Is it observed that the borrow checker considers Rust function pointer to have statefulness?

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No, the borrow checker does not consider Rust function pointers to have statefulness. Function pointers in Rust are considered to be stateless, meaning that they don't have any internal state that can be mutated or changed. The borrow checker only checks the borrow and ownership rules for data types that have mutable state, such as references or mutable data structures. Function pointers are simply a reference to a specific function in memory, and as such, do not have any borrow or ownership semantics that need to be checked by the borrow checker.