julia.html.markdown

language	contributors	filename
Julia	Leah Hanson http://leahhanson.us	learnjulia.jl

Julia is a new homoiconic functional language focused on technical computing. While having the full power of homoiconic macros, first-class functions, and low-level control, Julia is as easy to learn and use as Python.

This is based on Julia 0.3.

# Single line comments start with a hash (pound) symbol.
#= Multiline comments can be written
   by putting '#=' before the text  and '=#' 
   after the text. They can also be nested.
=#

####################################################
## 1. Primitive Datatypes and Operators
####################################################

# Everything in Julia is a expression.

# There are several basic types of numbers.
3 # => 3 (Int64)
3.2 # => 3.2 (Float64)
2 + 1im # => 2 + 1im (Complex{Int64})
2//3 # => 2//3 (Rational{Int64})

# All of the normal infix operators are available.
1 + 1 # => 2
8 - 1 # => 7
10 * 2 # => 20
35 / 5 # => 7.0
5 / 2 # => 2.5 # dividing an Int by an Int always results in a Float
div(5, 2) # => 2 # for a truncated result, use div
5 \ 35 # => 7.0
2 ^ 2 # => 4 # power, not bitwise xor
12 % 10 # => 2

# Enforce precedence with parentheses
(1 + 3) * 2 # => 8

# Bitwise Operators
~2 # => -3   # bitwise not
3 & 5 # => 1 # bitwise and
2 | 4 # => 6 # bitwise or
2 $ 4 # => 6 # bitwise xor
2 >>> 1 # => 1 # logical shift right
2 >> 1  # => 1 # arithmetic shift right
2 << 1  # => 4 # logical/arithmetic shift left

# You can use the bits function to see the binary representation of a number.
bits(12345)
# => "0000000000000000000000000000000000000000000000000011000000111001"
bits(12345.0)
# => "0100000011001000000111001000000000000000000000000000000000000000"

# Boolean values are primitives
true
false

# Boolean operators
!true # => false
!false # => true
1 == 1 # => true
2 == 1 # => false
1 != 1 # => false
2 != 1 # => true
1 < 10 # => true
1 > 10 # => false
2 <= 2 # => true
2 >= 2 # => true
# Comparisons can be chained
1 < 2 < 3 # => true
2 < 3 < 2 # => false

# Strings are created with "
"This is a string."

# Character literals are written with '
'a'

# A string can be indexed like an array of characters
"This is a string"[1] # => 'T' # Julia indexes from 1
# However, this is will not work well for UTF8 strings,
# so iterating over strings is recommended (map, for loops, etc).

# $ can be used for string interpolation:
"2 + 2 = $(2 + 2)" # => "2 + 2 = 4"
# You can put any Julia expression inside the parentheses.

# Another way to format strings is the printf macro.
@printf "%d is less than %f" 4.5 5.3 # 5 is less than 5.300000

# Printing is easy
println("I'm Julia. Nice to meet you!")

####################################################
## 2. Variables and Collections
####################################################

# You don't declare variables before assigning to them.
some_var = 5 # => 5
some_var # => 5

# Accessing a previously unassigned variable is an error
try
    some_other_var # => ERROR: some_other_var not defined
catch e
    println(e)
end

# Variable names start with a letter.
# After that, you can use letters, digits, underscores, and exclamation points.
SomeOtherVar123! = 6 # => 6

# You can also use unicode characters
☃ = 8 # => 8
# These are especially handy for mathematical notation
2 * π # => 6.283185307179586

# A note on naming conventions in Julia:
#
# * Word separation can be indicated by underscores ('_'), but use of
#   underscores is discouraged unless the name would be hard to read
#   otherwise.
#
# * Names of Types begin with a capital letter and word separation is shown
#   with CamelCase instead of underscores.
#
# * Names of functions and macros are in lower case, without underscores.
#
# * Functions that modify their inputs have names that end in !. These
#   functions are sometimes called mutating functions or in-place functions.

# Arrays store a sequence of values indexed by integers 1 through n:
a = Int64[] # => 0-element Int64 Array

# 1-dimensional array literals can be written with comma-separated values.
b = [4, 5, 6] # => 3-element Int64 Array: [4, 5, 6]
b[1] # => 4
b[end] # => 6

# 2-dimentional arrays use space-separated values and semicolon-separated rows.
matrix = [1 2; 3 4] # => 2x2 Int64 Array: [1 2; 3 4]

# Add stuff to the end of a list with push! and append!
push!(a,1)     # => [1]
push!(a,2)     # => [1,2]
push!(a,4)     # => [1,2,4]
push!(a,3)     # => [1,2,4,3]
append!(a,b) # => [1,2,4,3,4,5,6]

# Remove from the end with pop
pop!(b)        # => 6 and b is now [4,5]

# Let's put it back
push!(b,6)   # b is now [4,5,6] again.

a[1] # => 1 # remember that Julia indexes from 1, not 0!

