1 // A simple lexer inspired by work of Sulzmann & Lu

     2 //==================================================

     3 //

     4 // Call the test cases with 

     5 //

     6 //   amm lexer.sc small

     7 //   amm lexer.sc fib

     8 //   amm lexer.sc loops

     9 //

    10 //   amm lexer.sc all

    11 

    12 

    13 // regular expressions including records

    14 abstract class Rexp 

    15 case object ZERO extends Rexp

    16 case object ONE extends Rexp

    17 case class CHAR(c: Char) extends Rexp

    18 case class ALT(r1: Rexp, r2: Rexp) extends Rexp 

    19 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 

    20 case class STAR(r: Rexp) extends Rexp 

    21 case class RECD(x: String, r: Rexp) extends Rexp  

    22                 // records for extracting strings or tokens

    23   

    24 // values  

    25 abstract class Val

    26 case object Empty extends Val

    27 case class Chr(c: Char) extends Val

    28 case class Sequ(v1: Val, v2: Val) extends Val

    29 case class Left(v: Val) extends Val

    30 case class Right(v: Val) extends Val

    31 case class Stars(vs: List[Val]) extends Val

    32 case class Rec(x: String, v: Val) extends Val

    33    

    34 // some convenience for typing in regular expressions

    35 import scala.language.implicitConversions    

    36 import scala.language.reflectiveCalls

    37 

    38 def charlist2rexp(s : List[Char]): Rexp = s match {

    39   case Nil => ONE

    40   case c::Nil => CHAR(c)

    41   case c::s => SEQ(CHAR(c), charlist2rexp(s))

    42 }

    43 implicit def string2rexp(s : String) : Rexp = 

    44   charlist2rexp(s.toList)

    45 

    46 implicit def RexpOps(r: Rexp) = new {

    47   def | (s: Rexp) = ALT(r, s)

    48   def % = STAR(r)

    49   def ~ (s: Rexp) = SEQ(r, s)

    50 }

    51 

    52 implicit def stringOps(s: String) = new {

    53   def | (r: Rexp) = ALT(s, r)

    54   def | (r: String) = ALT(s, r)

    55   def % = STAR(s)

    56   def ~ (r: Rexp) = SEQ(s, r)

    57   def ~ (r: String) = SEQ(s, r)

    58   def $ (r: Rexp) = RECD(s, r)

    59 }

    60 

    61 def nullable(r: Rexp) : Boolean = r match {

    62   case ZERO => false

    63   case ONE => true

    64   case CHAR(_) => false

    65   case ALT(r1, r2) => nullable(r1) || nullable(r2)

    66   case SEQ(r1, r2) => nullable(r1) && nullable(r2)

    67   case STAR(_) => true

    68   case RECD(_, r1) => nullable(r1)

    69 }

    70 

    71 def der(c: Char, r: Rexp) : Rexp = r match {

    72   case ZERO => ZERO

    73   case ONE => ZERO

    74   case CHAR(d) => if (c == d) ONE else ZERO

    75   case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))

    76   case SEQ(r1, r2) => 

    77     if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))

    78     else SEQ(der(c, r1), r2)

    79   case STAR(r) => SEQ(der(c, r), STAR(r))

    80   case RECD(_, r1) => der(c, r1)

    81 }

    82 

    83 

    84 // extracts a string from value

    85 def flatten(v: Val) : String = v match {

    86   case Empty => ""

    87   case Chr(c) => c.toString

    88   case Left(v) => flatten(v)

    89   case Right(v) => flatten(v)

    90   case Sequ(v1, v2) => flatten(v1) ++ flatten(v2)

    91   case Stars(vs) => vs.map(flatten).mkString

    92   case Rec(_, v) => flatten(v)

    93 }

    94 

    95 

    96 // extracts an environment from a value;

    97 // used for tokenising a string

    98 def env(v: Val) : List[(String, String)] = v match {

    99   case Empty => Nil

   100   case Chr(c) => Nil

   101   case Left(v) => env(v)

   102   case Right(v) => env(v)

   103   case Sequ(v1, v2) => env(v1) ::: env(v2)

   104   case Stars(vs) => vs.flatMap(env)

   105   case Rec(x, v) => (x, flatten(v))::env(v)

   106 }

   107 

   108 

   109 // The injection and mkeps part of the lexer

   110 //===========================================

   111 

   112 def mkeps(r: Rexp) : Val = r match {

   113   case ONE => Empty

   114   case ALT(r1, r2) => 

   115     if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))

   116   case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))

   117   case STAR(r) => Stars(Nil)

   118   case RECD(x, r) => Rec(x, mkeps(r))

   119 }

   120 

   121 def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {

   122   case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)

   123   case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)

   124   case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)

   125   case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))

   126   case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))

   127   case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))

   128   case (CHAR(d), Empty) => Chr(c) 

   129   case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))

   130 }

   131 

   132 // some "rectification" functions for simplification

   133 def F_ID(v: Val): Val = v

   134 def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))

   135 def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))

   136 def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {

   137   case Right(v) => Right(f2(v))

   138   case Left(v) => Left(f1(v))

   139 }

   140 def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {

   141   case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))

   142 }

   143 def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 

   144   (v:Val) => Sequ(f1(Empty), f2(v))

   145 def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 

   146   (v:Val) => Sequ(f1(v), f2(Empty))

