Difference between intent(out) and intent(inout)

Solution 1:

intent(inout) and intent(out) are certainly not the same. You have noted why, although you don't draw the correct conclusion. On entering the subroutine useless a is undefined, rather than defined.

Having a variable "undefined" means that you cannot rely on a specific behaviour when you reference it. You observed that the variable a had a value 5 but this does not mean that the only value you could observe is 5. In particular "undefined" does not mean "takes a specific value like NaN".

Your code is not standard conforming because of this reference to an undefined variable. See Fortran 2008 6.2 (similar meaning will be somewhere in Fortran 90 as initially tagged). Of particular note is that the compiler doesn't have to point out your mistake.

With intent(inout) the variable a would be defined when referenced and it will be guaranteed to have the value 5 (for a conforming processor).

More widely, there are other differences between the two intent attributes and this "coincidental" appearance of the similarity of the definition of the variable a could be more troublesome.

Allocatable arrays and objects with deferred type parameters, for example, are deallocated; derived types become undefined (and any allocatable components deallocated) and components with default initialization are "re-initalized"; pointers have their association status become undefined.

All of these latter things have potential for very awkward results, much more so than with a scalar integer, if they are referenced without being defined first.