--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/exps/token1.scala Wed Jan 30 12:28:44 2019 +0000
@@ -0,0 +1,598 @@
+
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec
+
+def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
+ case Nil => Nil
+ case (x::xs) => {
+ val res = f(x)
+ if (acc.contains(res)) distinctBy(xs, f, acc)
+ else x::distinctBy(xs, f, res::acc)
+ }
+}
+
+abstract class Bit
+case object Z extends Bit
+case object S extends Bit
+case class C(c: Char) extends Bit
+
+
+type Bits = List[Bit]
+
+abstract class Action
+case object ST extends Action
+case object NST extends Action
+case object AL extends Action
+
+abstract class PartialValue
+case object Plhdr extends PartialValue
+case object STS extends PartialValue
+case object ENDSTS extends PartialValue
+case class Ch(c: Char) extends PartialValue
+case object Empt extends PartialValue
+case object Seque extends PartialValue
+case class Posi(i: Int) extends PartialValue
+case class RECRD(x: String) extends PartialValue
+case object ALTSTART extends PartialValue
+case object ALTEND extends PartialValue
+case object RIG extends PartialValue
+case object LEF extends PartialValue
+
+abstract class Rexp
+case object ZERO extends Rexp
+case object ONE extends Rexp
+case class PRED(f: Char => Boolean) extends Rexp
+case class ALTS(rs: List[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
+
+// abbreviations
+def CHAR(c: Char) = PRED(_ == c)
+def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))
+def PLUS(r: Rexp) = SEQ(r, STAR(r))
+
+abstract class ARexp
+case object AZERO extends ARexp
+case class AONE(bs: Bits) extends ARexp
+case class APRED(bs: Bits, f: Char => Boolean) extends ARexp
+case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp
+case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp
+case class ASTAR(bs: Bits, r: ARexp) extends ARexp
+
+
+def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
+
+abstract class Val
+case object Empty 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
+case class Pos(i: Int, v: Val) extends Val
+case object Prd extends Val
+
+// some convenience for typing in regular expressions
+def charlist2rexp(s : List[Char]): Rexp = s match {
+ case Nil => ONE
+ case c::Nil => CHAR(c)
+ case c::s => SEQ(CHAR(c), charlist2rexp(s))
+}
+implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
+
+implicit def RexpOps(r: Rexp) = new {
+ def | (s: Rexp) = ALT(r, s)
+ def % = STAR(r)
+ def ~ (s: Rexp) = SEQ(r, s)
+}
+
+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)
+}
+
+// translation into ARexps
+def fuse(bs: Bits, r: ARexp) : ARexp = r match {
+ case AZERO => AZERO
+ case AONE(cs) => AONE(bs ++ cs)
+ case APRED(cs, f) => APRED(bs ++ cs, f)
+ case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
+ case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
+ case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
+}
+
+def internalise(r: Rexp) : ARexp = r match {
+ case ZERO => AZERO
+ case ONE => AONE(Nil)
+ case PRED(f) => APRED(Nil, f)
+ case ALTS(List(r1, r2)) =>
+ AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
+ case ALTS(r1::rs) => {
+ val AALTS(Nil, rs2) = internalise(ALTS(rs))
+ AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
+ }
+ case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
+ case STAR(r) => ASTAR(Nil, internalise(r))
+ case RECD(x, r) => internalise(r)
+}
+
+internalise(("a" | "ab") ~ ("b" | ""))
+val action_stack = scala.collection.mutable.ArrayBuffer.empty[Action]
+val next_stack = scala.collection.mutable.ArrayBuffer.empty[Int]
+val regx_stack = scala.collection.mutable.ArrayBuffer.empty[Rexp]
+val pv_stack = scala.collection.mutable.ArrayBuffer.empty[PartialValue]
+var top = 0
+//st is the global var stack, made with a linked list?
+@tailrec
+def decode_stack(sp: Int, bs: Bits): Unit = {
+if(action_stack.isEmpty){
+ return
+}
+val action = action_stack.last
+action_stack.trimEnd(1)
+val r = regx_stack.last
+regx_stack.trimEnd(1)
+if(action == ST)//we have the rest of the star to finish(ST -> STAR)
+{
+ bs match {
+ case Z::bs => {//pv -> partial value Each grid in a stack does not hold a whole value but a partial one.
