Monadic Parsers using Haskell
An introduction
Tony Morris
Copyright © 2009 Tony Morris
Abstract
A hands-on introductory tutorial to monadic parsers using the Haskell Programming Language http://haskell.org/. Students will require an installation of the Glasgow Haskell Compiler http://haskell.org/ghc and a text editor. Upon completion of the tutorial students will have created a parser library.
Students will be expected to have a basic understanding of Haskell syntax and familiarity with tools -- in particular, the GHC interpreter (GHCi).
This document is released under a Creative Commons - Attribution, Non-Commercial, No Derivative Works licence. Appendix D, Licence

Table of Contents
Get Started 	 # 
What is a Parser? 	 # 

A data structure 	 # 
Errors? 	 # 
Our First Parser 	 # 

value 	 # 
Experiment 	 # 
Failing Parser 	 # 
Character Parser 	 # 

character 	 # 
Experiment 	 # 
Choice Parser 	 # 

||| 	 # 
Experiment 	 # 
Mapping Parser 	 # 

mapParser 	 # 
Experiment 	 # 
Binding Parser 	 # 

bindParser 	 # 
Experiment 	 # 
>>> 	 # 
Sequencing Parser 	 # 

sequenceParser 	 # 
Experiment 	 # 
Sequence N Parser 	 # 

thisMany 	 # 
Zero or Many Parser 	 # 

list / many1 	 # 
Experiment 	 # 
Satisfy 	 # 

satisfy 	 # 
Experiment 	 # 
Satisfiers 	 # 

satisfy 	 # 
Experiment 	 # 
Introspection 	 # 

Bits and Pieces 	 # 
Person 	 # 
ageParser 	 # 
firstNameParser 	 # 
surnameParser 	 # 
genderParser 	 # 
phoneBodyParser 	 # 
phoneParser 	 # 
Person Parser 	 # 

Experiment 	 # 
personParser 	 # 
Experiment 	 # 
Bind/Map 	 # 

bindParser/mapParser 	 # 
You Bet 	 # 
Then? 	 # 
Conclusion 	 # 
A. MyParser.hs 	 # 
B. MyParser.scala 	 # 
C. MyParser.java 	 # 
D. Licence 	 # 

Get Started
Let us start by creating a file called MyParser.hs. Then in that file the contents:
module MyParser where

import Data.Char
Start the GHC interpreter ghci and load the source file.
$ ghci
GHCi, version 6.10.2: http://www.haskell.org/ghc/  :? for help
Prelude> :load MyParser.hs
[1 of 1] Compiling MyParser         ( MyParser.hs, interpreted )
Ok, modules loaded: MyParser.
*MyParser>                                                         

What is a Parser?

A data structure
A parser is a function that accepts an input String and either fails or produces a value and the remaining input String.
data Parser a = P { 
  parse :: String -> Maybe (String, a)
} 
Examine the type of parse

*MyParser> :type parse
parse :: Parser a -> String -> Maybe (String, a)
parse accepts a parser and input and either fails or produces a value and the remaining input.

Errors?
Our parser is trivial such that error messages or positions of parse failure are not handled. This is done to simplify this exercise.

Our First Parser

value
Let’s create a parser that consumes no input and produces a given value.
value :: a -> Parser a
value a = P (\ s -> Just (s, a))
This parser always succeeds (Just).

Experiment
Experiment with this parser
*MyParser> :type parse (value “boo”)
parse (value “boo”) :: String -> Maybe (String, [Char])
*MyParser> parse (value 7) “input”
Just (”input”,7)
*MyParser> parse (value “boo”) “input”
Just (”input”,”boo”)

Failing Parser
Let’s write a parser that always fails.
failed :: Parser a
failed = P (\ _ -> Nothing)
This parser always fails since it always produces Nothing.

Character Parser

character
Let’s create a parser that consumes one character and produces that character, unless the input is empty, in which case fail.
character :: Parser Char
character = P (\ s -> case s of [] -> Nothing
                               (c:r) -> Just (r, c))

Experiment
Experiment with the character parser
*MyParser> :type parse character
parse character :: String -> Maybe (String, Char)
*MyParser> parse character “abc”
Just (”bc”,’a’)
*MyParser> parse character “”
Nothing

Choice Parser

|||
Write a function that accepts two parsers and returns a parser that tries the first parser for success. If that parser fails, try the second parser.
(|||) :: Parser a -> Parser a -> Parser a
P p1 ||| P p2 = P (\ s -> case p1 s of v@(Just _) -> v
                                      Nothing -> p2 s)

