package greeter
object POSIX {
println("Posix Algorithm") //> Posix Algorithm
abstract class Rexp
case object NULL extends Rexp
case object EMPTY extends Rexp
case class CHAR(c: Char) extends Rexp
case class ALT(r1: Rexp, r2: Rexp) extends Rexp
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
case class STAR(r: Rexp) extends Rexp
case class RECD(x: String, r: Rexp) extends Rexp
abstract class Val
case object Void extends Val
case class Chr(c: Char) extends Val
case class Sequ(v1: Val, v2: Val) extends Val
case class Left(v: Val) extends Val
case class Right(v: Val) extends Val
case class Stars(vs: List[Val]) extends Val
case class Rec(x: String, v: Val) extends Val
def charlist2rexp(s: List[Char]): Rexp = s match {
case Nil => EMPTY
case c :: Nil => CHAR(c)
case c :: s => SEQ(CHAR(c), charlist2rexp(s))
} //> charlist2rexp: (s: List[Char])greeter.POSIX.Rexp
implicit def string2rexp(s: String): Rexp = charlist2rexp(s.toList)
//> string2rexp: (s: String)greeter.POSIX.Rexp
implicit def RexpOps(r: Rexp) = new {
def |(s: Rexp) = ALT(r, s)
def % = STAR(r)
def ~(s: Rexp) = SEQ(r, s)
} //> RexpOps: (r: greeter.POSIX.Rexp)AnyRef{def |(s: greeter.POSIX.Rexp): greete
//| r.POSIX.ALT; def %: greeter.POSIX.STAR; def ~(s: greeter.POSIX.Rexp): greet
//| er.POSIX.SEQ}
implicit def stringOps(s: String) = new {
def |(r: Rexp) = ALT(s, r)
def |(r: String) = ALT(s, r)
def % = STAR(s)
def ~(r: Rexp) = SEQ(s, r)
def ~(r: String) = SEQ(s, r)
def $(r: Rexp) = RECD(s, r)
} //> stringOps: (s: String)AnyRef{def |(r: greeter.POSIX.Rexp): greeter.POSIX.AL
//| T; def |(r: String): greeter.POSIX.ALT; def %: greeter.POSIX.STAR; def ~(r:
//| greeter.POSIX.Rexp): greeter.POSIX.SEQ; def ~(r: String): greeter.POSIX.SE
//| Q; def $(r: greeter.POSIX.Rexp): greeter.POSIX.RECD}
// size of a regular expressions - for testing purposes
def size(r: Rexp): Int = r match {
case NULL => 1
case EMPTY => 1
case CHAR(_) => 1
case ALT(r1, r2) => 1 + size(r1) + size(r2)
case SEQ(r1, r2) => 1 + size(r1) + size(r2)
case STAR(r) => 1 + size(r)
case RECD(_, r) => 1 + size(r)
} //> size: (r: greeter.POSIX.Rexp)Int
// nullable function: tests whether the regular
// expression can recognise the empty string
def nullable(r: Rexp): Boolean = r match {
case NULL => false
case EMPTY => true
case CHAR(_) => false
case ALT(r1, r2) => nullable(r1) || nullable(r2)
case SEQ(r1, r2) => nullable(r1) && nullable(r2)
case STAR(_) => true
case RECD(_, r1) => nullable(r1)
} //> nullable: (r: greeter.POSIX.Rexp)Boolean
// derivative of a regular expression w.r.t. a character
def der(c: Char, r: Rexp): Rexp = r match {
case NULL => NULL
case EMPTY => NULL
case CHAR(d) => if (c == d) EMPTY else NULL
case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
case SEQ(r1, r2) =>
if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
else SEQ(der(c, r1), r2)
case STAR(r) => SEQ(der(c, r), STAR(r))
case RECD(_, r1) => der(c, r1)
} //> der: (c: Char, r: greeter.POSIX.Rexp)greeter.POSIX.Rexp
// derivative w.r.t. a string (iterates der)
