1 // A parser and evaluator for the while language

     2 // 

     3 import matcher._

     4 import parser._

     5 

     6 

     7 // some regular expressions

     8 val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")

     9 val DIGIT = RANGE("0123456789")

    10 val ID = SEQ(SYM, STAR(ALT(SYM, DIGIT))) 

    11 val NUM = PLUS(DIGIT)

    12 val KEYWORD = ALTS("skip", "while", "do", "if", "then", "else", "true", "false") 

    13 val SEMI: Rexp = ";"

    14 val OP: Rexp = ALTS(":=", "=", "-", "+", "*", "!=", "<", ">")

    15 val WHITESPACE = PLUS(RANGE(" \n"))

    16 val RPAREN: Rexp = ")"

    17 val LPAREN: Rexp = "("

    18 val BEGIN: Rexp = "{"

    19 val END: Rexp = "}"

    20 

    21 // tokens for classifying the strings that have been recognised

    22 abstract class Token

    23 case object T_WHITESPACE extends Token

    24 case object T_SEMI extends Token

    25 case object T_LPAREN extends Token

    26 case object T_RPAREN extends Token

    27 case object T_BEGIN extends Token

    28 case object T_END extends Token

    29 case class T_ID(s: String) extends Token

    30 case class T_OP(s: String) extends Token

    31 case class T_NUM(s: String) extends Token

    32 case class T_KWD(s: String) extends Token

    33 

    34 val lexing_rules: List[(Rexp, List[Char] => Token)] = 

    35   List((KEYWORD, (s) => T_KWD(s.mkString)),

    36        (ID, (s) => T_ID(s.mkString)),

    37        (OP, (s) => T_OP(s.mkString)),

    38        (NUM, (s) => T_NUM(s.mkString)),

    39        (SEMI, (s) => T_SEMI),

    40        (LPAREN, (s) => T_LPAREN),

    41        (RPAREN, (s) => T_RPAREN),

    42        (BEGIN, (s) => T_BEGIN),

    43        (END, (s) => T_END),

    44        (WHITESPACE, (s) => T_WHITESPACE))

    45 

    46 // the tokenizer

    47 val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE))

    48 

    49 // the abstract syntax trees

    50 abstract class Stmt

    51 abstract class AExp

    52 abstract class BExp 

    53 type Block = List[Stmt]

    54 case object Skip extends Stmt

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

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

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

    58 

    59 case class Var(s: String) extends AExp

    60 case class Num(i: Int) extends AExp

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

    62 

    63 case object True extends BExp

    64 case object False extends BExp

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

    66 

    67 // atomic parsers

    68 case class TokParser(tok: Token) extends Parser[List[Token], Token] {

    69   def parse(ts: List[Token]) = ts match {

    70     case t::ts if (t == tok) => Set((t, ts)) 

    71     case _ => Set ()

    72   }

    73 }

    74 implicit def token2tparser(t: Token) = TokParser(t)

    75 

    76 case object NumParser extends Parser[List[Token], Int] {

    77   def parse(ts: List[Token]) = ts match {

    78     case T_NUM(s)::ts => Set((s.toInt, ts)) 

    79     case _ => Set ()

    80   }

    81 }

    82 

    83 case object IdParser extends Parser[List[Token], String] {

    84   def parse(ts: List[Token]) = ts match {

    85     case T_ID(s)::ts => Set((s, ts)) 

    86     case _ => Set ()

    87   }

    88 }

    89 

    90 def len(xs: List[(Int, Int)]): Int = xs match {

    91   case Nil => 0

    92   case (1, x)::xs => len(xs) + 1

    93   case (_, x)::xs => len(xs) 

    94 }

    95 

    96 def fst(p: (Int, Int)): Int = p match {

    97   case Nil => 0

    98   case (1, x)::xs => len(xs) + 1

    99   case (_, x)::xs => len(xs) 

   100 }

   101 

   102 

   103 

   104 // arithmetic expressions

   105 lazy val AExp: Parser[List[Token], AExp] = 

   106   (T ~ T_OP("+") ~ AExp) ==> { case ((x, y), z) => Aop("+", x, z): AExp } ||

   107   (T ~ T_OP("-") ~ AExp) ==> { case ((x, y), z) => Aop("-", x, z): AExp } || T  

   108 lazy val T: Parser[List[Token], AExp] = 

   109   (F ~ T_OP("*") ~ T) ==> { case ((x, y), z) => Aop("*", x, z): AExp } || F

   110 lazy val F: Parser[List[Token], AExp] = 

   111   (T_LPAREN ~> AExp <~ T_RPAREN) || 

   112   IdParser ==> Var || 

   113   NumParser ==> Num

   114 

   115 // boolean expressions

   116 lazy val BExp: Parser[List[Token], BExp] = 

   117   (AExp ~ T_OP("=") ~ AExp) ==> { case ((x, y), z) => Bop("=", x, z): BExp } || 

