3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
|
1 |
import scala.language.implicitConversions
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
|
2 |
import scala.language.reflectiveCalls
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
3 |
import scala.annotation.tailrec
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
4 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
5 |
abstract class Rexp
|
156
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
6 |
case object ZERO extends Rexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
7 |
case object ONE extends Rexp
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
8 |
case class CHAR(c: Char) extends Rexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
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|
9 |
case class ALT(r1: Rexp, r2: Rexp) extends Rexp
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
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|
10 |
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
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|
11 |
case class STAR(r: Rexp) extends Rexp
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
12 |
case class RECD(x: String, r: Rexp) extends Rexp
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
13 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
14 |
abstract class ARexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
15 |
case object AZERO extends ARexp
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
16 |
case class AONE(bs: List[Boolean]) extends ARexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
17 |
case class ACHAR(bs: List[Boolean], c: Char) extends ARexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
18 |
case class AALT(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
19 |
case class ASEQ(bs: List[Boolean], r1: ARexp, r2: ARexp) extends ARexp
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Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
20 |
case class ASTAR(bs: List[Boolean], r: ARexp) extends ARexp
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
21 |
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Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
22 |
abstract class Val
|
156
Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
23 |
case object Empty extends Val
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
24 |
case class Chr(c: Char) extends Val
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
25 |
case class Sequ(v1: Val, v2: Val) extends Val
|
13
Christian Urban <christian dot urban at kcl dot ac dot uk>
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|
26 |
case class Left(v: Val) extends Val
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
27 |
case class Right(v: Val) extends Val
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
28 |
case class Stars(vs: List[Val]) extends Val
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
29 |
case class Rec(x: String, v: Val) extends Val
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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changeset
|
30 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
31 |
// some convenience for typing in regular expressions
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
32 |
def charlist2rexp(s : List[Char]): Rexp = s match {
|
156
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
33 |
case Nil => ONE
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
34 |
case c::Nil => CHAR(c)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
35 |
case c::s => SEQ(CHAR(c), charlist2rexp(s))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
36 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
37 |
implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
38 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
39 |
implicit def RexpOps(r: Rexp) = new {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
40 |
def | (s: Rexp) = ALT(r, s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
41 |
def % = STAR(r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
42 |
def ~ (s: Rexp) = SEQ(r, s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
43 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
44 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
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|
45 |
implicit def stringOps(s: String) = new {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
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|
46 |
def | (r: Rexp) = ALT(s, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
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|
47 |
def | (r: String) = ALT(s, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
48 |
def % = STAR(s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
49 |
def ~ (r: Rexp) = SEQ(s, r)
|
81
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
50 |
def ~ (r: String) = SEQ(s, r)
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
51 |
def $ (r: Rexp) = RECD(s, r)
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
52 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
53 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
54 |
// translation into ARexps
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
55 |
def fuse(bs: List[Boolean], r: ARexp) : ARexp = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
56 |
case AZERO => AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
57 |
case AONE(cs) => AONE(bs ++ cs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
58 |
case ACHAR(cs, c) => ACHAR(bs ++ cs, c)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
59 |
case AALT(cs, r1, r2) => AALT(bs ++ cs, r1, r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
60 |
case ASEQ(cs, r1, r2) => ASEQ(bs ++ cs, r1, r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
61 |
case ASTAR(cs, r) => ASTAR(bs ++ cs, r)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
62 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
63 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
64 |
def internalise(r: Rexp) : ARexp = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
65 |
case ZERO => AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
66 |
case ONE => AONE(Nil)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
67 |
case CHAR(c) => ACHAR(Nil, c)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
68 |
case ALT(r1, r2) => AALT(Nil, fuse(List(false), internalise(r1)), fuse(List(true), internalise(r2)))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
69 |
case SEQ(r1, r2) => ASEQ(Nil, internalise(r1), internalise(r2))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
70 |
case STAR(r) => ASTAR(Nil, internalise(r))
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
71 |
case RECD(x, r) => internalise(r)
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
72 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
73 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
74 |
internalise(("a" | "ab") ~ ("b" | ""))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
75 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
76 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
77 |
def decode_aux(r: Rexp, bs: List[Boolean]) : (Val, List[Boolean]) = (r, bs) match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
78 |
case (ONE, bs) => (Empty, bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
79 |
case (CHAR(c), bs) => (Chr(c), bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
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|
80 |
case (ALT(r1, r2), false::bs) => {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
81 |
val (v, bs1) = decode_aux(r1, bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
82 |
(Left(v), bs1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
83 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
84 |
case (ALT(r1, r2), true::bs) => {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
85 |
val (v, bs1) = decode_aux(r2, bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
86 |
(Right(v), bs1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
87 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
88 |
case (SEQ(r1, r2), bs) => {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
89 |
val (v1, bs1) = decode_aux(r1, bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
90 |
val (v2, bs2) = decode_aux(r2, bs1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
91 |
(Sequ(v1, v2), bs2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
92 |
}
