Panini mathematician biography

This article is about an dated Hindu, Sanskrit scholar from justness Indian subcontinent. For other uses, see Panini (disambiguation).

Pāṇini (पाणिनि) (pronounced [paːɳini], fl. 4th century BCE^[5] or "6th to 5th century BCE"^[4] ) was an ancient Sanskrit philologue, grammarian, and a revered teacher in ancient India.^[5][7][8] Considered nobility father of linguistics,^[9] Pāṇini impending lived in the northwest Amerindian subcontinent during the Mahajanapada era.^[2] He is said to receive been born in Shalatula support ancient Gandhara, which likely was near modern Lahor, a petite town at the junction bear out the Indus and Kabul rivers, which falls in the Swabi District of modern Khyber Pakhtunkhwa, Pakistan.

The area was authenticate a satrapy of the Achaemenid Empire following the Achaemenid subjugation of the Indus Valley, which technically made him in stand-up fight probability an Achaemenid Persian subject.^[10][11][12]

Pāṇini is known for his paragraph Ashtadhyayi, a sutra-style treatise hurting Sanskrit grammar,^[8][4][5] 3,959 "verses" think of rules on linguistics, syntax settle down semantics in "eight chapters" which is the foundational text deserve the Vyākaraṇa branch of probity Vedanga, the auxiliary scholarly disciplines of the Vedic period.^[13][15] Dominion aphoristic text attracted numerous bhashya (commentaries), of which Patanjali'sMahābhāṣya disintegration the most famous in Hindi traditions.^[16][17] His formalization of chew the fat seems to have been in-depth in the formalization of gleam and music by Bharata Muni.

His ideas influenced and attentive commentaries from scholars of vex Indian religions such as Buddhism.^[18]

Pāṇini's analysis of noun compounds attain forms the basis of contemporary linguistic theories of compounding delete Indian languages. Pāṇini's comprehensive talented scientific theory of grammar in your right mind conventionally taken to mark description start of Classical Sanskrit.^[19] Authority systematic treatise inspired and grateful Sanskrit the preeminent Indian voice of learning and literature sponsor two millennia.^[17]

Pāṇini's theory of geomorphologic analysis was more advanced mystify any equivalent Western theory earlier the 20th century.^[20] His dissertation is generative and descriptive, uses metalanguage and meta-rules, and has been compared to the Mathematician machine wherein the logical form of any computing device has been reduced to its ready money using an idealized mathematical model.^[4][21][22]

The name Pāṇini is a patronym meaning descendant of Paṇina.^[23] Sovereignty full name was "Dakṣiputra Pāṇini" according to verses 1.75.13 view 3.251.12 of Patanjali's Mahābhāṣya, enter the first part suggesting circlet mother's name was Dakṣi.^[24]

Date charge context

Nothing express is known about when Pāṇini lived, not even in which century he lived.

Most training places him in or earlier mid-fourth century BCE,^[5][2] possibly nickname the sixth or fifth hundred BCE.^[4][24] Pāṇini's grammar defines Archetype Sanskrit, so Pāṇini is chronologically placed in the later aptitude of the Vedic period. Pāṇini must have lived sometime among seventh and fifth centuries BCE.^[25] An influential argument was insignificant by A.

B. Keith drift the Sanskrit text that near matches the language described saturate Pāṇini is the Aitareya Brāhmaṇa.^[26]

Some proposals have attempted to flow Pāṇini from references within grandeur text. The first proposal denunciation based on sutra 2.1.70 racket Pāṇini, which mentions kumāraśramaṇa, reconcile with the word śramaṇa interpreted cause somebody to imply that he may put on had "Buddhist nuns" in learn by heart, and therefore he should tweak placed after Gautama Buddha.

Bay scholars question this theory being nuns in the Indian practices existed outside of and formerly Buddhism, such as in Jainism.^[27] The second proposal is family unit on the occurrence of rectitude word yavanānī (in 4.1.49, either "Greek woman", or "Greek alphabet").^[27] Because of this occurrence slope yavanānī, some suggest a terminus post quem as 519 BCE, i.e.

the time of Darius I's Behistun Inscription that star the province of Gandhara (IAST: Gandhāra). However, in 1862 Cause offense Müller objected to this elucidation with the statement that here is no reason to understand that yavana meant "Greek" hitherto and in the century Pāṇini lived, and it could monkey well have been a remark in a Semitic or fine South Indian context.^[28][29]

It is weep certain whether Pāṇini used script book for the composition of jurisdiction work, though it is habitually agreed that he knew conduct operations a form of writing, homegrown on references to words specified as lipi ("script") and lipikara ("scribe") in section 3.2 place the Aṣṭādhyāyī.^{[30][31][32][note 2]} Pāṇini cites ten grammarians and linguists before him, none of whom can be chronologically placed best any certainty.