   118   (AExp ~ T_OP("!=") ~ AExp) ==> { case ((x, y), z) => Bop("!=", x, z): BExp } || 

   119   (AExp ~ T_OP("<") ~ AExp) ==> { case ((x, y), z) => Bop("<", x, z): BExp } || 

   120   (AExp ~ T_OP(">") ~ AExp) ==> { case ((x, y), z) => Bop(">", x, z): BExp } || 

   121   (T_KWD("true") ==> ((_) => True)) || 

   122   (T_KWD("false") ==> ((_) => False: BExp))

   123 

   124 lazy val Stmt: Parser[List[Token], Stmt] =

   125   (T_KWD("skip") ==> ((_) => Skip: Stmt)) ||

   126   (IdParser ~ T_OP(":=") ~ AExp) ==> { case ((x, y), z) => Assign(x, z): Stmt } ||

   127   (T_KWD("if") ~ BExp ~ T_KWD("then") ~ Block ~ T_KWD("else") ~ Block) ==>

   128     { case (((((x,y),z),u),v),w) => If(y, u, w): Stmt } ||

   129   (T_KWD("while") ~ BExp ~ T_KWD("do") ~ Block) ==> { case (((x, y), z), w) => While(y, w) } 

   130  

   131 lazy val Stmts: Parser[List[Token], Block] =

   132   (Stmt ~ T_SEMI ~ Stmts) ==> { case ((x, y), z) => x :: z : Block } ||

   133   (Stmt ==> ((s) => List(s) : Block))

   134 

   135 lazy val Block: Parser[List[Token], Block] =

   136   (T_BEGIN ~> Stmts <~ T_END) || 

   137   (Stmt ==> ((s) => List(s)))

   138 

   139 

   140 // examples

   141 val p1 = "x := 5"

   142 val p1_toks = Tok.fromString(p1) 

   143 val p1_ast = Block.parse_all(p1_toks)

   144 println(p1_toks)

   145 println(p1_ast)

   146 

   147 val p1a = "{ x := 5; y := 8}"

   148 val p1a_toks = Tok.fromString(p1a) 

   149 val p1a_ast = Block.parse_all(p1a_toks)

   150 println(p1a_ast)

   151 

   152 val p2 = "5 = 6"

   153 val p2_toks = Tok.fromString(p2) 

   154 val p2_ast = BExp.parse_all(p2_toks)

   155 println(p2_ast)

   156 

   157 val p2a = "true"

   158 val p2a_toks = Tok.fromString(p2a) 

   159 val p2a_ast = BExp.parse_all(p2a_toks)

   160 println(p2a_ast)

   161 

   162 val p3 = "if true then skip else skip"

   163 val p3_toks = Tok.fromString(p3) 

   164 val p3_ast = Stmt.parse_all(p3_toks)

   165 println(p3_ast)

   166 

   167 val p3a = "if true then x := 5 else x := 10"

   168 val p3a_toks = Tok.fromString(p3a) 

   169 val p3a_ast = Stmt.parse_all(p3a_toks)

   170 println(p3a_ast)

   171 

   172 val p3b = "if false then x := 5 else x := 10"

   173 val p3b_toks = Tok.fromString(p3b) 

   174 val p3b_ast = Stmt.parse_all(p3b_toks)

   175 println(p3b_ast)

   176 

   177 // multiplication

   178 val p4 = """{ x := 5;

   179               y := 4;

   180               r := 0;

   181               while y > 0 do {

   182                  r := r + x;

   183                  y := y - 1

   184               } 

   185             }"""

   186 val p4_toks = Tok.fromString(p4) 

   187 val p4_ast = Block.parse_all(p4_toks)

   188 println(p4_ast)

   189 

   190 val p5 = """

   191  n := 9;

   192  minus1 := 0;

   193  minus2 := 1;

   194  temp := 0;

   195  while n > 0 do  {

   196    temp := minus2;

   197    minus2 := minus1 + minus2;

   198    minus1 := temp;

   199    n := n - 1

   200  };

   201  fib_res := minus2

   202 """

   203 val p5_toks = Tok.fromString(p5) 

   204 val p5_ast = Stmts.parse_all(p5_toks)

   205 

   206 // interpreter

   207 type Env = Map[String, Int]

   208 

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

   210   case True => true

   211   case False => false

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

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

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

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

   216 }

   217 

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

   219   case Num(i) => i

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

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

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

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

   224 }

   225 

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

   227   case Skip => env

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

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

   230   case While(b, bl) => 

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

   232     else env

   233 }

   234 

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

   236   case Nil => env

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

   238 }

   239 

   240 //examples

   241 println(eval_stmt(p3a_ast.head, Map.empty))

   242 println(eval_stmt(p3b_ast.head, Map.empty))

   243 println(eval_bl(p4_ast.head, Map.empty))

   244 println(eval_bl(p5_ast.head, Map.empty))