Experiment
Experiment with the choice parser
*MyParser> let p = character ||| value ‘x’ in parse p “abc”
Just (”bc”,’a’)
*MyParser> let p = character ||| value ‘x’ in parse p “”
Just (””,’x’)
*MyParser> let p = character ||| failed in parse p “abc”
Just (”bc”,’a’)
*MyParser> let p = character ||| failed in parse p “”
Nothing

Mapping Parser

mapParser
Write a function that accepts a parser and a function from its produced value to another value to return a parser that potentially produces that value. We will see later why this function is useful.
mapParser :: Parser a -> (a -> b) -> Parser b
mapParser (P p) f = P (\ s -> case p s of Just (r, c) -> Just (r, f c)
                                         Nothing -> Nothing)

Experiment
Experiment with the mapping parser
*MyParser> let p = mapParser character toUpper in parse p “abc”
Just (”bc”,’A’)
*MyParser> let p = mapParser character toUpper in parse p “”
Nothing

Binding Parser

bindParser
Write a function that accepts a parser and a function from its produced value to another parser producing values of some type and returns a parser producing values of that same type. Again, we will see later why this function is useful.
bindParser :: Parser a -> (a -> Parser b) -> Parser b
bindParser (P p) f = P (\ s -> case p s of Just (r, c) -> parse (f c) r
                                          Nothing -> Nothing)

Experiment
Experiment with the binding parser
*MyParser> let p = bindParser character (\ c -> if isUpper c then value c else failed) in parse p “”
Nothing
*MyParser> let p = bindParser character (\ c -> if isUpper c then value c else failed) in parse p “abc”
Nothing
*MyParser> let p = bindParser character (\ c -> if isUpper c then value c else failed) in parse p “Abc”
Just (”bc”,’A’)

>>>
Write a function that uses bindParser but ignores the value that is produced by the given parser. This will be useful for example, when we wish for a parser to consume white-space but not do anything with that white-space.
(>>>) :: Parser a -> Parser b -> Parser b
p >>> q = bindParser p (\ _ -> q)

Sequencing Parser

sequenceParser
Write a function that accepts a list of parsers and produces a parser of lists by calling bindParser and mapParser as you go along the list.
sequenceParser :: [Parser a] -> Parser [a]
sequenceParser [] = value []
sequenceParser (h:t) = bindParser h (\ a -> mapParser (sequenceParser t) (\ as -> a : as))

Experiment
Experiment with the sequencing parser
*MyParser> let p = sequenceParser [character, value ‘b’, character] in parse p “”
Nothing
*MyParser> let p = sequenceParser [character, value ‘b’, character] in parse p “a”
Nothing
*MyParser> let p = sequenceParser [character, value ‘b’, character] in parse p “ab”
Just (””,”abb”)
*MyParser> let p = sequenceParser [character, value ‘b’, character] in parse p “abc”
Just (”c”,”abb”)

Sequence N Parser

thisMany
Write a function that accepts an integer (n) and a parser and returns a parser that binds ‘n’ times. We can do this by using the library function replicate.
thisMany :: Int -> Parser a -> Parser [a]
thisMany n p = sequenceParser (replicate n p)

Zero or Many Parser

list / many1
Let’s now write two functions. One takes a parser and applies itself zero or many times (list) and the other takes a parser and applies itself one or many times (many1). These functions are useful for such things as parsing white-space, where we may take a parser of a single white-space character and obtain a parser of e.g. one or many white-space characters.
list :: Parser a -> Parser [a]
list k = many1 k ||| value []

many1 :: Parser a -> Parser [a]
many1 k = bindParser k (\ k’ -> mapParser (list k) (\ kk’ -> k’ : kk’))

Experiment
Experiment with the new parsers
*MyParser> let p = many1 character in parse p “”
Nothing
*MyParser> let p = many1 character in parse p “abc”
Just (””,”abc”)
*MyParser> let p = list character in parse p “”
Just (””,””)
*MyParser> let p = list character in parse p “abc”
Just (””,”abc”)

Satisfy

satisfy
Write a parser that consumes a character (or fails if there isn’t one) and ensures that character meets a given predicate. We might also use this parser to write another parser (is) that parses a specific character.
satisfy :: (Char -> Bool) -> Parser Char
satisfy p = bindParser character (\ c -> if p c then value c else failed)

is :: Char -> Parser Char
is c = satisfy (== c)

Experiment
Experiment with these parsers
*MyParser> let p = satisfy isUpper in parse p “”
Nothing
*MyParser> let p = satisfy isUpper in parse p “abc”
Nothing
*MyParser> let p = satisfy isUpper in parse p “Abc”
Just (”bc”,’A’)
*MyParser> let p = is ‘a’ in parse p “”
Nothing
*MyParser> let p = is ‘a’ in parse p “abc”
Just (”bc”,’a’)
*MyParser> let p = is ‘a’ in parse p “xbc”
Nothing

