A single text from about 500 BCE, the Ashtadhyayi (Eight chapters), is usually credited with forming this later “classical Sanskrit”; with this one book, the grammarian Panini created the fields of descriptive and generative linguistics. Drawing on the sophisticated regimes already developed, he attempted to create a “complete, maximally concise, and theoretically consistent analysis of Sanskrit grammatical structure.”⁵ His objects of study were both the spoken language of his time, and the language of the Vedas, already a thousand years behind him. He systemized both of these variations by formulating 3,976 rules that — over eight chapters — allow the generation of Sanskrit words and sentences from roots, which are in turn derived from phonemes and morphemes.⁶ In addition to these rules, he provides a list of all Sanskrit phonemes, along with a metalinguistic scheme that allows him to refer to entire classes of phonological segments with just one syllable; a classified lexicon of about two thousand Sanskrit verbal roots along with markers that encode the properties of these roots; and another classified list of lexical items that are idiosyncratically acted upon by certain rules.

The rules are of four types: (1) rules that function as definitions; (2) metarules — that is, rules that apply to other rules; (3) headings — rules that form the bases for other rules; and (4) operational rules. Some rules are universal while others are context sensitive; the sequence of rule application is clearly defined. Some rules can override others. Rules can call other rules, recursively. The application of one rule to a linguistic form can cause the application of other rules, which may in turn trigger other rules, until no more rules are applicable. The operational rules “carry out four basic types of operations on strings: replacement, affixation, augmentation, and compounding.”⁷

In addition to ordered rules, Panini also pioneered the use of linguistic “zero elements” for constituents posited in analysis but omitted in usage, as in the sentence “Women adore him,” in which the determiner “the” is assumed to precede “women.”⁸ He also created a metalanguage comprising special technical terms and markers which enabled him to speak precisely and unambiguously about the language he was analyzing.⁹

In Sanskrit, word order is not important other than for stylistic purposes; the verb can be placed anywhere in a sentence. So the Ashtadhyayi concerns itself mainly with word formation. When it does concern itself with sentence formation

Panini accounts for sentence structure by a set of grammatical categories which allow syntactic relationship to be represented as identity at the appropriate level of abstraction. The pivotal syntactico-semantic categories which do this are roles assigned to nominal expressions in relation to a verbal root, called karakas. A sentence is seen as a little drama played out by an Agent and a set of other actors, which may include Goal, Recipient, Instrument, Location, and Source.¹⁰

The rules of the Ashtadhyayi are extremely concise; here are numbers 58 through 77 of the fifth chapter: ¹¹

Only a few rules are more than two or three words long, so the entire rule set comprises only 32,000 syllables and fits into about forty pages of printed text.¹² The economy of Panini’s prose is such that a recent translation into English ran to over 1,300 pages. Panini somehow caught, the saying goes, an ocean in a cow’s hoof print. With this very finite analysis, Panini not only comprehensively described the functioning of his language, he also opened it up to infinity. S. D. Joshi points out:

The Astadhyayi is not a grammar in [the] general Western sense of the word. It is a device, a derivational word-generating device … It derives an infinite number of correct Sanskrit words, even though we lack the means to check whether the words derived form part of actual usage. As later grammarians put it, we are lakṣaṇaikacakṣuṣka, solely guided by rules. Correctness is guaranteed by the correct application of rules.¹³

The systematic, deterministic workings of these rules may remind you of the orderly on-and-off workings of logic gates. The Ashtadhyayi is, of course, an algorithm, a machine that consumes phonemes and morphemes and produces words and sentences. Panini’s machine — which is sometimes compared to the Turing machine — is also the first known instance of the application of algorithmic thinking to a domain outside of logic and mathematics. The influence of the Ashtadhyayi was and remains immense. In the Sanskrit ecumene, later grammarians suggested some additions and modifications, and other grammars were written before and after Panini’s intervention, but all have been overshadowed by this one “tersest and yet most complete grammar of any language.”¹⁴

The West discovered the Ashtadhyayi during the great flowering of Orientalist research and translation in the eighteenth and nineteenth centuries. Ferdinand de Saussure, “the father of structural linguistics,” was a professor of Sanskrit and influenced by Panini and his successor, Bhartrihari; Saussure’s notion of the linguistic “sign” is heavily reminiscent of Bhartrihari’s theory of sphota (explosion, bursting), which tries to account for the production of meaning from linguistic units.¹⁵ Leonard Bloomfield — the renowned scholar of structural linguistics whose work determined the direction linguistic science would take through the twentieth century, particularly in America — studied Sanskrit as a graduate student at the University of Wisconsin and later in Germany. As an assistant professor at the University of Illinois, he taught elementary Sanskrit even as he began his own research, “using Paninian methods … and studying Panini.”¹⁶ In his own writing, Bloomfield was unstinting in his praise of Panini’s grammar: it was “a linguistic achievement beyond any it [i.e., European scholarship] had known”; it was “one of the greatest monuments of human intelligence” and “an indispensable model for the description of language.”¹⁷ He summarized the impact of Panini’s work on modern linguistics as follows:

Around the beginning of the nineteenth century the Sanskrit grammar of the ancient Hindus became known to European scholars. Hindu grammar described the Sanskrit language completely and in scientific terms, without prepossessions or philosophical intrusions. It was from this model that Western scholars learned, in the course of a few decades, to describe a language in terms of its own structure.¹⁸

Paul Kiparsky tells us:

Western grammatical theory has been influenced by [Panini’s work] at every stage of its development for the last two centuries. The early nineteenth-century comparativists learned from it the principles of morphological analysis. Bloomfield modelled both his classic Algonquian grammars and the logical-positivist axiomatization of his Postulates on it.¹⁹

Further:

Theoretical linguists of all persuasions are … impressed by its remarkable conciseness, and by the rigorous consistency with which it deploys its semi-formalized metalanguage, a grammatically and lexically regimented form of Sanskrit … Generative linguists for their part have marveled especially at its ingenious technical devices, and at intricate system of conventions governing rule application and rule interaction that it presupposes, which seem to uncannily anticipate ideas of modern linguistic theory (if only because many of them were originally borrowed from Panini in the first place).²⁰

Modern linguistic theory, in its turn, became the seedbed for high-level computer languages. To ease the pain of programming in low-level languages like machine code and assembly, computer scientists were driven to create artificial, formal languages. The efforts of linguists toward understanding language in formal and generative terms led to the work of John Backus, the IBM language designer whose team created FORTRAN, the first widely used high-level programming language. Backus proposed using “metalinguistic formulae” to describe the working of a programming language in 1959. This method was further simplified by Peter Naur, and the resulting “Backus — Naur Form” remains the primary method of describing and generating formal computer languages. Backus apparently came up with his ideas knowing nothing of Panini, at least directly, but, as the Sanskritist Murray Emeneau put it, “Most of the specific features that are taken … to distinguish an ‘American’ school of linguistics from others are Bloomfieldian, and … many are Paninean.”²¹ In 1967 a programmer named Peter Zilahy Ingerman wrote to the Communications of the ACM (Association for Computing Machinery) to argue that “since it is traditional in professional circles to give credit where credit is due, and since there is clear evidence that Panini was the earlier independent inventor of the notation, may I suggest the name ‘Panini-Backus Form’ as being a more desirable one?”²²