Monads and their composition via distributive laws have many applications in program semantics and functional programming. For many interesting monads, distributive laws fail to exist, and this has motivated investigations into weaker notions. In this line of research, Petri\c{s}an and Sarkis recently introduced a construction called the semifree monad in order to study semialgebras for a monad and weak distributive laws. In this paper, we prove that an algebraic presentation of the semifree monad M^s on a monad M can be obtained uniformly from an algebraic presentation of M. This result was conjectured by Petri\c{s}an and Sarkis. We also show that semifree monads are ideal monads, that the semifree construction is not a monad transformer, and that the semifree construction is a comonad on the category of monads.

翻译：通过分配法,修道院及其组成在方案语义和功能编程中有许多应用。对于许多有趣的寺院来说,分配法并不存在,这促使人们调查较弱的概念。在这个研究领域,Petri\c{s}an和Sarkis最近推出一个名为半无月经的建筑,以研究月经和弱弱分配法的半无月经。在本文中,我们证明,从M的代数演示中可以统一获得对月经M半无月经M的代数表达。这个结果由Petri\c{s}an和Sarkis预测。我们还表明,半无月经是理想的月经,半无的建筑不是月经变异体,而半无半无的建筑是月经类的同音。