Retributivist Ethics is rooted in five assumptions.
The first is that something of the following form is true:
(1) x is Morally permissible = x harms no one or R1x , or R2x, …Rnx.
Where x ranges over actions.
The second assumption is that there are properties answering to R1… Rn and actions which satisfy them. That is, that there are some features of some actions which make them morally permissible even though those actions do cause harm to others.
The third is that it is possible to describe what constitutes harming someone in non moral terms.
The fourth is that is also possible to describe those R-properties-- those circumstances which harming others is permissible -- in non-moral terms.
The third and fourth assumption make Retributivism a reductive thesis. Note that "=" in (1) expresses an identity on a par with:
(2) X is water = x is H2O .
Retributivism is not a thesis about "the meanings" of moral terms-- whatever "the meanings" might be. It is a thesis about what moral permissibility is. It aims to say that to do something morally wrong just is to do one of those things that harms another and is not R1… or Rn, just as (2) says that to be water just is to be two parts hydrogen and one part Oxygen.
Finally, Retributivism is the assumption that all of ethics, everything worth saying about moral right and wrong, will have been exhausted when we have spelt out (1) .
Spelling out the R's -- saying when it is permissible to harm another-- is a matter of describing agents moral rights and claims.
Thus, it is permissible to harm another if one acts in self-defense, so we may speak of the "right of self defense".
To say that someone X has a moral claim against someone Y that Y do something A (e.g. because Y has promised X that Y will do A) is to say that it would be permissible in certain circumstances for X to harm Y in certain ways (e.g. to force Y to keep his promise).
To say that someone X has right to compensation from Y because of some harm Y has done X is to say that X has a right to force Y to perform some compensating act.
Note the Retributivist may not say that the right of self defense makes it permissible to use force in a certain way. Nor may he explain the permissibility by appealing to the right. His thesis is that the right is the permission. On the other hand the Retributivist need not argue for the existence of any right beyond the permissions it entrains. Once it is conceded that the relevant harmings are permissible then the Retributive right has been wholly established.
I distinguish between causing harm to others and allowing harm to come to others and assume that absent prior promises the latter are always permissible. One might revise this assumption, including at least certain kinds of allowing to harm as impermissible and still call oneself a Retributivist if one accepted the other premises.