Covariance with pl.class: a specialized List of numbers

array.lua

require 'pl'

class.Array(List)

function Array.__add (a1,a2)
    return a1:map2('+',a2)
end

function Array.__sub (a1,a2)
    return a1:map2('-',a2)
end

function Array.__mul (a1,a2)
    if type(a1) == 'number' then
        a1,a2 = a2,a1
    end
    return a1:map('*',a2)
end

function Array.__div (a,num)
    return a:map('/',num)
end

function Array:sum ()
    return self:reduce '+', #self
end

function Array:length ()
    local res = 0.0
    for i = 1,#self do
        res = self[i]^2
    end
    return res
end

a1 = Array {1,2,3}
a2 = Array {10,20,30}

print(a1 + a2, a2 - a1)

print(3*(a1 + a2), a2/2)

print(a1:slice(1,2)+a2:slice(1,2))

print(a1:sum())