Syntax

Elementary syntax: Matlab heritage

Very much like matlab:

• indexing from 1

• array as first-class A=[1 2 3]

Useful links

• Cheat sheet: https://cheatsheets.quantecon.org/

• Introduction: https://juliadocs.github.io/Julia-Cheat-Sheet/

Arrays are first-class citizens

Many design choices were motivated considering matrix arguments:

• x *= 2 is implemented as x = x*2 causing new allocation (vectors).

The reason is consistency with matrix operations: A *= B works as A = A*B.

Broadcasting operator

Julia generalizes matlabs .+ operation to general use for any function.

a = [1 2 3]
sin.(a)
f(x)=x^2+3x+8
f.(a)

Solves the problem of inplace multiplication

• x .*= 2

Functional roots of Julia

Function is a first-class citizen.

Repetition of functional programming:

function mymap(f::Function,a::AbstractArray)
    b = similar(a)
    for i in eachindex(a)
        b[i]=f(a[i])
    end
    b
end

Allows for anonymous functions:

mymap(x->x^2+2,[1.0,2.0])

Function properties:

• Arguments are passed by reference (change of mutable inputs inside the function is visible outside)

• Convention: function changing inputs have a name ending by "!" symbol

• return value

  • the last line of the function declaration,

  • return keyword

• zero cost abstraction

Different style of writing code

Definitions of multiple small functions and their composition

fsum(x) = x
fsum(x,p...) = x+fsum(p[1],p[2:end]...)

a single methods may not be sufficient to understand the full algorithm. In procedural language, you may write:

function out=fsum(x,varargin)
    if nargin==2 # TODO: better treatment
        out=x
    else
        out = fsum(varargin{1},varargin{2:end})
    end

The need to build intuition for function composition.

Dispatch is easier to optimize by the compiler.

Operators are functions

operator	function name
[A B C ...]	hcat
[A; B; C; ...]	vcat
[A B; C D; ...]	hvcat
A'	adjoint
A[i]	getindex
A[i] = x	setindex!
A.n	getproperty
A.n = x	setproperty!

struct Foo end

Base.getproperty(a::Foo, x::Symbol) = x == :a ? 5 : error("does not have property $(x)")

Can be redefined and overloaded for different input types. The getproperty method can define access to the memory structure.

Broadcasting revisited

The a.+b syntax is a syntactic sugar for broadcast(+,a,b).

The special meaning of the dot is that they will be fused into a single call:

• f.(g.(x .+ 1)) is treated by Julia as broadcast(x -> f(g(x + 1)), x).

• An assignment y .= f.(g.(x .+ 1)) is treated as in-place operation broadcast!(x -> f(g(x + 1)), y, x).

The same logic works for lists, tuples, etc.