+ pv_stack(sp) = ENDSTS
+ if(next_stack.isEmpty)
+ return
+ val n = next_stack.last
+ next_stack.trimEnd(1)
+ decode_stack(n, bs)
+ }
+ case S::bs => {
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 1
+ }
+ next_stack += (sp + 1)
+ regx_stack += r
+ action_stack += ST
+ pv_stack.insert(sp + 1, Plhdr)
+ action_stack += NST
+ regx_stack += r
+ decode_stack(sp, bs)
+ }
+ case _ => println("Sequence not decodable")
+ }
+
+}
+else if(action == NST){
+ (r, bs) match{
+ case (ONE, bs) => {
+ pv_stack(sp) = Empt
+ if(next_stack.isEmpty)
+ return
+ val n = next_stack.last
+ next_stack.trimEnd(1)
+ decode_stack(n, bs)
+ }
+ case (PRED(f), C(c)::bs) => {
+ pv_stack(sp) = Ch(c)
+ if(next_stack.isEmpty)
+ return
+ val n = next_stack.last
+ next_stack.trimEnd(1)
+ decode_stack(n, bs)
+ }
+ case (ALTS(rs), Z::bs1) => {
+ pv_stack(sp) = ALTSTART
+ pv_stack.insert(sp + 1, LEF)
+ pv_stack.insert(sp + 2, Plhdr)
+ pv_stack.insert(sp + 3, ALTEND)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 3
+ }
+ regx_stack += rs.head
+ action_stack += NST
+ decode_stack(sp + 2, bs1)
+ }
+ case (ALTS(rs), S::bs1) => {
+ pv_stack(sp) = ALTSTART
+ pv_stack.insert(sp + 1, RIG)
+ pv_stack.insert(sp + 2, Plhdr)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 2
+ }
+ regx_stack += ALTS(rs.tail)
+ action_stack += AL
+ decode_stack(sp + 2, bs1)
+ }
+ /*
+ val le = rs.length
+ val det = bs.take(le - 1)
+ val chosen = det.indexWhere(_ == Z)
+ action_stack += NST
+ pv_stack.insert(sp + 1, Plhdr)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 1
+ }
+ if(chosen == -1){
+ pv_stack(sp) = Posi(le)
+ regx_stack += rs(le - 1)
+ decode_stack(sp + 1, bs.drop(le - 1))
+ }
+ else{
+ pv_stack(sp) = Posi(chosen + 1)
+ regx_stack += rs(chosen)
+ decode_stack(sp + 1, bs.drop(chosen + 1))
+ }*/
+ case (SEQ(r1, r2), bs) => {
+ action_stack += NST
+ action_stack += NST
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 2
+ }
+ next_stack += (sp + 2)
+ regx_stack += r2
+ regx_stack += r1
+ pv_stack.insert(sp + 1, Plhdr)
+ pv_stack.insert(sp + 2, Plhdr)
+ pv_stack(sp) = Seque
+ decode_stack(sp + 1, bs)
+ }
+ case (STAR(r1), S::bs) => {
+ action_stack += ST
+ regx_stack += r1
+ action_stack += NST
+ regx_stack += r1
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 2
+ }
+ next_stack += sp + 2
+ pv_stack(sp) = STS
+ pv_stack.insert(sp + 1, Plhdr)
+ pv_stack.insert(sp + 1, Plhdr)
+ decode_stack(sp + 1, bs)
+ }
+ case (STAR(_), Z::bs) => {
+ pv_stack(sp) = STS
+ pv_stack.insert(sp + 1, ENDSTS)
+ if(next_stack.isEmpty)
+ return
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 1
+ }
+ val n = next_stack.last
+ next_stack.trimEnd(1)
+ decode_stack(n, bs)
+ }
+ case (RECD(x, r1), bs) => {
+ pv_stack(sp) = RECRD(x)
+ pv_stack.insert(sp + 1, Plhdr)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 1
+ }
+ action_stack += NST
+ regx_stack += r1
+ decode_stack(sp + 1, bs)
+ }//shouldn't go beyond this point
+ case (_, _) => println("Error with NST")
+ }
+}
+else{//action is AL
+ r match {
+ case (ALTS(r1::Nil)) => {
+ pv_stack.insert(sp + 1, ALTEND)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 1
+ }
+ action_stack += NST
+ regx_stack += r1
+ decode_stack(sp, bs)
+ }
+ case (ALTS(rs)) => {
+ bs match {
+ case (Z::bs1) => {
+ pv_stack(sp) = LEF
+ pv_stack.insert(sp + 1, ALTEND)
+ pv_stack.insert(sp + 1, Plhdr)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 2
+ }
+ regx_stack += rs.head
+ action_stack += NST
+ decode_stack(sp + 1, bs1)
+ }
+ case (S::bs2) => {
+ pv_stack(sp) = RIG
+ pv_stack.insert(sp + 1, Plhdr)
