Functional Programming (H) - Examinable
1. Study the Haskell function f below. What does f() evaluate to?
f :: () -> String f () = let x = (Just Nothing) in case x of (Just _) -> "something" Nothing -> "nothing"
"something"
"nothing"
Nothing
2. Give one reason why the following code is incorrect in Haskell:
x = 4 x = ((x * 2))
Because you can assign an expression to a name only once
Because there are too many parentheses
3. Which one of the following expressions generates an infinite list of successive factorial numbers? (Recall that the nth factorial is the product of the first n positive integers.)
facts = (*) [1..]
facts = map (\x-> (foldr (*) 1 [1..x])) [1..]
facts = [1,2,6,...]
4. How do you find the type of a defined function f in ghci?
:type f
:show f
:load f
5. What is the effect of the following fold?
foldl (\acc elt -> acc++[elt]) "" "A string"
It will return “gnirts Aâ€
It will return the string except its last character
It will return “A stringâ€
6. Which one of the following expressions does not evaluate to 42?
(*) 21 2
[7,23,42] !! ((+) 1 1)
head (zip [42] [True])
7. How do we generate an infinite list of integer 1 values?
[1..]
repeat 1
[1..1]
take 1
8. What is wrong with the following definition of filter?
filter :: (a -> Bool) -> [a] -> [a] filter pred [] = [] filter pred (x:xs) | pred x = x : filter pred xs | otherwise = filter pred (x:xs)
The predicate should operate on xs, not on x
The base case is wrong
The recursion for the non-matching case should operate on xs, not on (x:xs)
The recursion for the matching case should work on (x:xs), not on xs
9. A recursive function must have at least two cases. What are these called?
base case and induction case
base case and general case
general case and specific case
10. Given a list xs, what does the following expression evaluate to?
[]++xs == xs++[]
False
True
11. Does the evaluation order of Haskell sub-expressions affect the overall value of the expression?
No, evaluation order does not affect the final value.
If expressions are evaluated in a different order, then the final value might be different.
12. Which one of the following functions will not loop infinitely, if we evaluate it in ghci?
tail [1..]
take 10 [1..]
length [1..]
13. What is the type of this function?
f name = putStrLn ("hello " ++ name)
IO [Char]
[Char] -> ()
[Char] -> IO ()
14. What is the type of the following function:
\f -> f f
Bottom
True
It is not possible to type this expression correctly in Haskell
15. What is wrong with this line of code, to return the number of characters typed by a user?
let x = getLine in length(x)
Because getLine is a function, it needs arguments. There are no arguments given in this code.
The code associates the name x with the getLine function, rather than receiving a line of input from the user — and we can’t take length of a function.
nothing is wrong — the code should work fine
the code loops for ever
16. In a Haskell guard expression, each of the guards evaluates to a Bool value, either True or False. What is the Bool value for the otherwise case?
True
Maybe True
False
17. What is the result of the following expression in Haskell, where sqrt returns the square root of its argument:
sqrt (16+9)
13
5
18. Does the following expression terminate?
let bot = bot bottomList = repeat bot in length(take 5 bottomList)
no, it loops forever
yes, returning integer value 5
19. Is it valid to write
n = n + 1
in Haskell
Yes, it is a valid expression
No, it is a syntax error
20. What is the result of evaluating the following expression?
(\x -> 1) 2
2
a type error
1
21. Given the following type declarations:
f :: T1 -> T2 g :: T2 -> T3
And given that the following expression typechecks:
v :: T1 v = h f g
What is the type of h?
h :: T3 -> T2 -> T1
h :: (T1 -> T2) -> (T2 -> T3) -> T1
h :: T1 -> T2 -> T3
h :: (T3 -> T2) -> (T2 -> T1) -> T3
22. Given these definitions:
a = "england" b = "scotland"
then which one of the following expressions has the greatest integer value?
length (zip a b)
length (zip a a)
length (zip b b)
23. What is the difference between
->
and
<-
in Haskell syntax?
<-
indicates less than, whereas
->
indicates greater than
they are both two ways of representing the same thing.
<-
is for associating names with values in do blocks whereas
->
is used for defining functions.
