Homework 1 # one can write arbitrary comments in this file after hashes constants of type e : a b-d constants of type : P Q; display as: one-place predicate constants of type : R; display as: two-place predicate variables of type e : x-z variables of type : X Y; display as: one-place predicate exercise semantic types title Semantic Types directions Give the semantic type of the following lambda-expressions. You may want to simplify them in your mind if necessary before assigning a type. points per exercise 20 Lx[P(x) & Q(x)] 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. points per exercise 10 [Lx.P(x) & Q(x)] (a) [LxLy.R(a,y) & Q(x)] (a) (b) [Lx.Ey[R(y,x)]] (y) [Lx.a] (b) [Lx.P(x) -> Ex.R(x,b)] (a) [LxLx.P(x) -> R(x,c)] (a) (b)