TEST 16

matricola: ______________________________

nome (solo se non si ricorda la matricola): __________________________________

• Write a let expression whose semantics is equivalent to the following  expression                                                     ((lambda (a b) (a b)) (lambda (x) x) 3)
  

• Define in Haskell the parametric data type (Stack a)
  

•  Define (possibly without using any auxiliary function) a Scheme function  F that takes as input a predicate 'P?' on natural numbers and a natural number n . It returns a predicate on natural numbers which it is true on m if and only if 'P?' is true at least n times on the numbers between 0 and m.                              Example: ((F odd? 2) 5) --> #t
  

(define (F P? n)
  (lambda (m)
    (cond ((= n 0) #t)
          ((= m 0) (and (P? 0) (= n 1)))
          ((not (P? m)) ((F P? n) (- m 1)))
          (else ((F P? (- n 1)) (- m 1))))))