   147 def F_RECD(f: Val => Val) = (v:Val) => v match {

   148   case Rec(x, v) => Rec(x, f(v))

   149 }

   150 def F_ERROR(v: Val): Val = throw new Exception("error")

   151 

   152 // simplification

   153 def simp(r: Rexp): (Rexp, Val => Val) = r match {

   154   case ALT(r1, r2) => {

   155     val (r1s, f1s) = simp(r1)

   156     val (r2s, f2s) = simp(r2)

   157     (r1s, r2s) match {

   158       case (ZERO, _) => (r2s, F_RIGHT(f2s))

   159       case (_, ZERO) => (r1s, F_LEFT(f1s))

   160       case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))

   161                 else (ALT (r1s, r2s), F_ALT(f1s, f2s)) 

   162     }

   163   }

   164   case SEQ(r1, r2) => {

   165     val (r1s, f1s) = simp(r1)

   166     val (r2s, f2s) = simp(r2)

   167     (r1s, r2s) match {

   168       case (ZERO, _) => (ZERO, F_ERROR)

   169       case (_, ZERO) => (ZERO, F_ERROR)

   170       case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))

   171       case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))

   172       case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))

   173     }

   174   }

   175   case r => (r, F_ID)

   176 }

   177 

   178 // lexing functions including simplification

   179 def lex_simp(r: Rexp, s: List[Char]) : Val = s match {

   180   case Nil => if (nullable(r)) mkeps(r) else 

   181     { throw new Exception("lexing error") } 

   182   case c::cs => {

   183     val (r_simp, f_simp) = simp(der(c, r))

   184     inj(r, c, f_simp(lex_simp(r_simp, cs)))

   185   }

   186 }

   187 

   188 def lexing_simp(r: Rexp, s: String) = 

   189   env(lex_simp(r, s.toList))

   190 

   191 

   192 // The Lexing Rules for the WHILE Language

   193 

   194 def PLUS(r: Rexp) = r ~ r.%

   195 

   196 def Range(s : List[Char]) : Rexp = s match {

   197   case Nil => ZERO

   198   case c::Nil => CHAR(c)

   199   case c::s => ALT(CHAR(c), Range(s))

   200 }

   201 def RANGE(s: String) = Range(s.toList)

   202 

   203 val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")

   204 val DIGIT = RANGE("0123456789")

   205 val ID = SYM ~ (SYM | DIGIT).% 

   206 val NUM = PLUS(DIGIT)

   207 val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" 

   208 val SEMI: Rexp = ";"

   209 val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"

   210 val WHITESPACE = PLUS(" " | "\n" | "\t")

   211 val RPAREN: Rexp = "{"

   212 val LPAREN: Rexp = "}"

   213 val STRING: Rexp = "\"" ~ SYM.% ~ "\""

   214 

   215 

   216 val WHILE_REGS = (("k" $ KEYWORD) | 

   217                   ("i" $ ID) | 

   218                   ("o" $ OP) | 

   219                   ("n" $ NUM) | 

   220                   ("s" $ SEMI) | 

   221                   ("str" $ STRING) |

   222                   ("p" $ (LPAREN | RPAREN)) | 

   223                   ("w" $ WHITESPACE)).%

   224 

   225 

   226 // Two Simple While Tests

   227 //========================

   228 

   229 @doc("small tests")

   230 @main

   231 def small() = {

   232 

   233   val prog0 = """read n"""

   234   println(s"test: $prog0")

   235   println(lexing_simp(WHILE_REGS, prog0))

   236 

   237   val prog1 = """read  n; write n"""  

   238   println(s"test: $prog1")

   239   println(lexing_simp(WHILE_REGS, prog1))

   240 }

   241 

   242 // Bigger Tests

   243 //==============

   244 

   245 // escapes strings and prints them out as "", "\n" and so on

   246 def esc(raw: String): String = {

   247   import scala.reflect.runtime.universe._

   248   Literal(Constant(raw)).toString

   249 }

   250 

   251 def escape(tks: List[(String, String)]) =

   252   tks.map{ case (s1, s2) => (s1, esc(s2))}

   253 

   254 

   255 val prog2 = """

   256 write "Fib";

   257 read n;

   258 minus1 := 0;

   259 minus2 := 1;

   260 while n > 0 do {

   261   temp := minus2;

   262   minus2 := minus1 + minus2;

   263   minus1 := temp;

   264   n := n - 1

   265 };

   266 write "Result";

   267 write minus2

   268 """

   269 

   270 @doc("Fibonacci test")

   271 @main

   272 def fib() = {

   273   println("lexing fib program")

   274   println(escape(lexing_simp(WHILE_REGS, prog2)).mkString("\n"))

   275 }

   276 

   277 

   278 val prog3 = """

   279 start := 1000;

   280 x := start;

   281 y := start;

   282 z := start;

   283 while 0 < x do {

   284  while 0 < y do {

   285   while 0 < z do {

   286     z := z - 1

   287   };

   288   z := start;

   289   y := y - 1

   290  };     

   291  y := start;

   292  x := x - 1

   293 }

   294 """

   295 

   296 @doc("Loops test")

   297 @main

   298 def loops() = {

   299   println("lexing Loops")

   300   println(escape(lexing_simp(WHILE_REGS, prog3)).mkString("\n"))

   301 }

   302 

   303 

   304 

   305 

   306 @doc("All tests.")

   307 @main

   308 def all() = { small(); fib() ; loops() }