Haskell Basics
Stephen A. Edwards
Columbia University
Fall 2019
Useful Websites
Ï
https://www.haskell.org/
Downloads, documentation
E.g., the Haskell Wiki, the GHC User’s Guide, The Haskell 2010 language
report, Hackage (package library), Hoogle (Haskell API search)
Ï
http://docs.haskellstack.org
The Haskell Tool Stack: a powerful system for downloading and installing
packages, etc.
We will be using the Haskell Stack to make sure everybody’s environment
is consistent.
GHCi
GHC is the Glasgow Haskell Compiler (the major Haskell compiler release)
GHCi is the REPL (Read-Eval-Print Loop, a.k.a., command-line interface)
Run ghci with stack:
$ stack ghci
Configuring GHCi with the following packages:
GHCi, version 8.6.5: http://www.haskell.org/ghc/ :? for help
Loaded GHCi configuration from /tmp/haskell-stack-ghci/2a3bbd58/..
Prelude> :?
Commands available from the prompt:
<statement> evaluate/run <statement>
:quit exit GHCi
Comments
Single-line comments start with two dashes: --
Prelude> -- Single-line comment
Multi-line comments start with {-, end with -}, and may nest.
In GHCi only, multi-line definitions, etc.
may be written with :{ and :}; these are
unnecessary in source (.hs) files.
Prelude> :{
Prelude| {- This is a
Prelude| multi-line comment -}
Prelude| :}
Alternately enable multi-line input
mode in GHCi:
Prelude> :set +m
Prelude> {-
Prelude| A multi-line
Prelude| Comment
Prelude| -}
Prelude> {- Another
Prelude| one -}
Basic Arithmetic
Prelude> 2 + 15
17
Prelude> 42 - 10
32
Prelude> 1 + 2
*
3
7
Prelude> 5 / 2
2.5
Prelude> 3 + -2
<interactive>:4:1: error:
Precedence parsing error
cannot mix '+' [infixl 6] and prefix '-' [infixl 6] in the same
infix expression
Prelude> 3 + (-2)
1
Booleans and Equality
Haskell is case-sensitive
Prelude> True && False
False
Prelude> False || True
True
Prelude> not True || True
True
Prelude> not (True || True)
False
Prelude> 5 == 5
True
Prelude> 5 == 0
False
Prelude> 5 /= 5
False
Prelude> 5 /= 0
True
Prelude> "hello" == "hello"
True
Prelude> "llama" == 5
<interactive>:25:12: error:
*
No instance for (Num [Char]) arising from the literal '5'
*
In the second argument of '(==)', namely '5'
In the expression: "llama" == 5
In an equation for 'it': it = "llama" == 5
Function Application
Juxtaposition indicates function application. Don’t use parentheses or
commas for arguments.
Prelude> succ 41
42
Prelude> min 42 17
17
Prelude> max 42 17
42
Juxtaposition binds tightly; use parentheses to group arguments
Prelude> succ 3
*
2
8
Prelude> succ (3
*
2)
7
Backticks and parentheses
Backticks make a function an infix operator. This is sometimes a more natural
way to write expressions.
Prelude> 5 `max` 3
5
Prelude> 5 `max` 8
8
Parentheses around a binary operator turns it into a two-argument function.
This is most useful when you want to pass it as an argument (later).
Prelude> (+) 17 25
42
User-Defined Names and Functions
In recent versions of GHCi, just use = to bind things to names
Prelude> x = 7
Prelude> x
*
x
49
Just add one or more arguments to define a function
Prelude> sqr x = x
*
x
Prelude> sqr 7
49
Prelude> y = 8
Prelude> sqr y
64
Defining Functions
You can similarly define a function in a source file:
sqr.hs:
sqr x = x
*
x
In GHCi, :l means “load”
Prelude> :l sqr
[1 of 1] Compiling Main ( sqr.hs, interpreted )
Ok, one module loaded.
*
Main> sqr 7
49
Lists: Homogeneous Sequences
Square brackets and commas denote list literals
Prelude> fiveprimes = [2,3,5,7,11]
Prelude> fiveprimes
[2,3,5,7,11]
Strings are just lists of characters
Prelude> ['h','e','l','l','o']
"hello"
++ performs list concatenation
Prelude> [1,2,3] ++ [4,5]
[1,2,3,4,5]
Prelude> ['h','e','l','l','o'] ++ " world"
"hello world"
The Cons Operator : Prepends a List Element
The bracket notation is just syntactic sugar for Cons.
Prelude> 1 : [2,3,4]
[1,2,3,4]
Prelude> 1 : 2 : [3,4]
[1,2,3,4]
Prelude> 1 : 2 : 3 : 4 : []
[1,2,3,4]
List elements must all be the same type
Prelude> 1 : ['h','e']
<interactive>:10:1: error:
*
No instance for (Num Char) arising from the literal '1'
*
In the first argument of '(:)', namely '1'
In the expression: 1 : ['h', 'e']
In an equation for 'it': it = 1 : ['h', 'e']
From Learn You a Haskell for Great Good!
