Exercise 4 a) Construct a program transformer (-:-): PX PP which implements the sequential composition of programs, i.e. satisfies {(F;G)} = {G}_{F} for all programs F, G EP. b) is the sequential composition of programs associative? In other words, does it satisfy the equation ((F;G); H) (F;(G;)) for all F,G,H E P? If it is, prove that it is. If it is not, explain why not. c) Show that the sequential composition of programs is associative with respect to extensional equivalence of computations, i.e. that for all F,G,H EP holds ((F:G); H) = (F:(G;H)) where X =Y = {x} = {Y}. Exercise 4 a) Construct a program transformer (-:-): PX PP which implements the sequential composition of programs, i.e. satisfies {(F;G)} = {G}_{F} for all programs F, G EP. b) is the sequential composition of programs associative? In other words, does it satisfy the equation ((F;G); H) (F;(G;)) for all F,G,H E P? If it is, prove that it is. If it is not, explain why not. c) Show that the sequential composition of programs is associative with respect to extensional equivalence of computations, i.e. that for all F,G,H EP holds ((F:G); H) = (F:(G;H)) where X =Y = {x} = {Y}