[’a’,’b’,’c’]
(’a’,’b’,’c’)
[(False,’0’),(True,’1’)]
([False,True],[’0’,’1’])
[tail,init,reverse]
second xs = head (tail xs)
swap (x,y) = (y,x)
pair x y = (x,y)
double x = x*2
palindrome xs = reverse xs == xs
twice f x = f (f x)
What functions define the typeclasses Real
and Integral
,
respectively? Read the documentation (find them either
through Hayoo
or Hoogle) of these functions and try
invoking each of them in ghci
. Show your trials and explain in English
what the functions do.
What are the example types that are instances of Real
and Integral
,
respectively. Try invoking the Real
and Integral
functions on
values of the example types that you give.
Define a function f
as follows:
f x = toRational $ rem x 5
What is f
's type?
f
's type.
Redefine the following version of (&&) using conditionals rather than patterns:
True && True = True
_ && _ = False
Give three possible definitions for the logical or operator (||
)
using pattern matching.
What does the init
function in Prelude^{1} do? Define init
in
terms of functions length
and take
.
The scalar product of two lists of integers xs
and ys
of length n
is
give by the sum of the products of the corresponding integers:
Using a list comprehension, define a function that returns the scalar product of two lists. (Hint: You could start from the following program stub.)
scalarProduct :: [Int] -> [Int] -> Int
scalarProduct xs ys = undefined
A positive integer is perfect if it equals the sum of all of its factors, excluding the number itself. Using a list comprehension, define a function
perfects :: Int -> [Int]
perfects n = undefined
that returns the list of all perfect numbers up to a given limit, such that, e.g.:
Prelude λ> perfects 500
[6,28,496]
^{1.}Prelude is a standard module loaded by default when you start ghci
. Information about Prelude can be found on the Prelude Hackage page.
↩