1 // Parser Combinators: Simple Version

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

     3 

     4 

     5 // more convenience for the map parsers later on

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

     7 

     8 /* 

     9   Note, in the lectures I did not show the implicit type constraint

    10   I : IsSeq, which means that the input type 'I' needs to be

    11   a sequence. 

    12 */

    13 

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

    15 

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

    17   def parse(in: I): Set[(T, I)]

    18 

    19   def parse_all(in: I) : Set[T] =

    20     for ((hd, tl) <- parse(in); 

    21         if tl.isEmpty) yield hd

    22 }

    23 

    24 // parser combinators

    25 

    26 // sequence parser

    27 class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], 

    28                                  q: => Parser[I, S]) extends Parser[I, ~[T, S]] {

    29   def parse(in: I) = 

    30     for ((hd1, tl1) <- p.parse(in); 

    31          (hd2, tl2) <- q.parse(tl1)) yield (new ~(hd1, hd2), tl2)

    32 }

    33 

    34 // alternative parser

    35 class AltParser[I : IsSeq, T](p: => Parser[I, T], 

    36                               q: => Parser[I, T]) extends Parser[I, T] {

    37   def parse(in: I) = p.parse(in) ++ q.parse(in)   

    38 }

    39 

    40 // map parser

    41 class MapParser[I : IsSeq, T, S](p: => Parser[I, T], 

    42                                  f: T => S) extends Parser[I, S] {

    43   def parse(in: I) = for ((hd, tl) <- p.parse(in)) yield (f(hd), tl)

    44 }

    45 

    46 

    47 

    48 // atomic parser for (particular) strings

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

    50   def parse(sb: String) = {

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

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

    53   }

    54 }

    55 

    56 // atomic parser for identifiers (variable names)

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

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

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

    60     case None => Set()

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

    62   }

    63 }

    64 

    65 

    66 // atomic parser for numbers (transformed into ints)

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

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

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

    70     case None => Set()

    71     case Some(s) => {

    72       val (hd, tl) = sb.splitAt(s.length)

    73       Set((hd.toInt, tl)) 

    74     }

    75   }

    76 }

    77 

    78 // the following string interpolation allows us to write 

    79 // StrParser(_some_string_) more conveniently as 

    80 //

    81 // p"<_some_string_>" 

    82 

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

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

    85 }    

    86 

    87 // more convenient syntax for parser combinators

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

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

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

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

    92 }

    93 

    94 

    95 

    96 // the abstract syntax trees for the WHILE language

    97 abstract class Stmt

    98 abstract class AExp

    99 abstract class BExp 

   100 

   101 type Block = List[Stmt]

   102 

   103 case object Skip extends Stmt

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

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

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

   107 case class Write(s: String) extends Stmt

   108 

   109 case class Var(s: String) extends AExp

   110 case class Num(i: Int) extends AExp

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

   112 

   113 case object True extends BExp

   114 case object False extends BExp

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

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

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

   118 

   119 

   120 // arithmetic expressions

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

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

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

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

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

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

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

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

   129    IdParser.map(Var) || 

   130    NumParser.map(Num)

   131 

   132 // boolean expressions with some simple nesting

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

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

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

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

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

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

   139    (p"(" ~ BExp ~ p")" ~ p"||" ~ BExp).map[BExp]{ case _ ~ y ~ _ ~ _ ~ v => Or(y, v) } ||

   140    (p"true".map[BExp]{ _ => True }) || 

   141    (p"false".map[BExp]{ _ => False }) ||

   142    (p"(" ~ BExp ~ p")").map[BExp]{ case _ ~ x ~ _ => x }

   143 

   144 // statement 

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

   146   ((p"skip".map[Stmt]{_ => Skip }) ||

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

   148    (p"write(" ~ IdParser ~ p")").map[Stmt]{ case _ ~ y ~ _ => Write(y) } ||

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

   150      .map[Stmt]{ case _ ~ y ~ _ ~ u ~ _ ~ w => If(y, u, w) } ||

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

   152  

   153 // statements

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

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

   156   (Stmt.map[Block]{ s => List(s) })

   157 

   158 // blocks (enclosed in curly braces)

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

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

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

   162 

   163 

   164 // Examples

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

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

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

   168 

   169 

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

   171              minus1 := 0;

   172              minus2 := 1;

   173              temp := 0;

   174              while (n > 0) do {

   175                  temp := minus2;

   176                  minus2 := minus1 + minus2;

   177                  minus1 := temp;

   178                  n := n - 1

   179              };

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

   181 

   182 Stmts.parse_all(fib)

   183 

   184 

   185 // an interpreter for the WHILE language

   186 type Env = Map[String, Int]

   187 

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

   189   case Num(i) => i

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

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

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

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

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

   195 }

   196 

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

   198   case True => true

   199   case False => false

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

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

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

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

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

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

   206 }

   207 

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

   209   case Skip => env

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

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

   212   case While(b, bl) => 

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

   214     else env

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

   216 }

   217 

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

   219   case Nil => env

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

   221 }

   222 

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

   224 

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

   226 // stored under the variable result 

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

   228 

   229 

   230 // more examles

   231 

   232 // calculate and print all factors bigger 

   233 // than 1 and smaller than n

   234 println("Factors")

   235 

   236 val factors =  

   237    """n := 12;

   238       f := 2;

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

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

   241         f := f + 1

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

   243 

   244 println(eval(Stmts.parse_all(factors).head))

   245 

   246 // calculate all prime numbers up to a number 

   247 println("Primes")

   248 

   249 val primes =  

   250    """end := 100;

   251       n := 2;

   252       while (n < end) do {

   253         f := 2;

   254         tmp := 0;

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

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

   257           f := f + 1

   258         };

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

   260         n  := n + 1

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

   262 

   263 println(eval(Stmts.parse_all(primes).head))