tk3369

The Julian Master Game

The following is a set of problems that I organized with some friends at work in 2018.

Day 1 - π

This is an interesting one because the infinite sequence below converges to a number that relates to π. There are several ways to prove that although I like this one the most https://www.youtube.com/watch?v=d-o3eB9sfls.

1/1 + 1/4 + 1/9 + 1/16 + … = π / 6

tk3369

tk3369

julia> foo(x,y) = reshape(collect(Iterators.product(x,y)), :, 1)
foo (generic function with 1 method)

julia> bar(x,y) = [(i,j) for j in y for i in x]
bar (generic function with 1 method)

julia> x = rand(100); y = rand(100);

julia> @btime foo($x,$y);

tk3369

# start window number from 1
set -g base-index 1

# rebind prefix hot-key from C-b to C-j
set -g prefix C-j
unbind-key C-b
bind-key C-j send-prefix

# use vi binding
setw -g mode-keys vi

tk3369

using Plots

function batman(; lw = 4)
    let sqrt = x -> x > 0 ? Base.sqrt(x) : NaN
        v1(x) = 2*sqrt(-abs(abs(x)-1)*abs(3-abs(x))/((abs(x)-1)*(3-abs(x)))) * (1+abs(abs(x)-3)/(abs(x)-3)) * sqrt(1-(x/7)^2)+(5+0.97(abs(x-.5)+abs(x+.5))-3(abs(x-.75)+abs(x+.75))) * (1+abs(1-abs(x))/(1-abs(x))) 
        v2(x) = (2.71052 + 1.5 - 0.5 * abs(x) - 1.35526 * sqrt(4-(abs(x)-1)^2)) * sqrt(abs(abs(x)-1)/(abs(x)-1)) + 0.9
        v3(x) = (-3)*sqrt(1-(x/7)^2)*sqrt(abs(abs(x)-4)/(abs(x)-4))
        v4(x) = abs(x/2)-0.0913722*x^2-3+sqrt(1-(abs(abs(x)-2)-1)^2)

        x = -8:0.0005:8

tk3369

From Mason Protter in Slack:

struct FullyCurried end

macro curried(fdef)
    f = fdef.args[1].args[1]
    fargs = fdef.args[1].args[2:end]
    arity = length(fargs)
 body = fdef.args[2]

tk3369

julia> macro name(ex)
           ex.head === :function || 
               error("can be used for function defintions only")
           name = ex.args[1].args[1]
           assignment = :(local __NAME__ = $name)
           pushfirst!(ex.args[2].args, assignment)
           return ex
       end
@name (macro with 1 method)

tk3369

What are functors?

Functors are types that can be mapped over.

Two laws (https://wiki.haskell.org/Functor#Functor_Laws):

1. mapping an identity function over a functor would return the same functor
2. mapping function g then f is equivalent to mapping the composed function (f ∘ g)

fmap is a mapping function that operates on functors. It can be defined for specific objects so that the provided mapping function can be applied in the

tk3369

Some notes from Julia Slack

My initial question was why this expression returns false:

julia> Vector{Any} === Vector
false

The answer is quite simply that Vector{Any} is just like any other Vector{T}, for which is a subtype of Vector. Then, we wonder what is Vector.

tk3369

Custom cache

Generic function

julia> const fib_cache = Dict()
Dict{Any,Any} with 0 entries

julia> _fib(n) = n < 3 ? 1 : fib(n-1) + fib(n-2)
_fib (generic function with 1 method)