map2D.lua

local serpent = require 'serpent'

return function(defaultValue)
	local t = {}

	--[[
	Cantor pairing function
	\pi(k_1,k_2) := \frac{1}{2}(k_1 + k_2)(k_1 + k_2 + 1)+k_2.
	--]]
	local function primitiveCantorPair(k1, k2)
		return 0.5 * (k1 + k2) * ((k1 + k2) + 1) + k2
	end

	local function generalizedCantorPair(arg)
		if #arg == 2 then
			return primitiveCantorPair(unpack(arg))
		elseif #arg > 2 then
			return primitiveCantorPair(generalizedCantorPair(arg), table.remove(arg))
		else
			error('Cantor pairing function need at least 2 arguments!')
		end
	end

	local function cantorPair(...)
		return generalizedCantorPair({...})
	end

	local load = function(data)
		r, t = serpent.load(data)
		return r
	end

	local save = function()
		return serpent.dump(t)
	end

	setmetatable(t, {
		__index = function(_, k)
   			if type(k)=="table" then
   				local i = rawget(t, cantorPair(k[1] or 1, k[2] or 1))
   				return i or defaultValue
   			elseif type(k)=="string" then
   				if k=="load" then
   					return load
   				elseif k=="save" then
   					return save
   				end
   			end
   		end,
   		__newindex = function(_, k, v)
   			if type(k)=="table" then
				rawset(t, cantorPair(k[1] or 1, k[2] or 1), v)
			else
				rawset(t, k, v)
   			end
   		end,
   	})

	return t
end