pr3-sose2026-fork/haskell/01-expressions/README.md

Haskell - Expressions

The following illustrates some haskell basics. It can be reproduced using ghci.

Types, Literals, and Constants along with Arithmetic and Boolean Operations

Expression	Type (:t)	Value	Comment
2	Num a => a	2
2.03	Fractional a => a	2.03
'c'	Char	'c'
"hallo"	String	"hallo"
True	Bool	True
x=5	Num a => a	5	Constant named x
2 + 3	Num a => a	5	Similar -,*,^
2 / 3	Fractional a => a	0.6666666666666666
1 > 2	Bool	False	Similar <, <=, >=, ==, /=
True && False	Bool	False	Similar ||,not
((2+3)*5 > 1) || not (1 > 2)	Bool	True	Right part is not evaluated due to lazy evaluation

Unary Functions

Expression	Type (:t)	Value	Comment
sqrt(4)	Floating a => a	2.0
sqrt 4	Floating a => a	2.0	Similar abs,negate,signum,recip
sqrt	Floating a => a -> a
sqrt 3^2 + 4^2	Floating a => a	19.0
sqrt (3^2 + 4^2)	Floating a => a	5.0
negate(sqrt (3^2 + 4^2))	Floating a => a	-5.0
negate $ sqrt (3^2 + 4^2)	Floating a => a	-5.0	Function application operator $
(negate . sqrt) (3^2 + 4^2)	Floating a => a	-5.0	Function composition operator . Reads negate after negate . sqrt
(negate . length) "hallo"	Int	-5
negatedRoot = negate . sqrt	Floating c => c -> c		Constant named negatedRoot

Binary Functions

Expression	Type (:t)	Value	Comment
div 8 4	Integral a => a	2	Similar mod,gcd,lcm,not
8 `div` 4	Integral a => a	2	Infix notation using backticks
8 + 4	Num a => a	12	-,*,^,<, <=, >=, ==, /=
(+) 8 4	Num a => a	12	Prefix notation using parenthesis
div	Integral a => a -> a -> a		Currying represents multi-argument functions as a chain of single-argument functions
div 8	Integral a => a -> a		binds the first argument; Similar (8/),(8*),(8+),(8-)
div8bySomething = div 8	Integral a => a -> a
div8bySomething 4	Integral a => a	2
uncurry div	Integral c => (c, c) -> c		accepts a single tuple argument
uncurry div (8,4)	Integral c => c	2
uncurry	(a -> b -> c) -> (a, b) -> c
(`div` 4)	Integral a => a -> a		Sectioning binds the second argument of infix functions; Similar (/8),(*8),(+8),(-8)
divSomethingBy4 = (`div` 4)	Integral a => a -> a
divSomethingBy4 8	Integral a => a	2

Tuples

Expression	Type (:t)	Value	Comment
(1, 2)	(Num a, Num b) => (a, b)	(1, 2)
(1, "hello", True)	(Num a => (a, String, Bool)	(1, "hello", True)
fst (1, 2)	Num a => a	1
snd (1, 2)	Num b => b	2
(,) 1 2	Num a => a -> a -> (a, a)	(1, 2)

Strings

Expression	Type (:t)	Value	Comment
"hello" ++ " world"	String	"hello world"	String concatenation
length "hello"	Int	5	Length of the string
null ""	Bool	True	Checks if the string is empty

Control Structures

Expression	Type (:t)	Value	Comment
if 10/2==5 then "five" else "something else"	String	"five"
case 1 of { 1 -> "small"; 2 -> "medium"; _ -> "large"}	String	"small"	patterns are overlapping
(let x = 5*2 in (x * 2,x /2))	(Fractional b, Num a) => (a, b)	(20,5.0)

Lists

Expression	Type (:t)	Value	Comment
[1,7,4]	Num a => [a]	[1,7,4]
[]	[a]	[]
8 : [1,7,4]	Num a => [a]	[8,1,7,4]	cons operator, short for construct
1:7:4:[]	Num a => [a]	[1,7,4]	actual construction of a list
[1,7,4] ++ [8]	Num a => [a]	[1,7,4,8]
(++)	[a] -> [a] -> [a]
[1,7,4]	[Num a] => [a]	[1,7,4]
head [1,7,4]	Num a => a	1	Similar last
tail [1,7,4]	[Num a] => [a]	[7,4]	Similar init
length [1,7,4]	Int	3
null []	Bool	True
reverse [1,7,4]	[Num a] => [a]	[4,7,1]	Similar Data.List.sort
take 2 [1,7,4]	[Num a]=>[a]	[1,7]	Similar drop
take	Int -> [a] -> [a]
sum [1,7,4]	Num a=>a	12	Similar product,maximum,minimum,length
foldl (-) 0 [1,7,4]	Num a => a	-12	(((0-1)-7)-4)
foldl	Foldable t => (b -> a -> b) -> b -> t a -> b
foldr (-) 0 [1,7,4]	Num a => a	-2	(1-(7-(4-0)))
elem 7 [1,7,4]	Bool	True
all even [1,7,4]	Bool	False	Similar any
filter even [1,7,4]	[Integral a] => [a]	[1,7,4]	Similar odd,(>1),(/=3)
(length . filter (>1) ) [1,7,4]	Int	2
Data.List.partition (>1) [1,7,4]	(Ord a, Num a) => ([a], [a])	([7,4],[1])
zip [1,7,4] ["one","seven","four","eight"]	Num a => [(a, String)]	[(1,"one"),(7,"seven"),(4,"four")]	truncating to the shorter list
Data.List.sortOn fst $ zip [1,7,4] ["one", "seven", "four"]	(Ord b, Num b) => [(b, String)]	[(1,"one"),(4,"four"),(7,"seven")]
Data.List.sort ["one","seven","four","eight"]	[String]	["eight","four","one","seven"]
reverse $ Data.List.sort ["one","seven","four","eight"]	[String]	["seven","one","four","eight"]
Data.List.sortBy compare ["one","seven","four","eight"]	[String]	["eight","four","one","seven"]
Data.List.sortBy (flip compare) ["one","seven","four","eight"]	[String]	["seven","one","four","eight"]
Data.List.sortBy (curry( (uncurry compare) . (uncurry(Control.Arrow.***) (length,length)))) ["one","seven","four","eight","ten"]	[String]	["one","ten","four","seven","eight"]
Data.List.sortBy (Data.Ord.comparing length) ["one","seven","four","eight","ten"]	[String]	["one","ten","four","seven","eight"]
map (+1) [1,7,4]	Num a => [a]	[2,8,5]
map length ["one", "seven", "four"]	[Int]	[3,5,4]
map (negate . abs) [1,-7,4]	Num a => [a]	[-1,-7,-4]
map even [1,7,4]	[Bool]	[False,False,True]
[1..5]	(Num a, Enum a) => [a]	[1,2,3,4,5]
[1,3..9]	(Num a, Enum a) => [a]	[1,3,5,7,9]
[1..]	(Num a, Enum a) => [a]	[1,2,3,4,5,...]	infinite sequence
take 4 [10..]	(Num a, Enum a) => [a]	[1,2,3,4]	laziness in action
[x*2 | x <- [1..5]]	[Num a] => [a]	[2, 4, 6, 8, 10]	List comprehension
[x*2 | x <- [1..5], x `mod` 3 == 0]	[Num a] => [a]	[6]
[ (a,b,c) | c <- [1..10], b <- [1..c], a <- [1..b], a^2 + b^2 == c^2]	(Num c, Eq c, Enum c) => [(c, c, c)]	[(3,4,5),(6,8,10)]