1 // A parser and interpreter for the While language

     2 // 

     3 

     4 import scala.language.implicitConversions

     5 import scala.language.reflectiveCalls

     6 import scala.collection.immutable._

     7 

     8 // more convenience for the semantic actions later on

     9 case class ~[+A, +B](_1: A, _2: B)

    10 

    11 

    12 type IsSeq[A] = A => Seq[_]

    13 

    14 abstract class Parser[I : IsSeq, T] {

    15   def parse(ts: I): Set[(T, I)]

    16 

    17   def parse_all(ts: I) : Set[T] =

    18     for ((head, tail) <- parse(ts); if tail.isEmpty) yield head

    19 }

    20 

    21 class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], q: => Parser[I, S]) extends Parser[I, ~[T, S]] {

    22   def parse(sb: I) = 

    23     for ((head1, tail1) <- p.parse(sb); 

    24          (head2, tail2) <- q.parse(tail1)) yield (new ~(head1, head2), tail2)

    25 }

    26 

    27 class AltParser[I : IsSeq, T](p: => Parser[I, T], q: => Parser[I, T]) extends Parser[I, T] {

    28   def parse(sb: I) = p.parse(sb) ++ q.parse(sb)   

    29 }

    30 

    31 class MapParser[I : IsSeq, T, S](p: => Parser[I, T], f: T => S) extends Parser[I, S] {

    32   def parse(sb: I) = 

    33     for ((head, tail) <- p.parse(sb)) yield (f(head), tail)

    34 }

    35 

    36 case class StrParser(s: String) extends Parser[String, String] {

    37   def parse(sb: String) = {

    38     val (prefix, suffix) = sb.splitAt(s.length)

    39     if (prefix == s) Set((prefix, suffix)) else Set()

    40   }

    41 }

    42 

    43 case object NumParser extends Parser[String, Int] {

    44   val reg = "[0-9]+".r

    45   def parse(sb: String) = reg.findPrefixOf(sb) match {

    46     case None => Set()

    47     case Some(s) => {

    48       val (head, tail) = sb.splitAt(s.length)

    49       Set((head.toInt, tail)) 

    50     }

    51   }

    52 }

    53 

    54 

    55 implicit def parser_interpolation(sc: StringContext) = new {

    56     def p(args: Any*) = StrParser(sc.s(args:_*))

    57 }

    58 

    59 // this string interpolation allows us to write 

    60 // things like the following for a StrParser

    61 //

    62 // p"<_some_string_>" 

    63 //

    64 // instead of StrParser(<_some_string_>)

    65 

    66 

    67 implicit def ParserOps[I : IsSeq, T](p: Parser[I, T]) = new {

    68   def ||(q : => Parser[I, T]) = new AltParser[I, T](p, q)

    69   def ~[S](q : => Parser[I, S]) = new SeqParser[I, T, S](p, q)

    70   def map[S](f: => T => S) = new MapParser[I, T, S](p, f)

    71 }

    72 

    73 // these implicits allow us to use infic notation for

    74 // sequences and alternatives; we also can write map

    75 // for a parser

    76 

    77 

    78 // the abstract syntax trees for the WHILE language

    79 abstract class Stmt

    80 abstract class AExp

    81 abstract class BExp 

    82 

    83 type Block = List[Stmt]

    84 

    85 case object Skip extends Stmt

    86 case class If(a: BExp, bl1: Block, bl2: Block) extends Stmt

    87 case class While(b: BExp, bl: Block) extends Stmt

    88 case class Assign(s: String, a: AExp) extends Stmt

    89 case class Write(s: String) extends Stmt

    90 

    91 

    92 case class Var(s: String) extends AExp

    93 case class Num(i: Int) extends AExp

    94 case class Aop(o: String, a1: AExp, a2: AExp) extends AExp

    95 

    96 case object True extends BExp

    97 case object False extends BExp

    98 case class Bop(o: String, a1: AExp, a2: AExp) extends BExp

    99 case class And(b1: BExp, b2: BExp) extends BExp

   100 case class Or(b1: BExp, b2: BExp) extends BExp

   101 

   102 case object IdParser extends Parser[String, String] {

   103   val reg = "[a-z][a-z,0-9]*".r

   104   def parse(sb: String) = reg.findPrefixOf(sb) match {

   105     case None => Set()