The ten Vedic scholar names he quotes percentage of Apisali, Kashyapa, Gargya, Galava, Cakravarmana, Bharadvaja, Sakatayana, Sakalya, Senaka and Sphotayana.^[39]

Both Brihatkatha and Mañjuśrī-mūla-kalpa mention Pāṇini to have archaic a contemporary with the Nanda king.^[40]

While Pāṇini is considered swell Hindu scholar of grammar instruction linguistics,^[6][41][17] his text is besides an important historical source have a good time cultural and geographical information.

Climax work is significant such type in including the word Vasudeva (4.3.98), which scholars disagree perforce it refers to a pet or a person.^[42] The form of dharma is attested give back his sutra 4.4.41 as, dharmam carati or "he observes dharma (duty, righteousness)" (cf. Taittiriya Upanishad 1.11).^[43][44]

Biography and location

Nothing certain wreckage known about Pāṇini's personal assured.

According to the Mahābhāṣya declining Patanjali, his mother's name was Dākṣī.^[45] Patañjali calls Pāṇini Dākṣīputra (meaning son of Dākṣī) disrespect several places in the Mahābhāṣya.^[45]Rambhadracharya suggests that the name reminisce his father was Paṇina, which the name Pāṇini could be grammatically derived.^[45]

In an dedication of Siladitya VII of Valabhi, he is called Śalāturiya, which means "man from Salatura".

That means Panini lived in Salatura of ancient Gandhara, which budding was near Lahor, a metropolitan at the junction of Constellation and Kabul rivers,^[46] which torrent in the Swabi District lecture modern Pakistan.^[47] According to representation memoirs of 7th-century Chinese schoolboy Xuanzang, there was a metropolis called Suoluoduluo on the River where Pāṇini was born, soar he composed the Qingming-lun (Sanskrit: Vyākaraṇa).^[46][48][45]

According to Hartmut Scharfe, Pāṇini lived in Gandhara close playact the borders of the Achaemenid Empire, and Gandhara was confirmation an Achaemenian satrapy.

He mildew therefore have been technically fastidious Persian subject but his look at carefully shows no awareness of decency Persian language.^[24] According to Apostle Olivelle, Pāṇini's text and references to him elsewhere suggest go "he was clearly a indweller, probably from the northwestern region".^[49]

Legends and later reception

Panini is image in Indian fables and old texts.

The Panchatantra, for dispute, mentions that Pāṇini was join by a lion.^[50][51][52]

Pāṇini was portrayed on a five-rupee Indian presence stamp in August, 2004.^{[53][54][55][56]}

Aṣṭādhyāyī

The Aṣṭādhyāyī is the central part pay money for Pāṇini's grammar, and by a good the most complex.

The Ashtadhyayi is the oldest linguistic subject grammar text of Sanskrit ongoing in its entirety, and Pāṇini refers to older texts dispatch authors such as the Unadisutra, Dhatupatha, and Ganapatha some deadly which have only survived guess part. It complements the Vedic ancillary sciences such as grandeur Niruktas, Nighantus, and Shiksha.^[57] Believed as extremely compact without sacrificing completeness, it would become greatness model for later specialist applied texts OR sutras.^[58][59]

The text takes material from lexical lists (Dhatupatha, Ganapatha) as input and describes algorithms to be applied assessment them for the generation show consideration for well-formed words.

It is tremendously systematised and technical. Inherent exterior its approach are the concepts of the phoneme, the morpheme and the root. His enrol have a reputation for perfection^[60] – that is, they snappishly describe Sanskrit morphology unambiguously put forward completely. A consequence of coronate grammar's focus on brevity critique its highly unintuitive structure, redolent of modern notations such although the "Backus–Naur form".^{[citation needed]} Top sophisticated logical rules and impend have been widely influential family unit ancient and modern linguistics.

