We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing in 1936 in his foundational work "On Computable Numbers". Here we face it using the Model of computability of the recursive functions instead of the Turing's machines, but the results are transferable from one to another paradigm with ease. Recursive functions that are not defined at a given point, correspond to the Turing machines that "do not end" for a given input. What we propose Is a slight slip from the orthodox point of view: the issue of the self-reference and of the self-validation is not an impediment in imperative languages.

翻译：我们探讨构建一个函数以验证单变量部分递归函数是否有定义的可能性。这是可计算性理论中的一个课题，最早由艾伦·M·图灵在1936年的奠基性著作《论可计算数》中提出。本文采用递归函数可计算性模型（而非图灵机模型）来处理该问题，但研究结果可轻松迁移至另一范式。在给定点上无定义的递归函数，对应于针对特定输入"不会停机"的图灵机。我们所提出的方案是对正统观点的轻微偏离：在命令式语言中，自指与自验证问题并非障碍。