Arranging the sacrifice in space

Mīmāṃsā, Grammar and Kalpasūtra share a common terminology and the more one looks at it, the better one realises how it reflects a spatial (and not temporal) organization of concepts (see these comments). Let me focus on one example.

According to Śabara and all subsequent Mīmāṃsakas, prasaṅga is the topic of 12. Its standard definitions in mature Mīmāṃsā run more or less as follows:

so ’yam anyārthānuṣṭhitāṅgair anyasyo ’pakārarūpaḥ prasaṅgo dvādaśa ucyate (MNS 12.1.1).
This is prasaṅga, which has the form of assistance for one thing by means of subsidiaries performed for the sake of another, and which is spoken of in the Twelfth Book ([Benson 2010, 766]).

In other words, prasaṅga refers to:
• a function
• which applies to more than one item
• insofar as it has been made for the purpose of one item, but then ends up helping another, too.

A further requirement, which is explicit in Śabara and only implicit in the above definition is an explicit prescription prescribing for a certain occurrence the assistance originally performed for a previous one. In fact, since the assistance which is given through prasaṅga is, unlike tantra, not necessary present insofar as it pertains to the structure of the rite, it is only through an explicit prescription that one understands that it is needed.
In other words, all elements prescribed in the context of the Darśapūrṇamāsa sacrifice apply through tantra to all the six rites composing it, independently of whether they are actually needed there, just because the six rite share the same basic procedure (another meaning of tantra). By contrast, the assistance offered through prasaṅga applies to a sacrifice different from the one it had been initially performed for. Therefore it only applies to this later sacrifice if it is explicitly needed there, i.e., if in the later sacrifice there is a prescription enjoining the
same assistance.
To summarize:

tantra | prasaṅga
structural | non structural
applies anyway | applies only if prescribed
same sacrifice |different sacrifice or rite

On tantra and prasaṅga, see here. On tantra and absence, see here. On tantra as a technical term, see here and here.