Derive constraints and annotations for the following program:

(lambda (f)
  (lambda (x)
    (lambda (y)
       (cons x (f (f y))))))







------------- Solution ----------------------


[1] (lambda (f)
  [2] (lambda (x)
    [3] (lambda (y)
       [4] (cons x [5] (f [6] (f y))))))

Constraints:

[1] = [f] -> [2]  from 1
-------------------
[2] = [x] -> [3]  from 2
-------------------
[3] = [y] -> [4]  from 3
-------------------
[4] = list[alpha] from 4
[x] = alpha
[5] = list[alpha]
-------------------
[f] = [6] -> [5]  from 5
-------------------
[f] = [y] -> [6]  from 6

Inferred types (written as annotations)

(lambda (f : t1) t2
  (lambda (x : t3) t4
    (lambda (y : t5) t6
       (cons x (f (f y))))))

where
t1 = list[alpha] -> list[alpha]
t2 = alpha -> (list[alpha] -> list[alpha])
t3 = alpha
t4 = list[alpha] -> list[alpha]
t5 = list[alpha]
t6 = list[alpha]