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