+ for(i <- 0 to next_stack.length - 1){
+ next_stack(i) = next_stack(i) + 1
+ }
+ regx_stack += ALTS(rs.tail)
+ action_stack += AL
+ decode_stack(sp + 1, bs2)
+ }
+ case _ => println("Not decodable")
+ }
+ }
+ case (rs) => println(r,bs)
+ }
+}
+}
+//advantage: may decode chunks of bits
+def decode(r: Rexp, bs: Bits) = {
+ action_stack.clear()
+ next_stack.clear()
+ regx_stack.clear()
+ pv_stack.clear()
+
+ action_stack += NST
+ regx_stack += r
+ pv_stack += Plhdr
+
+ decode_stack(0, bs)
+}
+/*
+def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
+ case (v, Nil) => v
+ case _ => throw new Exception("Not decodable")
+}
+*/
+
+//erase function: extracts the regx from Aregex
+def erase(r:ARexp): Rexp = r match{
+ case AZERO => ZERO
+ case AONE(_) => ONE
+ case APRED(bs, f) => PRED(f)
+ case AALTS(bs, rs) => ALTS(rs.map(erase(_)))
+ case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
+ case ASTAR(cs, r)=> STAR(erase(r))
+}
+
+// nullable function: tests whether the aregular
+// expression can recognise the empty string
+def nullable (r: ARexp) : Boolean = r match {
+ case AZERO => false
+ case AONE(_) => true
+ case APRED(_,_) => false
+ case AALTS(_, rs) => rs.exists(nullable)
+ case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)
+ case ASTAR(_, _) => true
+}
+
+def mkepsBC(r: ARexp) : Bits = r match {
+ case AONE(bs) => bs
+ case AALTS(bs, rs) => {
+ val n = rs.indexWhere(nullable)
+ bs ++ mkepsBC(rs(n))
+ }
+ case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
+ case ASTAR(bs, r) => bs ++ List(Z)
+}
+
+// derivative of a regular expression w.r.t. a character
+def der(c: Char, r: ARexp) : ARexp = r match {
+ case AZERO => AZERO
+ case AONE(_) => AZERO
+ case APRED(bs, f) => if (f(c)) AONE(bs:::List(C(c))) else AZERO
+ case AALTS(bs, rs) => AALTS(bs, rs.map(der(c, _)))
+ case ASEQ(bs, r1, r2) =>
+ if (nullable(r1)) AALT(bs, ASEQ(Nil, der(c, r1), r2), fuse(mkepsBC(r1), der(c, r2)))
+ else ASEQ(bs, der(c, r1), r2)
+ case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), der(c, r)), ASTAR(Nil, r))
+}
+
+// derivative w.r.t. a string (iterates der)
+@tailrec
+def ders (s: List[Char], r: ARexp) : ARexp = s match {
+ case Nil => r
+ case c::s => ders(s, der(c, r))
+}
+
+// main unsimplified lexing function (produces a value)
+def lex(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
+ case c::cs => lex(der(c, r), cs)
+}
+
+def pre_lexing(r: Rexp, s: String) = lex(internalise(r), s.toList)
+//def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))
+
+
+def flats(rs: List[ARexp]): List[ARexp] = rs match {
+ case Nil => Nil
+ case AZERO :: rs1 => flats(rs1)
+ case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
+ case r1 :: rs2 => r1 :: flats(rs2)
+ }
+
+def simp(r: ARexp): ARexp = r match {
+ case ASEQ(bs1, r1, r2) => (simp(r1), simp(r2)) match {
+ case (AZERO, _) => AZERO
+ case (_, AZERO) => AZERO
+ case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
+ case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
+ }
+ case AALTS(bs1, rs) => distinctBy(flats(rs.map(simp)), erase) match {
+ case Nil => AZERO
+ case s :: Nil => fuse(bs1, s)
+ case rs => AALTS(bs1, rs)
+ }
+ case r => r
+}
+
+def ders_simp (s: List[Char], r: ARexp) : ARexp = s match {
+ case Nil => r
+ case c::s => ders_simp(s, simp(der(c, r)))
+}
+
+def lex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => {
+ if (nullable(r)) {
+ //println(asize(r))
+ mkepsBC(r)
+ }
+ else throw new Exception("Not matched")
+ }
+ case c::cs => lex_simp(simp(der(c, r)), cs)
+}
+
