|
1 import scala.language.implicitConversions |
|
2 import scala.language.reflectiveCalls |
|
3 |
|
4 abstract class Rexp |
|
5 |
|
6 case object NULL extends Rexp |
|
7 case object EMPTY extends Rexp |
|
8 case class CHAR(c: Char) extends Rexp |
|
9 case class ALT(r1: Rexp, r2: Rexp) extends Rexp |
|
10 case class SEQ(r1: Rexp, r2: Rexp) extends Rexp |
|
11 case class STAR(r: Rexp) extends Rexp |
|
12 |
|
13 abstract class Pat |
|
14 |
|
15 case class VAR(x: String, r: Rexp) extends Pat |
|
16 case class GRP(x: String, p: Pat) extends Pat |
|
17 case class PSEQ(p1: Pat, p2: Pat) extends Pat |
|
18 case class PALT(p1: Pat, p2: Pat) extends Pat |
|
19 case class PSTAR(p: Pat) extends Pat |
|
20 |
|
21 |
|
22 def nullable (r: Rexp) : Boolean = r match { |
|
23 case NULL => false |
|
24 case EMPTY => true |
|
25 case CHAR(_) => false |
|
26 case ALT(r1, r2) => nullable(r1) || nullable(r2) |
|
27 case SEQ(r1, r2) => nullable(r1) && nullable(r2) |
|
28 case STAR(_) => true |
|
29 } |
|
30 |
|
31 def down (p: Pat) : Rexp = p match { |
|
32 case VAR(x: String, w: String, r: Rexp) => r |
|
33 case GRP(x: String, w: String, p: Pat) => down(p) |
|
34 case PSEQ(p1: Pat, p2: Pat) => SEQ(down(p1), down(p2)) |
|
35 case PALT(p1: Pat, p2: Pat) => ALT(down(p1), down(p2)) |
|
36 case PSTAR(p: Pat) => STAR(down(p)) |
|
37 } |
|
38 |
|
39 def patnullable (p: Pat) : Boolean = p match { |
|
40 case PVar(_, r) => nullable(r) |
|
41 case PSEQ(p1, p2) => patnullable(p1) && patnullable(p2) |
|
42 case PCHOICE(p1, p2) => patnullable(p1) || patnullable(p2) |
|
43 case PSTAR(p) => true |
|
44 case PatVar(_, p) => patnullable(p) |
|
45 } |
|
46 |
|
47 //type Env = Set[List[(String, String)]] |
|
48 type Env = Map[Int, String] |
|
49 |
|
50 def update(n: Int, c: Char) (env: Env) = |
|
51 env + (n -> (env.getOrElse(n, "") + c.toString)) |
|
52 |
|
53 def pderivPat (p: Pat, c: Char) : Set[(Pat, Env => Env)] = p match { |
|
54 case PVar(n: Int, r: Rexp) => { |
|
55 val pds = pderiv(r, c) |
|
56 if (pds.isEmpty) Set() |
|
57 else Set((PVar(n, toRexp(pds.toList)), update(n, c))) |
|
58 } |
|
59 case PSEQ(p1: Pat, p2: Pat) => { |
|
60 val pats : Set[(Pat, Env => Env)] = |
|
61 for ((p, f) <- pderivPat(p1, c)) yield (PSEQ(p, p2), f) |
|
62 if (nullable(strip(p1))) pats ++ pderivPat(p2, c) |
|
63 else pats |
|
64 } |
|
65 case PCHOICE(p1: Pat, p2: Pat) => pderivPat(p1, c) ++ pderivPat(p2, c) |
|
66 case PSTAR(p1: Pat) => |
|
67 for ((p, f) <- pderivPat(p1, c)) yield (PSEQ(p, PSTAR(p1)), f) |
|
68 case PatVar(n: Int, p1: Pat) => |
|
69 for ((p, f) <- pderivPat(p1, c)) yield (PatVar(n, p), f compose (update (n, c))) |
|
70 } |
|
71 |
|
72 |
|
73 val p2 = PSEQ(PVar(1, STAR("A")), PVar(2, STAR("A"))) |
|
74 pderivPat(p2, 'A').mkString("\n") |
|
75 |
|
76 |
|
77 def greedy_aux(env: Set[(Pat, Env)], w: List[Char]) : Set[Env] = w match { |
|
78 case Nil => |
|
79 for ((p, e) <- env if patnullable(p)) yield e |
|
80 case c::cs => { |
|
81 val env2 = for ((p, e) <- env; (p1, f) <- pderivPat(p, c)) yield (p1, f(e)) |
|
82 greedy_aux(env2, cs) |
|
83 } |
|
84 } |
|
85 |
|
86 def greedy(p: Pat, w: String) = { |
|
87 val res = greedy_aux(Set((p, Map())), w.toList) |
|
88 if (res.isEmpty) None else Some(res) |
|
89 } |
|
90 |
|
91 // some convenience for typing in regular expressions |
|
92 def charlist2rexp (s : List[Char]) : Rexp = s match { |
|
93 case Nil => EMPTY |
|
94 case c::Nil => CHAR(c) |
|
95 case c::s => SEQ(CHAR(c), charlist2rexp(s)) |
|
96 } |
|
97 implicit def string2rexp (s : String) : Rexp = charlist2rexp(s.toList) |
|
98 |
|
99 implicit def RexpOps (r: Rexp) = new { |
|
100 def | (s: Rexp) = ALT(r, s) |
|
101 def % = STAR(r) |
|
102 def ~ (s: Rexp) = SEQ(r, s) |
|
103 } |
|
104 |
|
105 implicit def stringOps (s: String) = new { |
|
106 def | (r: Rexp) = ALT(s, r) |
|
107 def | (r: String) = ALT(s, r) |
|
108 def % = STAR(s) |
|
109 def ~ (r: Rexp) = SEQ(s, r) |
|
110 def ~ (r: String) = SEQ(s, r) |
|
111 } |
|
112 |
|
113 implicit def PatOps (p: Pat) = new { |
|
114 def | (q: Pat) = PALT(p, q) |
|
115 def % = PSTAR(p) |
|
116 def ~ (q: Pat) = PSEQ(p, q) |
|
117 } |
|
118 |
|
119 val p3 = PSTAR(PSEQ(PVar(1, "A"), PVar(2, "B"))) |
|
120 |
|
121 greedy2(Set((p3, Map())), "ABAB".toList) |
|
122 |
|
123 |
|
124 val p4 = PVar(1, "A") |
|
125 greedy2(Set((p4, Map())), "A".toList) |
|
126 |
|
127 val p5 = PSEQ(PVar(1, "A"), PVar(1, "B")) |
|
128 greedy2(Set((p5, Map())), "AB".toList) |
|
129 |
|
130 val res = pderivPat(p5, 'A') |
|
131 for ((_, f) <- res) yield f(Map()) |
|
132 |
|
133 |
|
134 val p6 = PatVar(4,PSTAR(PCHOICE(PCHOICE(PVar(1, "A"), PVar(2, "AB")), PVar(3, "B")))) |
|
135 |
|
136 greedy(p6, "ABA") |