Even Haskell doesn't have a way to declare a value precisely of type Bottom. As far as the connection with monoids goes, Bottom is a subtype of all types in th

Even Haskell doesn't have a way to declare a value precisely of type Bottom. As far as the connection with monoids goes, Bottom is a subtype of all types in the same way that the empty element of a monoid is a "zero" of the elements of the monoid. I don't know if that helps, but the similarity is that the types form a lattice, and so do the elements of the monoid. AIUI lattices (in the mathematical sense) have top and bottom elements, and in between they look like a DAG...