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package POSIX
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object PosixAlgo {
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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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case class RECD(x: String, r: Rexp) extends Rexp
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abstract class Val
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case object Void extends Val
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case class Chr(c: Char) extends Val
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case class Sequ(v1: Val, v2: Val) extends Val
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case class Left(v: Val) extends Val
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case class Right(v: Val) extends Val
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case class Stars(vs: List[Val]) extends Val
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case class Rec(x: String, v: Val) extends Val
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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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case RECD(_, r1) => nullable(r1)
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} //> nullable: (r: POSIX.PosixAlgo.Rexp)Boolean
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def der(c: Char, r: Rexp): Rexp = r match {
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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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case RECD(_, r1) => der(c, r1)
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} //> der: (c: Char, r: POSIX.PosixAlgo.Rexp)POSIX.PosixAlgo.Rexp
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} |