24 def nullable (r: Rexp) : Boolean = r match { |
25 def nullable (r: Rexp) : Boolean = r match { |
25 case NULL => false |
26 case NULL => false |
26 case EMPTY => true |
27 case EMPTY => true |
27 case CHAR(_) => false |
28 case CHAR(_) => false |
28 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
29 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
29 case SEQ(r1, r2) => if (nullable(r1)) (zeroable(r1) && zeroable(r2)) else zeroable(r1) |
30 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
30 case STAR(_) => true |
31 case STAR(_) => true |
31 case NOT(r) => !(nullable(r)) |
32 case NOT(r) => !(nullable(r)) |
32 } |
33 } |
33 |
34 |
34 // tests whether a regular expression |
35 // tests whether a regular expression |
35 // recognises nothing |
36 // cannot recognise more |
36 def zeroable (r: Rexp) : Boolean = r match { |
37 def no_more (r: Rexp) : Boolean = r match { |
37 case NULL => true |
38 case NULL => true |
38 case EMPTY => false |
39 case EMPTY => false |
39 case CHAR(_) => false |
40 case CHAR(_) => false |
40 case ALT(r1, r2) => zeroable(r1) && zeroable(r2) |
41 case ALT(r1, r2) => no_more(r1) && no_more(r2) |
41 case SEQ(r1, r2) => if (nullable(r1)) (zeroable(r1) && zeroable(r2)) else zeroable(r1) |
42 case SEQ(r1, r2) => if (nullable(r1)) (no_more(r1) && no_more(r2)) else no_more(r1) |
42 //case SEQ(r1, r2) => zeroable(r1) || zeroable(r2) |
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43 case STAR(_) => false |
43 case STAR(_) => false |
44 case NOT(r) => !(zeroable(r)) |
44 case NOT(r) => !(no_more(r)) |
45 } |
45 } |
46 |
46 |
47 |
47 |
48 // derivative of a regular expression w.r.t. a character |
48 // derivative of a regular expression w.r.t. a character |
49 def der (c: Char, r: Rexp) : Rexp = r match { |
49 def der (c: Char, r: Rexp) : Rexp = r match { |
56 else SEQ(der(c, r1), r2) |
56 else SEQ(der(c, r1), r2) |
57 case STAR(r) => SEQ(der(c, r), STAR(r)) |
57 case STAR(r) => SEQ(der(c, r), STAR(r)) |
58 case NOT(r) => NOT(der (c, r)) |
58 case NOT(r) => NOT(der (c, r)) |
59 } |
59 } |
60 |
60 |
61 // derivative w.r.t. a string (iterates der) |
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62 def ders (s: List[Char], r: Rexp) : Rexp = s match { |
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63 case Nil => r |
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64 case c::s => ders(s, der(c, r)) |
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65 } |
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66 |
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67 // main matcher function |
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68 def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r)) |
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69 |
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70 |
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71 // regular expression for specifying |
61 // regular expression for specifying |
72 // ranges of characters |
62 // ranges of characters |
73 def RANGE(s : List[Char]) : Rexp = s match { |
63 def RANGE(s : List[Char]) : Rexp = s match { |
74 case Nil => NULL |
64 case Nil => NULL |
75 case c::Nil => CHAR(c) |
65 case c::Nil => CHAR(c) |
76 case c::s => ALT(CHAR(c), RANGE(s)) |
66 case c::s => ALT(CHAR(c), RANGE(s)) |
77 } |
67 } |
78 |
68 |
79 //one or more |
69 // one or more |
80 def PLUS(r: Rexp) = SEQ(r, STAR(r)) |
70 def PLUS(r: Rexp) = SEQ(r, STAR(r)) |
81 |
71 |
82 |
72 // some regular expressions |
83 //some regular expressions |
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84 val LOWERCASE = RANGE("abcdefghijklmnopqrstuvwxyz".toList) |
73 val LOWERCASE = RANGE("abcdefghijklmnopqrstuvwxyz".toList) |
85 val UPPERCASE = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZ".toList) |
74 val UPPERCASE = RANGE("ABCDEFGHIJKLMNOPQRSTUVWXYZ".toList) |
86 val LETTER = ALT(LOWERCASE, UPPERCASE) |
75 val LETTER = ALT(LOWERCASE, UPPERCASE) |
87 val DIGITS = RANGE("0123456789".toList) |
76 val DIGIT = RANGE("0123456789".toList) |
88 val NONZERODIGITS = RANGE("123456789".toList) |
77 val NONZERODIGIT = RANGE("123456789".toList) |
89 |
78 |
90 val IDENT = SEQ(LETTER, STAR(ALT(LETTER,DIGITS))) |
