1. CS383 Programming Languages Quiz 6

2. 1. Which one is a term schema? a.‘a b.s :: = ‘a| int | bool c.fun f (x: int) : bool = e d.fun f (x: s1) : s2 = e

3. 2. Which one is not a step of type inference? a.Add type schemas b.Generate type constraints c.Determine subtypes d.Solve type constraints

4. 3. In the step of constraint generation, which simple rule is not totally correct? a.G |-- x ==> x : s, {} b.G |-- 2 ==> 2 : int, {} c.G |-- false ==> false : bool, {} d.G |-- true ==> true : bool, {}

5. 4. In the step of constraint generation, which rule is not correct? G |-- u1 ==> e1 : t1, q1 G |-- u2 ==> e2 : t2, q2 ------------------------------------------------------------------------ G |-- u1 + u2 ==> e1 + e2 : int, q1 U q2 U {t1 = int, t2 = int} G |-- u1 ==> e1 : t1, q1 G |-- u2 ==> e2 : t2, q2 ------------------------------------------------------------------------ G |-- u1 e1 < e2 : bool, q1 U q2 U {t1 = int, t2 = int} G |-- u1 ==> e1 : t1, q1 G |-- u2 ==> e2 : t2, q2 ---------------------------------------------------------------- G |-- u1 u2==> e2 e1: a, q1 U q2 U {t1 = t2 -> a} G, f : a -> b, x : a |-- u ==> e : t, q ---------------------------------------------------------------- G|-- fun f(x)=u ==> fun f(x:a):b=e : a -> b, q U {t = b} a. b. c. d.

6. a.a solution to a system of type constraints is called a substitution b.substitution is a function from type variables to type schemes c.composition (U o S) applies the substitution U and then applies the substitution S d.any substitution is less general than the identity substitution I 5. Which statement is incorrect?

7. 6. if S(a) = int, S(b) = c  c ; T(a) = int, T(b) = c  c, T(c) = int ; then we can conclude: a. T = S b. T >= S c. T <=S d. T is unrelated to S

8. 7. Which of the following principal solution is incorrect? a.q = {a=int, b=a, b=bool} S : does not exist b.q = {x=int->x} S: does not exist c.q = {} S: does not exist d.q = {a=bool, b=a} S(a) = S(b) = bool, S(c) = c

9. 8.Which one of the following constraint equation is impossible of a stuck state? a. int = bool b.‘a  ’b = int c.a = s (s contains a) d. They are all possible

10. 9. Which of the following rules is incorrect? a. ---------------------------------------------- (S, {s11 -> s12= s21 -> s22} U q) -> (S, {s11 = s21, s12 = s22} U q) b. ----------------------------------------(a not in FV(s)) (S,{a=s} U q) -> ([a=s] o S, q[s/a]) c. ----------------------------------------(a not in FV(s)) (S,{s=a} U q) -> ([a=s] o S, q[s/a]) d. They are all correct

11. 10. Which of the following statement is incorrect? a. A complete solution for (S, q) is a substitution T such that T <= S and T |= q b. Every final state (S, { }) has a complete solution. c. No stuck state has a complete solution (or any solution at all) d. If (S, q) -> (S’, q’) then T is complete for (S,q) iff T is principal for (S’,q’)