def ders(s: List[Char], r: Rexp): Rexp = s match {
case Nil => r
case c :: s => ders(s, der(c, r))
} //> ders: (s: List[Char], r: greeter.POSIX.Rexp)greeter.POSIX.Rexp
// extracts a string from value
def flatten(v: Val): String = v match {
case Void => ""
case Chr(c) => c.toString
case Left(v) => flatten(v)
case Right(v) => flatten(v)
case Sequ(v1, v2) => flatten(v1) + flatten(v2)
case Stars(vs) => vs.map(flatten).mkString
case Rec(_, v) => flatten(v)
} //> flatten: (v: greeter.POSIX.Val)String
// extracts an environment from a value
def env(v: Val): List[(String, String)] = v match {
case Void => Nil
case Chr(c) => Nil
case Left(v) => env(v)
case Right(v) => env(v)
case Sequ(v1, v2) => env(v1) ::: env(v2)
case Stars(vs) => vs.flatMap(env)
case Rec(x, v) => (x, flatten(v)) :: env(v)
} //> env: (v: greeter.POSIX.Val)List[(String, String)]
def mkeps(r: Rexp): Val = r match {
case EMPTY => Void
case ALT(r1, r2) =>
if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
case STAR(r) => Stars(Nil)
case RECD(x, r) => Rec(x, mkeps(r))
} //> mkeps: (r: greeter.POSIX.Rexp)greeter.POSIX.Val
def inj(r: Rexp, c: Char, v: Val): Val = (r, v) match {
case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1) :: vs)
case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
case (CHAR(d), Void) => Chr(d)
case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
} //> inj: (r: greeter.POSIX.Rexp, c: Char, v: greeter.POSIX.Val)greeter.POSIX.Va
//| l
// main lexing function (produces a value)
def lex(r: Rexp, s: List[Char]): Val = s match {
case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
case c :: cs => inj(r, c, lex(der(c, r), cs))
} //> lex: (r: greeter.POSIX.Rexp, s: List[Char])greeter.POSIX.Val
def lexing(r: Rexp, s: String): Val = lex(r, s.toList)
//> lexing: (r: greeter.POSIX.Rexp, s: String)greeter.POSIX.Val
val r = (("1" $ "a") | (("2" $ "b") | ("3" $ "ab"))).%
//> r : greeter.POSIX.STAR = STAR(ALT(RECD(1,CHAR(a)),ALT(RECD(2,CHAR(b)),RECD
//| (3,SEQ(CHAR(a),CHAR(b))))))
env(lexing(r, "ba")) //> res0: List[(String, String)] = List((2,b), (1,a))
val r1 = "a" | "b" //> r1 : greeter.POSIX.ALT = ALT(CHAR(a),CHAR(b))
lexing(r1, "a") //> res1: greeter.POSIX.Val = Left(Chr(a))
// Lexing Rules for a Small While Language
def PLUS(r: Rexp) = r ~ r.% //> PLUS: (r: greeter.POSIX.Rexp)greeter.POSIX.SEQ
val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"
//> SYM : greeter.POSIX.ALT = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(
//| ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(a),CHAR(b)),CHAR(c
//| )),CHAR(d)),CHAR(e)),CHAR(f)),CHAR(g)),CHAR(h)),CHAR(i)),CHAR(j)),CHAR(k)),
//| CHAR(l)),CHAR(m)),CHAR(n)),CHAR(o)),CHAR(p)),CHAR(q)),CHAR(r)),CHAR(s)),CHA
//| R(t)),CHAR(u)),CHAR(v)),CHAR(w)),CHAR(x)),CHAR(y)),CHAR(z))
val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
//> DIGIT : greeter.POSIX.ALT = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),CH
//| AR(1)),CHAR(2)),CHAR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHAR(
