SIE 550 – Formal Languages
Lecture for SIE 550
Matt Dube
Doctoral Student – Spatial
IGERT Fellow
Languages
What do we think of when we think of languages?
letters
numbers
punctuation
syllables
words
parts ofspeech
grammar
phrases
sentences
BUILDING BLOCKS
BUILDINGS INTHELANGUAGE
What are we going to do today?
•Not quite what you bargained for
•We are going to learn how to write in aforeign language that none of us canactually speak
•We will then use that language to set upthe constructs that govern computers anddatabase constructs
The Language Is….
KOREAN
Korean Words
말하다
This is a one word English physical action. So everyone take aguess by doing a physical action.
SPEAK
Now That You UnderstandKorean…
•(pause for raucous laughter)
•Korean appears to be a graphicallanguage, like Chinese and quite unlikeEnglish
•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 isactually 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 aconsonant
•All characters in written Korean follow either of those twopatterns
•A syllable is thus a composite of characters in aspecified order (and they all exist ironically enough).
•Words, phrases, sentences, etc. are composite ofsyllables.
What About English?
NOT SO SIMPLE!
Example
What then does “qeb” mean?
A
B
S
O
L
U
T
E
L
Y
N
O
T
H
I
N
G
!
“dog”
CUTE, CUDDLY, FURRYANIMAL 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 toan 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 orproduction 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 arecalled well formed formulas (sentences)
•Example:
–Jack in the box
–We should say: Jack is in the box.
JACK
BOX
IN
![MCj04315210000[1]](data/images/img13.png)
![MCj03970440000[1]](data/images/img14.png)
Forming a WFF
•Operators are needed for theselanguages:
•| = 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 ifnecessary
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 KoreanSyllables
•Start with what we are trying to create
•Establish the form of the creation
•Establish the terminal symbols
•Congratulations! We can now generateany 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?
![MCj04315210000[1]](data/images/img15.png)
Syllables aren’t enough though…
•We speak and write in words
•What do we need to do to make ourprogram 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 syllable
0 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 semanticsare not accounted for in a formallanguage.
The Problem with English…
DOG
SHY
BEE
AXE
QEV
No matter what, we can’t define syllables orwords 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 positiveintegers on the board.
Why Formal Languages?
•Mathematical Induction
–How many syllables exist in Korean?
•14 Consonants * 10 Vowels * (14 Consonants + 1Blank) = 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 onone (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 ownexercise:
•Create a formal language that will outputaddition and subtraction questions forpositive integers, namely 4+9-7=?
–Should be able to do arbitrary amount ofcalculations
–No leading zeroes for a number
•Discuss on Friday