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INFORMATICS 1 — FUNCTIONAL PROGRAMMING

 UNIVERSITY OF EDINBURGH

COLLEGE OF SCIENCE AND ENGINEERING
SCHOOL OF INFORMATICS
INFORMATICS 1 — FUNCTIONAL PROGRAMMING
CLASS TEST
due 4pm Wednesday 4 November 2020
INSTRUCTIONS TO CANDIDATES
• Unless otherwise stated, you may define any number of helper functions and use any
function from the standard prelude, including the libraries Char and List. You need
not write import declarations.
• As an aid to memory, some functions from the standard prelude that you may wish
to use are listed on the next page. You need not use all the functions.
Unlike tutorials, you should not consult other students or Piazza when
answering the class exam, and CodeGrade is not available to help you check
your answers.
Good Scholarly Practice: Please remember the good scholarly practice re￾quirements of the University regarding work for credit. You can find guidance
at the School page
http://web.inf.ed.ac.uk/infweb/admin/policies/academic-misconduct.
This also has links to the relevant University pages. Please do not publish
solutions to these exercises on the internet or elsewhere, to avoid others copying
your solutions.
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div, mod :: Integral a => a -> a -> a
even, odd :: Integral a => a -> Bool
(+), (*), (-), (/) :: Num a => a -> a -> a
(<), (<=), (>), (>=) :: Ord => a -> a -> Bool
(==), (/=) :: Eq a => a -> a -> Bool
(&&), (||) :: Bool -> Bool -> Bool
not :: Bool -> Bool
max, min :: Ord a => a -> a -> a
isAlpha, isAlphaNum, isLower, isUpper, isDigit :: Char -> Bool
toLower, toUpper :: Char -> Char
ord :: Char -> Int
chr :: Int -> Char
Figure 1: Basic functions
sum, product :: (Num a) => [a] -> a and, or :: [Bool] -> Bool
sum [1.0,2.0,3.0] = 6.0 and [True,False,True] = False
product [1,2,3,4] = 24 or [True,False,True] = True
maximum, minimum :: (Ord a) => [a] -> a reverse :: [a] -> [a]
maximum [3,1,4,2] = 4 reverse "goodbye" = "eybdoog"
minimum [3,1,4,2] = 1
concat :: [[a]] -> [a] (++) :: [a] -> [a] -> [a]
concat ["go","od","bye"] = "goodbye" "good" ++ "bye" = "goodbye"
(!!) :: [a] -> Int -> a length :: [a] -> Int
[9,7,5] !! 1 = 7 length [9,7,5] = 3
head :: [a] -> a tail :: [a] -> [a]
head "goodbye" = 'g' tail "goodbye" = "oodbye"
init :: [a] -> [a] last :: [a] -> a
init "goodbye" = "goodby" last "goodbye" = 'e'
takeWhile :: (a->Bool) -> [a] -> [a] take :: Int -> [a] -> [a]
takeWhile isLower "goodBye" = "good" take 4 "goodbye" = "good"
dropWhile :: (a->Bool) -> [a] -> [a] drop :: Int -> [a] -> [a]
dropWhile isLower "goodBye" = "Bye" drop 4 "goodbye" = "bye"
elem :: (Eq a) => a -> [a] -> Bool replicate :: Int -> a -> [a]
elem 'd' "goodbye" = True replicate 5 '*' = "*****"
zip :: [a] -> [b] -> [(a,b)]
zip [1,2,3,4] [1,4,9] = [(1,1),(2,4),(3,9)]
Figure 2: Library functions
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1. (a) Write a function f :: String -> Bool that returns true if given a string where
every alphabetic character is upper case. For example:
f "" == True
f "..." == True
f "nope" == False
f "FAKE NEWS" == True
f "This is a Tweet." == False
f "THIS IS A TWEET!" == True
Use basic functions, list comprehension, and library functions, but not recursion.
(b) Write a second function g :: String -> Bool that behaves identically to f,
this time using basic functions and recursion, but not list comprehension or
other library functions.
(c) Write a QuickCheck property prop_fg to confirm that f and g behave identically.
2. (a) Write a function c :: String -> Bool that takes a string and returns true if
the string contains two adjacent characters that are identical.
c "" == False
c "s" == False
c "ss" == True
c "Misisipi" == False
c "Mississippi" == True
c "single-dash" == False
c "double--dash" == True
Your definition may use basic functions, list comprehension, and library func￾tions, but not recursion.
(b) Define a second function d :: String -> Bool that behaves identically to c,
this time using basic functions and recursion, but not list comprehension or other
library functions.
(c) Write a QuickCheck property prop_cd to confirm that c and d behave identically.
Give the type signature of prop_cd and its definition.
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