Satisfiers

satisfy
Let us now write a bunch of parsers that use satisfy and apply the predicate.
digit :: Parser Char
digit = satisfy isDigit

natural :: Parser Int
natural = mapParser (list digit) read

space :: Parser Char
space = satisfy isSpace

spaces :: Parser String
spaces = many1 space

lower :: Parser Char
lower = satisfy isLower

upper :: Parser Char
upper = satisfy isUpper

alpha :: Parser Char
alpha = satisfy isAlpha

alphanum :: Parser Char
alphanum = satisfy isAlphaNum

Experiment
Experiment with some of these parsers
*MyParser> parse upper “”
Nothing
*MyParser> parse upper “a”
Nothing
*MyParser> parse upper “A”
Just (””,’A’)
*MyParser> let p = list digit in parse p “”
Just (””,””)
*MyParser> let p = list digit in parse p “79abc”
Just (”abc”,”79”)

Introspection

Bits and Pieces
So far we have constructed a small library of parsers. Some of these parsers are constructed from other parsers. This notion of constructing units of work from other, smaller units of work is the essence of functional programming. Does it scale?
Can we write even more higher-level parsers with our library by gluing parsers?

Person
Suppose we have a data structure to represent a person. The person data structure has these attributes:Age: positive integer
First Name: non-empty string that starts with a capital letter
Surname: string that starts with a capital letter and is followed by 5 or more lower-case letters
Gender: character that must be ‘m’ or ‘f’
Phone: string of digits, dots or hyphens but must start with a digit and end with a hash (#)
data Person = Person { 
  age :: Int,
  firstName :: String,
  surname :: String,
  gender :: Char,
  phone :: String
}  deriving Show

ageParser
The age parser is easy
ageParser :: Parser Int
ageParser = natural
Age: positive integer

firstNameParser
The first name parser requires us to piece together the upper and list lower parser. We do this using bindParser and mapParser. These two functions are turning out to be quite helpful.
firstNameParser :: Parser String
firstNameParser = bindParser upper (\ c -> mapParser (list lower) (\ cs -> c : cs))
First Name: non-empty string that starts with a capital letter

surnameParser
The surname parser requires us to piece together the upper, thisMany 5 lower and list lower parsers. Again, we do this using bindParser and mapParser.
surnameParser :: Parser String
surnameParser = bindParser upper (\ c -> bindParser (thisMany 5 lower) (\ cs -> mapParser (list lower) (\ t -> c : cs ++ t)))
Surname: string that starts with a capital letter and is followed by 5 or more lower-case letters

genderParser
The gender parser uses choice (|||) and is.
genderParser :: Parser Char
genderParser = is ‘m’ ||| is ‘f’
Gender: character that must be ‘m’ or ‘f’

phoneBodyParser
We will break the parsing of a phone number into two parts for simplicity. This part will parse the phone number body (without the hash at the end). It uses the list, digit and is parsers along with choice.
phoneBodyParser :: Parser String
phoneBodyParser = list (digit ||| is ‘.’ ||| is ‘-’)
Phone: string of digits, dots or hyphens but must start with a digit and end with a hash (#)

phoneParser
We will use the phoneBodyParser and the is parser to create a parser for the phone number. Once again, we glue it all together using bindParser and mapParser. Notice that we ignore the hash character in the end when we produce the final string.
phoneParser :: Parser String
phoneParser = bindParser digit (\ d -> bindParser phoneBodyParser (\ z -> mapParser (is ‘#’) (\ _ -> d : z)))
Phone: string of digits, dots or hyphens but must start with a digit and end with a hash (#)

Person Parser

Experiment
Experiment with the person parsers
*MyParser> parse firstNameParser “”
Nothing
*MyParser> parse firstNameParser “fred”
Nothing
*MyParser> parse firstNameParser “Fred”
Just (””,”Fred”)
*MyParser> parse surnameParser “”
Nothing
*MyParser> parse surnameParser “fred”
Nothing
*MyParser> parse surnameParser “Fred”
Nothing
*MyParser> parse surnameParser “Frederick”
Just (””,”Frederick”)
*MyParser> parse genderParser “”
Nothing
*MyParser> parse genderParser “a”
Nothing
*MyParser> parse genderParser “m”
Just (””,’m’)
*MyParser> parse genderParser “moo”
Just (”oo”,’m’)
*MyParser> parse phoneBodyParser “”
Just (””,””)
*MyParser> parse phoneBodyParser “123”
Just (””,”123”)
*MyParser> parse phoneBodyParser “123-456”
Just (””,”123-456”)
*MyParser> parse phoneBodyParser “123-456.789”
Just (””,”123-456.789”)
*MyParser> parse phoneParser “”
Nothing
*MyParser> parse phoneParser “#”
Nothing
*MyParser> parse phoneParser “-#”
Nothing
*MyParser> parse phoneParser “12#”
Just (””,”12”)
*MyParser> parse phoneParser “1-2#”
Just (””,”1-2”)
*MyParser> parse phoneParser “123-456.789”
Nothing
*MyParser> parse phoneParser “123-456.789#”
Just (””,”123-456.789”)
*MyParser> parse phoneParser “123-456.789#”
Just (””,”123-456.789”)
*MyParser> parse phoneParser “123#”
Just (””,”123”)

