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1 // A parser and evaluator for the WHILE language |
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2 // |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 // some regular expressions |
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9 val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_") |
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10 val DIGIT = RANGE("0123456789") |
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11 val ID = SEQ(SYM, STAR(ALT(SYM, DIGIT))) |
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12 val NUM = PLUS(DIGIT) |
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13 val KEYWORD = ALTS("skip", "while", "do", "if", "then", "else", "true", "false", "write") |
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14 val SEMI: Rexp = ";" |
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15 val OP: Rexp = ALTS(":=", "=", "-", "+", "*", "!=", "<", ">") |
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16 val WHITESPACE = PLUS(RANGE(" \n")) |
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17 val RPAREN: Rexp = ")" |
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18 val LPAREN: Rexp = "(" |
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19 val BEGIN: Rexp = "{" |
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20 val END: Rexp = "}" |
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21 val COMMENT = SEQS("/*", NOT(SEQS(STAR(ALLC), "*/", STAR(ALLC))), "*/") |
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22 |
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23 // tokens for classifying the strings that have been recognised |
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24 abstract class Token |
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25 case object T_WHITESPACE extends Token |
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26 case object T_COMMENT extends Token |
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27 case object T_SEMI extends Token |
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28 case object T_LPAREN extends Token |
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29 case object T_RPAREN extends Token |
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30 case object T_BEGIN extends Token |
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31 case object T_END extends Token |
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32 case class T_ID(s: String) extends Token |
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33 case class T_OP(s: String) extends Token |
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34 case class T_NUM(s: String) extends Token |
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35 case class T_KWD(s: String) extends Token |
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36 |
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37 val lexing_rules: List[(Rexp, List[Char] => Token)] = |
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38 List((KEYWORD, (s) => T_KWD(s.mkString)), |
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39 (ID, (s) => T_ID(s.mkString)), |
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40 (OP, (s) => T_OP(s.mkString)), |
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41 (NUM, (s) => T_NUM(s.mkString)), |
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42 (SEMI, (s) => T_SEMI), |
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43 (LPAREN, (s) => T_LPAREN), |
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44 (RPAREN, (s) => T_RPAREN), |
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45 (BEGIN, (s) => T_BEGIN), |
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46 (END, (s) => T_END), |
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47 (WHITESPACE, (s) => T_WHITESPACE), |
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48 (COMMENT, (s) => T_COMMENT)) |
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49 |
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50 // the tokenizer |
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51 val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE, T_COMMENT)) |
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52 |
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53 // the abstract syntax trees |
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54 abstract class Stmt |
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55 abstract class AExp |
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56 abstract class BExp |
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57 type Block = List[Stmt] |
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58 case object Skip extends Stmt |
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59 case class If(a: BExp, bl1: Block, bl2: Block) extends Stmt |
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60 case class While(b: BExp, bl: Block) extends Stmt |
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61 case class Assign(s: String, a: AExp) extends Stmt |
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62 case class Write(s: String) extends Stmt |
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63 |
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64 case class Var(s: String) extends AExp |
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65 case class Num(i: Int) extends AExp |
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66 case class Aop(o: String, a1: AExp, a2: AExp) extends AExp |
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67 |
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68 case object True extends BExp |
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69 case object False extends BExp |
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70 case class Bop(o: String, a1: AExp, a2: AExp) extends BExp |
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71 |
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72 // atomic parsers |
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73 case class TokParser(tok: Token) extends Parser[List[Token], Token] { |
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74 def parse(ts: List[Token]) = ts match { |
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75 case t::ts if (t == tok) => Set((t, ts)) |
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76 case _ => Set () |
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77 } |
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78 } |
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79 implicit def token2tparser(t: Token) = TokParser(t) |
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80 |
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81 case object NumParser extends Parser[List[Token], Int] { |
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82 def parse(ts: List[Token]) = ts match { |
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83 case T_NUM(s)::ts => Set((s.toInt, ts)) |
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84 case _ => Set () |
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85 } |
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86 } |
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87 |
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88 case object IdParser extends Parser[List[Token], String] { |
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89 def parse(ts: List[Token]) = ts match { |
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90 case T_ID(s)::ts => Set((s, ts)) |
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91 case _ => Set () |
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92 } |
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93 } |
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94 |
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95 |
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96 // arithmetic expressions |
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97 lazy val AExp: Parser[List[Token], AExp] = |
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98 (T ~ T_OP("+") ~ AExp) ==> { case ((x, y), z) => Aop("+", x, z): AExp } || |
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99 (T ~ T_OP("-") ~ AExp) ==> { case ((x, y), z) => Aop("-", x, z): AExp } || T |
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100 lazy val T: Parser[List[Token], AExp] = |
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101 (F ~ T_OP("*") ~ T) ==> { case ((x, y), z) => Aop("*", x, z): AExp } || F |
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102 lazy val F: Parser[List[Token], AExp] = |
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103 (T_LPAREN ~> AExp <~ T_RPAREN) || |
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104 IdParser ==> Var || |
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105 NumParser ==> Num |
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106 |
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107 // boolean expressions |
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108 lazy val BExp: Parser[List[Token], BExp] = |
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109 (T_KWD("true") ==> ((_) => True: BExp)) || |
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110 (T_KWD("false") ==> ((_) => False: BExp)) || |
