Monadic CompositionalParsing with ContextUsing Maltese as a Case Study

Gordon J. Pace

September 2004

Monadic CompositionalParsing with ContextUsing Maltese as a Case Study

A Users’ Perspective.For the technical details, read the

paper!

Combinator-Based Programming

A Recipe Provide a class/type of objects you will be

talking about; Provide a few basic objects of that type; Provide a few combinators to combine

objects of the type into more complex ones.

Mix well and put on low heat for 35 min.

type Parser a = …

A basic type:A parser which consumes a

text stream, returning an object of type a

Combinator-Based Programming

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

Combinator-Based Programming

Some basic parsers

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

Combinator-Based Programming

And some combinatorswhich produce new parsers

out of old ones.

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

A parser which always fails

Combinator-Based Programming

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

Given a value, this parser leaves the input stream untouched,

returning the given value

Combinator-Based Programming

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

A parser which returns the first character on the input stream

Combinator-Based Programming

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

Non-deterministic choice between two parsers

Combinator-Based Programming

fail :: Parser a

return :: a -> Parser a

one :: Parser Char

<+> :: Parser a -> Parser a -> Parser a

mthen :: Parser a -> Parser a -> Parser a

Sequential composition of two parsers*

Combinator-Based Programming

* Actually, I’m cheating by somewhat simplifying the type …

p1 <*> p2 =

do

x1 <- p1

x2 <- p2

return (x1,x2)

Parse a pair of objects in sequence

New parsers are easy to derive

matchSat ::

(Char -> Bool) -> Parser Char

matchSat cond =

do

x <- one

if cond x

then return x

else fail

Parse a character, if it satisfies a given

condition

New parsers are easy to derive

matchChar c = matchSat (c==)

matchString “” = return “” matchString (c:cs) = do matchChar c matchString cs return (c:cs)

Parse a particular string

New parsers are easy to deriveParse a particular character

star :: Parser a -> Parser [a]

star p =

return []

<+>

do

(x,xs) <- p <*> star p

return (x:xs)

Kleene star

New parsers are easy to derive

p1 <**> p2 =

do

w1 <- p1

plus (parseSat isSpace)

w2 <- p2

return (w1,w2)

Space separated words

New parsers are easy to derive

Context: The Maltese Article

1. Basic form of definite article is il–.2. Nouns starting with a sun letter (xemxin)

transform the l to match the first letter of the noun.

3. Nouns starting with 2 or 3 consonants, the first being x or s, drop the initial i, and add an initial i to the noun.

4. Nouns starting with a vowel drop the initial i from the article.

5. The initial i is also dropped when the preceding word starts with a vowel.

Context: The Maltese Article

1. Basic form of definite article is il–.2. Nouns starting with a sun letter (xemxin)

transform the l to match the first letter of the noun.

3. Nouns starting with 2 or 3 consonants, the first being x or s, drop the initial i, and add an initial i to the noun.

4. Nouns starting with a vowel drop the initial i from the article.

5. The initial i is also dropped when the preceding word starts with a vowel.

Context

Context

Context

Context

Context: The Maltese Article

1. Basic form of definite article is il–.2. Nouns starting with a sun letter (xemxin)

transform the l to match the first letter of the noun.

3. Nouns starting with 2 or 3 consonants, the first being x or s, drop the initial i, and add an initial i to the noun.

4. Nouns starting with a vowel drop the initial i from the article.

5. The initial i is also dropped when the preceding word starts with a vowel.

Context

Context

Context

Context

How can we write a compositional parser –

one that parses a stand-alone article?

Looking at the Context

We would like to write:

definiteNoun =

article <**> noun

Looking at the Context

We can look at local context using other parsers:

article =

do

initial_i

c <- parseSat isXemxija

parseChar ‘-’

matchFuture (parseChar c)

Looking at the Context

We can look at local context using other parsers:

initial_i =

matchPast (

(parseSat isVowel <*> wordSep)

)`ifnot`

parseChar ‘i’

More Context: First Form Verbs

Example

rikeb

General case

c1 v1 c2 v2 c3

1st Person, Singular nirkeb n v1 c1 c2 v2 c3

2nd Person, Singular tirkeb t v1 c1 c2 v2 c3

3rd Person, Singular, Male jirkeb j v1 c1 c2 v2 c3

3rd Person, Singular, Female tirkeb t v1 c1 c2 v2 c3

1st Person, Plural nirkbu n v1 c1 c2 c3 u

2nd Person, Plural tirkbu t v1 c1 c2 c3 u

3rd Person, Plural jirkbu j v1 c1 c2 c3 u

More Context: First Form Verbs

Example

rikeb

General case

c1 v1 c2 v2 c3

1st Person, Singular nirkeb n v1 c1 c2 v2 c3

2nd Person, Singular tirkeb t v1 c1 c2 v2 c3

3rd Person, Singular, Male jirkeb j v1 c1 c2 v2 c3

3rd Person, Singular, Female tirkeb t v1 c1 c2 v2 c3

1st Person, Plural nirkbu n v1 c1 c2 c3 u

2nd Person, Plural tirkbu t v1 c1 c2 c3 u

3rd Person, Plural jirkbu j v1 c1 c2 c3 u

Context

Setting the Context

We would like to write something like:

sentence =

noun <**> verb <**> noun

Setting the Context

We set a context by setting attributes:

setAttribute (name, value)

getAttribute name

renameAttribute (name, name’)

Setting the Context

We set a context by setting attributes:

setAttribute (name, value)

getAttribute name

renameAttribute (name, name’)

Clashing values cause the parser to fail

Setting the Context

parsePersonSingular = do setAttribute ("SubjectNumber", "Singular") c <- anyCharOf ['n','t','j'] case c of 'n' -> setAttribute ("SubjectPerson" “1“) 'j' -> setAttributes [("SubjectPerson",“3"), ...] 't' -> setAttribute ("SubjectPerson",“2") <+> setAttributes [("SubjectPerson",“3"), ...]

Setting the Context

parseSubject = do n <- parseNoun renameAttributes [("Noun"++x, "Subject"++x) | x <- ["Gender", "Person", "Number"] ]parseObject = ...

parseSentence = parseSubject <**> parseVerb <**> parseObject

Contribution

Local context parsed using the same parser combinators;

Global, shared information shared via attributes;

All this done compositionally, and By enriching standard parser

combinators.

Conclusions

Optimise it, apply it to larger NL subset, compare with other, more traditional approaches.

Optimise the new context-aware combinators.

Extend it to work both as a language generator and parser.