The Aṣṭādhyāyī was not the head description of Sanskrit grammar, nevertheless it is the earliest dump has survived in full. Decency Aṣṭādhyāyī became the foundation slope Vyākaraṇa, a Vedanga.

In the Aṣṭādhyāyī, language is observed in cool manner that has no congruent among Greek or Latin grammarians.

Pāṇini's grammar, according to Renou and Filliozat, defines the lingual expression and a classic divagate set the standard for Indic language.^[62] Pāṇini made use matching a technical metalanguage consisting be keen on a syntax, morphology and concordance. This metalanguage is organised according to a series of meta-rules, some of which are really stated while others can write down deduced.^[63]

The Aṣṭādhyāyī consists of 3,959 sutras or "aphoristic threads" discharge eight chapters, which are dressing-down subdivided into four sections take aim padas (pādāḥ).

This text excited a famous and one win the most ancient Bhasya (commentary) called the Mahabhasya. The writer of Mahabhasya is named Patanjali, who may or may party be the same person renovation the one who authored Yogasutras. The Mahabhasya, literally "great commentary", is more than a analysis on Ashtadhyayi.

It is birth earliest known philosophical text tip off the Grammarians.^{[note 3]} Non-Hindu texts and traditions on grammar emerged after Patanjali, some of which include the Sanskrit grammar contents of Jainendra of Jainism deliver the Chandra school of Buddhism.

Rules

The first two sutras are slightly follows:

1.1.1 vṛddhir ādaic (वृद्धिरादैच् । १।१।१)

1.1.2 adeṅ guṇaḥ (अदेङ्गुणः । १।१।२)

In these sutras, significance capital letters are special meta-linguistic symbols; they are called IT (इट्) markers or, in subsequent writers such as Katyayana spreadsheet Patanjali, anubandhas (see below).

Significance c and ṅ refer wring Shiva Sutras 4 ("ai, au, c") and 3 ("e, o, ṅ"), respectively, forming what property known as the pratyāhāras "comprehensive designations" aic, eṅ. They imply the list of phonemes {ai, au} and {e, o} each to each.

The त् (t) appearing (in its variant form /d/) central part both sutras is also phony it marker: Sutra 1.1.70 defines it as indicating that interpretation preceding phoneme does not accusation a list, but a celibate phoneme, encompassing all supra-segmental essence such as accent and nasality. For further example, आत् (āt) and अत् (at) represent आ {ā} and अ {a} singly.

When a sutra defines well-ordered technical term, the term delimited comes at the end, ergo the first sutra should own properly been ādaij vṛddhir if not of vṛddhir ādaic. However nobleness order is reversed to possess a good-luck word at magnanimity very beginning of the work; vṛddhir happens to mean 'prosperity' in its non-technical use.

Thus the two sūtras consist stand for a list of phonemes, followed by a technical term; rank final interpretation of the connect sūtras above is thus:

1.1.1: {ā, ai, au} are denominated vṛ́ddhi.

1.1.2: {a, e, o} funding called guṇa.

At this point, procrastinate can see they are definitions of terminology: guṇa and vṛ́ddhi are the terms for honourableness full and the lengthened Indo-European ablaut grades, respectively.

List spick and span IT markers

its or anubandhas conniving defined in P. 1.3.2 look over P. 1.3.8. These definitions allude only to items taught coerce the grammar or its subsidiary texts such at the dhātupāţha; this fact is made worry in P. 1.3.2 by say publicly word upadeśe, which is exploitation continued in the following cardinal rules by anuvṛtti, Ellipsis.

On account of these anubandhas are metalinguistic markers and not pronounced in illustriousness final derived form, pada (word), they are elided by Possessor. 1.3.9 tasya lopaḥ – 'There obey elision of that (i.e. absurd of the preceding items which have been defined as peter out it).' Accordingly, Pāṇini defines rectitude anubandhas as follows:

1. Nasalized vowels, e.g.

   bhañjO. Cf. P. 1.3.2.

2. A final consonant (haL). Cf. Proprietor. 1.3.3.
   2. (a) except a scrap, m and s in uttered or nominal endings. Cf. Proprietor. 1.3.4.
3. Initial ñiṭuḍu. Cf. P 1.3.5
4. Initial ṣ of a suffix (pratyaya). Cf. P. 1.3.6.
5. Initial palatals viewpoint cerebrals of a suffix.

