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18
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// regular expressions
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7
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abstract class Rexp
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case object NULL extends Rexp
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case object EMPTY extends Rexp
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case class CHAR(c: Char) extends Rexp
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case class ALT(r1: Rexp, r2: Rexp) extends Rexp
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case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
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case class STAR(r: Rexp) extends Rexp
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18
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// some convenience for typing in regular expressions
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implicit def string2rexp(s : String) : Rexp = {
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s.foldRight (EMPTY: Rexp) ( (c, r) => SEQ(CHAR(c), r) )
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}
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// for example
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println(STAR("abc"))
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// produces STAR(SEQ(CHAR(a),SEQ(CHAR(b),SEQ(CHAR(c),EMPTY))))
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// a simple-minded regular expression matcher:
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// it loops for examples like STAR(EMPTY) with
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// strings this regular expression does not match
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def smatchers(rs: List[Rexp], s: List[Char]) : Boolean = (rs, s) match {
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case (NULL::rs, s) => false
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case (EMPTY::rs, s) => smatchers(rs, s)
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case (CHAR(c)::rs, Nil) => false
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case (CHAR(c)::rs, d::s) => (c ==d) && smatchers(rs, s)
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case (ALT(r1, r2)::rs, s) => smatchers(r1::rs, s) || smatchers(r2::rs, s)
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case (SEQ(r1, r2)::rs, s) => smatchers(r1::r2::rs, s)
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case (STAR(r)::rs, s) => smatchers(rs, s) || smatchers(r::STAR(r)::rs, s)
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case (Nil, s) => s == Nil
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}
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def smatcher(r: Rexp, s: String) = smatchers(List(r), s.toList)
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// regular expression: a
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println(smatcher(CHAR('a'), "ab"))
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// regular expression: a + (b o c)
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println(smatcher(ALT(CHAR('a'), SEQ(CHAR('b'), CHAR('c'))), "ab"))
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// regular expression: a + (b o c)
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println(smatcher(ALT(CHAR('a'), SEQ(CHAR('b'), CHAR('c'))), "bc"))
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// loops for regular expression epsilon*
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//println(smatcher(STAR(EMPTY), "a"))
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// Regular expression matcher that works properly
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//================================================
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// nullable function: tests whether the regular
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// expression can recognise the empty string
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7
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def nullable (r: Rexp) : Boolean = r match {
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case NULL => false
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case EMPTY => true
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case CHAR(_) => false
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case ALT(r1, r2) => nullable(r1) || nullable(r2)
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case SEQ(r1, r2) => nullable(r1) && nullable(r2)
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case STAR(_) => true
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}
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18
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// derivative of a regular expression w.r.t. a character
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def der (c: Char, r: Rexp) : Rexp = r match {
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7
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case NULL => NULL
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case EMPTY => NULL
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case CHAR(d) => if (c == d) EMPTY else NULL
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case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
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case SEQ(r1, r2) =>
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if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
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else SEQ(der(c, r1), r2)
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case STAR(r) => SEQ(der(c, r), STAR(r))
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}
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// derivative w.r.t. a string (iterates der)
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def ders (s: List[Char], r: Rexp) : Rexp = s match {
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case Nil => r
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case c::s => ders(s, der(c, r))
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}
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// main matcher function
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def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
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7
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18
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//examples
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7
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18
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println(matcher(SEQ(STAR("a"), STAR("b")), "bbaaa"))
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println(matcher(ALT(STAR("a"), STAR("b")), ""))
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println(matcher("abc", ""))
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println(matcher(STAR(ALT(EMPTY, "a")), ""))
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println(matcher(STAR(EMPTY), "a"))
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println(matcher("cab","cab"))
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println(matcher(STAR("a"),"aaa"))
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println(matcher("cab" ,"cab"))
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println(matcher(STAR("a"),"aaa"))
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7
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