There is already a very good analysis of Purple. It is suggested that we take a look at it first.
Pimple - A simple PHP dependency injection container
Read PHP - Pimple Source Notes (Part 1)
Read PHP - Pimple Source Notes (Part 2)

Here we supplement the description of the core method with examples:
Related types:

1. Services (similar singletons):

   $container['session'] = function ($c) {
       return new Session($c['session_storage']);
   };

2. Factory services (multiple instances)

   $container['session'] = $container->factory(function ($c) {
       return new Session($c['session_storage']);
   });

3. Parameters (just save some variables)

   $container['cookie_name'] = 'SESSION_ID';

4. Protect parameters (anonymous functions are all considered [1 service], but if you want to be just a parameter, you need to use this method)

   $container['random_func'] = $container->protect(function () {
       return rand();
   });

set assignment related source code:

    public function offsetSet($id, $value)
    {
         //If it is frozen, it cannot be assigned
        if (isset($this->frozen[$id])) {
            throw new FrozenServiceException($id);
        }
        //Deposit in values
        $this->values[$id] = $value;
        //Deposit in keys
        $this->keys[$id] = true;
    }

Take [1 service] as an example, after calling the offsetSet method:

    $this->values['session'] = function ($c) {
        return new Session($c['session_storage']);
    };
    $this->keys['session'] = true;

When using $session=$container['session'];, the offsetGet method is called:

    public function offsetGet($id)
    {
        //$this - > keys ['session'] exists
        if (!isset($this->keys[$id])) {
            throw new UnknownIdentifierException($id);
        }

        if (
            isset($this->raw[$id])//This - > raw ['session'], the first call is not there, so false, repeated calls are ture.
            || !\is_object($this->values[$id])//All anonymous functions are object s, so they are false. The corresponding case [3 parameters] is true
            || isset($this->protected[$this->values[$id]])//protected method is not invoked, so it is false, and the corresponding case [4 protection parameters] is true.
            || !\method_exists($this->values[$id], '__invoke')//All anonymous functions have the u invoke method, so it's false
        ) {
            //To sum up, if it's the first call, it won't do that. If it's related to repeated calls, parameters, and protected methods, it will.
            return $this->values[$id];
        }
        //Determine if there are multiple instances, corresponding to [2 Factory Service], because we did not call the factories method, so this step will not be executed?
        if (isset($this->factories[$this->values[$id]])) {
            return $this->values[$id]($this);
        }
        
        //At this point, $ray is the anonymous function ($c)
        $raw = $this->values[$id];
        
        //Reassigning $this - > values ['session'], passing in $this, which is equivalent to function ($this), passes in $this because the anonymous function may contain other services.
        //For example, the above $c['session_storage'], $this is equivalent to $container['session_storage'], when passed in, triggers the call to offsetGet.
        $val = $this->values[$id] = $raw($this);
        
        //Save the original anonymous function in $this - > ray, $this - > raw ['session'] has value at this time, and return directly to the upper decision when repeated access, which is equivalent to the singleton mode.
        $this->raw[$id] = $raw;
        
        //Markup is frozen, offsetSet or extension is not allowed after get
        $this->frozen[$id] = true;
        
        //Return $this - > values ['session']
        return $val;
    }