+//size: of a Aregx for testing purposes
+def size(r: Rexp) : Int = r match {
+ case ZERO => 1
+ case ONE => 1
+ case PRED(_) => 1
+ case SEQ(r1, r2) => 1 + size(r1) + size(r2)
+ case ALTS(rs) => 1 + rs.map(size).sum
+ case STAR(r) => 1 + size(r)
+}
+
+def asize(a: ARexp) = size(erase(a))
+
+
+// decoding does not work yet
+def lexing_simp(r: Rexp, s: String) = {
+ val final_derivative = lex_simp(internalise(r), s.toList)
+ println("The length of bit sequence:")
+ println((final_derivative.length))
+ //println(final_derivative)
+ decode(r, final_derivative)
+ //println(vsize(value))
+}
+
+
+def vsize(v: Val): Int = v match {
+ case Empty => 1
+ case Chr(c) => 1
+ case Sequ(v1, v2) => vsize(v1) + vsize(v2) + 1
+ case Left(v1) => vsize(v1) + 1
+ case Right(v1) => vsize(v1) + 1
+ case Stars(vs) => vs.map(vsize(_)).sum + 1
+ case Rec(x, v1) => vsize(v1) + 1
+ case Pos(i, v1) => vsize(v1) + 1
+ case Prd => 1
+}
+
+
+// Lexing Rules for a Small While Language
+
+//symbols
+val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_))
+//digits
+val DIGIT = PRED("0123456789".contains(_))
+//identifiers
+val ID = SYM ~ (SYM | DIGIT).%
+//numbers
+val NUM = PLUS(DIGIT)
+//keywords
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
+//semicolons
+val SEMI: Rexp = ";"
+//operators
+val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
+//whitespaces
+val WHITESPACE = PLUS(" " | "\n" | "\t")
+//parentheses
+val RPAREN: Rexp = ")"
+val LPAREN: Rexp = "("
+val BEGIN: Rexp = "{"
+val END: Rexp = "}"
+//strings...but probably needs not
+val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+
+
+val WHILE_REGS = (("k" $ KEYWORD) |
+ ("i" $ ID) |
+ ("o" $ OP) |
+ ("n" $ NUM) |
+ ("s" $ SEMI) |
+ ("str" $ STRING) |
+ ("p" $ (LPAREN | RPAREN)) |
+ ("b" $ (BEGIN | END)) |
+ ("w" $ WHITESPACE)).%
+
+// filters out all white spaces
+//def tokenise(r: Rexp, s: String) =
+// env(lexing_simp(r, s)).filterNot { _._1 == "w"}
+
+
+//reads the string from a file
+//def fromFile(name: String) : String =
+// io.Source.fromFile(name).mkString
+
+//def tokenise_file(r: Rexp, name: String) =
+// tokenise(r, fromFile(name))
+
+
+// Some Tests
+//============
+def compute_and_print(r: Rexp, s: String){
+ //println(r)
+ //println(s)
+ lexing_simp(r, s)
+ println(pv_stack)
+}
+println("simple tests:")
+/*
+println(lexing_simp((SYM.%), "abcd"))
+println(lexing_simp(((SYM.%) | NUM), "12345"))
+println(lexing_simp((WHILE_REGS), "abcd"))
+println(lexing_simp((WHILE_REGS), "12345"))
+println(lexing_simp((WHILE_REGS), "\nwrite \"Fib\";"))
+*/
+compute_and_print((SYM.%), "abcd")
+compute_and_print(((SYM.%) | NUM), "12345")
+compute_and_print((WHILE_REGS), "abcd")
+compute_and_print((WHILE_REGS), "12345")
+compute_and_print((WHILE_REGS), "\nwrite \"Fib\";")
+
+def time[T](code: => T) = {
+ val start = System.nanoTime()
+ val result = code
+ val end = System.nanoTime()
+ println((end - start)/1.0e9)
+ result
+}
+
+val prog2 = """
+write "Fib";
+read n;
+minus1 := 0;
+minus2 := 1;
+while n > 0 do {
+ temp := minus2;
+ minus2 := minus1 + minus2;
+ minus1 := temp;
+ n := n -x 1
+};
+write "Result";
+write minus2
+"""
+/*
+
+val prog2 = """
+write "Fib";
+"""
+
+*/
+
+println("Iteration test with fib")
+for (i <- 900 to 1000 by 50) {
+ print(i.toString + ": ")
+ time(lexing_simp((WHILE_REGS), (prog2 * i)))
+ //time(lex_simp(internalise(WHILE_REGS), (prog2 * i).toList))
+}
+
+
+/*
+def recurseTest(i:Int):Unit={
+ try{
+ recurseTest(i+1)
+ } catch { case e:java.lang.StackOverflowError =>
+ println("Recursion depth on this system is " + i + ".")