   106     case Some(s) => Set(sb.splitAt(s.length))

   107   }

   108 }

   109 

   110 // arithmetic expressions

   111 lazy val AExp: Parser[String, AExp] = 

   112   (Te ~ p"+" ~ AExp).map[AExp]{ case x ~ _ ~ z => Aop("+", x, z) } ||

   113   (Te ~ p"-" ~ AExp).map[AExp]{ case x ~ _ ~ z => Aop("-", x, z) } || Te

   114 lazy val Te: Parser[String, AExp] = 

   115   (Fa ~ p"*" ~ Te).map[AExp]{ case x ~ _ ~ z => Aop("*", x, z) } || 

   116   (Fa ~ p"/" ~ Te).map[AExp]{ case x ~ _ ~ z => Aop("/", x, z) } || Fa  

   117 lazy val Fa: Parser[String, AExp] = 

   118    (p"(" ~ AExp ~ p")").map{ case _ ~ y ~ _ => y } || 

   119    IdParser.map(Var) || 

   120    NumParser.map(Num)

   121 

   122 // boolean expressions with some simple nesting

   123 lazy val BExp: Parser[String, BExp] = 

   124    (AExp ~ p"==" ~ AExp).map { case x ~ _ ~ z => Bop("==", x, z): BExp } || 

   125    (AExp ~ p"!=" ~ AExp).map { case x ~ _ ~ z => Bop("!=", x, z): BExp } || 

   126    (AExp ~ p"<" ~ AExp).map { case x ~ _ ~ z => Bop("<", x, z): BExp } || 

   127    (AExp ~ p">" ~ AExp).map { case x ~ _ ~ z => Bop(">", x, z): BExp } ||

   128    (p"(" ~ BExp ~ p")" ~ p"&&" ~ BExp).map { case _ ~ y ~ _ ~ _ ~ v => And(y, v): BExp } ||

   129    (p"(" ~ BExp ~ p")" ~ p"||" ~ BExp).map { case _ ~ y ~ _ ~ _ ~ v => Or(y, v): BExp } ||

   130    (p"true".map { _ => True: BExp }) || 

   131    (p"false".map { _ => False: BExp }) ||

   132    (p"(" ~ BExp ~ p")").map { case _ ~ x ~ _ => x }

   133 

   134 // statement / statements

   135 lazy val Stmt: Parser[String, Stmt] =

   136   ((p"skip".map {_ => Skip: Stmt}) ||

   137    (IdParser ~ p":=" ~ AExp).map { case x ~ _ ~ z => Assign(x, z): Stmt } ||

   138    (p"write(" ~ IdParser ~ p")").map { case _ ~ y ~ _ => Write(y): Stmt } ||

   139    (p"if" ~ BExp ~ p"then" ~ Block ~ p"else" ~ Block)

   140     .map{ case _ ~ y ~ _ ~ u ~ _ ~ w => If(y, u, w): Stmt } ||

   141    (p"while" ~ BExp ~ p"do" ~ Block).map { case _ ~ y ~ _ ~ w => While(y, w) }) 

   142  

   143 lazy val Stmts: Parser[String, Block] =

   144   (Stmt ~ p";" ~ Stmts).map { case x ~ _ ~ z => x :: z : Block } ||

   145   (Stmt.map { s => List(s) : Block})

   146 

   147 // blocks (enclosed in curly braces)

   148 lazy val Block: Parser[String, Block] =

   149   ((p"{" ~ Stmts ~ p"}").map{ case _ ~ y ~ _ => y } || 

   150    (Stmt.map(s => List(s))))

   151 

   152 

   153 Stmts.parse_all("x2:=5+3;")

   154 Block.parse_all("{x:=5;y:=8}")

   155 Block.parse_all("if(false)then{x:=5}else{x:=10}")

   156 

   157 val fib = """n := 10;

