PROGRAMMING IN HASKELL
Modules, I/O and functors
Based on lecture notes by Graham Hutton
The book “Learn You a Haskell for Great Good”
(and a few other sources)
0
Modules
So far, we’ve been using built-in functions
provided in the Haskell prelude. This is a subset
of a larger library that is provided with any
installation of Haskell. (Google for Hoogle to see a
handy search engine for these.)
Examples of other modules:
- lists
- concurrent programming
- complex numbers
- char
- sets
-…
1
Example: Data.List
To load a module, we need to import it:
import Data.List
All the functions in this module are immediately
available:
numUniques :: (Eq a) => [a] -> Int
numUniques = length . nub
function
concatenation
This is a function in Data.List
that removes duplicates from a
list.
2
You can also load modules from the command
prompt:
ghci> :m + Data.List
Or several at once:
ghci> :m + Data.List Data.Map Data.Set
Or import only some, or all but some:
import Data.List (nub, sort)
import Data.List hiding (nub)
3
If duplication of names is an issue, can extend the
namespace:
import qualified Data.Map
This imports the functions, but we have to use
Data.Map to use them – like Data.Map.filter.
When the Data.Map gets a bit long, we can
provide an alias:
import qualified Data.Map as M
And now we can just type M.filter, and the
normal list filter will just be filter.
4
Data.List has a lot more functionality than we’ve
seen. A few examples:
ghci> intersperse '.' "MONKEY"
"M.O.N.K.E.Y"
ghci> intersperse 0 [1,2,3,4,5,6]
[1,0,2,0,3,0,4,0,5,0,6]
ghci> intercalate " " ["hey","there","guys"]
"hey there guys"
ghci> intercalate [0,0,0] [[1,2,3],[4,5,6],
[7,8,9]]
[1,2,3,0,0,0,4,5,6,0,0,0,7,8,9]
5
And even more:
ghci> transpose [[1,2,3],[4,5,6],
[7,8,9]]
[[1,4,7],[2,5,8],[3,6,9]]
ghci> transpose ["hey","there","guys"] ["
htg","ehu","yey","rs","e"]
ghci> concat ["foo","bar","car"]
"foobarcar"
ghci> concat [[3,4,5],[2,3,4],[2,1,1]]
[3,4,5,2,3,4,2,1,1]
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And even more:
ghci> and $ map (>4) [5,6,7,8]
True
ghci> and $ map (==4) [4,4,4,3,4]
False
ghci> any (==4) [2,3,5,6,1,4]
True
ghci> all (>4) [6,9,10]
True
7
A nice example: adding functions
Functions are often represented as vectors: 8x^3 +
5x^2 + x - 1 is [8,5,1,-1].
So we can easily use List functions to add these
vectors:
ghci> map sum $ transpose [[0,3,5,9],
[10,0,0,9],[8,5,1,-1]]
[18,8,6,17]
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There are a ton of these functions, so I could spend
all semester covering just lists.
More examples: group, sort, dropWhile, takeWhile,
partition, isPrefixOf, find, findIndex, delete, words,
insert,…
Instead, I’ll make sure to post a link to a good
overview of lists on the webpage, in case you need
them.
In essence, if it’s a useful thing to do to a list,
Haskell probably supports it!
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The Data.Char module: includes a lot of useful
functions that will look similar to python, actually.
Examples: isAlpha, isLower, isSpace, isDigit,
isPunctuation,…
ghci> all isAlphaNum "bobby283"
True
ghci> all isAlphaNum "eddy the fish!"Fal
se
ghci> groupBy ((==) `on` isSpace)
"hey guys its me"
["hey"," ","guys"," ","its"," ","me"]
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The Data.Char module has a datatype that is a set
of comparisons on characters. There is a function
called generalCategory that returns the information.
(This is a bit like the Ordering type for numbers,
which returns LT, EQ, or GT.)
ghci> generalCategory ' '
Space
ghci> generalCategory 'A'
UppercaseLetter
ghci> generalCategory 'a'
LowercaseLetter
ghci> generalCategory '.'