+ }
+}
+recurseTest(0)
+*/
\ No newline at end of file
--- a/token1.scala Wed Jan 30 12:13:41 2019 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,598 +0,0 @@
-
-import scala.language.implicitConversions
-import scala.language.reflectiveCalls
-import scala.annotation.tailrec
-
-def distinctBy[B, C](xs: List[B], f: B => C, acc: List[C] = Nil): List[B] = xs match {
- case Nil => Nil
- case (x::xs) => {
- val res = f(x)
- if (acc.contains(res)) distinctBy(xs, f, acc)
- else x::distinctBy(xs, f, res::acc)
- }
-}
-
-abstract class Bit
-case object Z extends Bit
-case object S extends Bit
-case class C(c: Char) extends Bit
-
-
-type Bits = List[Bit]
-
-abstract class Action
-case object ST extends Action
-case object NST extends Action
-case object AL extends Action
-
-abstract class PartialValue
-case object Plhdr extends PartialValue
-case object STS extends PartialValue
-case object ENDSTS extends PartialValue
-case class Ch(c: Char) extends PartialValue
-case object Empt extends PartialValue
-case object Seque extends PartialValue
-case class Posi(i: Int) extends PartialValue
-case class RECRD(x: String) extends PartialValue
-case object ALTSTART extends PartialValue
-case object ALTEND extends PartialValue
-case object RIG extends PartialValue
-case object LEF extends PartialValue
-
-abstract class Rexp
-case object ZERO extends Rexp
-case object ONE extends Rexp
-case class PRED(f: Char => Boolean) extends Rexp
-case class ALTS(rs: List[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
-
-// abbreviations
-def CHAR(c: Char) = PRED(_ == c)
-def ALT(r1: Rexp, r2: Rexp) = ALTS(List(r1, r2))
-def PLUS(r: Rexp) = SEQ(r, STAR(r))
-
-abstract class ARexp
-case object AZERO extends ARexp
-case class AONE(bs: Bits) extends ARexp
-case class APRED(bs: Bits, f: Char => Boolean) extends ARexp
-case class AALTS(bs: Bits, rs: List[ARexp]) extends ARexp
-case class ASEQ(bs: Bits, r1: ARexp, r2: ARexp) extends ARexp
-case class ASTAR(bs: Bits, r: ARexp) extends ARexp
-
-
-def AALT(bs: Bits, r1: ARexp, r2: ARexp) = AALTS(bs, List(r1, r2))
-
-abstract class Val
-case object Empty 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
-case class Pos(i: Int, v: Val) extends Val
-case object Prd extends Val
-
-// some convenience for typing in regular expressions
-def charlist2rexp(s : List[Char]): Rexp = s match {
- case Nil => ONE
- case c::Nil => CHAR(c)
- case c::s => SEQ(CHAR(c), charlist2rexp(s))
-}
-implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
-
-implicit def RexpOps(r: Rexp) = new {
- def | (s: Rexp) = ALT(r, s)
- def % = STAR(r)
- def ~ (s: Rexp) = SEQ(r, s)
-}
-
-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)
-}
-
-// translation into ARexps
-def fuse(bs: Bits, r: ARexp) : ARexp = r match {
- case AZERO => AZERO
- case AONE(cs) => AONE(bs ++ cs)
- case APRED(cs, f) => APRED(bs ++ cs, f)
- case AALTS(cs, rs) => AALTS(bs ++ cs, rs)
- case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
- case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
-}
-
-def internalise(r: Rexp) : ARexp = r match {
- case ZERO => AZERO
- case ONE => AONE(Nil)
- case PRED(f) => APRED(Nil, f)
- case ALTS(List(r1, r2)) =>
- AALTS(Nil, List(fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2))))
- case ALTS(r1::rs) => {
- val AALTS(Nil, rs2) = internalise(ALTS(rs))
- AALTS(Nil, fuse(List(Z), internalise(r1)) :: rs2.map(fuse(List(S), _)))
- }
- case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
- case STAR(r) => ASTAR(Nil, internalise(r))
- case RECD(x, r) => internalise(r)
-}
-
-internalise(("a" | "ab") ~ ("b" | ""))
-val action_stack = scala.collection.mutable.ArrayBuffer.empty[Action]
-val next_stack = scala.collection.mutable.ArrayBuffer.empty[Int]
-val regx_stack = scala.collection.mutable.ArrayBuffer.empty[Rexp]
-val pv_stack = scala.collection.mutable.ArrayBuffer.empty[PartialValue]
-var top = 0
-//st is the global var stack, made with a linked list?
-@tailrec
-def decode_stack(sp: Int, bs: Bits): Unit = {
-if(action_stack.isEmpty){
- return
-}
-val action = action_stack.last
-action_stack.trimEnd(1)
-val r = regx_stack.last
-regx_stack.trimEnd(1)
-if(action == ST)//we have the rest of the star to finish(ST -> STAR)
-{
- bs match {
- case Z::bs => {//pv -> partial value Each grid in a stack does not hold a whole value but a partial one.