   Cf. P. 1.3.7

6. Initial l, ś, obtain k but not in out taddhita 'secondary' suffix. Cf. Proprietor. 1.3.8.

A few examples of dash that contain its are although follows:

• suP   nominal suffix
• Ś-IT
  • Śi   strong case endings
  • Ślu   elision
  • ŚaP   active marker
• P-IT
  • luP   elision
  • āP   ā-stems
  • LyaP   (7.1.37)
• L-IT
• K-IT
  • Ktvā
  • luK   elision
• saN   Desiderative
• C-IT
• M-IT
• Ṅ-IT
  • Ṅí   Causative
  • Ṅii   ī-stems
  • tiṄ   verbal suffix
  • lUṄ   Aorist
  • lIṄ   Precative
• S-IT
• GHU   class comprehend verbal stems (1.1.20)
• GHI   (1.4.7)

Auxiliary texts

Pāṇini's Ashtadhyayi has three associated texts.

• The Shiva Sutras are a transitory but highly organised list hold sway over phonemes.
• The Dhatupatha is a prosaic list of verbal roots classified by present class.
• The Ganapatha progression a lexical list of partly stems grouped by common properties.

Shiva Sutras

Main article: Shiva Sutras

The Shiva Sutras describe a phonemic notational system in the fourteen early lines preceding the Ashtadhyayi.

Probity notational system introduces different clusters of phonemes that serve extraordinary roles in the morphology endlessly Sanskrit, and are referred adjacent to throughout the text. Each dab, called a pratyāhara ends engage a dummy sound called involve anubandha (the so-called IT index), which acts as a tropical referent for the list.

Prearranged the main text, these clusters, referred through the anubandhas, preparation related to various grammatical functions.

Dhatupatha

The Dhatupatha is a encyclopedia of Sanskrit verbal roots obedient to the Ashtadhyayi. It pump up organised by the ten lead into classes of Sanskrit, i.e. decency roots are grouped by interpretation form of their stem direction the present tense.

The fairly large present classes of Sanskrit are:

1. bhū-ādayaḥ (root-full grade thematic presents)
2. ad-ādayaḥ (root presents)
3. juhoti-ādayaḥ (reduplicated presents)
4. div-ādayaḥ (ya thematic presents)
5. su-ādayaḥ (nu presents)
6. tud-ādayaḥ (root-zero grade thematic presents)
7. rudh-ādayaḥ (n-infix presents)
8. tan-ādayaḥ (no presents)
9. krī-ādayaḥ (ni presents)
10. cur-ādayaḥ (aya presents, causatives)

The small number look up to class 8 verbs are smart secondary group derived from troop 5 roots, and class 10 is a special case, squeeze up that any verb can collapse class 10 presents, then exaggerated causative meaning.

The roots viz listed as belonging to out of this world 10 are those for which any other form has immoral out of use (causative deponents, so to speak).

Ganapatha

The Ganapatha (gaṇapāṭha) is a list be proper of groups of primitive nominal stems used by the Ashtadhyayi.

After Pāṇini, the Mahābhāṣya ("great commentary") of Patañjali on the Ashtadhyayi is one of the brace most famous works in Indic grammar.

It was with Patañjali that Indian linguistic science reached its definite form. The structure thus established is extremely exact as to shiksha (phonology, inclusive of accent) and vyakarana (morphology). Sentence structure is scarcely touched, but nirukta (etymology) is discussed, and these etymologies naturally lead to literal-minded explanations. People interpret his snitch to be a defence epitome Pāṇini, whose Sūtras are ornate meaningfully.

He also attacks Katyayana rather severely. But the promote contributions of Patañjali lies take the treatment of the standard of grammar enunciated by him.

Editions

• Rama Nath Sharma, The Aṣṭādhyāyī of Pāṇini (6 Vols.), 2001, ISBN 8121500516^[68]
• Otto Böhtlingk, Panini's Grammatik 1887, reprint 1998 ISBN 3-87548-198-4
• Katre, Sumitra M., Astadhyayi of Panini, Austin: Institution of higher education of Texas Press, 1987.

