Tuesday, August 9, 2011

Six degrees of Sutras

One of the memorable humour tracks of Tamil movies is from arivAli (The Intelligent) made in early 1960s. A black white film, with simple clean humour. Very likely such movies were made in other Indian languages too. The husband asks his wife to make puri. Wife does not know how to make it, so husband gives instructions to her:

Husband: Take a vessel and put some wheat flour in it
Wife: Yeah, I know that!
Husband: Pour some water and salt and mix with flour
Wife: Yeah, I know that!
Husband: Make it into small round balls
Wife: Yeah, I know that!
Husband: Flatten it and make it round like appalam
Wife: Yeah, I know that!
Husband: Then what?
Wife: Aah, I dont know that...

In an earlier post we saw how a sutram's definition can be applied to naming convention of variables in modern programming context. A natural question arises - what are the types of sutram-s? As I have mentioned before, classification is ancient Indians' forte. There are six types of sutram-s which is defined, yeah you guessed it, in a shloka:

संज्ञा च परिभाषा च विधि: नियम एव च ।
अतिदेशो अधिकारश्च षड्विधम् सूत्र-लक्षणम् ॥

A lot has been described about this classification in wiki articles and elsewhere. Here we will just look at the parallels between this classification and programming concepts.
संज्ञा - definition; परिभाषा - interpretation; विधि- rules; नियम - restriction; अतिदेश- extension; अधिकार - header/domain.

संज्ञा is a definition sutram. It gives a meaningful name for one or more symbols. Do you remember your early programming days where you are told that a good practice is to give a name for constants? (Do you still follow that?)

वृद्धिरादैच् |  [1.1.1]  {a, e, o} are called vRuddhi |

In programming terms, this is like the classic C #define statement or final static/const statements in Java/C# world. 

#define PI 3.14

#define IK_PRATYAHARA {i, u, Ru, Lu}

परिभाषा sutram is an interpretation or meta-rules sutram. Its function is to tell how to interpret other sutram-s.
तस्मात् इति उत्तरस्य | [1.1.67] When a sutra has a word in panchamI vibhakti, then the word next to it will undergo some modification. 

A very good equivalent to interpretation rules is Annotations. This example will make it clear:

public void updateUser() {

The annotation says that the method updateUser() must respond to only a http post call. It helps the runtime interpret the method in a certain way.

विधि sutram: What is the fundamental difference between a calculator and a computer? The calculator (a regular) deals with numbers only, while the computer can make logical decisions.

विधि sutram is the classic if-else-condition. In fact, the way पाणिनि has applied it - its closer to aspect-based rules than just a vanilla if-else condition. There is a slight difference between "if do this" and "when apply this". While the if-condition has to be encountered during the execution process thread, a when-rule applies anytime during the happening of a certain condition. "if" is thread-execution based, while "when" is time based, a trigger with an "if".पाणिनि defines several rules in his अष्टाध्यायी. For example there is a famous sandhi rule with just three words, that covers a matrix of sandhi-s.
इको यण् अचि | [6.1.78]
When a vowel follows, the letters i, u, Ru, Lu change to y v r l.

Obviously any if-else condition would be a vidhi sutram. If we were to follow paaNini's technique, we would not write it as a simple if condition. Instead we would define all "when rules" in a separate section of the code, and provide aspects of applying. When code executes, the aspects will monitor the code and "apply" a rule when those conditions are satisfied. For eg the (now) Oracle's Haley is one of the very popular Rules Engine products, in which Rules can be defined in simple English.

नियम sutram
If programming was based on socialistic ideologies, rules would apply uniformly to all cases (except the political class, of course). But reality is somewhat capitalistic, so there is always some case which disagrees to agree. Remember the business requirements like "should apply to all but one or two cases" and the complex if-conditions you would have to write to handle just the boundaries?

Restriction is not Exception. Exception is an alternative flow, but restriction is about applying a rule to a lesser number of or rarer cases. In general, it is achieved by if-else conditions, but doesn't always have to be so.

अतिदेश sutram-s are extensions. They qualify a pre-existing rule with another property, not originally possessed.
Using pratyaya-s vat and mat, paaNini extends the behaviour of one rule and applies to another rule.
लोट: लङ्वत् | [] would mean "लोट् vibhakti-s are to be conjugated just like लङ्"
Imagine that
लोट्, लङ् etc implement an interface called "ल". Panini's technique essentially casts लोट् as लङ्.
Class extensions are very common in OO languages. Using the Extension mechanism offered by Ruby, C# etc, one can improve the functionality of an existing class. For eg, String class does not have intrinsic methods to check if the value is null or empty . One could add a IsNullOrEmpty(this String) method and operate directly on a string instead of a new helper class.
It does not end there. Imagine two objects User and LockedUser:
User user; //normal user behaviour
LockedUser lockedUser; //a locked user behaviour, imagine a Trait (see Scala which allows partially implemented interfaces)
if (user.failedAttempts(3)) { user.setBehaviour(lockedUser)); } //user now behaves like a lockedUser

Instead of changing the state of the object (commonly via isLocked() or status = LOCKED), the behaviour of the object itself is changed. Upon certain conditions, the regular user adapts the behaviour of a locked user. We do not directly deal with properties and state changes, instead work with behaviour changes. For eg, Scala offers Traits, with partially implementable methods, which are much more than interfaces. In a way you are describing or coding to the behaviour of an object rather than the states.
अधिकार sutram: If you have done database modeling, you know Subject Areas. In programming terms, think of package, namespace etc. They all define a domain underwhich certain rules/classes/tables are grouped. Thats exactly what adhikara sutram is. More information on adhikara sutram can be found in this post.
संहितायाम् | []  "During the closeness of words"
प्रत्यय: | [3.1.1] "Affix"
package com.microsoft.office;
namespace Com.Sun.Oracle.Java;
//ok, I was being facetious :-)

Apart from these core sutram-s there are a few more.

