For the uninitiated: Semantic Versioning is one of the true pearls of standardization out there.
The idea is extremely simple:

Given a version number MAJOR.MINOR.PATCH, increment the:

1. MAJOR version when you make incompatible API changes,
2. MINOR version when you add functionality in a backwards-compatible manner, and
3. PATCH version when you make backwards-compatible bug fixes.
   Additional labels for pre-release and build metadata are available as extensions to the MAJOR.MINOR.PATCH format.

When you follow these rules, then anyone who depends on your library has a strong guarantee about which version of your library could be used together with their library version.

A single module can only exist in one version on the VM. So this gives restrictions on the application structure. This basically means everybody needs to agree on a single version.

To clarify the naming: every mix project is an OTP application and that’s usually what the “application” means in Elixir.

Libraries and applications in the erlang world are one and the same. The notion of an application is used because while libraries are often thought of as just bundles of code, libraries in Erlang can also start stateful processes when loaded to manage the state of that library, and are thus better thought of as applications.

A good example would be the package Briefly, which generates temporary file paths. It has code / functions that let you ask for a temporary file path, but it also manages in memory process state to ensure that the paths are deleted when no longer in use.

As noted by @Ankhers, applications define a range of acceptable versions for each dependency ( ie ~> 1.0). When you to a mix deps.get for the first time mix will attempt to find a specific version for each application that falls within all the defined versions. If it cannot, you have the option to override the version to be whatever you want, and see if things work anyway.

Most of the time though it isn’t too hard to get a set of versions acceptable to all relevant libraries.

Does that apply to “libraries” as well? (Sorry if some of the terminology from the Elixir/Erlang ecosystem is not so clear in mind yet, but I believe that you are referring to something else with “application.”) Suppose I want to use library “moment” to handle date/time in Elixir but I also want to use library “anotherlib”, which also uses library “moment”. Is that not possible at all?

Wow, thanks a lot for all the detailed responses, @benwilson512, @Ankhers, and @michalmuskala – the concepts are much clearer to me now.

I suppose that minor versions (1.0, 1.1, etc.) are never expected to introduce breaking changes then. If I intend to publish an application for consumption by 3rd parties, it is good practice to always define its dependencies in the range format instead of targeting a single specific version?