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111 (T_LPAREN ~> BExp <~ T_RPAREN) || |
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112 (AExp ~ T_OP("=") ~ AExp) ==> { case ((x, y), z) => Bop("=", x, z): BExp } || |
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113 (AExp ~ T_OP("!=") ~ AExp) ==> { case ((x, y), z) => Bop("!=", x, z): BExp } || |
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114 (AExp ~ T_OP("<") ~ AExp) ==> { case ((x, y), z) => Bop("<", x, z): BExp } || |
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115 (AExp ~ T_OP(">") ~ AExp) ==> { case ((x, y), z) => Bop("<", z, x): BExp } |
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116 |
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117 lazy val Stmt: Parser[List[Token], Stmt] = |
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118 (T_KWD("skip") ==> ((_) => Skip: Stmt)) || |
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119 (IdParser ~ T_OP(":=") ~ AExp) ==> { case ((x, y), z) => Assign(x, z): Stmt } || |
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120 (T_KWD("if") ~ BExp ~ T_KWD("then") ~ Block ~ T_KWD("else") ~ Block) ==> |
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121 { case (((((x,y),z),u),v),w) => If(y, u, w): Stmt } || |
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122 (T_KWD("while") ~ BExp ~ T_KWD("do") ~ Block) ==> { case (((x, y), z), w) => While(y, w) } || |
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123 (T_KWD("write") ~ IdParser) ==> { case (x, y) => Write(y) } |
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124 |
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125 lazy val Stmts: Parser[List[Token], Block] = |
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126 (Stmt ~ T_SEMI ~ Stmts) ==> { case ((x, y), z) => x :: z : Block } || |
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127 (Stmt ==> ((s) => List(s) : Block)) |
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128 |
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129 lazy val Block: Parser[List[Token], Block] = |
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130 (T_BEGIN ~> Stmts <~ T_END) || |
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131 (Stmt ==> ((s) => List(s))) |
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132 |
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133 // interpreter |
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134 type Env = Map[String, Int] |
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135 |
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136 def eval_bexp(b: BExp, env: Env) : Boolean = b match { |
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137 case True => true |
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138 case False => false |
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139 case Bop("=", a1, a2) => eval_aexp(a1, env) == eval_aexp(a2, env) |
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140 case Bop("!=", a1, a2) => !(eval_aexp(a1, env) == eval_aexp(a2, env)) |
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141 case Bop("<", a1, a2) => eval_aexp(a1, env) < eval_aexp(a2, env) |
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142 } |
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143 |
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144 def eval_aexp(a: AExp, env : Env) : Int = a match { |
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145 case Num(i) => i |
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146 case Var(s) => env(s) |
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147 case Aop("+", a1, a2) => eval_aexp(a1, env) + eval_aexp(a2, env) |
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148 case Aop("-", a1, a2) => eval_aexp(a1, env) - eval_aexp(a2, env) |
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149 case Aop("*", a1, a2) => eval_aexp(a1, env) * eval_aexp(a2, env) |
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150 } |
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151 |
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152 def eval_stmt(s: Stmt, env: Env) : Env = s match { |
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153 case Skip => env |
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154 case Assign(x, a) => env + (x -> eval_aexp(a, env)) |
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155 case If(b, bl1, bl2) => if (eval_bexp(b, env)) eval_bl(bl1, env) else eval_bl(bl2, env) |
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156 case While(b, bl) => |
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157 if (eval_bexp(b, env)) eval_stmt(While(b, bl), eval_bl(bl, env)) |
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158 else env |
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159 case Write(x) => { println(env(x)); env } |
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160 } |
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161 |
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162 def eval_bl(bl: Block, env: Env) : Env = bl match { |
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163 case Nil => env |
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164 case s::bl => eval_bl(bl, eval_stmt(s, env)) |
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165 } |
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166 |
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167 def eval_prog(name: String) : Env = { |
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168 val tks = Tok.fromFile(name) |
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169 val ast = Stmts.parse_single(tks) |
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170 eval_bl(ast, Map.empty) |
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171 } |
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172 |
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173 |
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174 //examples |
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175 |
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176 //eval_prog("loops.while") |
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177 eval_prog("fib.while") |
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178 |
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179 |
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180 def time_needed[T](i: Int, code: => T) = { |
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181 val start = System.nanoTime() |
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182 for (j <- 1 to i) code |
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183 val end = System.nanoTime() |
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184 (end - start)/(i * 1.0e9) |
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185 } |
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186 |
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187 |
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188 val test_prog = """ |
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189 start := XXX; |
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190 x := start; |
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191 y := start; |
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192 z := start; |
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193 while 0 < x do { |
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194 while 0 < y do { |
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195 while 0 < z do { |
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196 z := z - 1 |
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197 }; |
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198 z := start; |
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199 y := y - 1 |
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200 }; |
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201 y := start; |
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202 x := x - 1 |
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203 } |
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204 """ |
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205 |
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206 |
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207 |
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208 def eval_test(n: Int) : Unit = { |
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209 val tks = Tok.fromString(test_prog.replaceAllLiterally("XXX", n.toString)) |
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210 val ast = Stmts.parse_single(tks) |
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211 println(n + " " + time_needed(2, eval_bl(ast, Map.empty))) |
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212 } |
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213 |
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214 List(1, 200, 400, 600, 800, 1000, 1200, 1400, 1600).map(eval_test(_)) |
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215 |
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216 |
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217 |
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218 |
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219 |
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220 |
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221 |