Prelude> x = [0,1,2,3,4]
Prelude> head x
0
Prelude> tail x
[1,2,3,4]
Prelude> last x
4
Prelude> length x
5
Prelude> init x
[0,1,2,3]
Prelude> reverse x
[4,3,2,1,0]
Prelude> null x
False
Prelude> null []
True
Prelude> [5,6,7] !! 2
7
Prelude> "Monty Python" !! 6
'P'
Prelude> take 3 x
[0,1,2]
Prelude> drop 2 x
[2,3,4]
Prelude> maximum x
4
Prelude> minimum x
0
Prelude> sum x
10
Prelude> product x
0
List Ranges
Prelude> [1..20]
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
Prelude> [2,4..20]
[2,4,6,8,10,12,14,16,18,20]
Prelude> [20,19..1]
[20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1]
Prelude> ['a'..'z']
"abcdefghijklmnopqrstuvwxyz"
Linear sequences only
Floating point numbers problematic
Infinite Lists
Haskell supports infinite lists (and other infinite data structures).
Hint: don’t print out the whole thing. E.g., use take to see the first elements
Prelude> take 5 [1..]
[1,2,3,4,5]
Prelude> take 10 [1..]
[1,2,3,4,5,6,7,8,9,10]
Prelude> take 10 [1,2,3]
[1,2,3]
Prelude> take 10 (cycle [1,2,3])
[1,2,3,1,2,3,1,2,3,1]
Prelude> take 16 (cycle [1,2,3])
[1,2,3,1,2,3,1,2,3,1,2,3,1,2,3,1]
Prelude> take 17 (repeat 5)
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
Prelude> replicate 15 6
[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
List Comprehensions
[ expression | generator-guard-let, generator-guard-let, . . . ]
Prelude> [ x^2 | x <- [1..19] ]
[1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361]
Prelude> [ x^2 | x <- [1..20], (x^2) `mod` 2 == 0 ]
[4,16,36,64,100,144,196,256,324,400]
Prelude> [ x^2 | x <- [1..20], even (x^2) ]
[4,16,36,64,100,144,196,256,324,400]
Prelude> [ y | x <- [1..20], let y = x^2, even y ]
[4,16,36,64,100,144,196,256,324,400]
List Comprehensions
Multiple guards must all be true
Prelude> [ x | x <- [1..100], x `mod` 7 == 0 ]
[7,14,21,28,35,42,49,56,63,70,77,84,91,98]
Prelude> [ x | x <- [1..100], x `mod` 7 == 0, x `mod` 5 == 0 ]
[35,70]
Multiple generators apply right-to-left:
Prelude> [ x + y | x <- [100,200..400], y <- [0..3] ]
[100,101,102,103,200,201,202,203,300,301,302,303,400,401,402,403]
Application: CS Research Jargon Generator
Prelude> :set +m
Prelude> [ adjective ++ " " ++ noun |
Prelude| adjective <- ["An integrated","A type-safe"],
Prelude| noun <- ["network","architecture","hypervisor"] ]
["An integrated network","An integrated architecture",
"An integrated hypervisor","A type-safe network",
"A type-safe architecture","A type-safe hypervisor"]
https://www.cs.purdue.edu/homes/dec/essay.topic.generator.html
List Comprehensions
Here’s an awkward way to code the standard Prelude’s length function:
Prelude> length' xs = sum [ 1 | _ <- xs ]
Prelude> length' [5,6,2,1,0]
5
Prelude> length' (replicate 11 []) -- List of eleven empty lists
11
Names (variable identifiers) start with a lowercase letter followed by zero or
more letters, digits, underscores, and single quotes.
_ alone means “don’t give this a name”
Prelude> onlyLetters s = [ c | c <- s,
Prelude| c `elem` ['A'..'Z'] ++ ['a'..'z'] ]
Prelude> onlyLetters "Does this do what I think it 5hould?"
"DoesthisdowhatIthinkithould"
Tuples: Pairs and More of Heterogeneous Objects
Lists are zero or more things of the same type; a tuple is two or more of
(potentially) different types.
Prelude> (5,10)
(5,10)
Prelude> ("a",15)
("a",15)
Prelude> ("Douglas","Adams",42)
("Douglas","Adams",42)
Prelude> sae = ("Stephen", "Edwards")
Prelude> fst sae
"Stephen"
Prelude> snd sae
"Edwards"
Zip and Pythagorean Triples
Form a list of pairs from two lists. Shorter of the two lists dominates;
convenient with infinite lists
Prelude> zip [1,2,3] [100,200,300]
[(1,100),(2,200),(3,300)]
Prelude> zip "Stephen" [1..]
[('S',1),('t',2),('e',3),('p',4),('h',5),('e',6),('n',7)]
Prelude> [ (a,b,c) | c <- [1..20], b <- [1..c], a <- [1..b],
Prelude| a^2 + b^2 == c^2 ]
[(3,4,5),(6,8,10),(5,12,13),(9,12,15),(8,15,17),(12,16,20)]
The Handshake Problem
Number of handshakes among a group of n friends?
Prelude> handshakes n = [ (a,b) | a <- [1..n-1], b <- [a+1..n] ]
Prelude> handshakes 3
[(1,2),(1,3),(2,3)]
Prelude> handshakes 5
[(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)]
Prelude> length (handshakes 5)
10
Prelude> [ length (handshakes n) | n <- [1..10] ]
[0,1,3,6,10,15,21,28,36,45]
Prelude> [ n
*
(n-1) `div` 2 | n <- [1..10] ]
[0,1,3,6,10,15,21,28,36,45]
