Semigroup / Monoid / Group types

[AshleyYakeley]

datatype Semigroup a of
    Mk of
        (<>): a -> a -> a;
    end;
end;

datatype Monoid a <: Semigroup a of
    Mk <: Mk.Semigroup of
        empty: a;
    end;
end;

datatype Group a <: Monoid a of
    Mk <: Mk.Monoid of
        invert: a -> a;
    end;
end;