OtherPunctuation
ghci> generalCategory '9'
DecimalNumber
ghci> map generalCategory " ¥t¥nA9?|"
[Space,Control,Control,UppercaseLetter,DecimalNumber,OtherPunctuation,M
athSymbol] ]
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There are also functions that can convert between
Ints and Chars:
ghci> map digitToInt "FF85AB"
[15,15,8,5,10,11]
ghci> intToDigit 15
'f'
ghci> intToDigit 5
'5'
ghci> chr 97
'a'
ghci> map ord "abcdefgh"
[97,98,99,100,101,102,103,104]
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Neat application: Ceasar ciphers
A primitive encryption cipher which encodes
messages by shifted them a fixed amount in the
alphabet.
Example: hello with shift of 3
encode :: Int -> String -> String
encode shift msg =
let ords = map ord msg
shifted = map (+ shift) ords
in map chr shifted
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Now to use it:
ghci> encode 3 "Heeeeey"
"Khhhhh|"
ghci> encode 4 "Heeeeey"
"Liiiii}"
ghci> encode 1 "abcd"
"bcde"
ghci> encode 5 "Marry Christmas! Ho ho ho!”
"Rfww~%Hmwnxyrfx&%Mt%mt%mt&"
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Decoding just reverses the encoding:
decode :: Int -> String -> String
decode shift msg =
encode (negate shift) msg
ghci> encode 3 "Im a little teapot"
"Lp#d#olwwoh#whdsrw"
ghci> decode 3 "Lp#d#olwwoh#whdsrw"
"Im a little teapot"
ghci> decode 5 . encode 5 $ "This is a sentence
"
"This is a sentence"
15
Making our own modules
We specify our own modules at the beginning of a
file. For example, if we had a set of geometry
functions:
module Geometry
( sphereVolume
, sphereArea
, cubeVolume
, cubeArea
, cuboidArea
, cuboidVolume
) where
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Then, we put the functions that the module uses:
sphereVolume :: Float -> Float
sphereVolume radius = (4.0 / 3.0) * pi *
(radius ^ 3)
sphereArea :: Float -> Float
sphereArea radius = 4 * pi * (radius ^ 2)
cubeVolume :: Float -> Float
cubeVolume side = cuboidVolume side side side
…
17
Note that we can have “private” helper functions,
also:
cuboidVolume :: Float -> Float -> Float
-> Float
cuboidVolume a b c = rectangleArea a b * c
cuboidArea :: Float -> Float ->
Float -> Float
cuboidArea a b c = rectangleArea a b * 2 + rectangl
eArea a c * 2 + rectangleArea c b * 2
rectangleArea :: Float -> Float -> Float
rectangleArea a b = a * b
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Can also nest these. Make a folder called
Geometry, with 3 files inside it:
• Sphere.hs
• Cubiod.hs
• Cube.hs
Each will hold a separate group of functions.
To load:
import Geometry.Sphere
Or (if functions have same names):
import qualified Geometry.Sphere as Sphere
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The modules:
module Geometry.Sphere
( volume
, area
) where
volume :: Float -> Float
volume radius = (4.0 / 3.0) * pi * (radius ^
3)
area :: Float -> Float
area radius = 4 * pi * (radius ^ 2)
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module Geometry.Cuboid
( volume
, area
) where
volume :: Float -> Float -> Float -> Float
volume a b c = rectangleArea a b * c
…
21
File I/O
So far, we’ve worked mainly at the prompt, and
done very little true input or output. This is logical
in a functional language, since nothing has side
effects!
However, this is a problem with I/O, since the whole
point is to take input (and hence change some
value) and then output something (which requires
changing the state of the screen or other I/O
device.
Luckily, Haskell offers work-arounds that separate
the more imperative I/O.
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A simple example: save the following file as
helloword.hs
main = putStrLn "hello, world"
Now we actually compile a program:
$ ghc --make helloworld
[1 of 1] Compiling Main
( helloworld.hs, helloworld.o )
Linking helloworld ...
$ ./helloworld
hello, world
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What are these functions?
ghci> :t putStrLn
putStrLn :: String -> IO ()
ghci> :t putStrLn "hello, world"
putStrLn "hello, world" :: IO ()
So putStrLn takes a string and returns an I/O action
(which has a result type of (), the empty tuple).
In Haskell, an I/O action is one with a side effect usually either reading or printing. Usually some kind
of a return value, where () is a dummy value for no
return.
24
An I/O action will only be performed when you give
it the name “main” and then run the program.
A more interesting example:
main = do
putStrLn "Hello, what's your name?”
name <- getLine
putStrLn ("Hey " ++ name ++ ",
you rock!")