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
93 |
case (STAR(r1), false::bs) => {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
94 |
val (v, bs1) = decode_aux(r1, bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
95 |
val (Stars(vs), bs2) = decode_aux(STAR(r1), bs1)
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
96 |
(Stars(v::vs), bs2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
97 |
}
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
98 |
case (STAR(_), true::bs) => (Stars(Nil), bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
99 |
case (RECD(x, r1), bs) => {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
100 |
val (v, bs1) = decode_aux(r1, bs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
101 |
(Rec(x, v), bs1)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
102 |
}
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
103 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
104 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
105 |
def decode(r: Rexp, bs: List[Boolean]) = decode_aux(r, bs) match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
106 |
case (v, Nil) => v
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
107 |
case _ => throw new Exception("Not decodable")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
108 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
109 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
110 |
// nullable function: tests whether the aregular
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
111 |
// expression can recognise the empty string
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
112 |
def nullable (r: ARexp) : Boolean = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
113 |
case AZERO => false
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
114 |
case AONE(_) => true
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
115 |
case ACHAR(_,_) => false
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
116 |
case AALT(_, r1, r2) => nullable(r1) || nullable(r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
117 |
case ASEQ(_, r1, r2) => nullable(r1) && nullable(r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
118 |
case ASTAR(_, _) => true
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
119 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
120 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
121 |
def mkepsBC(r: ARexp) : List[Boolean] = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
122 |
case AONE(bs) => bs
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
123 |
case AALT(bs, r1, r2) =>
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
124 |
if (nullable(r1)) bs ++ mkepsBC(r1) else bs ++ mkepsBC(r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
125 |
case ASEQ(bs, r1, r2) => bs ++ mkepsBC(r1) ++ mkepsBC(r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
126 |
case ASTAR(bs, r) => bs ++ List(true)
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
127 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
128 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
129 |
// derivative of a regular expression w.r.t. a character
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
130 |
def der (c: Char, r: ARexp) : ARexp = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
131 |
case AZERO => AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
132 |
case AONE(_) => AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
133 |
case ACHAR(bs, d) => if (c == d) AONE(bs) else AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
134 |
case AALT(bs, r1, r2) => AALT(bs, der(c, r1), der(c, r2))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
135 |
case ASEQ(bs, r1, r2) =>
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
136 |
if (nullable(r1)) AALT(bs, ASEQ(Nil, der(c, r1), r2), fuse(mkepsBC(r1), der(c, r2)))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
137 |
else ASEQ(bs, der(c, r1), r2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
138 |
case ASTAR(bs, r) => ASEQ(bs, fuse(List(false), der(c, r)), ASTAR(Nil, r))
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
139 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
140 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
141 |
// derivative w.r.t. a string (iterates der)
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
142 |
@tailrec
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
143 |
def ders (s: List[Char], r: ARexp) : ARexp = s match {
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
144 |
case Nil => r
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
145 |
case c::s => ders(s, der(c, r))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
146 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
147 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
148 |
// main unsimplified lexing function (produces a value)
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
149 |
def lex(r: ARexp, s: List[Char]) : List[Boolean] = s match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
150 |
case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
151 |
case c::cs => lex(der(c, r), cs)
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
152 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
153 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
154 |
def lexing(r: Rexp, s: String) : Val = decode(r, lex(internalise(r), s.toList))
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
155 |
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
156 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
157 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
158 |
def simp(r: ARexp): ARexp = r match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
159 |
case ASEQ(bs1, r1, r2) => (simp(r1), simp(r2)) match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
160 |
case (AZERO, _) => AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
161 |
case (_, AZERO) => AZERO
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
162 |
case (AONE(bs2), r2s) => fuse(bs1 ++ bs2, r2s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
163 |
case (r1s, r2s) => ASEQ(bs1, r1s, r2s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
164 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
165 |
case AALT(bs1, r1, r2) => (simp(r1), simp(r2)) match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
166 |
case (AZERO, r2s) => fuse(bs1, r2s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
167 |
case (r1s, AZERO) => fuse(bs1, r1s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
168 |
case (r1s, r2s) => AALT(bs1, r1s, r2s)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
169 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
170 |
case r => r
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
171 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
172 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
173 |
def lex_simp(r: ARexp, s: List[Char]) : List[Boolean] = s match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
174 |
case Nil => if (nullable(r)) mkepsBC(r) else throw new Exception("Not matched")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
175 |
case c::cs => lex(simp(der(c, r)), cs)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
176 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
177 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
178 |
def lexing_simp(r: Rexp, s: String) : Val = decode(r, lex_simp(internalise(r), s.toList))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
179 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
180 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
181 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
182 |
// extracts a string from value
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
183 |
def flatten(v: Val) : String = v match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
184 |
case Empty => ""
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
185 |
case Chr(c) => c.toString
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
186 |
case Left(v) => flatten(v)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
187 |
case Right(v) => flatten(v)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
188 |
case Sequ(v1, v2) => flatten(v1) + flatten(v2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
189 |
case Stars(vs) => vs.map(flatten).mkString
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
190 |
case Rec(_, v) => flatten(v)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
