True or false.
When a variable occurs in a logic programming goal, the interpreter is being asked whether that goal holds for all values of the variable.
False. It is being asked whether the goal holds for some value of the variables, and if so, for which values.
In logic programming, a variable in an axiom might be used as an input variable sometimes, and as an output variable at other times, when computation uses that axiom.
True. Some predicates can be used in different modes.
Cuts are used to reduce memory requirements and to speed up computation.
True.
In a typeless language, all type checking done at run time.
True. The idea of a typeless language is that no type checking is done at compile time.
Standard ML is a strongly typed language. Therefore, in Standard ML, it is not possible to get a type error at run time.
True.
Polymorphism is most useful in designing custom applications, and is rarely used in function libraries.
False. Polymorphism is most useful for designing general purpose libraries.
C++ uses name equivalence of types defined using typedef.
False. Typedef just gives a new name to an old type, so one type can have more than one name. If name equivalence is used, then a type can only have one name.
Unification is a form of pattern matching. Which of the following is not a characteristic of unification?
In a logic programming style, write axioms for computing predicate samelength(X,Y), which is true just when X and Y are lists that have the same length.
Here is it written in Prolog.
samelength([],[]).
samelength([_|A],[_|B]) :- samelength(A,B).
In a logic programming style, write axioms for computing predicate allsame(X), which is true just when all members of list X are the same. For example, allsame([5,5,5]) is true, as is allsame([a,a]), but allsame([2,4,4]) is false. Note that allsame([]) is true, and allsame([b]) is true.
Here it is written in Prolog.
allsame([]).
allsame([_]).
allsame([H,H|R]) :- allsame([H|R]).
Show the logic programming search tree for goal (member(X,[3,4,5]), member(X,[4])), up to the point where a success is found. The definition of the member predicate is as follows, written in Prolog syntax.
member(M, [M|X]).
member(M, [X|T]) :- member(M, T).
member(X,[3,4,5]), member(X,[4])
/ \
| X = 3 member(X,[4,5]), member(X,[4])
| / \
member(3,[4]) | X = 4
\ |
member(3,[]) |
|
member(4,[4])
/ \
success
Why do most modern languages employ name equivalence instead of structural equivalence for types?
Name equivalence gives stronger type checking.
What is the most general polymorphic type of function f defined by f(x) = tail(right(x))? Use type variables. Function right takes the right-hand member of an ordered pair. (Try an example. What kind of thing makes sense?)
I will use A and B f
type variables. Try an example. f(true, ['a', 'b', 'c']) = ['b', 'c'].
Evidently, f takes an ordered pair where the right-hand member is a list.
It produces the same kind of list as that right-hand parameter. The
left-hand member of the ordered pair is not used, so it can be anything.
f: (A,[B]) -> [B]
What is the most general polymorphic type of the Astarte function filter? Use type variables. Filter is defined so that (filter p L) returns a list of all members x of list L such that p(x) is true. For example, if function positive returns true on a positive number and false on a nonpositive number, then (filter positive [9,-2,-3,6]) = [9,6]. Notice that p is a predicate.
Look at the example. The parameter of filter is positive, a predicate. Clearly, the parameter of filter is a function that produces a boolean result. So you should expect to find filter: (T -> boolean) -> S for some T and S.
(filter positive) is a function that takes a list and produces another list. The members of both lists have the same type. Also notice that the predicate has to be run on each member of the parameter list. So you should find that, whatever type T is, type S should be [T] -> [T]. Now just let T be a type variable.
filter: (T -> boolean) -> ([T] -> [T])