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Principles of Programming Languages 2015.07.06 Notes • NAME: __________________________________ • Did you present a small project? YES / NO • Total available time: 2h. • Y ou may use any written material you need. • Y ou cannot use computers or phones during the exam. 1 Scheme 1.1 Closures (6 points) Consider this code: (define (producer ag1 ag2) (let loop ((i 1)) (if (< i 10) (begin ((if (odd? i) ag1 ag2) i) (loop (+ i 1))) (cons (ag2 ’end) (ag1 ’end))))) Define two closuresclos1 and clos2 for passing them toproducer such that it returns the list’(20 9 7 5 3 1) (note that 20 = 2 + 4 + 6 + 8 ). 1.2 Macro (6 points) Define a macro multiple-apply, (multiple-apply (fun-1 fun-2 ...) to list-1 list-2 ...) where fun-i are functions and to is a keyword, which returns a list containing the result of applying fun-i to list-i. E.g. > (multiple-apply (+ - *) to ’(1 2 3) ’(3 4) ’(9 -2)) (6 -1 -18) 1 2 Haskell 2.1 Split (5 points) Assume this is a possible Haskell variant of producer in Exercise 1, in which the closures’ states are made explicit. producer ag1 ag2 = prod’ ag1 [] ag2 0 1 where prod’ ag1 st1 ag2 st2 i | i >= 10 = (st2:st1) prod’ ag1 st1 ag2 st2 i | odd i = prod’ ag1 (ag1 i st1) ag2 st2 (i+1) prod’ ag1 st1 ag2 st2 i | even i = prod’ ag1 st1 ag2 (ag2 i st2) (i+1) 1. Define two suitable functions for producer’s two arguments, such that its call returns [20,9,7,5,3,1]. 2. Write the type of prod’, assuming that all the numbers have type Int. 2.2 Duo-fold (6 points) Define an higher-order function called duofold, which takes two binary functions f and g, a starting value t and a (finite) list [e1, e2, . . .], and returns . . . f(g(f (t, e1), e2), e3), .... Please, write also its type. Example: duofold (+) (-) 0 [1,2,3,4] returns −2 (i.e. 0 + 1 − 2 + 3 − 4). 3 Prolog 3.1 Check…