Asiddhatva and the Tripādī: Ordering by Blocking
Chapter Forty-One
Syllabus topic Module 1, "Context-sensitive operations", "Conflict resolution mechanisms"
Pages 134 to 136 of 378
In one line
The last three quarters of book eight are treated as not having happened, as far as every rule before them is concerned, and that turns a rule list into two ordered phases.
In the wording you can write in an examination: sūtra 8.2.1, pūrvatrāsiddham, provides that the rules of the last three quarters of book eight, known as the tripādī, are asiddha, that is, treated as not having taken effect, with respect to all the preceding rules. Within the tripādī itself a later rule is likewise asiddha with respect to an earlier one. The grammar therefore operates in two successive phases, and no rule in the earlier phase can see the results of the later one.
The provision, as Vasu states it
With regard to whatever has been taught in the preceding Seven Books and a quarter, the rules contained in these three last chapters are considered as asiddha. And further, in these three chapters, a subsequent rule is, as if it had not taken effect, so far as any preceding rule is concerned.
And elsewhere, naming the section:
the tripādī or the last three chapters of Aṣṭādhyāyī; and the tripādī are considered asiddha for the purposes of previous sūtras (VIII. 2. 1).
The word asiddha he glosses as not-accomplished: the operation caused by a rule's having taken effect is not produced, for the purposes of the rule now being considered.
What the rule actually does
There are two separate provisions in it, and students usually notice only the first.
Provision one: a boundary. The grammar is divided at the end of the first quarter of book eight. Everything after that point is invisible to everything before it. Call the earlier part phase one and the tripādī phase two.
Provision two: an internal ordering. Inside the tripādī, a later rule is also asiddha for an earlier one. So within phase two the rules are effectively applied in textual order, each blind to the ones after it.
The second provision is the reverse of what 1.4.2 does elsewhere. Under 1.4.2 a later rule prevails in a conflict; inside the tripādī an earlier rule proceeds as though the later one had not happened. That is not an inconsistency: it is a different mechanism for a different section, and knowing that the tripādī is governed differently is worth a mark.
Why a grammar would want this
Think about what goes wrong without it.
Suppose a phase-one rule's condition is "a stem ending in a consonant". Suppose a phase-two rule deletes a final consonant in certain words. Without 8.2.1, the phase-one rule would have to ask: has the deletion happened yet? And the answer would depend on the order in which the two rules were tried, which is exactly the kind of dependence that makes a rule system unpredictable.
Asiddhatva and the Tripādī: Ordering by Blocking
8.2.1 removes the question. Phase-one rules always see the form before any phase-two rule has touched it. Their conditions are therefore stable, and a reader can reason about phase one without knowing anything about phase two.
That is a real engineering benefit and it has a modern name.
The modern name: phase ordering
| Feature of 8.2.1 | The modern counterpart |
|---|---|
| a fixed boundary in the rule list | a compiler pass boundary |
| earlier rules cannot see later results | a pass operates on the output of the previous pass only |
| later rules may see earlier results | passes run in order and each sees what the last produced |
| the boundary is declared, not inferred | the pass pipeline is written down |
| inside the later section, order is textual | a single pass that traverses its input once |
A multi-pass compiler makes exactly this choice. Constant folding does not need to know what the register allocator will do, because the allocator runs later and the folder is finished. The benefit is the same: each pass can be reasoned about in isolation.
Worked example, from Vasu's own discussion
He gives the mechanism at work, and the example is worth following because it shows why the rule is needed rather than merely stating it.
He is discussing a case in which a final consonant could be elided by either of two rules of the tripādī, at 8.2.7 and at 8.2.23. His report is that the form could not have had its final elided by 8.2.7 if the elision by 8.2.23 had taken effect, and that therefore, because within the last three quarters a subsequent rule is as if it had not taken effect so far as a preceding rule is concerned, 8.2.23 is treated as not having operated and 8.2.7 finds its scope.
Read what that does. The earlier rule of the tripādī gets to operate on the form as it stands, without having to know that a later rule of the tripādī would have changed the very thing its condition depends on. The blocking is what makes the earlier rule usable.
The one that is not 8.2.1: the ābhīya section
The grammar has a second, narrower asiddhatva, and a complete answer mentions it.
Sūtra 6.4.22, confirmed in the digital sūtrapāṭha, establishes a section within which, as Vasu puts it, when one of the rules of the section is to be brought into operation having the same place of operation as another of the section which has already taken effect, the one that has taken effect is regarded as not having taken effect.
So the same device is used twice, at two scales. Once for the whole tripādī, and once for a smaller neighbourhood within book six. That is a designed mechanism rather than a one-off patch, and pointing that out is the strongest form of the claim.
Asiddhatva and the Tripādī: Ordering by Blocking
What asiddhatva is NOT
It is not deletion. The later rule does still operate. It is invisible to the earlier rules, not absent.
It is not the same as the antaraṅga maxim. That maxim also uses the words "not having taken effect", and Vasu quotes it that way, but it compares two rules by the closeness of their conditions, not by their section. Two mechanisms, similar wording, different tests.
It is not a general principle of the grammar. It is declared for two specific sections. Outside them, 1.4.2 and the other precedence principles apply.
It is not a proof of consistency. It makes the phases independent; it does not show that the resulting derivations are all correct.
Quick revision
- 8.2.1 pūrvatrāsiddham: the last three quarters of book eight, the tripādī, are asiddha for every preceding rule, and inside the tripādī a later rule is asiddha for an earlier one.
- Asiddha means treated as not having taken effect; Vasu glosses it as not-accomplished.
- Effect: two phases, with phase one blind to phase two, so phase-one conditions are stable.
- The modern counterpart is a compiler pass boundary, declared rather than inferred.
- Inside the tripādī the internal rule reverses 1.4.2's effect, which is a different mechanism for a different section.
- A second, narrower asiddhatva is established by 6.4.22 for a section of book six.
- It is not deletion, not the antaraṅga maxim, and not a general principle.
Test yourself
1. State 8.2.1 and both of its provisions.
The rules of the last three quarters of book eight are treated as not having taken effect with respect to all preceding rules; and within those three quarters a later rule is treated as not having taken effect with respect to an earlier one.
2. Why does a grammar benefit from making one section invisible to another?
Because a rule's condition then does not depend on whether a rule from the other section has already run. The conditions of the earlier section are stable, so it can be reasoned about without knowing anything about the later one.
3. Give the modern counterpart of asiddhatva and one property they share.
A compiler pass boundary. Both make each pass or phase operate only on what the previous one produced, so each can be reasoned about in isolation, and in both the boundary is declared rather than discovered.
4. How does the tripādī's internal rule relate to 1.4.2, and why is that not a contradiction?
Under 1.4.2 the later of two conflicting rules prevails. Inside the tripādī an earlier rule proceeds as though the later one had not taken effect, which is the opposite effect. It is not a contradiction because 8.2.1 declares a different mechanism for that section, and 1.4.2 governs elsewhere.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself for the same subject.