So we have parsers for the components of a Person. But we need a parser for a person. How can we get one of those?

personParser
By gluing them together with bindParser and mapParser (of course!).
personParser1 :: Parser Person
personParser1 = bindParser ageParser (\ age ->
                spaces >>>
                bindParser firstNameParser (\ firstName ->
                spaces >>>
                bindParser surnameParser (\ surname ->
                spaces >>>
                bindParser genderParser (\ gender ->
                spaces >>>
                bindParser phoneParser (\ phone ->
                value (Person age firstName surname gender phone))))))

Experiment
Experiment with the person parser
*MyParser> parse personParser1 “”
Nothing
*MyParser> parse personParser1 “123 Fred Clarkson m 123-456.789#”
Just (””,Person { age = 123, firstName = “Fred”, surname = “Clarkson”, gender = ‘m’, phone = “123-456.789”} )
*MyParser> parse personParser1 “123 Fred Clarkson m 123-456.789# the rest of the input”
Just (” the rest of the input”,Person { age = 123, firstName = “Fred”, surname = “Clarkson”, gender = ‘m’, phone = “123-456.789”} )
*MyParser> parse personParser1 “123 Fred Clark m 123-456.789# the rest of the input”
Nothing
We are successfully parsing a string into a Person object with potential failure.

Bind/Map

bindParser/mapParser
We have advanced quite far ahead of what we do with traditional languages. We have glued smaller parts to make larger parts, then glued those larger parts to make even larger parts again.
So what with this bindParser and mapParser business? They seem rather fundamental. Can we somehow remove the noise to make them easier to use?

You Bet
Haskell has do notation to take care of this pattern for us, since it occurs all over the place, not just parsers. First we must implement a type-class:
instance Monad Parser where
  (>>=) = bindParser
  return = value

Then?
zing!
personParser2 :: Parser Person
personParser2 = do age <- ageParser
                   spaces
                   firstName <- firstNameParser
                   spaces
                   surname <- surnameParser
                   spaces
                   gender <- genderParser
                   spaces
                   phone <- phoneParser
                   return (Person age firstName surname gender phone)

Conclusion
We have seen how to create a small parser library then use that library to create our own custom parsers. We did this by putting together parts to create more specialised parts. 1
This process is the essence of functional programming. It scales up to larger programs and demonstrates that functional programming is incredibly practical for solving real-world problems, much more so than traditional methods.
We observed a programming pattern called the monadic model and we exploited Haskell’s built-in support for it.
What other types of problems fit this model? The answer(s!) to this question run deep, but that’s for another day.

A. MyParser.hs
module MyParser where

import Data.Char
      
data Parser a = P { 
  parse :: String -> Maybe (String, a)
} 

value :: a -> Parser a
value a = P (\ s -> Just (s, a))

failed :: Parser a
failed = P (\ _ -> Nothing)

character :: Parser Char
character = P (\ s -> case s of [] -> Nothing
                               (c:r) -> Just (r, c))

(|||) :: Parser a -> Parser a -> Parser a
P p1 ||| P p2 = P (\ s -> case p1 s of v@(Just _) -> v
                                      Nothing -> p2 s)

mapParser :: Parser a -> (a -> b) -> Parser b
mapParser (P p) f = P (\ s -> case p s of Just (r, c) -> Just (r, f c)
                                         Nothing -> Nothing)

bindParser :: Parser a -> (a -> Parser b) -> Parser b
bindParser (P p) f = P (\ s -> case p s of Just (r, c) -> parse (f c) r
                                          Nothing -> Nothing)