79 val IDENT = SEQ(LETTER, STAR(ALT(LETTER,DIGIT))) |
91 val NUMBER = ALT(SEQ(NONZERODIGITS, STAR(DIGITS)), "0") |
80 val NUMBER = ALT(SEQ(NONZERODIGIT, STAR(DIGIT)), "0") |
92 val WHITESPACE = RANGE(" \n".toList) |
81 val WHITESPACE = RANGE(" \n".toList) |
93 val WHITESPACES = PLUS(WHITESPACE) |
82 val WHITESPACES = PLUS(WHITESPACE) |
94 |
83 |
95 val ALL = ALT(ALT(LETTER, DIGITS), WHITESPACE) |
84 val ALL = ALT(ALT(LETTER, DIGIT), WHITESPACE) |
96 |
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97 val COMMENT = SEQ(SEQ("/*", NOT(SEQ(SEQ(STAR(ALL), "*/"), STAR(ALL)))), "*/") |
85 val COMMENT = SEQ(SEQ("/*", NOT(SEQ(SEQ(STAR(ALL), "*/"), STAR(ALL)))), "*/") |
98 |
86 |
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87 |
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88 // for classifying the strings that have been recognised |
99 abstract class Token |
89 abstract class Token |
100 |
90 |
101 case object T_WHITESPACE extends Token |
91 case object T_WHITESPACE extends Token |
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92 case object T_COMMENT extends Token |
102 case class T_IDENT(s: String) extends Token |
93 case class T_IDENT(s: String) extends Token |
103 case class T_OP(s: String) extends Token |
94 case class T_OP(s: String) extends Token |
104 case class T_NUM(n: Int) extends Token |
95 case class T_NUM(n: Int) extends Token |
105 case class T_KEYWORD(s: String) extends Token |
96 case class T_KEYWORD(s: String) extends Token |
106 case object T_COMMENT extends Token |
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107 |
97 |
108 |
98 |
109 // an example list of rules |
99 // an example list of syntactic rules |
110 type Rule = (Rexp, List[Char] => Token) |
100 type Rule = (Rexp, List[Char] => Token) |
111 |
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112 val rules: List[Rule]= |
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113 List(("if", (s) => T_KEYWORD(s.mkString)), |
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114 ("then", (s) => T_KEYWORD(s.mkString)), |
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115 ("else", (s) => T_KEYWORD(s.mkString)), |
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116 ("+", (s) => T_OP(s.mkString)), |
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117 (IDENT, (s) => T_IDENT(s.mkString)), |
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118 (NUMBER, (s) => T_NUM(s.mkString.toInt)), |
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119 (WHITESPACES, (s) => T_WHITESPACE)) |
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120 |
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121 |
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122 def error (s: String) = throw new IllegalArgumentException ("Could not lex " + s) |
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123 |
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124 def munch(r: Rexp, action: List[Char] => Token, s: List[Char], t: List[Char]) : Option[(List[Char], Token)] = |
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125 s match { |
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126 case Nil if (nullable(r)) => Some(Nil, action(t)) |
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127 case Nil => None |
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128 case c::s if (zeroable(der (c, r)) && nullable(r)) => Some(c::s, action(t)) |
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129 case c::s if (zeroable(der (c, r))) => None |
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130 case c::s => munch(der (c, r), action, s, t ::: List(c)) |
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131 } |
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132 |
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133 def lex_one (rs: List[Rule], s: List[Char]) : (List[Char], Token) = { |
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134 val somes = rs.map { (r) => munch(r._1, r._2, s, Nil) } .flatten |
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135 if (somes == Nil) error(s.mkString) else (somes sortBy (_._1.length) head) |