# end is a shorthand for the last index. It can be used in any
# indexing expression
a[end] # => 6

# we also have shift and unshift
shift!(a) # => 1 and a is now [2,4,3,4,5,6]
unshift!(a,7) # => [7,2,4,3,4,5,6]

# Function names that end in exclamations points indicate that they modify
# their argument.
arr = [5,4,6] # => 3-element Int64 Array: [5,4,6]
sort(arr) # => [4,5,6]; arr is still [5,4,6]
sort!(arr) # => [4,5,6]; arr is now [4,5,6]

# Looking out of bounds is a BoundsError
try
    a[0] # => ERROR: BoundsError() in getindex at array.jl:270
    a[end+1] # => ERROR: BoundsError() in getindex at array.jl:270
catch e
    println(e)
end

# Errors list the line and file they came from, even if it's in the standard
# library. If you built Julia from source, you can look in the folder base
# inside the julia folder to find these files.

# You can initialize arrays from ranges
a = [1:5;] # => 5-element Int64 Array: [1,2,3,4,5]

# You can look at ranges with slice syntax.
a[1:3] # => [1, 2, 3]
a[2:end] # => [2, 3, 4, 5]

# Remove elements from an array by index with splice!
arr = [3,4,5]
splice!(arr,2) # => 4 ; arr is now [3,5]

# Concatenate lists with append!
b = [1,2,3]
append!(a,b) # Now a is [1, 2, 3, 4, 5, 1, 2, 3]

# Check for existence in a list with in
in(1, a) # => true

# Examine the length with length
length(a) # => 8

# Tuples are immutable.
tup = (1, 2, 3) # => (1,2,3) # an (Int64,Int64,Int64) tuple.
tup[1] # => 1
try:
    tup[1] = 3 # => ERROR: no method setindex!((Int64,Int64,Int64),Int64,Int64)
catch e
    println(e)
end

# Many list functions also work on tuples
length(tup) # => 3
tup[1:2] # => (1,2)
in(2, tup) # => true

# You can unpack tuples into variables
a, b, c = (1, 2, 3) # => (1,2,3)  # a is now 1, b is now 2 and c is now 3

# Tuples are created even if you leave out the parentheses
d, e, f = 4, 5, 6 # => (4,5,6)

# A 1-element tuple is distinct from the value it contains
(1,) == 1 # => false
(1) == 1 # => true

# Look how easy it is to swap two values
e, d = d, e  # => (5,4) # d is now 5 and e is now 4


# Dictionaries store mappings
empty_dict = Dict() # => Dict{Any,Any}()

# You can create a dictionary using a literal
filled_dict = ["one"=> 1, "two"=> 2, "three"=> 3]
# => Dict{ASCIIString,Int64}

# Look up values with []
filled_dict["one"] # => 1

# Get all keys
keys(filled_dict)
# => KeyIterator{Dict{ASCIIString,Int64}}(["three"=>3,"one"=>1,"two"=>2])
# Note - dictionary keys are not sorted or in the order you inserted them.

# Get all values
values(filled_dict)
# => ValueIterator{Dict{ASCIIString,Int64}}(["three"=>3,"one"=>1,"two"=>2])
# Note - Same as above regarding key ordering.

# Check for existence of keys in a dictionary with in, haskey
in(("one", 1), filled_dict) # => true
in(("two", 3), filled_dict) # => false
haskey(filled_dict, "one") # => true
haskey(filled_dict, 1) # => false

# Trying to look up a non-existent key will raise an error
try
    filled_dict["four"] # => ERROR: key not found: four in getindex at dict.jl:489
catch e
    println(e)
end

# Use the get method to avoid that error by providing a default value
# get(dictionary,key,default_value)
get(filled_dict,"one",4) # => 1
get(filled_dict,"four",4) # => 4

# Use Sets to represent collections of unordered, unique values
empty_set = Set() # => Set{Any}()
# Initialize a set with values
filled_set = Set(1,2,2,3,4) # => Set{Int64}(1,2,3,4)

