SIE 550 – Formal Languages

Lecture for SIE 550Matt Dube

Doctoral Student – SpatialIGERT Fellow

Languages

What do we think of when we think of languages?

letters numbers punctuationsyllables

words

parts of speech

grammar

phrases

sentences

BUILDING BLOCKS

BUILDINGS IN THE

LANGUAGE

What are we going to do today?

• Not quite what you bargained for

• We are going to learn how to write in a foreign language that none of us can actually speak

• We will then use that language to set up the constructs that govern computers and database constructs

The Language Is….

KOREAN

Korean Words

말하다

This is a one word English physical action. So everyone take a guess by doing a physical action.

SPEAK

Now That You Understand Korean…

• (pause for raucous laughter)

• Korean appears to be a graphical language, like Chinese and quite unlike English

• Looks are very deceiving though

말하다

KOREAN ALPHABET

Korean is an alphabetical language!

Consonants Vowels

Consonants Vowels

말하다

But wait….Those characters aren’t in the alphabet!

Let’s take a closer look:So what exactly is each character in the phrase “speak”?

Syllables

• Each character in written Korean is actually a syllable!

• Any patterns?

Consonants Vowels

말하다

Syllables

• Korean characters are syllables!• Any patterns?

– Consonant followed by a vowel– Consonant followed by a vowel followed by a

consonant• All characters in written Korean follow either of those two

patterns• A syllable is thus a composite of characters in a

specified order (and they all exist ironically enough).• Words, phrases, sentences, etc. are composite of

syllables.

What About English?

NOT SO SIMPLE!

Example

What then does “qeb” mean?

ABSOLUTELY NOTHING!

“dog”

CUTE, CUDDLY, FURRY ANIMAL THAT BARKS

English Language

• Syllables do not work with our alphabet

• Thus some are not valid

• Syllables are phonetically based

• Korean is a phonetically based language

• English is the hardest language to learn

• Korean is the easiest language to learn

Why Did We Do That?

• Necessity

• Computers and databases need a “Korean” type of language as opposed to an English type of language– Parsing– Relevancy

• Korean is a formal language

Formal Languages• Characters

– Letters, numbers, punctuation– Building blocks– We call these terminal symbols or axioms

• Uses of characters– Syllables, words, phrases, grammar, sentences,

etc.– Buildings– We call these non-terminal symbols or production

rules or predicates

Where do we find them?• Music• Mathematics• World Languages• Art• Computer Languages• Almost Anywhere

Conventions

• The production rules form the syntax (grammar/spelling) of a language

• Valid combinations under the syntax are called well formed formulas (sentences)

• Example:– Jack in the box– We should say: Jack is in the box.

JACK

BOX

IN

Forming a WFF

• Operators are needed for these languages:

• | = exclusive or• ::= = is replaced by• [ ] = optional (0 or 1)• { } = optional (0 to many)• “ ” = designators of terminal symbols• Examples of situations for these?

Assigning a sign (+ or -)

Fullname ::= First Last

Area code

Letters in a name

Programming Korean Syllables

• Start with what we are trying to create

Korean Syllables

• start ::= syllable

start “is replaced by” syllable

Programming Korean Syllables

• Start with what we are trying to create

• Establish the form of the creation

Korean Syllables

• start ::= syllable

• syllable ::= consonant vowel [consonant]

consonant followed by a vowel

another consonant if necessary

Programming Korean Syllables

• Start with what we are trying to create

• Establish the form of the creation

• Establish the terminal symbols

Korean Syllables

can be substituted for consonant

can be substituted for vowel

• start ::= syllable

• syllable ::= consonant vowel [consonant]

• consonant ::= “A” | “B” | “C” | “D” | “E” | “F” | “G” | “H” | “I” | “J” | “K” | “L” | “M” | “N”

• vowel ::= “0” | “1” | “2” | “3” | “4” | “5” | “6” | “7” | “8” | “9”

Let’s Try to Program Korean Syllables

• Start with what we are trying to create

• Establish the form of the creation

• Establish the terminal symbols

• Congratulations! We can now generate any Korean syllable mechanically

• Let’s test a few examples

• start ::= syllable

• syllable ::= consonant vowel [consonant]

• consonant ::= “A” | “B” | “C” | “D” | “E” | “F” | “G” | “H” | “I” | “J” | “K” | “L” | “M” | “N”

• vowel ::= “0” | “1” | “2” | “3” | “4” | “5” | “6” | “7” | “8” | “9”

Korean Syllables

A3A?100?AAA?K9?M4?O7K?3D?C3P0?

Syllables aren’t enough though…

• We speak and write in words

• What do we need to do to make our program generate possible Korean words?

Korean Words

• start ::= word

• word ::= {syllable}

arbitrary number of syllables

What is wrong with this?A word can have 0 syllables???

How can we deal with this?

Korean Words Revised

• start ::= word

• word ::= syllable {syllable}

one syllable0 to n more possible

Now add the lines from syllable

Korean Words

• start ::= word

• word ::= syllable {syllable}

• syllable ::= consonant vowel [consonant]

• consonant ::= “A” | “B” | “C” | “D” | “E” | “F” | “G” | “H” | “I” | “J” | “K” | “L” | “M” | “N”

• vowel ::= “0” | “1” | “2” | “3” | “4” | “5” | “6” | “7” | “8” | “9”

This goes to show that semantics are not accounted for in a formal

language.

The Problem with English…

DOG SHY BEE AXE

QEVNo matter what, we can’t define syllables or words such that we get all “words” as results (provided we don’t code all words in)!

• start ::= syllable

• syllable ::= consonant vowel [consonant]

• consonant ::= “B” | “C” | “D” | “F” | “G” | “H” | “J” | “K” | “L” | “M” | “N” | “P” | “Q” | “R” | “S” | “T” | “V” | “W” | “X” | “Y” | “Z” |

• vowel ::= “A” | “E” | “I” | “O” | “U”

Positive Integers

• Let’s construct a language for positive integers on the board.

Why Formal Languages?

• Mathematical Induction– How many syllables exist in Korean?

• 14 Consonants * 10 Vowels * (14 Consonants + 1 Blank) = 2,100

– How many syllables in English?• Can’t tell without counting one by one

Why Formal Languages?

• Parsing– Conversion to other useful information

• Φ = “ph”• 1/2 = ½

Why Formal Languages?

• Grafiti Palm Pilots– Allow for symbolic recognition– Writing on a small object easier than typing on

one (texting on a cell phone)

Why Formal Languages?

• Sequential Operations on a Computer– Selecting text– Drawing– Menu browsing

Why Formal Languages?

• Mechanical recognition of commands– Spell checkers– Proper commands in DOS prompt

To think about

• Won’t be collected, but for your own exercise:

• Create a formal language that will output addition and subtraction questions for positive integers, namely 4+9-7=?– Should be able to do arbitrary amount of

calculations– No leading zeroes for a number

• Discuss on Friday