Homework on Lambda Conversion # a comment here constants of type e: a b c constants of type : P-Q constants of type : R variables of type e : x-z variables of type : X Y variables of type >: W #exercise semantic types #title Semantic Types #directions Give the semantic type of the following lambda-expressions. #Lx.Ly. P(y) exercise lambda conversion title Lambda Conversion directions After checking that the type of the function and the type of the directions argument(s) match, simplify the following expressions performing directions one lambda-conversion at a time. Lx.Ly.Lz. [Q(z) & (R(y,x) -> P(z))] (a) (b) (c) Lx.Ly. [P(x) -> Q(x)] (a) (b) Lx.Ly.Lz. [P(x) & Ey[R(y,z)] & Ax[Q(x) -> R(z,y)] ] (a) (b) (c) Lx.Ly. Ez[R(z,x) -> Q(y) & P(y)] (z) (b) Lx.Ly. [P(y) & P(x)] (y) (b) LX.LY. [Ax[X(x) -> Y(x)]] (P) (Q) LX.Ly. [X(c)] (P) (a) LX.Lx. [P(x) & X(c)] (Lx.Q(x)) (a) #####