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This (experimental) crate declares a single type FnMutant,

FnMutant has a field f: for<'a> Fn(X) -> Y, which acts much like a fn(X) -> Y function pointer, but is a Trait rather than a type. As such it can take generic parameters.

This specifies that the Fn must be valid for all lifetimes, even those less than the lifetime of f. any references given to f, through X, cannot not be captured by f.

This results in a function that can be called multiple times (unlike FnOnce), and can not capture the unique &mut borrows (unlike FnMut).

To explain why this type is not a simple type alias for for<'a> Fn(x) -> Y, we can add the type alias, FnMutantGoodError below, And the resulting compiler error from some changes in the tests.

pub type FnMutantGoodError<'a, In, Extra, Out, F=&'a dyn for<'b> Fn(In,Extra) -> Out> = FnMutant<In, Extra, Out, F>;

Specifying the default value of F for both helper and fps, works fine, However if you specify it in one place: fn helper(fps: &[FnMutantGoodError<&mut i32, i32, (), &dyn for<'b> Fn(&mut i32, i32)>], ...

And leave as the default, in the caller:

let fps: [FnMutantGoodError<&mut i32, i32, ()>; 3] = ...

You will see a nice compilation error:

--> src/lib.rs:91:20
    |
 91 |             helper(&fps, &mut xs, expect.clone());
    |                    ^^^^ one type is more general than the other
    |
    = note: expected struct `FnMutant<&mut i32, _, _, &dyn for<'r> std::ops::Fn(&'r mut i32, i32)>`
               found struct `FnMutant<&mut i32, _, _, &dyn std::ops::Fn(&mut i32, i32)>`

The reason is that aliases do not check bounds, thus current usage of the type is not pretty, since there is no way to specify default type parameters.