//| 9))
val ID = SYM ~ (SYM | DIGIT).% //> ID : greeter.POSIX.SEQ = SEQ(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(A
//| LT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(a),CHAR(b)),CHA
//| R(c)),CHAR(d)),CHAR(e)),CHAR(f)),CHAR(g)),CHAR(h)),CHAR(i)),CHAR(j)),CHAR(k
//| )),CHAR(l)),CHAR(m)),CHAR(n)),CHAR(o)),CHAR(p)),CHAR(q)),CHAR(r)),CHAR(s)),
//| CHAR(t)),CHAR(u)),CHAR(v)),CHAR(w)),CHAR(x)),CHAR(y)),CHAR(z)),STAR(ALT(ALT
//| (ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(AL
//| T(ALT(ALT(ALT(ALT(ALT(CHAR(a),CHAR(b)),CHAR(c)),CHAR(d)),CHAR(e)),CHAR(f)),
//| CHAR(g)),CHAR(h)),CHAR(i)),CHAR(j)),CHAR(k)),CHAR(l)),CHAR(m)),CHAR(n)),CHA
//| R(o)),CHAR(p)),CHAR(q)),CHAR(r)),CHAR(s)),CHAR(t)),CHAR(u)),CHAR(v)),CHAR(w
//| )),CHAR(x)),CHAR(y)),CHAR(z)),ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),C
//| HAR(1)),CHAR(2)),CHAR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHAR
//| (9)))))
val NUM = PLUS(DIGIT) //> NUM : greeter.POSIX.SEQ = SEQ(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),
//| CHAR(1)),CHAR(2)),CHAR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHA
//| R(9)),STAR(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(CHAR(0),CHAR(1)),CHAR(2)),CH
//| AR(3)),CHAR(4)),CHAR(5)),CHAR(6)),CHAR(7)),CHAR(8)),CHAR(9))))
val KEYWORD: Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
//> KEYWORD : greeter.POSIX.Rexp = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(SEQ(CHA
//| R(s),SEQ(CHAR(k),SEQ(CHAR(i),CHAR(p)))),SEQ(CHAR(w),SEQ(CHAR(h),SEQ(CHAR(i)
//| ,SEQ(CHAR(l),CHAR(e)))))),SEQ(CHAR(d),CHAR(o))),SEQ(CHAR(i),CHAR(f))),SEQ(C
//| HAR(t),SEQ(CHAR(h),SEQ(CHAR(e),CHAR(n))))),SEQ(CHAR(e),SEQ(CHAR(l),SEQ(CHAR
//| (s),CHAR(e))))),SEQ(CHAR(r),SEQ(CHAR(e),SEQ(CHAR(a),CHAR(d))))),SEQ(CHAR(w)
//| ,SEQ(CHAR(r),SEQ(CHAR(i),SEQ(CHAR(t),CHAR(e)))))),SEQ(CHAR(t),SEQ(CHAR(r),S
//| EQ(CHAR(u),CHAR(e))))),SEQ(CHAR(f),SEQ(CHAR(a),SEQ(CHAR(l),SEQ(CHAR(s),CHAR
//| (e))))))
val SEMI: Rexp = ";" //> SEMI : greeter.POSIX.Rexp = CHAR(;)
val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
//> OP : greeter.POSIX.Rexp = ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(SEQ(
//| CHAR(:),CHAR(=)),SEQ(CHAR(=),CHAR(=))),CHAR(-)),CHAR(+)),CHAR(*)),SEQ(CHAR(
//| !),CHAR(=))),CHAR(<)),CHAR(>)),SEQ(CHAR(<),CHAR(=))),SEQ(CHAR(>),CHAR(=))),
//| CHAR(%)),CHAR(/))
val WHITESPACE = PLUS(" " | "\n" | "\t") //> WHITESPACE : greeter.POSIX.SEQ = SEQ(ALT(ALT(CHAR( ),CHAR(
//| )),CHAR( )),STAR(ALT(ALT(CHAR( ),CHAR(
//| )),CHAR( ))))
val RPAREN: Rexp = ")" //> RPAREN : greeter.POSIX.Rexp = CHAR())
val LPAREN: Rexp = "(" //> LPAREN : greeter.POSIX.Rexp = CHAR(()
val BEGIN: Rexp = "{" //> BEGIN : greeter.POSIX.Rexp = CHAR({)
val END: Rexp = "}" //> END : greeter.POSIX.Rexp = CHAR(})
/*
* val WHILE_REGS = (("k" $ KEYWORD) |
("i" $ ID) |
("o" $ OP) |
("n" $ NUM) |
("s" $ SEMI) |
("p" $ (LPAREN | RPAREN)) |
("b" $ (BEGIN | END)) |
("w" $ WHITESPACE)).%
*/
val WHILE_REGS = (KEYWORD |
ID |
OP |
NUM |
SEMI |