Notice the do statement - more imperative style.
Each step is an I/O action, and these glue together.
25
More on getLine:
ghci> :t getLine
getLine :: IO String
This is the first I/O we’ve seen that doesn’t have an
empty tuple type - it has a String.
Once the string is returned, we use the <- to bind
the result to the specified identifier.
Notice this is the first non-functional action we’ve
seen, since this function will NOT have the same
value every time it is run! This is called “impure”
code, and the value name is “tainted”.
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An invalid example:
nameTag = "Hello, my name is " ++ getLine
What’s the problem? Well, ++ requires both
parameters to have the same type.
What is the return type of getLine?
Another word of warning: what does the following
do?
name = getLine
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Just remember that I/O actions are only performed
in a few possible places:
- A main function
- inside a bigger I/O block that we have composed
with a do (and remember that the last action can’t
be bound to a name, since that is the one that is the
return type).
-At the ghci prompt:
ghci> putStrLn "HEEY"
HEEY
28
You can use let statements inside do blocks, to call
other functions (and with no “in” part required):
import Data.Char
main = do
putStrLn "What's your first name?"
firstName <- getLine
putStrLn "What's your last name?"
lastName <- getLine
let bigFirstName = map toUpper firstName
bigLastName = map toUpper lastName
putStrLn $ "hey " ++ bigFirstName ++ " " ++
bigLastName ++ ", how are you?"
Note that <- is for I/O, and let for expressions.
29
What is return?
Does NOT signal the end of execution! Return
instead makes an I/O action out of a pure value.
main = do
a <- return "heck"
b <- return "yeah!"
putStrLn $ a ++ " " ++ b
In essence, return is the opposite of <-. Instead of
“unwrapping” I/O Strings, it wraps them.
30
Last example was a bit redundant, though – could
use a let instead:
main = do
let a = ”heck"
b = "yeah"
putStrLn $ a ++ " " ++ b
Usually, you’ll use return to create I/O actions that
don’t do anything (but you have to have one
anyway, like an if-then-else), or for the last line of a
do block, so it returns some value we want.
31
Takeaway: Return in haskell is NOT like other
languages.
main = do
line <- getLine
if null line
then return ()
else do
putStrLn $ reverseWords line
main
reverseWords :: String -> String
reverseWords = unwords . map reverse . words
Note: reverseWords = unwords . map reverse .
words is the same as
reverseWords st = nwords (map reverse (words st))
32
Other I/O functions:
-print (works on any type in show, but calls show
first)
-putStr - And as putStrLn, but no newline
-putChar and getChar
main = do print True
print 2
print "haha"
print 3.2
print [3,4,3]
main = do
c <- getChar
if c /= ' '
then do
putChar c
main
else return ()
33
More advanced functionality is available in
Control.Monad:
import Control.Monad
import Data.Char
main = forever $ do
putStr "Give me some input: "
l <- getLine
putStrLn $ map toUpper l
(Will indefinitely ask for input and print it back out
capitalized.)
34
Other functions:
• sequence: takes list of I/O actions and does them
one after the other
• mapM: takes a function (which returns an I/O)
and maps it over a list
Others available in Control.Monad:
• when: takes boolean and I/O action. If bool is
true, returns same I/O, and if false, does a return
instead
35
System Level programming
Scripting functionality deals with I/O as a necessity.
The module System.Environment has several to help
with this:
• getArgs: returns a list of the arguments that the
program was run with
• getProgName: returns the string which is the
program name
(Note: I’ll be assuming you compile using “ghc –
make myprogram” and then running “./myprogram”.
But you could also do “runhaskell myprogram.hs”.)
36
An example:
import System.Environment
import Data.List
main = do
args <- getArgs
progName <- getProgName
putStrLn "The arguments are:"
mapM putStrLn args
putStrLn "The program name is:"
putStrLn progName
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The output:
$ ./arg-test first second w00t "multi word
arg"
The arguments are:
first
second
w00t
multi word arg
The program name is:
arg-test
38
Functors
Functors are a typeclass, just like Ord, Eq, Show,
and all the others. This one is designed to hold
things that can be mapped over; for example, lists
are part of this typeclass.
class Functor f where
fmap :: (a -> b) -> f a -> f b
This type is interesting - not like previous exmaples,
like in EQ, where (==) :: (Eq a) => a -> a -> Bool.