# Add more values to a set
push!(filled_set,5) # => Set{Int64}(5,4,2,3,1)

# Check if the values are in the set
in(2, filled_set) # => true
in(10, filled_set) # => false

# There are functions for set intersection, union, and difference.
other_set = Set(3, 4, 5, 6) # => Set{Int64}(6,4,5,3)
intersect(filled_set, other_set) # => Set{Int64}(3,4,5)
union(filled_set, other_set) # => Set{Int64}(1,2,3,4,5,6)
setdiff(Set(1,2,3,4),Set(2,3,5)) # => Set{Int64}(1,4)


####################################################
## 3. Control Flow
####################################################

# Let's make a variable
some_var = 5

# Here is an if statement. Indentation is not meaningful in Julia.
if some_var > 10
    println("some_var is totally bigger than 10.")
elseif some_var < 10    # This elseif clause is optional.
    println("some_var is smaller than 10.")
else                    # The else clause is optional too.
    println("some_var is indeed 10.")
end
# => prints "some var is smaller than 10"


# For loops iterate over iterables.
# Iterable types include Range, Array, Set, Dict, and String.
for animal=["dog", "cat", "mouse"]
    println("$animal is a mammal")
    # You can use $ to interpolate variables or expression into strings
end
# prints:
#    dog is a mammal
#    cat is a mammal
#    mouse is a mammal

# You can use 'in' instead of '='.
for animal in ["dog", "cat", "mouse"]
    println("$animal is a mammal")
end
# prints:
#    dog is a mammal
#    cat is a mammal
#    mouse is a mammal

for a in ["dog"=>"mammal","cat"=>"mammal","mouse"=>"mammal"]
    println("$(a[1]) is a $(a[2])")
end
# prints:
#    dog is a mammal
#    cat is a mammal
#    mouse is a mammal

for (k,v) in ["dog"=>"mammal","cat"=>"mammal","mouse"=>"mammal"]
    println("$k is a $v")
end
# prints:
#    dog is a mammal
#    cat is a mammal
#    mouse is a mammal

# While loops loop while a condition is true
x = 0
while x < 4
    println(x)
    x += 1  # Shorthand for x = x + 1
end
# prints:
#   0
#   1
#   2
#   3

# Handle exceptions with a try/catch block
try
   error("help")
catch e
   println("caught it $e")
end
# => caught it ErrorException("help")


####################################################
## 4. Functions
####################################################

# The keyword 'function' creates new functions
#function name(arglist)
#  body...
#end
function add(x, y)
    println("x is $x and y is $y")

    # Functions return the value of their last statement
    x + y
end

add(5, 6) # => 11 after printing out "x is 5 and y is 6"

# You can define functions that take a variable number of
# positional arguments
function varargs(args...)
    return args
    # use the keyword return to return anywhere in the function
end
# => varargs (generic function with 1 method)

varargs(1,2,3) # => (1,2,3)

# The ... is called a splat.
# We just used it in a function definition.
# It can also be used in a fuction call,
# where it will splat an Array or Tuple's contents into the argument list.
Set([1,2,3])    # => Set{Array{Int64,1}}([1,2,3]) # produces a Set of Arrays
Set([1,2,3]...) # => Set{Int64}(1,2,3) # this is equivalent to Set(1,2,3)

x = (1,2,3)     # => (1,2,3)
Set(x)          # => Set{(Int64,Int64,Int64)}((1,2,3)) # a Set of Tuples
Set(x...)       # => Set{Int64}(2,3,1)


# You can define functions with optional positional arguments
function defaults(a,b,x=5,y=6)
    return "$a $b and $x $y"
end

defaults('h','g') # => "h g and 5 6"
defaults('h','g','j') # => "h g and j 6"
defaults('h','g','j','k') # => "h g and j k"
try
    defaults('h') # => ERROR: no method defaults(Char,)
    defaults() # => ERROR: no methods defaults()
catch e
    println(e)
end

# You can define functions that take keyword arguments
function keyword_args(;k1=4,name2="hello") # note the ;
    return ["k1"=>k1,"name2"=>name2]
end

keyword_args(name2="ness") # => ["name2"=>"ness","k1"=>4]
keyword_args(k1="mine") # => ["k1"=>"mine","name2"=>"hello"]
keyword_args() # => ["name2"=>"hello","k1"=>4]

# You can combine all kinds of arguments in the same function
function all_the_args(normal_arg, optional_positional_arg=2; keyword_arg="foo")
    println("normal arg: $normal_arg")
    println("optional arg: $optional_positional_arg")
    println("keyword arg: $keyword_arg")
end

all_the_args(1, 3, keyword_arg=4)
# prints:
#   normal arg: 1
#   optional arg: 3
#   keyword arg: 4

# Julia has first class functions
function create_adder(x)
    adder = function (y)
        return x + y
    end
    return adder
end

