Three Papers on the Completeness Properties of Abelian Semi groups and Groups

The three papers presented here all arise from recent research into sets of operators which are sufficient to define a horizontal microlanguage for a computer and which are (in some undefined sense) natural for human beings to use. It is this criterion of naturalness which leads us to consider dyadic operators which are commutative and associative, that is, structures which are abelian semigroups.