-- Let table t = {k_1 = v_1, k_2 = v_2, ..., k_n = v_n} represent the set S.(∀s ∈ S ∃ k ∈ t.(v = true)).

--

-- Utility functions for working with this type of set.

--- Returns a ∪ b as a new set

function Union(a, b)

local u = {}

table.print(a)

table.print(b)

for k, v in a do

u[k] = v or u[k]

end

for k, v in b do

u[k] = v or u[k]

end

return u

end

--- Replaces a with a ∪ b

function DestructiveUnion(a, b)

for k, v in b do

a[k] = v or nil

end

return a

end

--- Returns a ∩ b as a new set

function Intersection(a, b)

local i = {}

for k, v in a do

if v and b[k] then

i[k] = true

end

end

for k, v in b do

if v and a[k] then

i[k] = true

end

end

return i

end

--- Returns a \ b as a new set

function Subtract(a, b)

local s = {}

for k, v in a do

if v and not b[k] then

s[k] = true

end

end

return s

end

--- Returns the set S = {a ∈ A.p(a)}

function PredicateFilter(A, p)

local s = {}

for k, v in A do

if v and p(k) then

s[k] = true

end

end

return s

end

--- Returns true iff A is the empty set

function Empty(A)

for k, v in A do

if v then

return false

end

end

return true

end