# This is "stabby lambda syntax" for creating anonymous functions
(x -> x > 2)(3) # => true

# This function is identical to create_adder implementation above.
function create_adder(x)
    y -> x + y
end

# You can also name the internal function, if you want
function create_adder(x)
    function adder(y)
        x + y
    end
    adder
end

add_10 = create_adder(10)
add_10(3) # => 13


# There are built-in higher order functions
map(add_10, [1,2,3]) # => [11, 12, 13]
filter(x -> x > 5, [3, 4, 5, 6, 7]) # => [6, 7]

# We can use list comprehensions for nicer maps
[add_10(i) for i=[1, 2, 3]] # => [11, 12, 13]
[add_10(i) for i in [1, 2, 3]] # => [11, 12, 13]

####################################################
## 5. Types
####################################################

# Julia has a type system.
# Every value has a type; variables do not have types themselves.
# You can use the `typeof` function to get the type of a value.
typeof(5) # => Int64

# Types are first-class values
typeof(Int64) # => DataType
typeof(DataType) # => DataType
# DataType is the type that represents types, including itself.

# Types are used for documentation, optimizations, and dispatch.
# They are not statically checked.

# Users can define types
# They are like records or structs in other languages.
# New types are defined using the `type` keyword.

# type Name
#   field::OptionalType
#   ...
# end
type Tiger
  taillength::Float64
  coatcolor # not including a type annotation is the same as `::Any`
end

# The default constructor's arguments are the properties
# of the type, in the order they are listed in the definition
tigger = Tiger(3.5,"orange") # => Tiger(3.5,"orange")

# The type doubles as the constructor function for values of that type
sherekhan = typeof(tigger)(5.6,"fire") # => Tiger(5.6,"fire")

# These struct-style types are called concrete types
# They can be instantiated, but cannot have subtypes.
# The other kind of types is abstract types.

# abstract Name
abstract Cat # just a name and point in the type hierarchy

# Abstract types cannot be instantiated, but can have subtypes.
# For example, Number is an abstract type
subtypes(Number) # => 6-element Array{Any,1}:
                 #     Complex{Float16}
                 #     Complex{Float32}
                 #     Complex{Float64}
                 #     Complex{T<:Real}
                 #     ImaginaryUnit
                 #     Real
subtypes(Cat) # => 0-element Array{Any,1}

# Every type has a super type; use the `super` function to get it.
typeof(5) # => Int64
super(Int64) # => Signed
super(Signed) # => Real
super(Real) # => Number
super(Number) # => Any
super(super(Signed)) # => Number
super(Any) # => Any
# All of these type, except for Int64, are abstract.

# <: is the subtyping operator
type Lion <: Cat # Lion is a subtype of Cat
  mane_color
  roar::String
end

# You can define more constructors for your type
# Just define a function of the same name as the type
# and call an existing constructor to get a value of the correct type
Lion(roar::String) = Lion("green",roar)
# This is an outer constructor because it's outside the type definition

type Panther <: Cat # Panther is also a subtype of Cat
  eye_color
  Panther() = new("green")
  # Panthers will only have this constructor, and no default constructor.
end
# Using inner constructors, like Panther does, gives you control
# over how values of the type can be created.
# When possible, you should use outer constructors rather than inner ones.

####################################################
## 6. Multiple-Dispatch
####################################################

# In Julia, all named functions are generic functions
# This means that they are built up from many small methods
# Each constructor for Lion is a method of the generic function Lion.

# For a non-constructor example, let's make a function meow:

# Definitions for Lion, Panther, Tiger
function meow(animal::Lion)
  animal.roar # access type properties using dot notation
end

function meow(animal::Panther)
  "grrr"
end

function meow(animal::Tiger)
  "rawwwr"
end

# Testing the meow function
meow(tigger) # => "rawwr"
meow(Lion("brown","ROAAR")) # => "ROAAR"
meow(Panther()) # => "grrr"

# Review the local type hierarchy
issubtype(Tiger,Cat) # => false
issubtype(Lion,Cat) # => true
issubtype(Panther,Cat) # => true

# Defining a function that takes Cats
function pet_cat(cat::Cat)
  println("The cat says $(meow(cat))")
end

pet_cat(Lion("42")) # => prints "The cat says 42"
try
    pet_cat(tigger) # => ERROR: no method pet_cat(Tiger,)
catch e
    println(e)
end

# In OO languages, single dispatch is common;
# this means that the method is picked based on the type of the first argument.
# In Julia, all of the argument types contribute to selecting the best method.