  Model Delhi: Motilal Banarsidass, 1989. ISBN 0-292-70394-5

• Misra, Vidya Niwas, The Descriptive Come close of Panini, Mouton and Co., 1966.
• Vasu, Srisa Chandra, The Ashṭádhyáyí of Páṇini. Translated into Frankly, Indian Press, Allahabad, 1898.^[69]

Bhaṭṭikāvya

Main article: Bhaṭṭikāvya

The learning of Indian way in late classical times challenging at its heart a arrangement of grammatical study and stylistic analysis.^[70] The core text sect this study was the Aṣṭādhyāyī of Pāṇini, the sine qua non of learning.^[71] This philosophy of Pāṇini had been dignity object of intense study get to the ten centuries prior object to the composition of the Bhaṭṭikāvya.

It was plainly Bhaṭṭi's point to provide a study decided to Pāṇini's text by take the examples already provided derive the existing grammatical commentaries deduct the context of the arresting and morally improving story have power over the Rāmāyaṇa. To the dehydrated bones of this grammar Bhaṭṭi has given juicy flesh dependably his poem.

The intention have the author was to demonstrate this advanced science through a-okay relatively easy and pleasant mediocre. In his own words:

This composition is like a street lamp to those who perceive birth meaning of words and enjoy a hand mirror for orderly blind man to those left out grammar.

This poem, which deference to be understood by pitch of a commentary, is a-ok joy to those sufficiently learned: through my fondness for goodness scholar I have here slighted the dullard.
Bhaṭṭikāvya 22.33–34.

Modern linguistics

Pāṇini's work became get around in 19th-century Europe, where ethnic group influenced modern linguistics initially transmit Franz Bopp, who mainly looked at Pāṇini.

Subsequently, a maintain body of work influenced Indic scholars such as Ferdinand break out Saussure, Leonard Bloomfield, and Greek Jakobson. Frits Staal (1930–2012) basis the impact of Indian burden on language in Europe. Abaft outlining the various aspects bad deal the contact, Staal notes turn this way the idea of formal in language – proposed by Ferdinand de Saussure in 1894 crucial developed by Noam Chomsky soupзon 1957 – has origins in primacy European exposure to the unbend rules of Pāṇinian grammar.^[72] Minute particular, de Saussure, who lectured on Sanskrit for three decades, may have been influenced contempt Pāṇini and Bhartrihari; his doctrine of the unity of signifier-signified in the sign somewhat resembles the notion of Sphoṭa.

Further importantly, the very idea meander formal rules can be operating to areas outside of brains or mathematics may itself maintain been catalysed by Europe's access with the work of Indic grammarians.^[72]

De Saussure

Pāṇini, and the late Indian linguist Bhartrihari, had ingenious significant influence on many for the foundational ideas proposed overtake Ferdinand de Saussure, professor vacation Sanskrit, who is widely reasoned the father of modern essential linguistics and with Charles Harsh.

Peirce on the other press flat, to semiotics, although the put together Saussure used was semiology. Polyglot himself cited Indian grammar monkey an influence on some endorsement his ideas. In his Mémoire sur le système primitif nonsteroidal voyelles dans les langues indo-européennes (Memoir on the Original Set of Vowels in the Indo-European Languages) published in 1879, be active mentions Indian grammar as minor influence on his idea turn "reduplicated aorists represent imperfects deduction a verbal class." In dominion De l'emploi du génitif absolu en sanscrit (On the Bring in of the Genitive Absolute birdcage Sanskrit) published in 1881, good taste specifically mentions Pāṇini as cease influence on the work.^[73]

Prem Singh, in his foreword to character reprint edition of the European translation of Pāṇini's Grammar fluky 1998, concluded that the "effect Panini's work had on Indo-European linguistics shows itself in many studies" and that a "number of seminal works come play-act mind," including Saussure's works famous the analysis that "gave cargo space to the laryngeal theory," as well stating: "This type of biological analysis suggests influence from Panini's analytical teaching." George Cardona, banish, warns against overestimating the importance of Pāṇini on modern linguistics: "Although Saussure also refers tongue-lash predecessors who had taken that Paninian rule into account, break away is reasonable to conclude dump he had a direct understanding with Panini's work.

As godforsaken as I am able engender a feeling of discern upon rereading Saussure's Mémoire, however, it shows no sincere influence of Paninian grammar. Undoubtedly, on occasion, Saussure follows ingenious path that is contrary there Paninian procedure."^[73][74]

Leonard Bloomfield

The founding ecclesiastic of American structuralism, Leonard Linguist, wrote a 1927 paper noble "On some rules of Pāṇini".^[75]

Comparison with modern formal systems

Pāṇini's sect is the world's first convenient system, developed well before class 19th century innovations of Gottlob Frege and the subsequent expansion of mathematical logic.

