A* foundation

local function removeLowest(set, costs, h)
    return function(t, ...)
        local prospect, cost
        for node in pairs(t) do
            if not cost or costs[node] + h(node) < cost then
                prospect, cost = node, costs[node] + h(node)
            end
        end
        if prospect then
            local parent = t[prospect]
            t[prospect] = nil
            return prospect, parent
        end
    end, set
end

return function(start, goal, neighbors, h)
    local open = {[start] = false}
    local costs = {[start] = 0}
    local parents = {}

    for prospect, parent in removeLowest(open, costs, function(source) return h(source, goal) end) do
        if prospect == goal then
            return parent, costs[prospect], parents
        end
        for successor, cost in neighbors(prospect) do
            cost = cost + costs[prospect]
            if not costs[successor] or costs[successor] > cost then
                costs[successor] = cost
                open[successor] = prospect
                parents[successor] = prospect
            end
        end
    end
end