lecture-02.lhs

University of Zagreb
Faculty of Electrical Engineering and Computing

PROGRAMMING IN HASKELL

Academic Year 2017/2018

LECTURE 2: Lists (cont.) and tuples

v1.0

(c) 2017 Jan Šnajder

==============================================================================

> import Data.Char
> import Data.List

=== LISTS (cont.) ============================================================

Lists cannot be heterogeneous (contain elements of different types). E.g., we
cannot have: [1,'a',3].

Replicate, cycle, and repeat:

> l9  = repeat 'a'
> l10 = cycle [1,2,3]
> l11 = replicate 10 'a'

How to implement 'replicate' with repeat?

> replicate' n x = take n $ repeat x

List intervals:

> l12 = [1..100]

> l13 = [1,3..999]

> l14 = take 10 [1,3..100]

> l15 = [1..]

> l16 = ['a'..'z']

Laziness in action:

> l17 = take 10 [1..]
> l18 = head [1..]

What's going on here?:

> l19 = tail [1..]
> n = length [1..]

A list without its first and last element:

> trim l = tail (init l)
> trim' l = init $ tail l

> blanks = repeat ' '

> padTo10 s = s ++ take (10 - length s) blanks

Be careful with this:

> l20 = head []

Lists of lists:

> l21 = [[1,2,3],[4,5,6],[7,8,9,10]]
> l22 = ["red","green","blue"]

Again, remember that lists cannot be heterogenous, thus we cannot have
[1,2,[3,4]] nor ["red",'a'].

Concatenating list of sublists:

> l23 = concat l21

Minimum and maximum of a list:

> m1 = minimum [4, 1, 2, 3]

> m2 = maximum "Haskell for the win!"

Looking up elements from a list:

> e1 = [1,3..100] !! 17

> e2 = l21 !! 1 !! 2

Our own implementation of 'chr':

> intToChar i = ['A'..] !! (i - 65)

What happens if i < 65? Let's fix this:

> intToChar' i | i >= 65   = ['A'..] !! (i - 65)
>              | otherwise = error "Index should be at least 65"

Logical operation on lists:

> r1 = and [True,True,False]
> r2 = or [True,True,False]

Removing duplicates with 'nub':

> l24 = nub [1, 2, 3, 1, 1, 2]
> l25 = nub "Give me every letter only once!"

Sorting a list:

> l26 = sort [1,4,5,6,1,2]
> l27 = sort "Alphabet"

Checking list membership: 'elem' and 'notElem':

> hasA xs = 'a' `elem` xs

Function 'null' returns True if the list is empty, otherwise it returns False.

> isEmpty = null l27

We now have three ways at our disposal to check whether a list is empty:
(1) length xs == 0
(2) xs == []
(3) null xs

Which one should you use? You should definitively use (3). Approach (1) won't
work for infinite list. Approach (2) is more restrictive than (3), because it
won't work for all list types (why this is so will be clear after Lecture 3).

=== EXERCISE 1 ===============================================================

1.1.
- Define a function that returns a list without the first three elements and 
  last three elements.

1.2.
- Define a function 'initals s1 s2' that takes a person's name and a surname 
  as input and returns a string consisting of person's initials.
  initials "James" "Bond" => "J. B."

1.3.
- Define a function that concatenates two strings, so that the longest string
  always comes first.

1.4.
- Define a function 'safeHead' that returns an empty list if 'l' is an empty
  list, otherwise it returns its first element wrapped inside a singleton list.

1.5.
- Define a function 'hasDuplicates' that checks whether a list contains
  duplicate elements (use 'nub').

=== LIST COMPREHENSIONS ======================================================

> doubles = [x*2 | x <- [1..10]]

> sums1 = [x + y | x <- [1..10], y <- [1..10]]

> sums2 = [x + y | x <- [1..10], y <- [1..10], x < y]

> sums3 = [x + y | x <- [1..10], y <- [1..10], x < y, odd x || even y]

List of sublist lengths:

> lengths xss = [length xs | xs <- xss]

> totalLength xss = sum $ lengths xss

Combining strings:

> food = [s1 ++ " " ++ s2 | 
>         s1 <- ["cold", "hot", "fresh"], 
>         s2 <- ["cake", "strudel", "salad"]]

Since strings are actually lists of characters, we can do list comprehensions
with strings:

> codes = [ [c1,c2] | c1 <- "abc", c2 <- "123"]

> caesarCode s = [succ c | c <- s, c /= ' ']

> onlyDigits s = [c | c <- s, isDigit c]

> upperCase s = [toUpper c | c <- s]

=== EXERCISE 2 ===============================================================

2.1
- Define 'doublesFromTo a b' that generates a sequence [a*2, (a+1)*2,... b*2]
  and also works when b<a.

