1. How would you characterize inheritance as applied in knowledge representation? Discuss the problems that arise due to non-monotony.
2. How would you render the meaning of an inheritance lattice? Give some examples.
3. What is the meaning of a type? How would you characterize the relation between a type and its subtypes?
4. Characterize the subtyping rules for ranges, functions, records and variant records. Give some examples.
5. What is the intuition underlying the function subtyping rule?
6. What is understood by the notion of objects as records? Explain the subtyping rule for objects.
7. Discuss the relative merits of typed formalisms and untyped formalisms.
8. What flavors of polymorphism can you think of? Explain how the various flavors are related to programming language constructs.
9. Discuss how inheritance may be understood as an incremental modification mechanism.
10. Characterize the simple type calculus $%l_\left\{<=\right\}$, that is the syntax, type assignment and refinement rules. Do the same for $F_\left\{ /\ \right\}$ and $F_\left\{<=\right\}$.
11. Type the following expressions: (a) $\left\{ a = 1, f = %l x:Int. x + 1 \right\}$, (b) $%l x:Int . x * x$, and (c) $%l x:\left\{ b:Bool, f:\left\{ a:Bool \right\} \right\} -> Int.x.f\left(x\right)$.
12. Verify whether: (a) $f\text{'} : 2..5 -> Int <= f:1..4 -> Int$, (b) $\left\{ a:Bool, f:Bool -> Int \right\} <= \left\{ a:Int, f: Int -> Int \right\}$, and (c) $%l x: \left\{ a:Bool \right\} -> Int <= %l x: \left\{ a:Bool, f:Bool -> Int \right\} -> Int$.
13. Explain how you may model abstract data types as existential types.
14. What realizations of the type $\E %a. \left\{ a:%a, f:%a -> Bool \right\}$ can you think of? Give at least two examples.
15. Prove that $%m %a . \left\{ c:%a, b:%a -> %a \right\} \not<= %m %a . \left\{ b : %a -> %a \right\}$.
16. Prove that $%m %a . \left\{ c : %a, b: %t -> %a \right\} <= %t$, for $%t = %m %a.\left\{ b: %a -> %a \right\}$.

slide: Questions