lambda calculus

Fibonacci series contains numbers 0, 1, 1, 2, 3, 5, ... where each number is the sum of the preceding two. The n^th fibonacci number can be computed recursively as follows:

fib(1) = 0

fib(2) = 1

fib(n) = fib(n-1) + fib(n-2)

Write a lambda expression for this function, because this is a recursive function, you will have to nest the lambda expression taking argument n within another lambda taking f the function which you will then recursively call within the body. Plus, you will have to precede this definition with the letter Y, which represents a special kind of lambda expression called the Y combinator, which actually makes the recursion happen. So, your solution will look something like:

Y lambda f . [rest of your solution]

expressions for boolean constants and operators:

true = x.y.(x) false = x.y.(y) not = v.w.x.(v x w) or = v.w.(v v w) and = v.w.(v w v)