   158              minus1 := 0;

   159              minus2 := 1;

   160              temp := 0;

   161              while (n > 0) do {

   162                  temp := minus2;

   163                  minus2 := minus1 + minus2;

   164                  minus1 := temp;

   165                  n := n - 1

   166              };

   167              result := minus2""".replaceAll("\\s+", "")

   168 

   169 Stmts.parse_all(fib)

   170 

   171 

   172 // an interpreter for the WHILE language

   173 type Env = Map[String, Int]

   174 

   175 def eval_aexp(a: AExp, env: Env) : Int = a match {

   176   case Num(i) => i

   177   case Var(s) => env(s)

   178   case Aop("+", a1, a2) => eval_aexp(a1, env) + eval_aexp(a2, env)

   179   case Aop("-", a1, a2) => eval_aexp(a1, env) - eval_aexp(a2, env)

   180   case Aop("*", a1, a2) => eval_aexp(a1, env) * eval_aexp(a2, env)

   181   case Aop("/", a1, a2) => eval_aexp(a1, env) / eval_aexp(a2, env)

   182 }

   183 

   184 def eval_bexp(b: BExp, env: Env) : Boolean = b match {

   185   case True => true

   186   case False => false

   187   case Bop("==", a1, a2) => eval_aexp(a1, env) == eval_aexp(a2, env)

   188   case Bop("!=", a1, a2) => !(eval_aexp(a1, env) == eval_aexp(a2, env))

   189   case Bop(">", a1, a2) => eval_aexp(a1, env) > eval_aexp(a2, env)

   190   case Bop("<", a1, a2) => eval_aexp(a1, env) < eval_aexp(a2, env)

   191   case And(b1, b2) => eval_bexp(b1, env) && eval_bexp(b2, env)

   192   case Or(b1, b2) => eval_bexp(b1, env) || eval_bexp(b2, env)

   193 }

   194 

   195 def eval_stmt(s: Stmt, env: Env) : Env = s match {

   196   case Skip => env

   197   case Assign(x, a) => env + (x -> eval_aexp(a, env))

   198   case If(b, bl1, bl2) => if (eval_bexp(b, env)) eval_bl(bl1, env) else eval_bl(bl2, env) 

   199   case While(b, bl) => 

   200     if (eval_bexp(b, env)) eval_stmt(While(b, bl), eval_bl(bl, env))

   201     else env

   202   case Write(x) => { println(env(x)) ; env }  

   203 }

   204 

   205 def eval_bl(bl: Block, env: Env) : Env = bl match {

   206   case Nil => env

   207   case s::bl => eval_bl(bl, eval_stmt(s, env))

   208 }

   209 

   210 def eval(bl: Block) : Env = eval_bl(bl, Map())

   211 

   212 // parse + evaluate fib program; then lookup what is

   213 // stored under the variable result 

   214 println(eval(Stmts.parse_all(fib).head)("result"))

   215 

   216 

   217 // more examles

   218 

   219 // calculate and print all factors bigger 

   220 // than 1 and smaller than n

   221 println("Factors")

   222 

   223 val factors =  

   224    """n := 12;

   225       f := 2;

   226       while (f < n / 2 + 1) do {

   227         if ((n / f) * f == n) then  { write(f) } else { skip };

   228         f := f + 1

   229       }""".replaceAll("\\s+", "")

   230 

   231 eval(Stmts.parse_all(factors).head)

   232 

   233 // calculate all prime numbers up to a number 

   234 println("Primes")

   235 

   236 val primes =  

   237    """end := 100;

   238       n := 2;

   239       while (n < end) do {

   240         f := 2;

   241         tmp := 0;

   242         while ((f < n / 2 + 1) && (tmp == 0)) do {

   243           if ((n / f) * f == n) then  { tmp := 1 } else { skip };

   244           f := f + 1

   245         };

   246         if (tmp == 0) then { write(n) } else { skip };

   247         n  := n + 1

   248       }""".replaceAll("\\s+", "")

   249 

   250 eval(Stmts.parse_all(primes).head)