--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/scala/re-annotated.sc Mon Feb 22 03:22:26 2021 +0000
@@ -0,0 +1,407 @@
+// uses bitcode sequences and annotated regular
+// expressions
+//
+// for basic regular expressions and RECD
+//
+// uses a non-standard extraction method for generating
+// tokens (this is tail-recursive)
+//
+// can match 60 copies of the fib-program (size 10500)
+// in about 20 secs
+
+
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec
+
+// standard regular expressions
+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
+case class RECD(x: String, r: Rexp) extends Rexp
+
+abstract class Bit
+case object Z extends Bit
+case object S extends Bit
+
+type Bits = List[Bit]
+
+// annotated regular expressions
+abstract class ARexp
+case object AZERO extends ARexp
+case class AONE(bs: Bits) extends ARexp
+case class ACHAR(bs: Bits, c: Char) 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
+
+// an abbreviation for binary alternatives
+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 Recd(x: String, v: 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)
+ def $ (r: Rexp) = RECD(s, r)
+}
+
+def size(r: Rexp) : Int = r match {
+ case ZERO => 1
+ case ONE => 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)
+}
+
+
+
+// Bitcoded + Annotation
+//=======================
+
+//erase function: extracts the Rexp from ARexp
+def erase(r:ARexp): Rexp = r match{
+ case AZERO => ZERO
+ case AONE(_) => ONE
+ case ACHAR(bs, c) => CHAR(c)
+ case AALTS(bs, Nil) => ZERO
+ case AALTS(bs, r::Nil) => erase(r)
+ case AALTS(bs, r::rs) => ALT(erase(r), erase(AALTS(bs, rs)))
+ case ASEQ(bs, r1, r2) => SEQ (erase(r1), erase(r2))
+ case ASTAR(cs, r)=> STAR(erase(r))
+}
+
+def fuse(bs: Bits, r: ARexp) : ARexp = r match {
+ case AZERO => AZERO
+ case AONE(cs) => AONE(bs ++ cs)
+ case ACHAR(cs, c) => ACHAR(bs ++ cs, c)
+ 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 CHAR(c) => ACHAR(Nil, c)
+ case ALT(r1, r2) => AALT(Nil, fuse(List(Z), internalise(r1)), fuse(List(S), internalise(r2)))
+ case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
+ case STAR(r) => ASTAR(Nil, internalise(r))
+ case RECD(_, r) => internalise(r)
+}
+
+// example
+// internalise(("a" | "ab") ~ ("b" | ""))
+
+
+// decoding of a value from a bitsequence
+// (this is not tail-recursive and therefore a potential bottleneck)
+def vdecode_aux(r: Rexp, bs: Bits) : (Val, Bits) = (r, bs) match {
+ case (ONE, bs) => (Empty, bs)
+ case (CHAR(c), bs) => (Chr(c), bs)
+ case (ALT(r1, r2), Z::bs) => {
+ val (v, bs1) = vdecode_aux(r1, bs)
+ (Left(v), bs1)
+ }
+ case (ALT(r1, r2), S::bs) => {
+ val (v, bs1) = vdecode_aux(r2, bs)
+ (Right(v), bs1)
+ }
+ case (SEQ(r1, r2), bs) => {
+ val (v1, bs1) = vdecode_aux(r1, bs)
+ val (v2, bs2) = vdecode_aux(r2, bs1)
+ (Sequ(v1, v2), bs2)
+ }
+ case (STAR(r1), Z::bs) => {
+ val (v, bs1) = vdecode_aux(r1, bs)
+ val (Stars(vs), bs2) = vdecode_aux(STAR(r1), bs1)
+ (Stars(v::vs), bs2)
+ }
+ case (STAR(_), S::bs) => (Stars(Nil), bs)
+ case (RECD(s, r1), bs) =>
+ val (v, bs1) = vdecode_aux(r1, bs)
+ (Recd(s, v), bs1)
+}
+
+def vdecode(r: Rexp, bs: Bits) = vdecode_aux(r, bs) match {
+ case (v, Nil) => v
+ case _ => throw new Exception("Not decodable")
+}
+
+// decoding of sequence of string tokens from a bitsequence