24. Why do you think the generation and use of pseudo-random numbers might occur inside a monad?
because it is defined in the Haskell Prelude library
because the sequence of pseudo-random numbers is important, and the programmer needs to control it.
because it is an interaction with ‘the outside world’
25. Is the following expression correctly typed?
join :: String -> [String] -> String join str strs = foldl (++) str strs
No
Yes
26. What is the result of evaluating the following expression?
(\x -> (\y -> y x)) "x" (\y -> y)
an error
(\x -> (\y -> y x)) "x"
(\y -> y x) "x"
"x"
27. What is the difference between an expression and a statement in an imperative programming language
Expressions denote small scale computations that return a value
Statements handle sequencing, looping, conditionals, and all the large scale operation of a program
Expressions determine control flow and are often composed of statements
28. Select which one of the following two let expressions will evaluate to the String
"prime minister"
let x = numeral ++ " minister" in x where numeral = "prime"
let x = numeral ++ " minister" where numeral = "prime" in x
29. What is the result of the following expression in Haskell, where sqrt returns the square root of its argument:
sqrt 16+9
13
5
30. In Haskell, what is another appropriate name for this style of expression:
n = n + 1
An equation
An assignment
31. What is the difference between a named function and a lambda function assigned to a variable? For example:
f x = x + 1 -- or f = \x -> x+1
There is no meaningful difference.
It is less efficient to define functions in terms of lambdas.
32. What does the following expression evaluate to?
['a','d' .. 'z']
“adzâ€
“adgjmpsvyâ€
33. What is the type of the following function (use a,b,c etc as type variables in order of occurence):
\x y -> y
\x y -> y :: a -> a -> a
\x y -> y :: a -> a -> b
\x y -> y :: a -> b -> b
\x y -> y :: a -> b -> c
34. What is the result of evaluating the following expression?
(\x -> (\y -> x y)) "x"
a type error
a partially applied function
a string value
35. What is the type of the
putStrLn
function?
putStrLn :: Char -> IO ()
putStrLn :: String -> ()
putStrLn :: Show a => a -> IO ()
putStrLn :: String -> IO ()
36. What is the result of evaluation of the following expression?
(\x y -> x*x-y*y) 3 4
-7
-20
7
20
37. What is the result of evaluating the following expression?
(\x f -> f x) 4 (\x -> x*x)
a partially applied function
16
4
38. Is the following expression correctly typed?
sq :: Int -> Float sq x = x*x
Yes
No
39. What is the result of evaluating the following expression?
map (\x -> length x) ["This","is", "a","test"]
[4,2,1,4]
an error
4
40. Given the definition:
sum_ratio = \x y z -> (x + y) / z
then what is the value of:
1 + 4* sum_ratio 4 2 3
5
9
41. What is the missing case clause in the following definition of a function to calculate the length of a Haskell list?
mylength l = case l of -- MISSING CLAUSE -- x:xs -> 1+mylength xs
[] <- 0
Null -> 0
[] -> 0
42. What is the result of the following computation?
foldr (/) 1 [2,4,8]
2.0
0.25
0.5
4.0
43. What is the result of the following computation?
foldl (/) 16 [8,4,2,1]
4.0
0.25
0.5
2.0
44. Complete the following type definition to define a binary tree with the values stored only in the leaf nodes:
data Tree a = Node __ __ | Leaf __
data Tree a = Node Leaf Leaf | Leaf (Tree a)
data Tree a = Node Tree Tree | Leaf
data Tree a = Node (Tree a) (Tree a) | Leaf a
data Tree a = Node a a | Leaf
45. What is the value of this expression?
let x = 5 in x == 5
True
False
5
46. Given a Tree data type as defined earlier in the course:
data Tree = Leaf | Node Int Tree Tree deriving Show
with Leaf and Node constructors, then how do we define an infinite tree?
mkInfiniteTree = Node 0 (mkInfiniteTree) (mkInfiniteTree)
mkInfiniteTree = Node 0 (mkInfiniteTree) (mkInfiniteTree)
mkInfiniteTree = mkInfiniteTree Node 0
47.
let x = y + 2 y = x/3 in x+y
This code defines a pair of simultaneous equations. Will this work in Haskell?
yes — it will compute the two values that have mutually recursive definitions
no — it will either fail with an error or loop forever.
48. Which one of the following expressions should always evaluate to True?
"haskell" < "python"
haskell < python
"haskell" <> "python"
49. What is the result of the expression
abs -6
in Haskell, where abs returns the absolute value of its argument.
6
An error
50. What’s wrong with the following Haskell expression?
if (1) then "true" else "false"
The condition is incorrectly typed, since it is an integer value
An endif statement is needed to show the end of the conditional expression
There should not be any brackets around the condition
51. What is the wrong with the following map/fold-based computation?
foldl (+) (map (*2) [1..8])
map should take a function like (*), not (*2)
foldl needs an accumulator argument.
The map and foldl functions should be swapped
52. What is the type of the
head
function?
head :: a -> a
head :: [a] -> a
head :: [a] -> Int
head :: a -> Int
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