When I mentioned to Richard Rasala that we
have now a new version of the Law of Demeter:
"Listen only to your friends" he referred to
his book about the brain that he is currently reading
and he said: that is the way a neuron works.
The neuron listens for inputs and when it has
enough inputs it fires information to its neighbors.

So here is an explanation of DemeterF in terms of neurons.

Think of each node in the object tree as a neuron.
Each neuron has two states: the DOWN state and the UP state.
Initially all neurons are in the DOWN state and once
a neuron in the DOWN state has fired, it switches to the UP state.

In the DOWN state, a neuron takes input from a parent (or the outside
if it is the root neuron) potentially
updates this information and sends it down to all children 
who are free to use or ignore this information.

The UP state has two substates, called TRANSFORM and COMBINE.
In the COMBINE state, the neuron listens for the inputs from
its children. If there are no children, the output from
the TRANSFORM state is used.
In the TRANSFORM state, if there are children,
the neuron takes input from the COMBINE state and otherwise
the information at the leaf is used.

The firing of the neurons starts with the root neuron.

The code executed at the neurons is specified based on the
types of the incoming information. The DemeterF program
that drives the neurons is checked statically. 
The type checker guarantees that each neuron will know
what to do in all states.