Why PHP Trait can't implement interfaces?

The really short version is simpler because you can't. That's not how Traits work.

When you write use SomeTrait; in PHP you are (effectively) telling the compiler to copy and paste the code from the Trait into the class where it's being used.

Because the use SomeTrait; is inside the class, it can't add implements SomeInterface to the class, because that has to be outside the class.

"why aren't Traits types in PHP? "

Because they can't be instantiated. Traits are really just a language construct (telling the compiler to copy and paste the trait code into this class) as opposed to an object or type that can be referenced by your code.

So, i want to "design" in the code that every class that want to use my trait have to implement the interface.

That can be enforced using an abstract class to use the trait and then extending classes from it.

interface SomeInterface{
    public function someInterfaceFunction();
}

trait SomeTrait {
    function sayHello(){
        echo "Hello my secret is ".static::$secret;
    }
}

abstract class AbstractClass implements SomeInterface{
    use SomeTrait;
}

class TestClass extends AbstractClass {
    static public  $secret = 12345;

    //function someInterfaceFunction(){
        //Trying to instantiate this class without this function uncommented will throw an error
        //Fatal error: Class TestClass contains 1 abstract method and must therefore be 
        //declared abstract or implement the remaining methods (SomeInterface::doSomething)
    //}
}

$test = new TestClass();

$test->sayHello();

However - if you do need to enforce that any class that uses a Trait has a particular method, I think you may be using traits where you should have been abstract classes in the first place.

Or that you have your logic the wrong way round. You're meant to require classes that implement interfaces have certain functions, not that if they have certain functions that they must declare themselves as implementing an interface.

Edit

Actually you can define abstract functions inside Traits to force a class to implement the method. e.g.

trait LoggerTrait {

    public function debug($message, array $context = array()) {
        $this->log('debug', $message, $context);
    }

    abstract public function log($level, $message, array $context = array());
}

However this still doesn't allow you to implement the interface in the trait, and still smells like a bad design, as interfaces are much better than traits at defining a contract that a class needs to fulfill.

There's a RFC: Traits with interfaces suggests following to be added to the language:

trait SearchItem implements SearchItemInterface
{
    ...
}

Methods required by the interface can either be implemented by the trait, or declared as abstract, in which case it is expected that class that uses the trait implements it.

This feature is currently not supported by the language, but it is under consideration (current status of the RFC is: Under Discussion).

[...] to "design" in the code that every class that want to use my trait have to implement the interface. That would allow the Trait to use class methods defined by the interface and be sure they are existing in the class.

This sounds very reasonable and I would not say that there has to be anything wrong with your design. Traits have been suggested with this idea in mind, see the second point here:

• A trait provides a set of methods that implement behaviour.
• A trait requires a set of methods that serve as parameters for the provided behaviour.
• [...]

Schärli et al, Traits: Composable Units of Behaviour, ECOOP’2003, LNCS 2743, pp. 248–274, Springer Verlag, 2003, Page 2

So it would be maybe more appropriate to say that you want a trait to require an interface, not to "implement" it.

I do not see a reason why it should be impossible to have this "trait requires (its consumer classes to implement) an interface" feature in PHP, but currently it seems to be missing.

As @Danack notes in his answer, you can use abstract functions in the trait to "require" them from classes that use the trait. Unfortunately you can not do this with private functions.