In Rust, closures can implement one or more of the Fn, FnMut, and FnOnce traits based on how they interact with their captured environment. Here are the specific conditions for each trait:
FnOnce
A closure implements the FnOnce trait if it can be called at least once. This is the most basic trait that all closures implement. A closure will only implement FnOnce if it moves captured values out of its body, meaning it takes ownership of the captured variables. This trait is named FnOnce because the closure can be called at least once, but not necessarily more than once.
FnMut
A closure implements the FnMut trait if it can be called multiple times and it mutates the captured variables. This trait requires mutable access to the environment. If a closure modifies any of the captured variables, it will implement FnMut but not Fn. Since FnMut is a superset of FnOnce, any closure that implements FnMut also implements FnOnce.
Fn
A closure implements the Fn trait if it does not mutate or move the captured variables. This means the closure can be called multiple times without changing the state of the captured environment. Closures that only read from their environment or do not capture any variables at all will implement the Fn trait. Since Fn is a superset of both FnMut and FnOnce, any closure that implements Fn also implements FnMut and FnOnce.