निषेध sutram-s are negation rules of other rules. While niyama sutram-s are positive restrictions, nishedha can be seen as negative orientation.
हलन्त्यम् | (consonant endings are it-markers)
न विभक्तौ तुस्माः | (but
letters t, th, d, dh, s, m are not it-markers if it is used for conjugations)
In programming, we can come up with a validation rules engine like this:
1. All Address Fields Required
2. Not if Address Line 2
Imagine the simplicity of a program using such a validation engine!
विभाषा sutram is an optional rule. For eg think of the sentence "I would like to goto a movie". You can also say it as "I'd like to goto a movie". The shortening of "I would" to I'd does not change the meaning, and is optional to use. पाणिनि uses this technique to provide alternative usages of words and grammar by using the shabda-s vaa, vibhaaShaa, anyatarasyaam. Optional rules are very common and are done using if conditions.

Besides these, some of the paaNini's techniques also strike a chord with modern techniques. For eg, there is an interpretation sutra विप्रतिषेधे परम् कार्यम्, which means "In case of rule-conflicts, the latter rule prevails". Virtual override feature?

Another unique technique is called स्थानी भाव where a substituting suffix can retain the characteristics of a substituted suffix. Heard of Liskov Substitution Principle? Yeah, something like that.

Panini also uses recursive techniques for some of the rule operations. We will see that in a subsequent post.

Yet another ingenious technique is seen in the last 3 pada-s of अष्टाध्यायी where every previous rule is oblivious to all the latter rule. The rules are arranged in such a way that every rule "thinks" that it is the last rule of the book.

So what is the benefit of comparing modern programming with a 2500+ old text book of grammar? Let it be पाणिनि:, Capellini or Linguini founded algorithms. As a software engineer, what do I care? I do not have an answer. After all, a programmer consultant in US writes a for-loop for $75 an hour, while the same for loop is written by some one in China for a few Yen. Can you judge which for-loop is better?

If several of modern programming concepts have indeed parallels in अष्टाध्यायी, how about some concepts in अष्टाध्यायी not yet formulated into modern programming theories? What if they could create a fundamental change in theory of programming?

What would पाणिनि: think about modern programming concepts? To find out, we shall send Donald Knuth back in time as our representative.

Knuth: Programming is about definitions, rules and algorithms.
पाणिनि: आम्, जानाम्येव !
Knuth: Using algorithms we derive and solve various equations.
पाणिनि: आम्, जानाम्येव !
Knuth: In object oriented programming, we do abstraction, polymorphism and other cool things.
पाणिनि: आम्, जानाम्येव !

Knuth: With functional programming, we define functions, recursions and closures.
पाणिनि: आम्, जानाम्येव !
Knuth: Then we create programs to play games like Grand Theft Auto all day long.
पाणिनि: अहो ! तदहम् न जानामि !!

1 comment:

ssriram said...

I am very fortunate to visit your site. It is bookmarked now.

The sUtrA technique existed way before Panini. His ingenuity was in how he used the sUtrA to represent the meta-linguistic features of saMskrtavyAkaranam.
That is, he programmed saMskrtam in saMskrtam what you call as bootstrapping a lisp interpreter in compiler techniques.

I am self taught saMskrta-hacker in part time. Here is my site https://xyzcompany.in

The below sUtrA-s actually resemble Newton's laws and is part of the vYSES'ika sUtrA.
I have tried to translate to the Newton's laws. But it would be better to understand how the sUtra reveals itself. I need some help in that.
If you indulge could you please translate the following sUtrA-s?

vEga saMskAra - mechanical force which causes change in motion (velocity)

1. vEgaH nimittaviSES'Ata karmaNW jAyatE

2. vEgaH nimittApEkS'Ata karmaNW jAyatE
niyatadik kri yApraband'ahEtuH

3. vEgaH saMyOgaviSES'avirOd'I

AkrS'Ti Saktistu mahI yat svast'am gurU svAb'imUk'am svaSaktya
AkrS'ytE tat patatIva b'Ati samE samantAt vaca vatatyyaM ravE

1. Any change in motion is due to an externally impressed force.
2. Any change in motion is proportional to the externally impressed force and is in the direction of the force.
3. The forces of action and reaction are equal and opposite in the same alignment

Note: I have used nUtanalipi (http://xyzcompany.in/2011/12/15/nutanalipi-new-script/). The quotes represent the aspirated axarA instead of an ambigous 'h'.

And I feel bad (and enticed in one way so I can develop my saMsktram skills) that I cannot post this post fully in saMskrtam.