On the other hand, it should be perfectly valid to make your functor application compository. You just take your proposition ∃x:τ.P(x), and your more different propositions B |- C and M : ∃a.B, and you cross-project their modularity functions in the opposite order. So then you get:
module AppTable(B |- C const M : ∃a.B) : TABLE =
struct
type t:τ
type x:τ.τ, y:2τ
val π1M:τ = unpack(B C)
τ.τ.τ ? ∃a.B : throw new ModularityException();;
let M unpack x in y with implicit(z)
return M:τ
end
no subject
module AppTable(B |- C const M : ∃a.B) : TABLE = struct type t:τ type x:τ.τ, y:2τ val π1M:τ = unpack(B C) τ.τ.τ ? ∃a.B : throw new ModularityException();; let M unpack x in y with implicit(z) return M:τ end