(>>>) :: Parser a -> Parser b -> Parser b
p >>> q = bindParser p (\ _ -> q)

sequenceParser :: [Parser a] -> Parser [a]
sequenceParser [] = value []
sequenceParser (h:t) = bindParser h (\ a -> mapParser (sequenceParser t) (\ as -> a : as))

thisMany :: Int -> Parser a -> Parser [a]
thisMany n p = sequenceParser (replicate n p)

list :: Parser a -> Parser [a]
list k = many1 k ||| value []

many1 :: Parser a -> Parser [a]
many1 k = bindParser k (\ k’ -> mapParser (list k) (\ kk’ -> k’ : kk’))

satisfy :: (Char -> Bool) -> Parser Char
satisfy p = bindParser character (\ c -> if p c then value c else failed)

is :: Char -> Parser Char
is c = satisfy (== c)

digit :: Parser Char
digit = satisfy isDigit

natural :: Parser Int
natural = mapParser (list digit) read

space :: Parser Char
space = satisfy isSpace

spaces :: Parser String
spaces = many1 space

lower :: Parser Char
lower = satisfy isLower

upper :: Parser Char
upper = satisfy isUpper

alpha :: Parser Char
alpha = satisfy isAlpha

alphanum :: Parser Char
alphanum = satisfy isAlphaNum

data Person = Person { 
  age :: Int,
  firstName :: String,
  surname :: String,
  gender :: Char,
  phone :: String
}  deriving Show

ageParser :: Parser Int
ageParser = natural

firstNameParser :: Parser String
firstNameParser = bindParser upper (\ c -> mapParser (list lower) (\ cs -> c : cs))

surnameParser :: Parser String
surnameParser = bindParser upper (\ c -> bindParser (thisMany 5 lower) (\ cs -> mapParser (list lower) (\ t -> c : cs ++ t)))

genderParser :: Parser Char
genderParser = is ‘m’ ||| is ‘f’

phoneBodyParser :: Parser String
phoneBodyParser = list (digit ||| is ‘.’ ||| is ‘-’)

phoneParser :: Parser String
phoneParser = bindParser digit (\ d -> bindParser phoneBodyParser (\ z -> mapParser (is ‘#’) (\ _ -> d : z)))

personParser1 :: Parser Person
personParser1 = bindParser ageParser (\ age ->
                spaces >>>
                bindParser firstNameParser (\ firstName ->
                spaces >>>
                bindParser surnameParser (\ surname ->
                spaces >>>
                bindParser genderParser (\ gender ->
                spaces >>>
                bindParser phoneParser (\ phone ->
                value (Person age firstName surname gender phone))))))

instance Monad Parser where
  (>>=) = bindParser
  return = value

personParser2 :: Parser Person
personParser2 = do age <- ageParser
                   spaces
                   firstName <- firstNameParser
                   spaces
                   surname <- surnameParser
                   spaces
                   gender <- genderParser
                   spaces
                   phone <- phoneParser
                   return (Person age firstName surname gender phone)

B. MyParser.scala
package MyParser

import Character._

case class Parser[A](parse: List[Char] => Option[(List[Char], A)]) { 
  def |||(p2: => Parser[A]): Parser[A] = Parser(s => this parse s match { 
    case v@Some(_) => v
    case None => p2 parse s
  } )

  def >>>[B](q: => Parser[B]): Parser[B] = Parser.bindParser[A, B](this, _ => q)
} 

object Parser { 
  def value[A](a: A): Parser[A] = Parser(s => Some(s, a))

  def failed[A]: Parser[A] = Parser(s => None)

  def character: Parser[Char] = Parser[Char] { 
    case Nil => None
    case c::r => Some(r, c)
  } 

  def mapParser[A, B](p: Parser[A], f: A => B): Parser[B] = Parser(s => p parse s match { 
    case Some((r, c)) => Some(r, f(c))
    case None => None
  } )

  def bindParser[A, B](p: Parser[A], f: A => Parser[B]): Parser[B] = Parser(s => p parse s match { 
    case Some((r, c)) => f(c) parse r
    case None => None
  } )

  def sequenceParser[A](ps: List[Parser[A]]): Parser[List[A]] = ps match { 
    case Nil => value(Nil)
    case h::t => bindParser(h, (a: A) => mapParser(sequenceParser(t), (as: List[A]) => a :: as))
  } 

  def thisMany[A](n: Int, p: Parser[A]): Parser[List[A]] = sequenceParser(List.make(n, p))

  def list[A](k: Parser[A]): Parser[List[A]] = many1(k) ||| value(Nil)

  def many1[A](k: Parser[A]): Parser[List[A]] = bindParser(k, (kx: A) => mapParser(list(k), (kkx: List[A]) => kx :: kkx))

  def satisfy(p: Char => Boolean): Parser[Char] = bindParser(character, (c: Char) => if(p(c)) value(c) else failed)

  def is(c: Char): Parser[Char] = satisfy(_ == c)

  val digit: Parser[Char] = satisfy(isDigit(_))

  val natural: Parser[Int] = mapParser(list(digit), (_: List[Char]).mkString.toInt)

  val space: Parser[Char] = satisfy(isWhitespace(_))

  val spaces: Parser[List[Char]] = many1(space)

