The HOL_Pure formalization, while serving as a simplified and transparent introduction to higher-order logic in Isabelle, has certain limitations compared to the full Isabelle/HOL system. One significant limitation is the lack of automation and advanced features present in Isabelle/HOL, such as built-in theories for various mathematical concepts, extensive libraries, and sophisticated proof tactics. This limitation can impact the efficiency and convenience of using HOL_Pure for more complex formalizations and advanced theorem proving tasks.
Additionally, HOL_Pure may lack certain meta-properties and advanced functionalities that are available in Isabelle/HOL, such as the ability to reason about semantics, completeness, and soundness of the logic system. This limitation could restrict the depth of understanding that students can achieve when studying higher-order logic using HOL_Pure, especially when compared to the comprehensive capabilities of Isabelle/HOL.
Despite these limitations, HOL_Pure can still be a valuable teaching tool for introducing students to the fundamental concepts of higher-order logic and proof assistants. By focusing on simplicity, clarity, and minimalism, HOL_Pure can provide a solid foundation for beginners to grasp the core principles of logic and formal reasoning before transitioning to more advanced systems like Isabelle/HOL.