diff -r c669b39debe3 -r b147a10be8dd progs/lexer/token2.scala --- a/progs/lexer/token2.scala Mon Jun 29 22:19:05 2020 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,463 +0,0 @@ -import scala.language.implicitConversions -import scala.language.reflectiveCalls -import scala.annotation.tailrec - -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 -case class CRANGE(cs: String) extends Rexp -case class PLUS(r: Rexp) extends Rexp -case class OPT(r: Rexp) extends Rexp -case class NTIMES(r: Rexp, n: Int) extends Rexp - -abstract class Val -case object Empty extends Val -case class Chr(c: Char) extends Val -case class Seq(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 - -// some convenience for typing in regular expressions -def charlist2rexp(s : List[Char]): Rexp = s match { - case Nil => EMPTY - 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) -} - -// 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(_, r) => nullable(r) - case CRANGE(_) => false - case PLUS(r) => nullable(r) - case OPT(_) => true - case NTIMES(r, n) => if (n == 0) true else nullable(r) -} - -// 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) - case CRANGE(cs) => if (cs.contains(c)) EMPTY else NULL - case PLUS(r) => SEQ(der(c, r), STAR(r)) - case OPT(r) => ALT(der(c, r), NULL) - case NTIMES(r, n) => if (n == 0) NULL else der(c, SEQ(r, NTIMES(r, n - 1))) -} - -// 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)) -} - -// 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 Seq(v1, v2) => flatten(v1) + flatten(v2) - case Stars(vs) => vs.map(flatten).mkString - case Rec(_, v) => flatten(v) -} - -// 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 Seq(v1, v2) => env(v1) ::: env(v2) - case Stars(vs) => vs.flatMap(env) - case Rec(x, v) => (x, flatten(v))::env(v) -} - -// injection part -def mkeps(r: Rexp) : Val = r match { - case EMPTY => Empty - case ALT(r1, r2) => - if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2)) - case SEQ(r1, r2) => Seq(mkeps(r1), mkeps(r2)) - case STAR(r) => Stars(Nil) - case RECD(x, r) => Rec(x, mkeps(r)) - case PLUS(r) => Stars(List(mkeps(r))) - case OPT(_) => Right(Empty) - case NTIMES(r, n) => if (n == 0) Stars(Nil) else Stars(Nil.padTo(n, mkeps(r))) - case _ => { println ("r : " + r.toString); - throw new Exception("mkeps error")} -} - - -def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match { - case (STAR(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs) - case (SEQ(r1, r2), Seq(v1, v2)) => Seq(inj(r1, c, v1), v2) - case (SEQ(r1, r2), Left(Seq(v1, v2))) => Seq(inj(r1, c, v1), v2) - case (SEQ(r1, r2), Right(v2)) => Seq(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(_), Empty) => Chr(c) - case (CRANGE(_), Empty) => Chr(c) - case (RECD(x, r1), _) => Rec(x, inj(r1, c, v)) - case (PLUS(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs) - case (OPT(r), Left(v1)) => Left(inj(r, c, v1)) - case (NTIMES(r, n), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs) - case (NTIMES(r, n), Left(Seq(v1, Stars(vs)))) => Stars(inj(r, c, v1)::vs) - case (NTIMES(r, n), Right(Stars(v::vs))) => Stars(mkeps(r)::inj(r, c, v)::vs) - case _ => { println ("r : " + r.toString + " v: " + v.toString); - throw new Exception("inj error")} -} - -// 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)) -} - -def lexing(r: Rexp, s: String) : Val = lex(r, s.toList) - -lexing(("ab" | "ab") ~ ("b" | EMPTY), "ab") - -lexing(OPT("ab"), "ab") - -lexing(NTIMES("1", 3), "111") -lexing(NTIMES("1" | EMPTY, 3), "11") - -// some "rectification" functions for simplification -def F_ID(v: Val): Val = v -def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v)) -def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v)) -def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match { - case Right(v) => Right(f2(v)) - case Left(v) => Left(f1(v)) -} -def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match { - case Seq(v1, v2) => Seq(f1(v1), f2(v2)) -} -def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = - (v:Val) => Seq(f1(Empty), f2(v)) -def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = - (v:Val) => Seq(f1(v), f2(Empty)) -def F_RECD(f: Val => Val) = (v:Val) => v match { - case Rec(x, v) => Rec(x, f(v)) -} -def F_ERROR(v: Val): Val = throw new Exception("error") - -// simplification of regular expressions returning also an -// rectification function; no simplification under STAR -def simp(r: Rexp): (Rexp, Val => Val) = r match { - case ALT(r1, r2) => { - val (r1s, f1s) = simp(r1) - val (r2s, f2s) = simp(r2) - (r1s, r2s) match { - case (NULL, _) => (r2s, F_RIGHT(f2s)) - case (_, NULL) => (r1s, F_LEFT(f1s)) - case _ => if (r1s == r2s) (r1s, F_LEFT(f1s)) - else (ALT (r1s, r2s), F_ALT(f1s, f2s)) - } - } - case SEQ(r1, r2) => { - val (r1s, f1s) = simp(r1) - val (r2s, f2s) = simp(r2) - (r1s, r2s) match { - case (NULL, _) => (NULL, F_ERROR) - case (_, NULL) => (NULL, F_ERROR) - case (EMPTY, _) => (r2s, F_SEQ_Empty1(f1s, f2s)) - case (_, EMPTY) => (r1s, F_SEQ_Empty2(f1s, f2s)) - case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s)) - } - } - case RECD(x, r1) => { - val (r1s, f1s) = simp(r1) - (RECD(x, r1s), F_RECD(f1s)) - } - case r => (r, F_ID) -} - -def lex_simp(r: Rexp, s: List[Char]) : Val = s match { - case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched") - case c::cs => { - val (r_simp, f_simp) = simp(der(c, r)) - inj(r, c, f_simp(lex_simp(r_simp, cs))) - } -} - -def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList) - -lexing_simp(("a" | "ab") ~ ("b" | ""), "ab") - -lexing_simp(OPT("ab"), "ab") - -// Lexing Rules for a Small While Language - -val SYM = CRANGE("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ") -val DIGIT = CRANGE("0123456789") -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 = (("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 { (s) => s._1 == "w"} - -// Testing -//============ - -def time[T](code: => T) = { - val start = System.nanoTime() - val result = code - val end = System.nanoTime() - println((end - start)/1.0e9) - result -} - -println(lexing_simp(OPT("1"), "1")) -println(lexing_simp(OPT("1"), "")) -println(ders("111".toList, NTIMES("1",3))) -println(lexing_simp(NTIMES("1",3), "111")) - -val r1 = ("a" | "ab") ~ ("bcd" | "c") -println(lexing(r1, "abcd")) - -val r2 = ("" | "a") ~ ("ab" | "b") -println(lexing(r2, "ab")) - - -// Two Simple While Tests -//======================== -println("prog0 test") - -val prog0 = """read n""" -println(env(lexing_simp(WHILE_REGS, prog0))) - -println("prog1 test") - -val prog1 = """read n; write (n)""" -println(env(lexing_simp(WHILE_REGS, prog1))) - - -// Big Test -//========== - -def escape(raw: String): String = { - import scala.reflect.runtime.universe._ - Literal(Constant(raw)).toString -} - -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 -""" - -val prog3 = """ -start := 1000; -x := start; -y := start; -z := start; -while 0 < x do { - while 0 < y do { - while 0 < z do { - z := z - 1 - }; - z := start; - y := y - 1 - }; - y := start; - x := x - 1 -} -""" - - -println("Tokens") -println(tokenise(WHILE_REGS, prog2).mkString("\n")) - -val fib_tokens = tokenise(WHILE_REGS, prog2) -fib_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n") - - -val test_tokens = tokenise(WHILE_REGS, prog3) -test_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n") - - -/* -for (i <- 1 to 120 by 10) { - print(i.toString + ": ") - time(lexing_simp(WHILE_REGS, prog2 * i)) -} -*/ - -val toks_fib = - List(("k","write"), - ("str","Fib"), - ("s",";"), - ("k","read"), - ("i","n"), - ("s",";"), - ("i","minus1"), - ("o",":="), - ("n","0"), - ("s",";"), - ("i","minus2"), - ("o",":="), - ("n","1"), - ("s",";"), - ("k","while"), - ("i","n"), - ("o",">"), - ("n","0"), - ("k","do"), - ("b","{"), - ("i","temp"), - ("o",":="), - ("i","minus2"), - ("s",";"), - ("i","minus2"), - ("o",":="), - ("i","minus1"), - ("o","+"), - ("i","minus2"), - ("s",";"), - ("i","minus1"), - ("o",":="), - ("i","temp"), - ("s",";"), - ("i","n"), - ("o",":="), - ("i","n"), - ("o","-"), - ("n","1"), - ("b","}"), - ("s",";"), - ("k","write"), - ("str","Result"), - ("s",";"), - ("k","write"), - ("i","minus2")) - -val toks_test = - List(("i","start"), - ("o",":="), - ("n","1000"), - ("s",";"), - ("i","x"), - ("o",":="), - ("i","start"), - ("s",";"), - ("i","y"), - ("o",":="), - ("i","start"), - ("s",";"), - ("i","z"), - ("o",":="), - ("i","start"), - ("s",";"), - ("k","while"), - ("n","0"), - ("o","<"), - ("i","x"), - ("k","do"), - ("b","{"), - ("k","while"), - ("n","0"), - ("o","<"), - ("i","y"), - ("k","do"), - ("b","{"), - ("k","while"), - ("n","0"), - ("o","<"), - ("i","z"), - ("k","do"), - ("b","{"), - ("i","z"), - ("o",":="), - ("i","z"), - ("o","-"), - ("n","1"), - ("b","}"), - ("s",";"), - ("i","z"), - ("o",":="), - ("i","start"), - ("s",";"), - ("i","y"), - ("o",":="), - ("i","y"), - ("o","-"), - ("n","1"), - ("b","}"), - ("s",";"), - ("i","y"), - ("o",":="), - ("i","start"), - ("s",";"), - ("i","x"), - ("o",":="), - ("i","x"), - ("o","-"), - ("n","1"), - ("b","}"))