- pv_stack(sp) = ENDSTS
- if(next_stack.isEmpty)
- return
- val n = next_stack.last
- next_stack.trimEnd(1)
- decode_stack(n, bs)
- }
- case S::bs => {
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 1
- }
- next_stack += (sp + 1)
- regx_stack += r
- action_stack += ST
- pv_stack.insert(sp + 1, Plhdr)
- action_stack += NST
- regx_stack += r
- decode_stack(sp, bs)
- }
- case _ => println("Sequence not decodable")
- }
-
-}
-else if(action == NST){
- (r, bs) match{
- case (ONE, bs) => {
- pv_stack(sp) = Empt
- if(next_stack.isEmpty)
- return
- val n = next_stack.last
- next_stack.trimEnd(1)
- decode_stack(n, bs)
- }
- case (PRED(f), C(c)::bs) => {
- pv_stack(sp) = Ch(c)
- if(next_stack.isEmpty)
- return
- val n = next_stack.last
- next_stack.trimEnd(1)
- decode_stack(n, bs)
- }
- case (ALTS(rs), Z::bs1) => {
- pv_stack(sp) = ALTSTART
- pv_stack.insert(sp + 1, LEF)
- pv_stack.insert(sp + 2, Plhdr)
- pv_stack.insert(sp + 3, ALTEND)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 3
- }
- regx_stack += rs.head
- action_stack += NST
- decode_stack(sp + 2, bs1)
- }
- case (ALTS(rs), S::bs1) => {
- pv_stack(sp) = ALTSTART
- pv_stack.insert(sp + 1, RIG)
- pv_stack.insert(sp + 2, Plhdr)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 2
- }
- regx_stack += ALTS(rs.tail)
- action_stack += AL
- decode_stack(sp + 2, bs1)
- }
- /*
- val le = rs.length
- val det = bs.take(le - 1)
- val chosen = det.indexWhere(_ == Z)
- action_stack += NST
- pv_stack.insert(sp + 1, Plhdr)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 1
- }
- if(chosen == -1){
- pv_stack(sp) = Posi(le)
- regx_stack += rs(le - 1)
- decode_stack(sp + 1, bs.drop(le - 1))
- }
- else{
- pv_stack(sp) = Posi(chosen + 1)
- regx_stack += rs(chosen)
- decode_stack(sp + 1, bs.drop(chosen + 1))
- }*/
- case (SEQ(r1, r2), bs) => {
- action_stack += NST
- action_stack += NST
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 2
- }
- next_stack += (sp + 2)
- regx_stack += r2
- regx_stack += r1
- pv_stack.insert(sp + 1, Plhdr)
- pv_stack.insert(sp + 2, Plhdr)
- pv_stack(sp) = Seque
- decode_stack(sp + 1, bs)
- }
- case (STAR(r1), S::bs) => {
- action_stack += ST
- regx_stack += r1
- action_stack += NST
- regx_stack += r1
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 2
- }
- next_stack += sp + 2
- pv_stack(sp) = STS
- pv_stack.insert(sp + 1, Plhdr)
- pv_stack.insert(sp + 1, Plhdr)
- decode_stack(sp + 1, bs)
- }
- case (STAR(_), Z::bs) => {
- pv_stack(sp) = STS
- pv_stack.insert(sp + 1, ENDSTS)
- if(next_stack.isEmpty)
- return
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 1
- }
- val n = next_stack.last
- next_stack.trimEnd(1)
- decode_stack(n, bs)
- }
- case (RECD(x, r1), bs) => {
- pv_stack(sp) = RECRD(x)
- pv_stack.insert(sp + 1, Plhdr)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 1
- }
- action_stack += NST
- regx_stack += r1
- decode_stack(sp + 1, bs)
- }//shouldn't go beyond this point
- case (_, _) => println("Error with NST")
- }
-}
-else{//action is AL
- r match {
- case (ALTS(r1::Nil)) => {
- pv_stack.insert(sp + 1, ALTEND)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 1
- }
- action_stack += NST
- regx_stack += r1
- decode_stack(sp, bs)
- }
- case (ALTS(rs)) => {
- bs match {
- case (Z::bs1) => {
- pv_stack(sp) = LEF
- pv_stack.insert(sp + 1, ALTEND)
- pv_stack.insert(sp + 1, Plhdr)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 2
- }
- regx_stack += rs.head
- action_stack += NST
- decode_stack(sp + 1, bs1)
- }
- case (S::bs2) => {
- pv_stack(sp) = RIG
- pv_stack.insert(sp + 1, Plhdr)
- for(i <- 0 to next_stack.length - 1){