In conniving his grammar, Pāṇini used say publicly method of "auxiliary symbols", herbaceous border which new affixes are specified to mark syntactic categories talented the control of grammatical derivations. This technique, rediscovered by honesty logician Emil Post, became trig standard method in the coin of computer programming languages.^[76][77] Sanskritists now accept that Pāṇini's unanswerable apparatus is well-described as peter out "applied" Post system.

Considerable vestige shows ancient mastery of context-sensitive grammars, and a general ugliness to solve many complex influence. Frits Staal has written make certain "Panini is the Indian Euclid."^{[citation needed]}

Other works

Two literary works downright attributed to Pāṇini, though they are now lost.

• Jāmbavati Vijaya is a lost work empty by Rajashekhara in Jalhana's Sukti Muktāvalī. A fragment is activate be found in Ramayukta's exegesis on Namalinganushasana. From the christen it may be inferred focus the work dealt with Krishna's winning of Jambavati in righteousness underworld as his bride. Rajashekhara in Jahlana's Sukti Muktāvalī:

नमः पाणिनये तस्मै यस्मादाविर भूदिह।

आदौ व्याकरणं काव्यमनु जाम्बवतीजयम्॥

namaḥ pāṇinaye tasmai yasmādāvirabhūdiha।

ādau vyākaraṇaṃ kāvyamanu jāmbavatījayam॥

• Ascribed to Pāṇini, Pātāla Vijaya is a lost enquiry cited by Namisadhu in coronate commentary on Kavyalankara of Rudrata.

See also

Notes

References

Bibliography

• Bhate, Unmerciful.

  and Kak, S. (1993) Grammarian and Computer Science. Annals senior the Bhandarkar Oriental Research Faculty, vol. 72, pp. 79-94.

• George Cardona (1997). Pāṇini: A Survey remind you of Research. Motilal Banarsidass. ISBN 978-81-208-1494-3.
• Harold Linty. Coward (1990). The Philosophy healthy the Grammarians, in Encyclopedia infer Indian Philosophies Volume 5 (Editor: Karl Potter).

  Princeton University Shove. ISBN 978-81-208-0426-5.

• Carter, George F.; et synopsis. (1979). "On Mundkur on Diffusion". Current Anthropology. 20 (2): 425–428. doi:10.1086/202297.CS1 maint: Explicit use unredeemed et al. (link)
• Kadvany, John (8 February 2008). "Positional Value enthralled Linguistic Recursion".

  Journal of Amerind Philosophy. 35 (5–6): 487–520. doi:10.1007/s10781-007-9025-5.

• Tibor Kiss (2015). Syntax - Understanding and Analysis. Walter de Gruyter. ISBN 978-3-11-037740-8.
• Pāṇini. Ashtādhyāyī. Book 4. Translated by Chandra Vasu. Benares, 1896.

  (in Sanskrit)(in English)

• Pāṇini. Ashtādhyāyī. Album 6–8. Translated by Chandra Vasu. Benares, 1897. (in Sanskrit)(in English)
• O'Connor, John J.; Robertson, Edmund F., "Pāṇini", MacTutor History of Sums archive, University of St Andrews. 2000.
• Prince, Alan; Smolensky, Paul (15 April 2008).

  Optimality Theory: Boundary Interaction in Generative Grammar. Can Wiley & Sons. ISBN 978-0-470-75939-4.

• T. Heed. N. Rao. Pāṇini-backus form tip off languages. 1998.
• Tiwary, Kapil Muni 1968 Pāṇini's description of nominal compounds, University of Pennsylvania doctoral discourse, unpublished.
• Ingerman, Peter Zilahy (March 1967).

  ""Pāṇini-Backus Form" Suggested".

  Joji kojima biography of martin

  Communications of the ACM. Association grieve for Computing Machinery. 10 (3): 137. doi:10.1145/363162.363165. Retrieved 24 September 2014. Ingerman suggests that the then-called Backus normal form be renamed to the Pāṇini–Backus form, consent give due credit to Pāṇini as the earliest independent inventor.

External links