+// tail-recursive version using an accumulator (alternative for
+// vdecode)
+@tailrec
+def sdecode_aux(rs: List[Rexp], bs: Bits, acc: List[String]) : List[String] = (rs, bs) match {
+ case (Nil, _) => acc
+ case (_, Nil) => acc
+ case (ONE::rest, bs) => sdecode_aux(rest, bs, acc)
+ case (CHAR(c)::rest, bs) =>
+ sdecode_aux(rest, bs, (acc.head ++ c.toString)::acc.tail)
+ case (ALT(r1, r2)::rest, Z::bs) => sdecode_aux(r1::rest, bs, acc)
+ case (ALT(r1, r2)::rest, S::bs) => sdecode_aux(r2::rest, bs, acc)
+ case (SEQ(r1, r2)::rest, bs) => sdecode_aux(r1::r2::rest, bs, acc)
+ case (STAR(r1)::rest, Z::bs) => sdecode_aux(r1::STAR(r1)::rest, bs, acc)
+ case (STAR(_)::rest, S::bs) => sdecode_aux(rest, bs, acc)
+ case (RECD(s, r1)::rest, bs) =>
+ sdecode_aux(r1::rest, bs, s"$s:"::acc)
+}
+
+def sdecode(r: Rexp, bs: Bits) : List[String] =
+ sdecode_aux(List(r), bs, List("")).reverse.tail
+
+
+
+// nullable function: tests whether the an (annotated)
+// regular expression can recognise the empty string
+def bnullable (r: ARexp) : Boolean = r match {
+ case AZERO => false
+ case AONE(_) => true
+ case ACHAR(_,_) => false
+ case AALTS(_, rs) => rs.exists(bnullable)
+ case ASEQ(_, r1, r2) => bnullable(r1) && bnullable(r2)
+ case ASTAR(_, _) => true
+}
+
+def bmkeps(r: ARexp) : Bits = r match {
+ case AONE(bs) => bs
+ case AALTS(bs, r::Nil) => bs ++ bmkeps(r)
+ case AALTS(bs, r::rs) =>
+ if (bnullable(r)) bs ++ bmkeps(r) else bmkeps(AALTS(bs, rs))
+ case ASEQ(bs, r1, r2) => bs ++ bmkeps(r1) ++ bmkeps(r2)
+ case ASTAR(bs, r) => bs ++ List(S)
+}
+
+// derivative of a regular expression w.r.t. a character
+def bder(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 AALTS(bs, rs) => AALTS(bs, rs.map(bder(c, _)))
+ case ASEQ(bs, r1, r2) =>
+ if (bnullable(r1)) AALT(bs, ASEQ(Nil, bder(c, r1), r2), fuse(bmkeps(r1), bder(c, r2)))
+ else ASEQ(bs, bder(c, r1), r2)
+ case ASTAR(bs, r) => ASEQ(bs, fuse(List(Z), bder(c, r)), ASTAR(Nil, r))
+}
+
+// derivative w.r.t. a string (iterates bder)
+@tailrec
+def bders (s: List[Char], r: ARexp) : ARexp = s match {
+ case Nil => r
+ case c::s => bders(s, bder(c, r))
+}
+
+// main unsimplified lexing function (produces a bitsequence)
+def blex(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => if (bnullable(r)) bmkeps(r) else throw new Exception("Not matched")
+ case c::cs => blex(bder(c, r), cs)
+}
+
+// calls blex and decodes the value
+def blexing(r: Rexp, s: String) : Val =
+ vdecode(r, blex(internalise(r), s.toList))
+
+
+// example by Tudor
+//val reg = (STAR("a") ~ ("b" | "c")).%
+
+//println(blexing(reg, "aab"))
+
+
+//=======================
+// simplification
+//
+
+def flts(rs: List[ARexp]) : List[ARexp] = rs match {
+ case Nil => Nil
+ case AZERO :: rs => flts(rs)
+ case AALTS(bs, rs1) :: rs => rs1.map(fuse(bs, _)) ++ flts(rs)
+ case r1 :: rs => r1 :: flts(rs)
+}
+
+def bsimp(r: ARexp): ARexp = r match {
+ case ASEQ(bs1, r1, r2) => (bsimp(r1), bsimp(r2)) match {
+ case (AZERO, _) => AZERO
+ case (_, AZERO) => AZERO
+ case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
+ // needed in order to keep the size down
+ case (AALTS(bs, rs), r2) => AALTS(bs1 ++ bs, rs.map(ASEQ(Nil, _, r2)))
+ case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
+ }
+ // distinctBy deletes copies of the same "erased" regex