- next_stack(i) = next_stack(i) + 1
- }
- regx_stack += ALTS(rs.tail)
- action_stack += AL
- decode_stack(sp + 1, bs2)
- }
- case _ => println("Not decodable")
- }
- }
- case (rs) => println(r,bs)
- }
-}
-}
-//advantage: may decode chunks of bits
-def decode(r: Rexp, bs: Bits) = {
- action_stack.clear()
- next_stack.clear()
- regx_stack.clear()
- pv_stack.clear()
-
- action_stack += NST
- regx_stack += r
- pv_stack += Plhdr
-
- decode_stack(0, bs)
-}
-/*
-def decode(r: Rexp, bs: Bits) = decode_aux(r, bs) match {
- case (v, Nil) => v
- case _ => throw new Exception("Not decodable")
-}
-*/
-
-//erase function: extracts the regx from Aregex
-def erase(r:ARexp): Rexp = r match{
- case AZERO => ZERO
- case AONE(_) => ONE
- case APRED(bs, f) => PRED(f)
- case AALTS(bs, rs) => ALTS(rs.map(erase(_)))
- case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
- case ASTAR(cs, r)=> STAR(erase(r))
-}
-
-// nullable function: tests whether the aregular
-// expression can recognise the empty string
-def nullable (r: ARexp) : Boolean = r match {
- case AZERO => false
- case AONE(_) => true
- case APRED(_,_) => false
- case AALTS(_, rs) => rs.exists(nullable)
- case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)
- case ASTAR(_, _) => true
-}
-
-def mkepsBC(r: ARexp) : Bits = r match {
- case AONE(bs) => bs
- case AALTS(bs, rs) => {
- val n = rs.indexWhere(nullable)
- bs ++ mkepsBC(rs(n))
- }
- case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
- case ASTAR(bs, r) => bs ++ List(Z)
-}
-
-// derivative of a regular expression w.r.t. a character
-def der(c: Char, r: ARexp) : ARexp = r match {
- case AZERO => AZERO
- case AONE(_) => AZERO
- case APRED(bs, f) => if (f(c)) AONE(bs:::List(C(c))) else AZERO
- case AALTS(bs, rs) => AALTS(bs, rs.map(der(c, _)))
- case ASEQ(bs, r1, r2) =>
- if (nullable(r1)) AALT(bs, ASEQ(Nil, der(c, r1), r2), fuse(mkepsBC(r1), der(c, r2)))
- else ASEQ(bs, der(c, r1), r2)
- case ASTAR(bs, r) => ASEQ(bs, fuse(List(S), der(c, r)), ASTAR(Nil, r))
-}
-
-// derivative w.r.t. a string (iterates der)
-@tailrec
-def ders (s: List[Char], r: ARexp) : ARexp = s match {
- case Nil => r
- case c::s => ders(s, der(c, r))
-}
-
-// main unsimplified lexing function (produces a value)
-def lex(r: ARexp, s: List[Char]) : Bits = s match {
- case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
- case c::cs => lex(der(c, r), cs)
-}
-
-def pre_lexing(r: Rexp, s: String) = lex(internalise(r), s.toList)
-//def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))
-
-
-def flats(rs: List[ARexp]): List[ARexp] = rs match {
- case Nil => Nil
- case AZERO :: rs1 => flats(rs1)
- case AALTS(bs, rs1) :: rs2 => rs1.map(fuse(bs, _)) ::: flats(rs2)
- case r1 :: rs2 => r1 :: flats(rs2)
- }
-
-def simp(r: ARexp): ARexp = r match {
- case ASEQ(bs1, r1, r2) => (simp(r1), simp(r2)) match {
- case (AZERO, _) => AZERO
- case (_, AZERO) => AZERO
- case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
- case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
- }
- case AALTS(bs1, rs) => distinctBy(flats(rs.map(simp)), erase) match {
- case Nil => AZERO
- case s :: Nil => fuse(bs1, s)
- case rs => AALTS(bs1, rs)
- }
- case r => r
-}
-
-def ders_simp (s: List[Char], r: ARexp) : ARexp = s match {
- case Nil => r
- case c::s => ders_simp(s, simp(der(c, r)))
-}
-
-def lex_simp(r: ARexp, s: List[Char]) : Bits = s match {
- case Nil => {
- if (nullable(r)) {
- //println(asize(r))
- mkepsBC(r)
- }
- else throw new Exception("Not matched")
- }
- case c::cs => lex_simp(simp(der(c, r)), cs)
-}
-
-//size: of a Aregx for testing purposes
