While reading the chapter on "A Simple One-Pass Compiler" in the Book "Compilers: Principles, Techniques and Tools", I came across the following sentence mentioned in the bibliography section.
Context-free grammars were introduced by Chomsky  as part of a natural languages. Their use in specifying the syntax of programming languages arose independently. While working with a draft of Algol 60, John Backus, "hastily adapted [Emil Post's productions[ to that use" (Wexelblat [1981, p.162]). The resulting notation was a variant of context-free grammar. The scholar panin devised an equivalent syntactic notation to specify the rules of Sanskrit grammar between 400 B.C and 200 B.C (Ingerman )
There is a section in the wikipedia on Panini's influence on Modern Linguistics.
Chomsky, during his visit to India and had an humble acknowledgment for generative grammar devised by Panini.. "happy to receive the honour in the land where his subject had its origin. "The first generative grammar in the modern sense was Panini's grammar","
G Cardona, Panini : a survey of research (Paris, 1976), quotes
Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.
There was a debate brought about on Ingerman's suggestion to name Backus-Naur Form has Panini-Backus form and author, who has studied both Panini's Asthadhyayi and BNF states that both are quite different.
The main point is that Panini's system of codes, abbreviations, and
redefined case endings is vastly more subtle and sophisticated than BNF,
and is aimed at doing a different job. BNF is really just a very simple
way of writing down the logical relationships between items in a program; a
linear version of Venn diagrams, almost. It is purely descriptive, where
as Panini's rules are operative. To put it differently, BNF notation is
useful for describing grammars; the Astadhyayi is a grammar.
Based on these references, I can see that Panini's was a definitive grammar for the Sanskrit language and can be regarded as scholarly approach to devise a system for the representation of the language. In days when we don't find any of his contemporaries making such attempt or even linguists for a hundreds of years to come.