--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Fahad/Scala/POSIX.sc Sun Oct 26 11:17:40 2014 +0000
@@ -0,0 +1,254 @@
+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 prog0 = """read n""" //> prog0 : String = read n
+ //env(lexing_simp(WHILE_REGS, prog0))
+
+ println("Next test") //> Next test
+}
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