--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/scala/re-bit.scala Fri Apr 01 16:29:33 2016 +0100
@@ -0,0 +1,213 @@
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec
+
+abstract class Rexp
+case object ZERO extends Rexp
+case object ONE 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
+
+abstract class ARexp
+case object AZERO extends ARexp
+case class AONE(bs: List[Boolean]) extends ARexp
+case class ACHAR(bs: List[Boolean], c: Char) extends ARexp
+case class AALT(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp
+case class ASEQ(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp
+case class ASTAR(bs: List[Boolean], r: ARexp) extends ARexp
+
+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
+
+// 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)
+}
+
+// translation into ARexps
+def fuse(bs: List[Boolean], r: ARexp) : ARexp = r match {
+ case AZERO => AZERO
+ case AONE(cs) => AONE(bs ++ cs)
+ case ACHAR(cs, c) => ACHAR(bs ++ cs, c)
+ case AALT(cs, r1, r2) => AALT(bs ++ cs, r1, r2)
+ 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 CHAR(c) => ACHAR(Nil, c)
+ case ALT(r1, r2) => AALT(Nil, fuse(List(false), internalise(r1)), fuse(List(true), internalise(r2)))
+ case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
+ case STAR(r) => ASTAR(Nil, internalise(r))
+}
+
+internalise(("a" | "ab") ~ ("b" | ""))
+
+
+def decode_aux(r: Rexp, bs: List[Boolean]) : (Val, List[Boolean]) = (r, bs) match {
+ case (ONE, bs) => (Empty, bs)
+ case (CHAR(c), bs) => (Chr(c), bs)
+ case (ALT(r1, r2), false::bs) => {
+ val (v, bs1) = decode_aux(r1, bs)
+ (Left(v), bs1)
+ }
+ case (ALT(r1, r2), true::bs) => {
+ val (v, bs1) = decode_aux(r2, bs)
+ (Right(v), bs1)
+ }
+ case (SEQ(r1, r2), bs) => {
+ val (v1, bs1) = decode_aux(r1, bs)
+ val (v2, bs2) = decode_aux(r2, bs1)
+ (Sequ(v1, v2), bs2)
+ }
+ case (STAR(r), false::bs) => {
+ val (v, bs1) = decode_aux(r, bs)
+ val (Stars(vs), bs2) = decode_aux(STAR(r), bs1)
+ (Stars(v::vs), bs2)
+ }
+ case (STAR(r), true::bs) => (Stars(Nil), bs)
+}
+
+def decode(r: Rexp, bs: List[Boolean]) = decode_aux(r, bs) match {
+ case (v, Nil) => v
+ case _ => throw new Exception("Not decodable")
+}
+
+// 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 ACHAR(_,_) => false
+ case AALT(_, r1, r2) => nullable(r1) || nullable(r2)
+ case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)
+ case ASTAR(_, _) => true
+}
+
+def mkepsBC(r: ARexp) : List[Boolean] = r match {
+ case AONE(bs) => bs
+ case AALT(bs, r1, r2) =>
+ if (nullable(r1)) bs ++ mkepsBC(r1) else bs ++ mkepsBC(r2)
+ case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
+ case ASTAR(bs, r) => bs ++ List(true)
+}
+
+// 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 ACHAR(bs, d) => if (c == d) AONE(bs) else AZERO
+ case AALT(bs, r1, r2) => AALT(bs, der(c, r1), der(c, r2))
+ 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(false), 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]) : List[Boolean] = s match {
+ case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
+ case c::cs => lex(der(c, r), cs)
+}
+
+def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))
+
+// Some Tests
+//============
+
+def time_needed[T](i: Int, code: => T) = {
+ val start = System.nanoTime()
+ for (j <- 1 to i) code
+ val end = System.nanoTime()
+ (end - start)/(i * 1.0e9)
+}
+
+
+
+
+val r0 = ("a" | "ab") ~ ("b" | "")
+println(lexing(r0, "ab"))
+
+val r1 = ("a" | "ab") ~ ("bcd" | "cd")
+println(lexing(r1, "abcd"))
+
+println(lexing((("" | "a") ~ ("ab" | "b")), "ab"))
+println(lexing((("" | "a") ~ ("b" | "ab")), "ab"))
+println(lexing((("" | "a") ~ ("c" | "ab")), "ab"))
+
+
+
+// Two Simple Tests for the While Language
+//========================================
+
+// Lexing Rules
+
+def PLUS(r: Rexp) = r ~ r.%
+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"
+val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
+val ID = SYM ~ (SYM | DIGIT).%
+val NUM = PLUS(DIGIT)
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
+val SEMI: Rexp = ";"
+val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
+val WHITESPACE = PLUS(" " | "\n" | "\t")
+val RPAREN: Rexp = ")"
+val LPAREN: Rexp = "("
+val BEGIN: Rexp = "{"
+val END: Rexp = "}"
+val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+val WHILE_REGS = (KEYWORD |
+ ID |
+ OP |
+ NUM |
+ SEMI |
+ LPAREN | RPAREN |
+ BEGIN | END |
+ WHITESPACE).%
+
+
+println("prog0 test")
+
+val prog0 = """read n"""
+println(lexing(WHILE_REGS, prog0))
+
+println("prog1 test")
+
+val prog1 = """read n; write (n)"""
+println(lexing(WHILE_REGS, prog1))
+
+
--- a/progs/scala/re-simp.scala Thu Mar 31 16:50:37 2016 +0100
+++ b/progs/scala/re-simp.scala Fri Apr 01 16:29:33 2016 +0100
@@ -69,6 +69,7 @@
}
// derivative w.r.t. a string (iterates der)
+@tailrec
def ders (s: List[Char], r: Rexp) : Rexp = s match {
case Nil => r
case c::s => ders(s, der(c, r))
@@ -191,14 +192,14 @@
// Some Tests
//============
-def time[T](code: => T) = {
+def time_needed[T](i: Int, code: => T) = {
val start = System.nanoTime()
- val result = code
+ for (j <- 1 to i) code
val end = System.nanoTime()
- println((end - start)/1.0e9)
- result
+ (end - start)/(i * 1.0e9)
}
+
val r0 = ("a" | "ab") ~ ("b" | "")
println(lexing(r0, "ab"))
println(lexing_simp(r0, "ab"))
@@ -266,8 +267,8 @@
println(env(lexing_simp(WHILE_REGS, prog1)))
-// Big Test
-//==========
+// Bigger Test
+//=============
val prog2 = """
i := 2;
max := 100;
@@ -311,3 +312,17 @@
}
*/
+// Sulzmann's tests
+//==================
+
+val sulzmann = ("a" | "b" | "ab").%
+
+println(lexing_simp(sulzmann, "a" * 10))
+
+for (i <- 1 to 4501 by 500) {
+ println(i + ": " + "%.5f".format(time_needed(1, lexing_simp(sulzmann, "a" * i))))
+}
+
+for (i <- 1 to 2001 by 500) {
+ println(i + ": " + "%.5f".format(time_needed(1, lexing_simp(sulzmann, "ab" * i))))
+}