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Amba Kulkarni Department of Sanskrit Studies University of Hyderabad Hyderabad ambapradeep@gmail.com. P āņ ini's Ash ţā dhy ā y ī : A Computer Scientist's Perspective. Circa 500 B.C.E. Extant Grammar of the then prevalent Sanskrit Language Around 4000 sutras; 8 chapters 4 sections each.

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slide1
Amba Kulkarni

Department of Sanskrit Studies

University of Hyderabad

Hyderabad

ambapradeep@gmail.com

Pāņini's Ashţādhyāyī: A Computer Scientist's Perspective

4th APCAP Dec 5th 2008, NIAS Bangalore

slide2
Circa 500 B.C.E.

Extant Grammar of the then prevalent Sanskrit Language

Around 4000 sutras;

8 chapters 4 sections each

Pāņini's Ashţādhyāyī

4th APCAP Dec 5th 2008, NIAS Bangalore

a computer scientist

Information Theory: Shannon

Computational Linguists:

(Language: Means of coding the information.)

Information Coding: How much, Where and How

Programming Languages: Concepts, Techniques and Models

A Computer Scientist

4th APCAP Dec 5th 2008, NIAS Bangalore

information coding

Claim:

Panini was aware of the strength of language as

an information coding device.

Evident from

a) His style of presenting the information in sUtra

b) His analysis of Sanskrit Language

Information Coding

4th APCAP Dec 5th 2008, NIAS Bangalore

information theory

Brevity

Kiparsky: Panini used Brevity to achieve generalisation.

– Maximum Use of anuvŗtti

Ramwent home.

Ramate an apple.

----------------------------------------------

Ramwent home, ate an apple.

Information Theory

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti

upadeSe ac anunAsika it 1.3.2

hal antyam 1.3.3

na vibhaktau tusmA 1.3.4

Adi ~nitudavAH 1.3.5

.saH pratyayasya 1.3.6

CutU 1.3.7

laSaku ataddhite 1.3.8

Anuvŗtti

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd

upadeSe

ac anunAsika (=it) 1.3.2

hal antyam 1.3.3

na vibhaktau tusmA (=it)1.3.4

Adi

~nitudavAH (=it)1.3.5

pratyayasya

.saH (=it)1.3.6

CutU (=it)1.3.7

ataddhite laSaku (=it)1.3.8

Anuvŗtti … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd9

upadeSe(a)

ac anunAsika(b)(=it)(c)1.3.2

hal antyam(d)1.3.3

na vibhaktau tusmA(e)(=it)1.3.4

Adi(f)

~nitudavAH(g)(=it)1.3.5

pratyaya(h)sya(i)

.saH(j)(=it)1.3.6

CutU(k)(=it)1.3.7

ataddhite laSaku(l)(=it)1.3.8

Anuvŗtti … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd10

a

b c

d

e c

f

gc

h_i

j c

k c

l c

a (b + de + f [g+ h_i{j + k + l }]) c

Anuvŗtti … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd11

No Proper Nesting; MandUka pluti:

Ad(a) guNaH(b) 6.1.84

v.rddhiH(c) eci(d){a} 6.1.85

etyedhatyUTsu (e) {a c d} 6.1.86

upasargAt(f)ŗti(g)dhAtO(h){a c}6.1.87

VA supyApiSale(i){f g h a c} 6.1.88

OtaH amSasoH(j) 6.1.89

e”ni(k) pararUpaM(l){ f h a} 6.1.90

a{b + c[d(1+e) + fh(g(1 + i)] + j + kl)}

Anuvŗtti … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd12

Maximum advantage of features of Natural Language:

How are the complete phrases reconstructed?

AkAnksha (Expectancy): Major role in deciding the anuvŗtti

Anuvŗtti … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd13

Example of borrowing from as many as 11 sūtras

Original sūtra:

3-3-65 क्वणः वीणायां च

After anuvŗtti:

3-3-65: क्वणः वीणायां च प्रत्ययःपरः चआद्युदात्तः चधातोःकृत्क्रियायां क्रियार्थायाम् भावे अकर्तरि च कारके सञ्ज्ञायाम् अप्उपसर्गे वानौ(anuvŗtti from 11 different sūtras)

Anuvŗtti … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

anuv tti contd14

Some Statistics:

Total sūtras : (3984) 4000

Total Words (with sandhi): (7007) 7000

Total Sandhi split words: 9843

Total words after repeating the

words with anuvŗtti: 40,000

Compression because of anuvŗtti: 1/6

In terms of byte size, compression is 1/3.

Anuvŗtti … Contd

4th APCAP Dec 5th 2008, NIAS Bangalore

information theory15

Normal Arrangement of Alphabet

a A i I u U ŗļ e E o O M H

k kh g gh “n

c ch j jh ~n

ţ ţh .d .dh .n

t th d dh n

p ph b bh m

y r l v

S ş s h

Information Theory

4th APCAP Dec 5th 2008, NIAS Bangalore

panini required several 42 subsets of this alphabet to describe various operations
Panini required several(42) subsets of this

alphabet to describe various operations.