191 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
192 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
193 |
// extracts an environment from a value
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
194 |
def env(v: Val) : List[(String, String)] = v match {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
195 |
case Empty => Nil
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
196 |
case Chr(c) => Nil
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
197 |
case Left(v) => env(v)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
198 |
case Right(v) => env(v)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
199 |
case Sequ(v1, v2) => env(v1) ::: env(v2)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
200 |
case Stars(vs) => vs.flatMap(env)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
201 |
case Rec(x, v) => (x, flatten(v))::env(v)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
202 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
203 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
204 |
// Some Tests
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
205 |
//============
|
75
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
206 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
207 |
def time_needed[T](i: Int, code: => T) = {
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
208 |
val start = System.nanoTime()
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
209 |
for (j <- 1 to i) code
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
210 |
val end = System.nanoTime()
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
211 |
(end - start)/(i * 1.0e9)
|
75
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
212 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
213 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
214 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
215 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
216 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
217 |
val r0 = ("a" | "ab") ~ ("b" | "")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
218 |
println(lexing(r0, "ab"))
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
219 |
println(lexing_simp(r0, "ab"))
|
75
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
220 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
221 |
val r1 = ("a" | "ab") ~ ("bcd" | "cd")
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
222 |
println(lexing(r1, "abcd"))
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
223 |
println(lexing_simp(r1, "abcd"))
|
78
279d0bc48308
updated the Isabelle theories with the totality proof
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
224 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
225 |
println(lexing((("" | "a") ~ ("ab" | "b")), "ab"))
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
226 |
println(lexing_simp((("" | "a") ~ ("ab" | "b")), "ab"))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
227 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
228 |
println(lexing((("" | "a") ~ ("b" | "ab")), "ab"))
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
229 |
println(lexing_simp((("" | "a") ~ ("b" | "ab")), "ab"))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
230 |
|
158
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
231 |
println(lexing((("" | "a") ~ ("c" | "ab")), "ab"))
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
232 |
println(lexing_simp((("" | "a") ~ ("c" | "ab")), "ab"))
|
78
279d0bc48308
updated the Isabelle theories with the totality proof
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
233 |
|
81
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
234 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
235 |
// Two Simple Tests for the While Language
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
236 |
//========================================
|
78
279d0bc48308
updated the Isabelle theories with the totality proof
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
237 |
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
238 |
// Lexing Rules
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
239 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
240 |
def PLUS(r: Rexp) = r ~ r.%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
241 |
val SYM = "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
242 |
val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
243 |
val ID = SYM ~ (SYM | DIGIT).%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
244 |
val NUM = PLUS(DIGIT)
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
245 |
val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
246 |
val SEMI: Rexp = ";"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
247 |
val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
248 |
val WHITESPACE = PLUS(" " | "\n" | "\t")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
249 |
val RPAREN: Rexp = ")"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
250 |
val LPAREN: Rexp = "("
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
251 |
val BEGIN: Rexp = "{"
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
252 |
val END: Rexp = "}"
|
41
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
253 |
val STRING: Rexp = "\"" ~ SYM.% ~ "\""
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
254 |
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
255 |
val WHILE_REGS = (("k" $ KEYWORD) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
256 |
("i" $ ID) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
257 |
("o" $ OP) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
258 |
("n" $ NUM) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
259 |
("s" $ SEMI) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
260 |
("str" $ STRING) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
261 |
("p" $ (LPAREN | RPAREN)) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
262 |
("b" $ (BEGIN | END)) |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
263 |
("w" $ WHITESPACE)).%
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
264 |
|
38
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
265 |
println("prog0 test")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
266 |
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
267 |
val prog0 = """read n"""
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
268 |
println(env(lexing(WHILE_REGS, prog0)))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
269 |
println(env(lexing_simp(WHILE_REGS, prog0)))
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
270 |
|
38
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
271 |
println("prog1 test")
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
272 |
|
3
Christian Urban <christian dot urban at kcl dot ac dot uk>
parents:
diff
changeset
|
273 |
val prog1 = """read n; write (n)"""
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
274 |
println(env(lexing(WHILE_REGS, prog1)))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
275 |
println(env(lexing_simp(WHILE_REGS, prog1)))
|
157
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
276 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
277 |
|
159
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
278 |
// Sulzmann's tests
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
279 |
//==================
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
280 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
281 |
val sulzmann = ("a" | "b" | "ab").%
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
282 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
283 |
println(lexing(sulzmann, "a" * 10))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
284 |
println(lexing_simp(sulzmann, "a" * 10))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
285 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
286 |
for (i <- 1 to 6501 by 500) {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
287 |
println(i + ": " + "%.5f".format(time_needed(1, lexing_simp(sulzmann, "a" * i))))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
288 |
}
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
289 |
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
290 |
for (i <- 1 to 16 by 5) {
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
291 |
println(i + ": " + "%.5f".format(time_needed(1, lexing_simp(sulzmann, "ab" * i))))
|
Christian Urban <christian dot urban at kcl dot ac dot uk>
diff
changeset
|
292 |
}
|