  val lower: Parser[Char] = satisfy(isLowerCase(_))

  val upper: Parser[Char] = satisfy(isUpperCase(_))

  val alpha: Parser[Char] = satisfy(isLetter(_))

  val alphaNum: Parser[Char] = satisfy(isLetterOrDigit(_))
} 

case class Person(age: Int, firstName: String, surname: String, gender: Char, phone: String)

object Person { 
  import Parser._

  val ageParser: Parser[Int] = natural

  val firstNameParser: Parser[String] = bindParser(upper, (c: Char) => mapParser(list(lower), (cs: List[Char]) => (c :: cs).mkString))

  val surnameParser: Parser[String] = bindParser(upper, (c: Char) => bindParser(thisMany(5, lower), (cs: List[Char]) => mapParser(list(lower), (t: List[Char]) => (c :: cs ::: t).mkString)))

  val genderParser: Parser[Char] = is(’m’) ||| is(’f’)

  val phoneBodyParser: Parser[String] = mapParser(list(digit ||| is(’.’) ||| is(’-’)), (_: List[Char]).mkString)

  val phoneParser: Parser[String] = bindParser(digit, (d: Char) => bindParser(phoneBodyParser, (z: String) => mapParser(is(’#’), (_: Char) => (d :: z.toList).mkString)))

  val personParser1: Parser[Person] = bindParser(ageParser, (age: Int) =>
                                      spaces >>>
                                      bindParser(firstNameParser, (firstName: String) =>
                                      spaces >>>
                                      bindParser(surnameParser, (surname: String) =>
                                      spaces >>>
                                      bindParser(genderParser, (gender: Char) =>
                                      spaces >>>
                                      bindParser(phoneParser, (phone: String) =>
                                      value(Person(age, firstName, surname, gender, phone)))))))

  implicit def PersonMonad[A](p: Parser[A]) = new { 
    def map[B](f: A => B) = mapParser(p, f)
    def flatMap[B](f: A => Parser[B]) = bindParser(p, f)
  } 

  val personParser2: Parser[Person] = for(age <- ageParser;
                                          _ <- spaces;
                                          firstName <- firstNameParser;
                                          _ <- spaces;
                                          surname <- surnameParser;
                                          _ <- spaces;
                                          gender <- genderParser;
                                          _ <- spaces;
                                          phone <- phoneParser)
                                      yield Person(age, firstName, surname, gender, phone)
} 

C. MyParser.java
package MyParser;

import fj.P2;
import fj.F;
import fj.P1;
import static fj.pre.Equal.charEqual;
import static fj.P.p;
import fj.data.Option;
import fj.data.List;
import static fj.data.Validation.parseInt;
import static fj.data.List.asString;
import static fj.data.List.fromString;
import static fj.data.Option.some;
import static fj.data.Option.none;

import static java.lang.Character.*;
import static MyParser.Parser.*;

abstract class Parser<A> { 
  abstract Option<P2<List<Character>, A>> parse(List<Character> s);

  Parser<A> or(final P1<Parser<A>> p2) { 
    return new Parser<A>() { 
      Option<P2<List<Character>, A>> parse(final List<Character> s) { 
        final Option<P2<List<Character>, A>> v = Parser.this.parse(s);
        return v.isSome()
            ? v
            : p2._1().parse(s);
      } 
    } ;
  } 

  <B> Parser<B> anonymousBind(final P1<Parser<B>> q) { 
    return bindParser(this, new F<A, Parser<B>>() { 
      public Parser<B> f(final A _) { 
        return q._1();
      } 
    } );
  } 

  static <A> Parser<A> value(final A a) { 
    return new Parser<A>() { 
      Option<P2<List<Character>, A>> parse(final List<Character> s) { 
        return some(p(s, a));
      } 
    } ;
  } 

  static <A> Parser<A> failed() { 
    return new Parser<A>() { 
      Option<P2<List<Character>, A>> parse(final List<Character> s) { 
        return none();
      } 
    } ;
  } 

  static Parser<Character> character() { 
    return new Parser<Character>() { 
      Option<P2<List<Character>, Character>> parse(final List<Character> s) { 
        return s.isEmpty()
            ? Option.<P2<List<Character>, Character>>none()
            : some(p(s.tail(), s.head()));
      } 
    } ;
  } 

  static <A, B> Parser<B> mapParser(final Parser<A> p, final F<A, B> f) { 
    return new Parser<B>() { 
      Option<P2<List<Character>, B>> parse(final List<Character> s) { 
        return p.parse(s).map(new F<P2<List<Character>, A>, P2<List<Character>, B>>() { 
          public P2<List<Character>, B> f(final P2<List<Character>, A> rc) { 
            return rc.map2(f);
          } 
        } );
      } 
    } ;
  } 

