What is the real responsibility of a Database?
A database at its core is a system to store and retrieve data. A CSV file on disk + suitable tools (e.g. Excel) is a simple example of this. In addition, a database might provide additional capabilities, such as transaction control, data integrity, and security.
Should we add Store procedures and functions to de Database or just let it to be a data repository with no logic?
What do you want from the database? If all you want is a "bit bucket", then by all means, store it in a plain file on disk and call it "the database". If you want a bit more than that, use a product that suits your needs. If you want to be able to query it using a 4GL like SQL, use MySQL. If you want transaction control, security, advanced query features, etc etc, use another DBMS if appropriate. Whatever product you choose, however, take advantage of that product. Otherwise you're wasting your time and money. Sure, you'll never use all of the features (only a subset will be useful to you), but if you use very few of them, you may as well downgrade to a simpler product.
If you're using Oracle, you can store procedures and functions (even better, whole packages) right there in the database alongside the data. The real question is, what do you need to write in those procedures and functions - business logic or presentation logic?
Personally, I usually prefer to keep business logic close to the data, whereas presentation logic is custom-made for each interface.
It is possible to create an API layer over your data so that no matter how your applications access your database, they will get a consistent view of it, and they will all modify it using a consistent mechanism. In other words, instead of writing the business logic multiple times (once for each interface), you write it once and once only, then re-use it everywhere.
There are two reasons I've heard why business logic should not be stored in the database:
1. Maintainability: it's hard to change. I never really understood this one. How hard is it to type CREATE OR REPLACE PACKAGE
? I suspect it's just the burden of having to learn "yet another language".
2. Database independence: what works in Oracle won't work elsewhere. This is a biggie, and better minds than I have written about this one. Basically, if you really need it to be "database agnostic", you won't be able to use any of the advanced features of the database you bought, so you may as well just use the simplest/cheapest one you can find; in which case, you don't need it to work on every database anyway!