-def size(r: Rexp) : Int = r match {
- case ZERO => 1
- case ONE => 1
- case PRED(_) => 1
- case SEQ(r1, r2) => 1 + size(r1) + size(r2)
- case ALTS(rs) => 1 + rs.map(size).sum
- case STAR(r) => 1 + size(r)
-}
-
-def asize(a: ARexp) = size(erase(a))
-
-
-// decoding does not work yet
-def lexing_simp(r: Rexp, s: String) = {
- val final_derivative = lex_simp(internalise(r), s.toList)
- println("The length of bit sequence:")
- println((final_derivative.length))
- //println(final_derivative)
- decode(r, final_derivative)
- //println(vsize(value))
-}
-
-
-def vsize(v: Val): Int = v match {
- case Empty => 1
- case Chr(c) => 1
- case Sequ(v1, v2) => vsize(v1) + vsize(v2) + 1
- case Left(v1) => vsize(v1) + 1
- case Right(v1) => vsize(v1) + 1
- case Stars(vs) => vs.map(vsize(_)).sum + 1
- case Rec(x, v1) => vsize(v1) + 1
- case Pos(i, v1) => vsize(v1) + 1
- case Prd => 1
-}
-
-
-// Lexing Rules for a Small While Language
-
-//symbols
-val SYM = PRED("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ".contains(_))
-//digits
-val DIGIT = PRED("0123456789".contains(_))
-//identifiers
-val ID = SYM ~ (SYM | DIGIT).%
-//numbers
-val NUM = PLUS(DIGIT)
-//keywords
-val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
-//semicolons
-val SEMI: Rexp = ";"
-//operators
-val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
-//whitespaces
-val WHITESPACE = PLUS(" " | "\n" | "\t")
-//parentheses
-val RPAREN: Rexp = ")"
-val LPAREN: Rexp = "("
-val BEGIN: Rexp = "{"
-val END: Rexp = "}"
-//strings...but probably needs not
-val STRING: Rexp = "\"" ~ SYM.% ~ "\""
-
-
-
-val WHILE_REGS = (("k" $ KEYWORD) |
- ("i" $ ID) |
- ("o" $ OP) |
- ("n" $ NUM) |
- ("s" $ SEMI) |
- ("str" $ STRING) |
- ("p" $ (LPAREN | RPAREN)) |
- ("b" $ (BEGIN | END)) |
- ("w" $ WHITESPACE)).%
-
-// filters out all white spaces
-//def tokenise(r: Rexp, s: String) =
-// env(lexing_simp(r, s)).filterNot { _._1 == "w"}
-
-
-//reads the string from a file
-//def fromFile(name: String) : String =
-// io.Source.fromFile(name).mkString
-
-//def tokenise_file(r: Rexp, name: String) =
-// tokenise(r, fromFile(name))
-
-
-// Some Tests
-//============
-def compute_and_print(r: Rexp, s: String){
- //println(r)
- //println(s)
- lexing_simp(r, s)
- println(pv_stack)
-}
-println("simple tests:")
-/*
-println(lexing_simp((SYM.%), "abcd"))
-println(lexing_simp(((SYM.%) | NUM), "12345"))
-println(lexing_simp((WHILE_REGS), "abcd"))
-println(lexing_simp((WHILE_REGS), "12345"))
-println(lexing_simp((WHILE_REGS), "\nwrite \"Fib\";"))
-*/
-compute_and_print((SYM.%), "abcd")
-compute_and_print(((SYM.%) | NUM), "12345")
-compute_and_print((WHILE_REGS), "abcd")
-compute_and_print((WHILE_REGS), "12345")
-compute_and_print((WHILE_REGS), "\nwrite \"Fib\";")
-
-def time[T](code: => T) = {
- val start = System.nanoTime()
- val result = code
- val end = System.nanoTime()
- println((end - start)/1.0e9)
- result
-}
-
-val prog2 = """
-write "Fib";
-read n;
-minus1 := 0;
-minus2 := 1;
-while n > 0 do {
- temp := minus2;
- minus2 := minus1 + minus2;
- minus1 := temp;
- n := n -x 1
-};
-write "Result";
-write minus2
-"""
-/*
-
-val prog2 = """
-write "Fib";
-"""
-
-*/
-
-println("Iteration test with fib")
-for (i <- 900 to 1000 by 50) {
- print(i.toString + ": ")
- time(lexing_simp((WHILE_REGS), (prog2 * i)))
- //time(lex_simp(internalise(WHILE_REGS), (prog2 * i).toList))
-}
-
-
-/*
-def recurseTest(i:Int):Unit={
- try{
- recurseTest(i+1)
- } catch { case e:java.lang.StackOverflowError =>
- println("Recursion depth on this system is " + i + ".")
- }
-}
-recurseTest(0)
-*/
\ No newline at end of file