Here, f is NOT a concrete type, but a type
constructor that takes one parameter.
39
Compare fmap to map:
fmap :: (a -> b) -> f a -> f b
map :: (a -> b) -> [a] -> [b]
So map is a lot like a functor! Here, map takes a
function and a list of type a, and returns a list of
type b.
In fact, can define map in terms of fmap:
instance Functor [] where
fmap = map
40
Notice what we wrote:
instance Functor [] where
fmap = map
We did NOT write “instance Functor [a] where…”,
since f has to be a type constructor that takes one
type.
Here, [a] is already a concrete type, while [] is a
type constructor that takes one type and can
produce many types, like [Int], [String], [[Int]], etc.
41
Another example:
instance Functor Maybe where
fmap f (Just x) = Just (f x)
fmap f Nothing = Nothing
Again, we did NOT write “instance Functor (Maybe
m) where…”, since functor wants a type constructor.
Mentally replace the f’s with Maybe, so fmap acts
like (a -> b) -> Maybe a -> Maybe b.
If we put (Maybe m), would have (a -> b) ->
(Maybe m) a -> (Maybe m) b, which looks wrong.
42
Using it:
ghci> fmap (++ " HEY GUYS IM INSIDE THE
JUST") (Just "Something serious.")
Just "Something serious. HEY GUYS IM INSIDE TH
E JUST"
ghci> fmap (++ " HEY GUYS IM INSIDE THE
JUST") Nothing
Nothing
ghci> fmap (*2) (Just 200)
Just 400
ghci> fmap (*2) Nothing
Nothing
43
Back to trees, as an example to put it all together:
Let’s make a binary search tree type. Need
comparisons to make sense, so want the type to be
in Eq.
Also going to have it be Show and Read, so anything
in the tree can be converted to a string and printed
(just to make displaying easier).
data Tree a = EmptyTree
| Node a (Tree a) (Tree a)
deriving (Show,Read,Eq)
44
Note that this is slightly different than our last class.
Node 5 (Node 3 (Node 1 EmptyTree EmptyTree) (Node 4
EmptyTree EmptyTree)) (Node 6 EmptyTree EmptyTree)
This will let us code an insert that’s a bit easier to
process, though!
First step – a function to make a single node tree:
singleton :: a -> Tree a
singleton x = Node x EmptyTree EmptyTree
45
Now – go code insert!
treeInsert :: (Ord a) => a -> Tree a -> Tree a
treeInsert x EmptyTree =
treeInsert x (Node a left right) =
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My insert:
treeInsert :: (Ord a) => a -> Tree a -> Tree a
treeInsert x EmptyTree = singleton x
treeInsert x (Node a left right)
| x == a = Node x left right
| x < a = Node a (treeInsert x left) right
| x > a = Node a left (treeInsert x right)
47
Find:
findInTree :: (Ord a) => a -> Tree a -> Bool
findInTree x EmptyTree = False
findInTree x (Node a left right)
| x == a = True
| x < a = findInTree x left
| x > a = findInTree x right
Note: This is a binary search tree, so can be
efficient. If it were an “unordered” tree, like we saw
last week, would need to search both left and right
subtrees.
48
An example run:
ghci> let nums = [8,6,4,1,7,3,5]
ghci> let numsTree = foldr treeInsert EmptyTre
e nums
ghci> numsTree
Node 5 (Node 3 (Node 1 EmptyTree EmptyTree) (N
ode 4 EmptyTree EmptyTree)) (Node 7 (Node 6 Em
ptyTree EmptyTree) (Node 8 EmptyTree EmptyTre
e))
49
Back to functors:
If we looked at fmap as though it were only for
trees, it would look something like:
(a -> b) -> Tree a -> Tree b
We can certainly phrase this as a functor, also:
instance Functor Tree where
fmap f EmptyTree = EmptyTree
fmap f (Node x leftsub rightsub) =
Node (f x) (fmap f leftsub)
(fmap f rightsub)
50
Using the tree functor:
ghci> fmap (*2) EmptyTree
EmptyTree
ghci> fmap (*4) (foldr treeInsert
EmptyTree [5,7,3,2,1,7])
Node 28 (Node 4 EmptyTree (Node 8 EmptyTree (N
ode 12 EmptyTree (Node 20 EmptyTree EmptyTree
)))) EmptyTree
51