  static <A, B> Parser<B> bindParser(final Parser<A> p, final F<A, Parser<B>> f) { 
    return new Parser<B>() { 
      Option<P2<List<Character>, B>> parse(final List<Character> s) { 
        return p.parse(s).bind(new F<P2<List<Character>, A>, Option<P2<List<Character>, B>>>() { 
          public Option<P2<List<Character>, B>> f(final P2<List<Character>, A> rc) { 
            return f.f(rc._2()).parse(rc._1());
          } 
        } );
      } 
    } ;
  } 

  static <A> Parser<List<A>> sequenceParser(final List<Parser<A>> ps) { 
    return ps.isEmpty()
        ? value(List.<A>nil())
        : bindParser(ps.head(), new F<A, Parser<List<A>>>() { 
      public Parser<List<A>> f(final A a) { 
        return mapParser(sequenceParser(ps.tail()), List.<A>cons().f(a));
      } 
    } );
  } 

  static <A> Parser<List<A>> thisMany(final int n, final Parser<A> p) { 
    return sequenceParser(List.replicate(n, p));
  } 

  static <A> Parser<List<A>> list(final Parser<A> k) { 
    return many1(k).or(new P1<Parser<List<A>>>() { 
      public Parser<List<A>> _1() { 
        return value(List.<A>nil());
      } 
    } );
  } 

  static <A> Parser<List<A>> many1(final Parser<A> k) { 
    return bindParser(k, new F<A, Parser<List<A>>>() { 
      public Parser<List<A>> f(final A kx) { 
        return mapParser(list(k), List.<A>cons().f(kx));
      } 
    } );
  } 

  static Parser<Character> satisfy(final F<Character, Boolean> p) { 
    return bindParser(character(), new F<Character, Parser<Character>>() { 
      public Parser<Character> f(final Character c) { 
        return p.f(c) ? value(c) : Parser.<Character>failed();
      } 
    } );
  } 

  static Parser<Character> is(final char c) { 
    return satisfy(charEqual.eq(c));
  } 

  final static Parser<Character> digit = satisfy(new F<Character, Boolean>() { 
    public Boolean f(final Character z) { 
      return isDigit(z);
    } 
  } );

  final static Parser<Integer> natural = mapParser(list(digit), new F<List<Character>, Integer>() { 
    public Integer f(final List<Character> z) { 
      return parseInt(asString(z)).success();
    } 
  } );

  final static Parser<Character> space = satisfy(new F<Character, Boolean>() { 
    public Boolean f(final Character z) { 
      return isWhitespace(z);
    } 
  } );

  final static Parser<List<Character>> spaces = many1(space);

  final static Parser<Character> lower = satisfy(new F<Character, Boolean>() { 
    public Boolean f(final Character z) { 
      return isLowerCase(z);
    } 
  } );

  final static Parser<Character> upper = satisfy(new F<Character, Boolean>() { 
    public Boolean f(final Character z) { 
      return isUpperCase(z);
    } 
  } );

  final static Parser<Character> alpha = satisfy(new F<Character, Boolean>() { 
    public Boolean f(final Character z) { 
      return isLetter(z);
    } 
  } );

  final static Parser<Character> alphaNum = satisfy(new F<Character, Boolean>() { 
    public Boolean f(final Character z) { 
      return isLetterOrDigit(z);
    } 
  } );
} 

class Person { 
  final int age;
  final String firstName;
  final String surname;
  final char gender;
  final String phone;

  Person(final int age, final String firstName, final String surname, final char gender, final String phone) { 
    this.age = age;
    this.firstName = firstName;
    this.surname = surname;
    this.gender = gender;
    this.phone = phone;
  } 

  final static Parser<Integer> ageParser = natural;

  final static Parser<String> firstNameParser = bindParser(upper, new F<Character, Parser<String>>() { 
    public Parser<String> f(final Character c) { 
      return mapParser(list(lower), new F<List<Character>, String>() { 
        public String f(final List<Character> cs) { 
          return asString(cs.cons(c));
        } 
      } );
    } 
  } );

  final static Parser<String> surnameParser = bindParser(upper, new F<Character, Parser<String>>() { 
    public Parser<String> f(final Character c) { 
      return bindParser(thisMany(5, lower), new F<List<Character>, Parser<String>>() { 
        public Parser<String> f(final List<Character> cs) { 
          return mapParser(list(lower), new F<List<Character>, String>() { 
            public String f(final List<Character> t) { 
              return asString(cs.cons(c).append(t));
            } 
          } );
        } 
      } );
    } 
  } );

