1 // A parser and evaluator for teh 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 

    91 // arithmetic expressions

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

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

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

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

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

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

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

    99   IdParser ==> Var || 

   100   NumParser ==> Num

   101 

   102 // boolean expressions

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

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

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

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

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

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

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

   110 

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

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

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

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

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

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

   117  

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

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

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

   121 

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

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

   124   (Stmt ==> ((s) => List(s)))

   125 

   126 

   127 // examples

   128 val p1 = "x := 5"

   129 val p1_toks = Tok.fromString(p1) 

   130 val p1_ast = Block.parse_all(p1_toks)

   131 println(p1_toks)

   132 println(p1_ast)

   133 

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

   135 val p1a_toks = Tok.fromString(p1a) 

   136 val p1a_ast = Block.parse_all(p1a_toks)

   137 println(p1a_ast)

   138 

   139 val p2 = "5 = 6"

   140 val p2_toks = Tok.fromString(p2) 

   141 val p2_ast = BExp.parse_all(p2_toks)

   142 println(p2_ast)

   143 

   144 val p2a = "true"

   145 val p2a_toks = Tok.fromString(p2a) 

   146 val p2a_ast = BExp.parse_all(p2a_toks)

   147 println(p2a_ast)

   148 

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

   150 val p3_toks = Tok.fromString(p3) 

   151 val p3_ast = Stmt.parse_all(p3_toks)

   152 println(p3_ast)

   153 

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

   155 val p3a_toks = Tok.fromString(p3a) 

   156 val p3a_ast = Stmt.parse_all(p3a_toks)

   157 println(p3a_ast)

   158 

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

   160 val p3b_toks = Tok.fromString(p3b) 

   161 val p3b_ast = Stmt.parse_all(p3b_toks)

   162 println(p3b_ast)

   163 

   164 // multiplication

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

   166               y := 4;

   167               r := 0;

   168               while y > 0 do {

   169                  r := r + x;

   170                  y := y - 1

   171               } 

   172             }"""

   173 val p4_toks = Tok.fromString(p4) 

   174 val p4_ast = Block.parse_all(p4_toks)

   175 println(p4_ast)

   176 

   177 val p5 = """

   178  n := 9;

   179  minus1 := 0;

   180  minus2 := 1;

   181  temp := 0;

   182  while n > 0 do  {

   183    temp := minus2;

   184    minus2 := minus1 + minus2;

   185    minus1 := temp;

   186    n := n - 1

   187  };

   188  fib_res := minus2

   189 """

   190 val p5_toks = Tok.fromString(p5) 

   191 val p5_ast = Stmts.parse_all(p5_toks)

   192 

   193 // interpreter

   194 type Env = Map[String, Int]

   195 

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

   197   case True => true

   198   case False => false

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

   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 }

   204 

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

   206   case Num(i) => i

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

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

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

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

   211 }

   212 

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

   214   case Skip => env

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

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

   217   case While(b, bl) => 

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

   219     else env

   220 }

   221 

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

   223   case Nil => env

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

   225 }

   226 

   227 //examples

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

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

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

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