CSE 428: Quizzes

Spring 2001, CSE 428: Quiz 10.3 - 11 April 2001

Please write your Name and Student ID at the top of the page. By default, this quiz will be returned in Section 1 (afternoon section).

[Pts 2] The type 'a list in ML is polymorphic because (only one answer, please)
- it is an equality type
- in a list the elements can be of different types
- a list can contain any number of elements
- 'a (the type of the elements) can be any type. The predefined functions on lists, hd, tl, etc. work for any 'a

[Pts 2] For each of the following functions on 'a list, say whether it is polymorphic or not

fun sum nil = 0  (* returns the sum of all the elements *)   no
  | sum (x::L)  = x + sum L;

fun length nil = 0  (* returns the length of the list *)   yes
  | length (x::L) = 1 + length L;

fun reverse nil = nil  (* reverse the list *)    yes
  | reverse (x::L) = append(reverse L, [x]); (* append is the usual function which concatenates two lists *)

fun add nil = nil  (* sums the components of each element of the list *)   no
  | add ((x,y)::L) = (x+y)::(add L);

[Pts 2] In logic programming, a rule A :- B1, B2,...,Bn. means (only one answer, please):
- if B1 or B2 or ... or Bn holds, then A holds
- if B1 and B2 and ... and Bn hold, then A holds
- if A holds, then B1 or B2 or ... or Bn holds
- if A holds, then B1 and B2 and ... and Bn hold
[Pts 4] Consider the following definition of the member-of-a-list predicate:
```
   memb(X,[X|L]).
   memb(X,[_|L]) :- memb(X,L).
```
For each of the following queries, please indicate all the answers that are returned (assuming that we interactively keep asking for more answers). If no answers are returned, write "no". If the query generates an error, write "error".
- ?- memb(X,[1]). X = 1
- ?- memb(X,[1,2]). X = 1 ; X = 2
- ?- memb(3,[1,2]). no
- ?- memb(3,[1,X]). X = 3