  final static Parser<Character> genderParser = is(’m’).or(new P1<Parser<Character>>() { 
    public Parser<Character> _1() { 
      return is(’f’);
    } 
  } );

  final static Parser<String> phoneBodyParser = mapParser(list(digit.or(new P1<Parser<Character>>() { 
    public Parser<Character> _1() { 
      return is(’.’);
    } 
  } ).or(new P1<Parser<Character>>() { 
    public Parser<Character> _1() { 
      return is(’-’);
    } 
  } )), new F<List<Character>, String>() { 
    public String f(final List<Character> z) { 
      return asString(z);
    } 
  } );

  final static Parser<String> phoneParser = bindParser(digit, new F<Character, Parser<String>>() { 
    public Parser<String> f(final Character d) { 
      return bindParser(phoneBodyParser, new F<String, Parser<String>>() { 
        public Parser<String> f(final String z) { 
          return mapParser(is(’#’), new F<Character, String>() { 
            public String f(final Character _) { 
              return asString(fromString(z).cons(d));
            } 
          } );
        } 
      } );
    } 
  } );

  final static Parser<Person> personParser1 = bindParser(ageParser, new F<Integer, Parser<Person>>() { 
    public Parser<Person> f(final Integer age) { 
      return spaces.anonymousBind(new P1<Parser<Person>>() { 
        public Parser<Person> _1() { 
          return bindParser(firstNameParser, new F<String, Parser<Person>>() { 
            public Parser<Person> f(final String firstName) { 
              return spaces.anonymousBind(new P1<Parser<Person>>() { 
                public Parser<Person> _1() { 
                  return bindParser(surnameParser, new F<String, Parser<Person>>() { 
                    public Parser<Person> f(final String surname) { 
                      return spaces.anonymousBind(new P1<Parser<Person>>() { 
                        public Parser<Person> _1() { 
                          return bindParser(genderParser, new F<Character, Parser<Person>>() { 
                            public Parser<Person> f(final Character gender) { 
                              return spaces.anonymousBind(new P1<Parser<Person>>() { 
                                public Parser<Person> _1() { 
                                  return bindParser(phoneParser, new F<String, Parser<Person>>() { 
                                    public Parser<Person> f(final String phone) { 
                                      return value(new Person(age, firstName, surname, gender, phone));
                                    } 
                                  } );
                                } 
                              } );
                            } 
                          } );
                        } 
                      } );
                    } 
                  } );
                } 
              } );
            } 
          } );
        } 
      } );
    } 
  } );
} 

D. Licence
This presentation is released under a Creative Commons - Attribution, Non-Commercial, No Derivatives Works licence.
THE WORK (AS DEFINED BELOW) IS PROVIDED UNDER THE TERMS OF THIS CREATIVE COMMONS PUBLIC LICENCE (”CCPL” OR “LICENCE”). THE WORK IS PROTECTED BY COPYRIGHT AND/OR OTHER APPLICABLE LAW. ANY USE OF THE WORK OTHER THAN AS AUTHORISED UNDER THIS LICENCE AND/OR APPLICABLE LAW IS PROHIBITED.

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   8. “Licence Elements” means the following high-level licence attributes as selected by Licensor and indicated in the title of this Licence: Attribution, NonCommercial, NoDerivatives, ShareAlike.

2. Fair Dealing and Other Rights. Nothing in this Licence excludes or modifies, or is intended to exclude or modify, (including by reducing, limiting, or restricting) the rights of You or others to use the Work arising from fair dealings or other limitations on the rights of the copyright owner or the Original Author under copyright law, moral rights law or other applicable laws.

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The above rights may be exercised in all media and formats whether now known or hereafter devised. The above rights include the right to make such modifications as are technically necessary to exercise the rights in other media and formats, but otherwise you have no rights to make Derivative Works. All rights not expressly granted by Licensor under this Licence are hereby reserved, including but not limited to the rights set forth in Sections 4(d) and 4(e).

4. Restrictions. The licence granted in Section 3 above is expressly made subject to and limited by the following restrictions:

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   2. in the case of services:
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         2. the payment of the cost of having the services supplied again.

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8. Miscellaneous.

   1. Each time You publish, communicate to the public, distribute or publicly digitally perform the Work or a Collective Work, the Licensor offers to the recipient a licence to the Work on the same terms and conditions as the licence granted to You under this Licence.
   2. If any provision of this Licence is invalid or unenforceable under applicable law, it shall not affect the validity or enforceability of the remainder of the terms of this Licence, and without further action by the parties to this agreement, such provision shall be reformed to the minimum extent necessary to make such provision valid and enforceable.
   3. No term or provision of this Licence shall be deemed waived and no breach consented to unless such waiver or consent shall be in writing and signed by the party to be charged with such waiver or consent.
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