2.2.
- Redefine 'ceasarCode n xs' so that it shifts all letters a specified number 
  of positions 'n', converts all input to lowercase, and ensures that letters 
  remain within the ['a'..'z'] interval.

==============================================================================

Breaking up a string into tokens:

> ws = words "I think we agree, the past is over."

Breaking up a string into lines:

> ls = lines "First line\nSecond line"

Concatenating lines into a single string:

> stream = unlines ls

Filtering words with initial uppercase letter:

> capitalized s = [w | w <- words s, isUpper $ head w]

> camelCase s = concat [toUpper (head w) : tail w | w <- words s]

Or, more succinctly, using pattern matching:

> camelCase' s = concat [toUpper h : t | (h:t) <- words s]

=== EXERCISE 3 ===============================================================

3.1.
- Define 'letterCount' that computes the total number of letters in a string,
  thereby ignoring the whitespaces and all words shorter than three letters.
  You can use 'totalLength'.

3.2
- Redefine 'isPalindrome' so that it's case insensitive and works correctly 
  for strings that contain whitespaces.

3.3.
- Define 'flipp xss' that takes a list of lists, reverts each individual list,
  and concatenates all of them, but in the reverse order.
  flip ["water","is","warm"] -> "mrawsiretaw"

=== TUPLES ===================================================================

> pair1 = (1, 2)
> pair2 = ("Vatroslav", "Lisinski")

> triplet1 = (10, 1, 8)
> triplet2 = ("Vatroslav", "Lisinski", 1819)

> e3 = pair1 == (1, 2)

What do we get if we type in 'pair1 == pair2' ?

Assigning values to tuples:

> (a,b) = (1,2)

Extract of the first and the second element of a tuple, respectively:

> p = fst (5,6)
> q = snd (5,6)

List of pairs:

> pairs = [(1,2),(3,4),(5,6)]

Pairs of numbers from 1 to 100:

> pairsUpTo100 = [(x,y) | x <- [0..100], y <- [0..100]]

Pairs of numbers that sum up to 100:

> pairsSumTo100 = [(x,y) | x <- [0..100], y <- [0..100], x + y == 100 ]

Integer lengths of triangle sides that satisfy the Pythagorean theorem
(Pythagorean triplets):

> pythagoreanTriplets = 
>   [(a,b,c) | a <- [1..10], b <- [1..10], c <- [1..10], a^2 + b^2 == c^2]

Can be optimized:

> pythagoreanTriplets' = 
>   [(a,b,c) | c <- [1..10], a <- [1..c], b <- [1..a], a^2 + b^2 == c^2]

'zip' function:

> pairs2 = zip [1,2,3] "abc"
> pairs3 = zip [1,2,3,4] "abc"
> pairs4 = zip [1..] "abc"
> pairs5 = zip [1..100] [2..100]

=== EXERCISE 4 ===============================================================

4.1.
- Define 'inCircle r x y' that returns the coordinates of all points within
  the ([-10..10],[-10..10]) interval that fall inside a circle of radius
  'r' with center '(x,y)'.
- Redefine the function so that it takes the resolution of the grid as an 
  additional argument.

4.2.
- Define 'steps xs' that, given a list xs=[x1,x2,..], generates the pairs
  [(x1,x2),(x2,x3),...]. Hint: have a look at 'pairs5'.

==============================================================================

Indexing elements of a list:

> index xs = zip [1..] xs

Filtering every second list element:

> evenElems xs = [ snd ix | ix <- index xs, even (fst ix)]

The same thing, but using pattern matching:

> evenElems' xs = [ x | (i,x) <- index xs, even i]

Zip3:

> triplets2 = zip3 [0..10] ['A'..] [100..]

=== EXERCISE 5 ===============================================================

5.1.
- Define 'indices x xs' that returns the indices of element 'x' in list 'xs'
  (if 'x' appears multiple times, there will be a number of such indices).
  indices 'a' "alphabet" => [0, 4]

5.2.
- Define 'showLineNumbers s' that prefixes all lines from string 's' with a
  line number.
  showLineNumbers "first line\nsecond line" => "1 first line\n2 second line\n"

5.3.
- Define 'haveAlignment xs ys' that returns 'True' if 'xs' and 'ys' have
  any identical elements that are aligned (appear at the same position in
  both lists).
- Define 'common xs ys' that returns the aligned subsequences.
  haveAlignment "water" "fire" => True
  common "witer" "fire" => "ie"

=== NEXT =====================================================================

So far we have deliberately avoided talking about types of values and
functions. Because Haskell is a strongly and statically typed language, we
cannot postpone this any longer. In the next lecture, we'll look into types 
and type inference system of Haskell.

To prepare, you may (but need not to) read Chapter 3 of LYH:
http://learnyouahaskell.com/types-and-typeclasses