ShivasUtra

4th APCAP Dec 5th 2008, NIAS Bangalore

shivasutra

Some of these subsets:

All vowels

All consonants

All vowels + semivowels

h y v r l + consonants

y v r l + consonants

v r l + consonants

r l + consonants

ShivasUtra

4th APCAP Dec 5th 2008, NIAS Bangalore

shivasutra18

It is not advisable to give 42 names to these sets.

It will be difficult to memorize the association.

These are Partially ordered sets.

Panini arranged them linearly in the form of

14 ShivasUtras.

ShivasUtra

4th APCAP Dec 5th 2008, NIAS Bangalore

slide19
4th APCAP Dec 5th 2008, NIAS Bangalore

a i u N

ŗļK

e o c

E O “N

h y v r T

l N

ň m “n N n M

Jh bh Ň

gh .dh dh Ş

j b g .d d S

kh ph ch .th th c .t t V

k p Y

SŞ s R

h L

S

H

I

V

A

S

U

T

R

A

S

slide20
Optimality of these sUtras is

proved independently by

Kiparsky (linguistically)

and Petersen (mathematically)

ShivasUtras .. contd

4th APCAP Dec 5th 2008, NIAS Bangalore

shivasutras contd

Given a set of Partially Ordered sets,

Now it is possible to tell

Whether the elements are

Shivasutra encodable or not.

Ref: Petersen(2008)

ShivasUtras ... contd

4th APCAP Dec 5th 2008, NIAS Bangalore

information dynamics

Information Theory:

Deals with

Measure of information, data compression, etc.

Information Dynamics:

Focuses on flow of information in a language

Information Dynamics

4th APCAP Dec 5th 2008, NIAS Bangalore

information dynamics23

For a Computer Scientist working in NLP

Where a language codes the information

How it codes the information

How much information it codes

are important.

Information Dynamics

4th APCAP Dec 5th 2008, NIAS Bangalore

where a language codes information useful to decide the parsing strategy
Where a language codes information:

Useful to decide the parsing Strategy

Information Dynamics … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

slide25
How a language codes information:

Useful to decide whether the information can be passed on to other language without any efforts or not

Information Dynamics … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

information dynamics contd

How much information a language codes:

Useful to decide whether the desired information can be extracted or not merely from a language string without appealing to the extra linguistic knowledge.

Information Dynamics … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

slide27
Where: anabhihite 3.1.1

How much: svatantraH kartA 1.4.54

How (the manner):

samAna kartŗkayoH pUrvakAle 3.4.21

Information Dynamics … Contd

4th APCAP Dec 5th 2008, NIAS Bangalore

programming languages

Data + Algorithm = Program

Algorithm: Around 4000 sUtras

Data: Shivasutra

gaNapAtha

DhAtupAtha

uNAdi sUtra

li”ngAnuSAsana

Programming Languages

4th APCAP Dec 5th 2008, NIAS Bangalore

programming languages contd

Data + Algorithm = Program

Object Oriented Programming:

Encapsulation of data with the (markers to the) functions

Bhaj + (gh)a(~n) : Presence of gh => j->g

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

programming languages contd30

Ordering of rules:

Two meta rules

a) viprati.sedhe param kAryam 1.4.2

(In case of conflict apply the later rule)

b) pUrvatra asiddham 8.2.1

(Apply the rules in last 3 sections

at the end and

in linear order)

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

slide31
Typical VaiyAkara.na's view:

Event driven Programming

Changes in the Data spaces: Event

==> Triggers the rules

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

typical vaiakara nas view
Typical vaiakara.nas view:Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

programming languages contd33

Control:

Certain rules block certain other rules.

Blocking is of 3 different types

a) Partial blocking (asiddhavat)

b) certain rules are not applicable (asiddhaH)

c) only certain rules are applicable (asiddham)

(direct implication on : passing of parameters)

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

ordering of the sutras
Ordering of the sUtrasProgramming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

programming languages contd36

Control:

a) If X then Y (mA.thara kau.ndi.nya nyAya)

b) If X then Y else Z (takra kau.ndi.nya nyAya)

c) If (not X) then Y (ni.sedha)

d) if X then (Y and Z) (vibhA.sA)

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

conflict resolution utsarga apavada general special rule
Conflict Resolution:

Utsarga / apavAda

General / special rule

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

slide38
Use of Special Features of Sanskrit

Use of Vibhaktis (case markers)

Order of parameters in a function

IkaH ya.n aci

Ik ac → ya.n ac

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

slide39
Use of Special Features of Sanskrit

Use of Pronouns as variables

Tasmin iti nirdis.te pUrvasya

TasmAt iti uttarasya

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore

slide40
Inheritance

Multiple inheritance → arranged as a linear inheritance

Taddhita pratyaya

Ashwini Deo 2007

Programming Languages … contd

4th APCAP Dec 5th 2008, NIAS Bangalore