Lambda calculus question:

Define terms first , second , such that

first N1, N2 N1 second N1, N2 N2

Define terms swap and incsnd such that

swap N1, N2 N2, N1 incsnd N1, N2 N2, N2 + 1

Verify their correct functioning when applied to the pair 3, 1 . (Here, means reduction by any number of -steps, and N2 + 1 stands for succ N2 ).