More trivially, adding types IS adding constraints that are verifiable at compile time.
If compile-time verification of that sort is not essential (or not desired, which is the more general form of not essential), then the constraints are non-essential (or not desired).
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Whether you choose to
1. Choose a particular data-structure and implement both modules to pass and receive that data-structure.
2. Specify an interface: The interface requires the data-structure to have certain properties (e.g. some methods work on them). The modules then build to the interface.
3. Specify that an adaptor exist to convert the data-structure to whatever the module requires.
is a somewhat different issue, although the kind of type system used does affect the implementation complexity and effort required.
I'm not sure exactly what you mean. Could you elaborate please?
I'll clarify my view with an analogous example: you can think of a database as having a set of types - its schema. Think of each of the applications that use that database as also having its own set of types - its classes or data structures in general. Now, an example of the "mechanism" I mean is that SQL provides a way for each app to translate data in the database's schema into its own data structures. If its data structures change, the SQL can change to adapt to that; similarly, if the DB's schema changes, it can also adapt by changing SQL (or even creating a virtual schema with another layer of SQL - a view). Of course, this only works if these are only changes of the representation of the information, and the information content itself is the same. If the information changes, in a way that the DB or an app depends on, then there's no avoiding that dependency.
A similar example are JSON/XML API's, where the JSON/XML is like the DB, and the data binding code is like SQL. The "type" of XML is often explicitly defined with an "XML Schema" document; JSON doesn't usually have that, but it is of an implicit expected form - which is still a type, just informally defined. There are also tools for converting between XML types - XSLT, and may GUI "XML mappers" that display two xml schema and let you draw lines between them.
tl;dr These enable "modules" with different types to interoperate without dependency. Each defines its own types at its own boundary, and so can be compiled independently. The middleware glue (SQL/databinder/XSLT/datamapper) facilitates interoperation by converting between types at the respective boundaries of two modules - provided those types are equivalent, i.e. contain the same information, just in a different schema/type.
Does your concept of "non-essential coupling" include the requirement of precisely identical types at the boundary? If so, by loosening that to only require the same information, this mechanism avoids that particular kind of non-essential coupling.