( w 1 , w 2 ) , ( w 2 , w 1 ) } . a . (4 point) State what is meant by M | = φ , where φ is a well formed formula and M is a Kripke model for ACL. b . (12 point) For the given model M 1 , Compute E M 1 ( Bob controls ( r ∨ s ) ) , where E M 1 is the evaluation function for the Kripke’s model M 1 . c . (4 point) From your computations in part b , can we say M 1 | = Bob controls ( r ∨ s ) ? Give reason(s) to support your answer. 6