# Let's define a function with more arguments, so we can see the difference
function fight(t::Tiger,c::Cat)
  println("The $(t.coatcolor) tiger wins!")
end
# => fight (generic function with 1 method)

fight(tigger,Panther()) # => prints The orange tiger wins!
fight(tigger,Lion("ROAR")) # => prints The orange tiger wins!

# Let's change the behavior when the Cat is specifically a Lion
fight(t::Tiger,l::Lion) = println("The $(l.mane_color)-maned lion wins!")
# => fight (generic function with 2 methods)

fight(tigger,Panther()) # => prints The orange tiger wins!
fight(tigger,Lion("ROAR")) # => prints The green-maned lion wins!

# We don't need a Tiger in order to fight
fight(l::Lion,c::Cat) = println("The victorious cat says $(meow(c))")
# => fight (generic function with 3 methods)

fight(Lion("balooga!"),Panther()) # => prints The victorious cat says grrr
try
  fight(Panther(),Lion("RAWR")) # => ERROR: no method fight(Panther,Lion)
catch
end

# Also let the cat go first
fight(c::Cat,l::Lion) = println("The cat beats the Lion")
# => Warning: New definition
#    fight(Cat,Lion) at none:1
# is ambiguous with
#    fight(Lion,Cat) at none:2.
# Make sure
#    fight(Lion,Lion)
# is defined first.
#fight (generic function with 4 methods)

# This warning is because it's unclear which fight will be called in:
fight(Lion("RAR"),Lion("brown","rarrr")) # => prints The victorious cat says rarrr
# The result may be different in other versions of Julia

fight(l::Lion,l2::Lion) = println("The lions come to a tie")
fight(Lion("RAR"),Lion("brown","rarrr")) # => prints The lions come to a tie


# Under the hood
# You can take a look at the llvm  and the assembly code generated.

square_area(l) = l * l      # square_area (generic function with 1 method)

square_area(5) #25

# What happens when we feed square_area an integer?
code_native(square_area, (Int32,))  
	#	    .section    __TEXT,__text,regular,pure_instructions
	#	Filename: none
	#	Source line: 1              # Prologue
	#	    push    RBP
	#	    mov RBP, RSP
	#	Source line: 1
	#	    movsxd  RAX, EDI        # Fetch l from memory?
	#	    imul    RAX, RAX        # Square l and store the result in RAX
	#	    pop RBP                 # Restore old base pointer
	#	    ret                     # Result will still be in RAX

code_native(square_area, (Float32,))
	#	    .section    __TEXT,__text,regular,pure_instructions
	#	Filename: none
	#	Source line: 1
	#	    push    RBP
	#	    mov RBP, RSP
	#	Source line: 1
	#	    vmulss  XMM0, XMM0, XMM0  # Scalar single precision multiply (AVX)
	#	    pop RBP
	#	    ret

code_native(square_area, (Float64,))
	#	    .section    __TEXT,__text,regular,pure_instructions
	#	Filename: none
	#	Source line: 1
	#	    push    RBP
	#	    mov RBP, RSP
	#	Source line: 1
	#	    vmulsd  XMM0, XMM0, XMM0 # Scalar double precision multiply (AVX)
	#	    pop RBP
	#	    ret
	#	
# Note that julia will use floating point instructions if any of the
# arguements are floats.
# Let's calculate the area of a circle 
circle_area(r) = pi * r * r     # circle_area (generic function with 1 method)
circle_area(5)                  # 78.53981633974483

code_native(circle_area, (Int32,))
	#	    .section    __TEXT,__text,regular,pure_instructions
	#	Filename: none
	#	Source line: 1
	#	    push    RBP
	#	    mov RBP, RSP
	#	Source line: 1
	#	    vcvtsi2sd   XMM0, XMM0, EDI          # Load integer (r) from memory
	#	    movabs  RAX, 4593140240              # Load pi
	#	    vmulsd  XMM1, XMM0, QWORD PTR [RAX]  # pi * r
	#	    vmulsd  XMM0, XMM0, XMM1             # (pi * r) * r
	#	    pop RBP
	#	    ret
	#

code_native(circle_area, (Float64,))
	#	    .section    __TEXT,__text,regular,pure_instructions
	#	Filename: none
	#	Source line: 1
	#	    push    RBP
	#	    mov RBP, RSP
	#	    movabs  RAX, 4593140496
	#	Source line: 1
	#	    vmulsd  XMM1, XMM0, QWORD PTR [RAX]
	#	    vmulsd  XMM0, XMM1, XMM0
	#	    pop RBP
	#	    ret
	#	

Further Reading

You can get a lot more detail from The Julia Manual

The best place to get help with Julia is the (very friendly) mailing list.