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136 } |
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137 |
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138 def lex_all (rs: List[Rule], s: List[Char]) : List[Token] = s match { |
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139 case Nil => Nil |
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140 case _ => lex_one(rs, s) match { |
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141 case (rest, t) => t :: lex_all(rs, rest) |
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142 } |
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143 } |
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144 |
101 |
145 val rules: List[Rule]= |
102 val rules: List[Rule]= |
146 List(("if", (s) => T_KEYWORD(s.mkString)), |
103 List(("if", (s) => T_KEYWORD(s.mkString)), |
147 ("then", (s) => T_KEYWORD(s.mkString)), |
104 ("then", (s) => T_KEYWORD(s.mkString)), |
148 ("else", (s) => T_KEYWORD(s.mkString)), |
105 ("else", (s) => T_KEYWORD(s.mkString)), |
150 (IDENT, (s) => T_IDENT(s.mkString)), |
107 (IDENT, (s) => T_IDENT(s.mkString)), |
151 (NUMBER, (s) => T_NUM(s.mkString.toInt)), |
108 (NUMBER, (s) => T_NUM(s.mkString.toInt)), |
152 (WHITESPACES, (s) => T_WHITESPACE), |
109 (WHITESPACES, (s) => T_WHITESPACE), |
153 (COMMENT, (s) => T_COMMENT)) |
110 (COMMENT, (s) => T_COMMENT)) |
154 |
111 |
155 println(lex_all(rules, "/*ifff if */ hhjj /*34 */".toList)) |
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156 |
112 |
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113 def error (s: String) = throw new IllegalArgumentException ("Cannot tokenize: " + s) |
157 |
114 |
158 munch(COMMENT, (s) => T_COMMENT , "/*ifff if */ hhjj /*34 */".toList, Nil) |
115 def munch(r: Rexp, action: List[Char] => Token, s: List[Char], t: List[Char]) : Option[(List[Char], Token)] = |
159 val COMMENT2 = NOT(SEQ(SEQ(STAR(ALL), "*/"), STAR(ALL))) |
116 s match { |
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117 case Nil if (nullable(r)) => Some(Nil, action(t)) |
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118 case Nil => None |
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119 case c::s if (no_more(der (c, r)) && nullable(r)) => Some(c::s, action(t)) |
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120 case c::s if (no_more(der (c, r))) => None |
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121 case c::s => munch(der (c, r), action, s, t ::: List(c)) |
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122 } |
160 |
123 |
161 der('/', COMMENT) |
124 def one_token (rs: List[Rule], s: List[Char]) : (List[Char], Token) = { |
162 zeroable(der('/', COMMENT)) |
125 val somes = rs.map { (r) => munch(r._1, r._2, s, Nil) } .flatten |
163 zeroable(der('a', COMMENT2)) |
126 if (somes == Nil) error(s.mkString) else (somes sortBy (_._1.length) head) |
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127 } |
164 |
128 |
165 matcher(COMMENT2, "ifff if 34") |
129 def tokenize (rs: List[Rule], s: List[Char]) : List[Token] = s match { |
166 munch(COMMENT2, "ifff if 34".toList, Nil) |
130 case Nil => Nil |
167 starts_with(COMMENT2, 'i') |
131 case _ => one_token(rs, s) match { |
168 lex_all(regs, "ifff if 34".toList) |
132 case (rest, token) => token :: tokenize(rs, rest) |
169 lex_all(regs, "ifff $ if 34".toList) |
133 } |
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134 } |
170 |
135 |
171 println(lex_all(rules, "/* if true then */ then 42 else +".toList)) |
136 //examples |
172 println(lex_all(rules, "if true then then 42 else +".toList)) |
137 println(tokenize(rules, "if true then then 42 else +".toList)) |
173 println(lex_all(rules, "ifff if 34 34".toList)) |
138 println(tokenize(rules, "if+true+then+then+42+else +".toList)) |
174 println(lex_all(rules, "ifff $ if 34".toList)) |
139 println(tokenize(rules, "ifff if 34 34".toList)) |
175 |
140 println(tokenize(rules, "/*ifff if */ hhjj /*34 */".toList)) |
176 |
141 println(tokenize(rules, "/* if true then */ then 42 else +".toList)) |
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142 //println(tokenize(rules, "ifff $ if 34".toList)) // causes an error because of the symbol $ |