[ux266478]

> It's a really weird language to reason with IMO

I know you likely mean regular Prolog, but that's actually fairly easy and intuitive to reason with (code dependent). Lambda Prolog is much, much harder to reason about IMO and there's a certain intractability to it because of just how complex the language is.

[cubefox]

What would be some applications it handles better than regular Prolog? Something that naturally requires second or higher order logic rather first order logic?

[ux266478]

Lambda Prolog isn't a "pure" HOL. It's a very restricted form of HOL using Higher-Order Hereditary Herrop formulas, granting us pretty solid generalized mechanisms of implication and universal quantification, which itself more or less means we get contextual reasoning and scoping rules baked into the grammar for free.

Implementing other programming languages and proving theorems are the low-hanging fruits since you get variable binding without name management, but I genuinely think it has profound implications for expert systems since it essentially removes a massive amount of complexity from contextual reasoning. Being able to account for patient history when providing a diagnosis, for example.