+ case AALTS(bs1, rs) => (flts(rs.map(bsimp))).distinctBy(erase) match {
+ case Nil => AZERO
+ case r::Nil => fuse(bs1, r)
+ case rs => AALTS(bs1, rs)
+ }
+ case r => r
+}
+
+def blex_simp(r: ARexp, s: List[Char]) : Bits = s match {
+ case Nil => if (bnullable(r)) bmkeps(r)
+ else throw new Exception("Not matched")
+ case c::cs => blex_simp(bsimp(bder(c, r)), cs)
+}
+
+// blexing_simp decodes a value from the bitsequence (potentially slow)
+// blexing2_simp decodes a string-list from the bitsequence
+def blexing_simp(r: Rexp, s: String) : Val =
+ vdecode(r, blex_simp(internalise(r), s.toList))
+
+def blexing2_simp(r: Rexp, s: String) : List[String] =
+ sdecode(r, blex_simp(internalise(r), s.toList))
+
+
+//println(blexing_simp(reg, "aab"))
+
+
+// extracts a string from value
+def flatten(v: Val) : String = v match {
+ case Empty => ""
+ 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
+}
+
+// extracts an environment from a value
+def env(v: Val) : List[(String, String)] = v match {
+ case Empty => 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 Recd(x, v) => (x, flatten(v))::env(v)
+}
+
+def bsize(a: ARexp) = size(erase(a))
+
+// 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 evil1 = STAR(STAR("a")) ~ "b"
+val evil2 = STAR(STAR(STAR("a"))) ~ "b"
+val evil3 = STAR("aa" | "a")
+
+for(i <- 0 to 10000 by 1000) {
+ println(time_needed(1, blexing2_simp(evil1, "a"*i ++ "b")))
+}
+
+for(i <- 0 to 10000 by 1000) {
+ println(time_needed(1, blexing2_simp(evil2, "a"*i ++ "b")))
+}
+
+for(i <- 0 to 10000 by 1000) {
+ println(time_needed(1, blexing2_simp(evil3, "a"*i)))
+}
+*/
+
+// WHILE LANGUAGE
+//================
+def PLUS(r: Rexp) = r ~ r.%
+
+def Range(s : List[Char]) : Rexp = s match {
+ case Nil => ZERO
+ case c::Nil => CHAR(c)
+ case c::s => ALT(CHAR(c), Range(s))
+}
+def RANGE(s: String) = Range(s.toList)
+
+val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")
+val DIGIT = RANGE("0123456789")
+val ID = SYM ~ (SYM | DIGIT).%
+val NUM = PLUS(DIGIT)
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write"
+val SEMI: Rexp = ";"
+val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"
+val WHITESPACE = PLUS(" " | "\n" | "\t")
+val RPAREN: Rexp = "{"
+val LPAREN: Rexp = "}"
+val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+
+val WHILE_REGS = (("k" $ KEYWORD) |
+ ("i" $ ID) |
+ ("o" $ OP) |
+ ("n" $ NUM) |
+ ("s" $ SEMI) |
+ ("str" $ STRING) |
+ ("p" $ (LPAREN | RPAREN)) |
+ ("w" $ WHITESPACE)).%
+
+
+// Some Simple While Tests
+//========================
+
+val prog0 = """read n"""
+println(s"test: $prog0")
+println(env(blexing_simp(WHILE_REGS, prog0)))
+println(blexing2_simp(WHILE_REGS, prog0))
+
+val prog1 = """read n; write n"""
+println(s"test: $prog1")
+println(env(blexing_simp(WHILE_REGS, prog1)))
+println(blexing2_simp(WHILE_REGS, prog1))
+
+val prog2 = """
+write "Fib";
+read n;
+minus1 := 0;
+minus2 := 1;
+while n > 0 do {
+ temp := minus2;
+ minus2 := minus1 + minus2;
+ minus1 := temp;
+ n := n - 1
+};
+write "Result";
+write minus2
+"""
+
+println("lexing fib program (once)")
+println(blexing2_simp(WHILE_REGS, prog2).filter(s => s == "" || !s.startsWith("w")))
+
+val n = 60
+println(s"lexing fib program ($n times, size ${prog2.length * n})")
+println(time_needed(1, blexing2_simp(WHILE_REGS, prog2 * n)))