Mīmāṃsā authors distinguish broadly between prescriptions (vidhi) and prohibitions (niṣedha). The first ones are linked with a result, so that if one has fulfilled them, they get a reward. The latter, if respected, don’t lead to any result, whereas they lead to sanctions if transgressed.
Prescriptions are further divided into three groups (fixed, occasional and elective). The first two groups are configured as strong obligations (leading to rewards if fulfilled, but omitted only at the risk of sanctions), whereas the latter are configured as recommendations. As for prohibitions, they are divided into prohibitions applying to the person throughout their lives and prohibitions applying only to a specific context.
Next comes the somehow controversial case of reparations or expiations (prāyaścitta). These are in fact contrary-to-duty prescriptions. Such prescriptions have as their addressee someone who did some- thing wrong during the performance of a sacrifice; therefore, they can be taken to be contrary-to- duty (ctd) prescriptions.
Expiations can be used to eliminate the negative consequences of a transgressed prohibition. That is, after having performed the corresponding expiation, a transgressed kratvartha prohibition does no longer lead to a negative output on the sacrifice, and a transgressed puruṣārtha prohibition does no longer lead to a sanction. In Dharmaśāstra (jurisprudence) texts, for instance, authors discuss expiations to be performed after having transgressed the duty to live in Āryāvarta (the part of South Asia where nobles people live and where liberation can be achieved).
There seems, however, to be a basic difference between the first and the second type of expiations, since the first ones seem to be routinely performed in case of contextual errors. By contrast, the second type of expiations seems to be an undesired alternative. In other words, more research is needed, but it is possible that puruṣārtha expiations are of this form:
F (p) → ¬ p ∨ p ∧ Expiation
By contrast, puruṣārtha expiations seem to have this form:
F (p) → ¬ p ∨ p ∧ Sanction ∨ Expiation ∧ Lesser Sanction
What do readers think? Does my understanding match your knowledge of Mīmāṃsā and/or Dharmaśāstra?