LPAREN | RPAREN |
BEGIN | END |
WHITESPACE).% //> WHILE_REGS : greeter.POSIX.STAR = STAR(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT
//| (ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(SEQ(CHAR(s),SEQ(CHAR(k),SEQ(CHAR(i),CH
//| AR(p)))),SEQ(CHAR(w),SEQ(CHAR(h),SEQ(CHAR(i),SEQ(CHAR(l),CHAR(e)))))),SEQ(C
//| HAR(d),CHAR(o))),SEQ(CHAR(i),CHAR(f))),SEQ(CHAR(t),SEQ(CHAR(h),SEQ(CHAR(e),
//| CHAR(n))))),SEQ(CHAR(e),SEQ(CHAR(l),SEQ(CHAR(s),CHAR(e))))),SEQ(CHAR(r),SEQ
//| (CHAR(e),SEQ(CHAR(a),CHAR(d))))),SEQ(CHAR(w),SEQ(CHAR(r),SEQ(CHAR(i),SEQ(CH
//| AR(t),CHAR(e)))))),SEQ(CHAR(t),SEQ(CHAR(r),SEQ(CHAR(u),CHAR(e))))),SEQ(CHAR
//| (f),SEQ(CHAR(a),SEQ(CHAR(l),SEQ(CHAR(s),CHAR(e)))))),SEQ(ALT(ALT(ALT(ALT(AL
//| T(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(ALT(A
//| LT(ALT(CHAR(a),CHAR(b)),CHAR(c)),CHAR(d)),CHAR(e)),CHAR(f)),CHAR(g)),CHAR(h
//| )),CHAR(i)),CHAR(j)),CHAR(k)),CHAR(l)),CHAR(m)),CHAR(n)),CHAR(o)),CHAR(p)),
//| CHAR(q)),CHAR(r)),CHAR(s)),CHAR(t)),CHAR(u)),CHAR(v)),CHAR(w)),CHAR(x)),CHA
//| R(y)),CHAR(z)),STAR(ALT
//| Output exceeds cutoff limit.
// Some Tests
//============
def time[T](code: => T) = {
val start = System.nanoTime()
val result = code
val end = System.nanoTime()
println((end - start) / 1.0e9)
result
} //> time: [T](code: => T)T
val abc = List('a', 'b', 'c') //> abc : List[Char] = List(a, b, c)
val nullRexp = null //> nullRexp : Null = null
val myRexp = charlist2rexp(abc) //> myRexp : greeter.POSIX.Rexp = SEQ(CHAR(a),SEQ(CHAR(b),CHAR(c)))
val myRexp2 = string2rexp("FahadAusaf") //> myRexp2 : greeter.POSIX.Rexp = SEQ(CHAR(F),SEQ(CHAR(a),SEQ(CHAR(h),SEQ(CHA
//| R(a),SEQ(CHAR(d),SEQ(CHAR(A),SEQ(CHAR(u),SEQ(CHAR(s),SEQ(CHAR(a),CHAR(f))))
//| ))))))
RexpOps(myRexp2) //> res2: AnyRef{def |(s: greeter.POSIX.Rexp): greeter.POSIX.ALT; def %: greete
//| r.POSIX.STAR; def ~(s: greeter.POSIX.Rexp): greeter.POSIX.SEQ} = greeter.PO
//| SIX$$anonfun$main$1$$anon$1@37ecb28e
stringOps("Fahad") //> res3: AnyRef{def |(r: greeter.POSIX.Rexp): greeter.POSIX.ALT; def |(r: Stri
//| ng): greeter.POSIX.ALT; def %: greeter.POSIX.STAR; def ~(r: greeter.POSIX.R
//| exp): greeter.POSIX.SEQ; def ~(r: String): greeter.POSIX.SEQ; def $(r: gree
//| ter.POSIX.Rexp): greeter.POSIX.RECD} = greeter.POSIX$$anonfun$main$1$$anon$
//| 2@14bea551
size(myRexp2) //> res4: Int = 19
nullable(nullRexp) //> scala.MatchError: null
//| at greeter.POSIX$$anonfun$main$1.nullable$1(greeter.POSIX.scala:59)
//| at greeter.POSIX$$anonfun$main$1.apply$mcV$sp(greeter.POSIX.scala:202)
//| at org.scalaide.worksheet.runtime.library.WorksheetSupport$$anonfun$$exe
//| cute$1.apply$mcV$sp(WorksheetSupport.scala:76)
//| at org.scalaide.worksheet.runtime.library.WorksheetSupport$.redirected(W
//| orksheetSupport.scala:65)
//| at org.scalaide.worksheet.runtime.library.WorksheetSupport$.$execute(Wor
//| ksheetSupport.scala:75)
//| at greeter.POSIX$.main(greeter.POSIX.scala:3)
//| at greeter.POSIX.main(greeter.POSIX.scala)
val newRexp = der('a',myRexp)
//this is some crap
}