--- a/progs/lexer.scala Tue Oct 01 15:00:09 2019 +0100
+++ b/progs/lexer.scala Tue Oct 01 23:40:25 2019 +0100
@@ -1,8 +1,11 @@
-// A Simple Lexer according to Sulzmann & Lu
+// A simple lexer inspired by work of Sulzmann & Lu
+//==================================================
+
import scala.language.implicitConversions
import scala.language.reflectiveCalls
+// regular expressions including records
abstract class Rexp
case object ZERO extends Rexp
case object ONE extends Rexp
@@ -11,7 +14,8 @@
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp
case class STAR(r: Rexp) extends Rexp
case class RECD(x: String, r: Rexp) extends Rexp
-
+
+// values
abstract class Val
case object Empty extends Val
case class Chr(c: Char) extends Val
@@ -45,12 +49,7 @@
def $ (r: Rexp) = RECD(s, r)
}
-// A test for more conveninet syntax
-val re : Rexp = ("ab" | "a") ~ ("b" | ONE)
-
-// the nullable function: tests whether the regular
-// expression can recognise the empty string
-def nullable (r: Rexp) : Boolean = r match {
+def nullable(r: Rexp) : Boolean = r match {
case ZERO => false
case ONE => true
case CHAR(_) => false
@@ -60,8 +59,7 @@
case RECD(_, r1) => nullable(r1)
}
-// the derivative of a regular expression w.r.t. a character
-def der (c: Char, r: Rexp) : Rexp = r match {
+def der(c: Char, r: Rexp) : Rexp = r match {
case ZERO => ZERO
case ONE => ZERO
case CHAR(d) => if (c == d) ONE else ZERO
@@ -73,11 +71,6 @@
case RECD(_, r1) => der(c, r1)
}
-// the derivative w.r.t. a string (iterates der)
-def ders (s: List[Char], r: Rexp) : Rexp = s match {
- case Nil => r
- case c::s => ders(s, der(c, r))
-}
// extracts a string from value
def flatten(v: Val) : String = v match {
@@ -90,8 +83,9 @@
case Rec(_, v) => flatten(v)
}
+
// extracts an environment from a value;
-// used for lexing a string
+// used for tokenise a string
def env(v: Val) : List[(String, String)] = v match {
case Empty => Nil
case Chr(c) => Nil
@@ -102,10 +96,8 @@
case Rec(x, v) => (x, flatten(v))::env(v)
}
-// The Injection Part of the Lexer
+// The Injection Part of the lexer
-// calculates a value for how a nullable regex
-// matches the empty string
def mkeps(r: Rexp) : Val = r match {
case ONE => Empty
case ALT(r1, r2) =>
@@ -115,7 +107,6 @@
case RECD(x, r) => Rec(x, mkeps(r))
}
-// injects back a character into a value
def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
@@ -127,19 +118,6 @@
case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
}
-// the main lexing function (produces a value)
-def lex(r: Rexp, s: List[Char]) : Val = s match {
- case Nil => if (nullable(r)) mkeps(r)
- else throw new Exception("Not matched")
- case c::cs => inj(r, c, lex(der(c, r), cs))
-}
-
-def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)
-
-// a simple test for extracting an environment
-val re1 : Rexp = ("first" $ ("a" | "ab")) ~ ("second" $ ("b" | ONE))
-env(lexing(re1, "ab"))
-
// some "rectification" functions for simplification
def F_ID(v: Val): Val = v
def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))
@@ -160,8 +138,6 @@
}
def F_ERROR(v: Val): Val = throw new Exception("error")
-// simplification of regular expressions returns now also
-// an rectification function; no simplification under STAR
def simp(r: Rexp): (Rexp, Val => Val) = r match {
case ALT(r1, r2) => {
val (r1s, f1s) = simp(r1)
@@ -193,33 +169,39 @@
// lexing functions including simplification
def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
- case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+ case Nil => if (nullable(r)) mkeps(r) else
+ { throw new Exception("lexing error") }
case c::cs => {
val (r_simp, f_simp) = simp(der(c, r))
inj(r, c, f_simp(lex_simp(r_simp, cs)))
}
}
-def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList)
+def lexing_simp(r: Rexp, s: String) =
+ env(lex_simp(r, s.toList))
-lexing_simp(("a" | "ab") ~ ("b" | ""), "ab")
-// The Lexing Rules for a Small While Language
+// The Lexing Rules for the Fun Language
def PLUS(r: Rexp) = r ~ r.%
-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"
-val DIGIT = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
+def Range(s : List[Char]) : Rexp = s match {
+ case Nil => ZERO
+ case c::Nil => CHAR(c)
+ case c::s => ALT(CHAR(c), Range(s))
+}
+def RANGE(s: String) = Range(s.toList)
+
+val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")
+val DIGIT = RANGE("0123456789")
val ID = SYM ~ (SYM | DIGIT).%
val NUM = PLUS(DIGIT)
-val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write"
val SEMI: Rexp = ";"
-val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
+val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">"
val WHITESPACE = PLUS(" " | "\n" | "\t")
-val RPAREN: Rexp = ")"
-val LPAREN: Rexp = "("
-val BEGIN: Rexp = "{"
-val END: Rexp = "}"
+val RPAREN: Rexp = "{"
+val LPAREN: Rexp = "}"
val STRING: Rexp = "\"" ~ SYM.% ~ "\""
@@ -230,45 +212,37 @@
("s" $ SEMI) |
("str" $ STRING) |
("p" $ (LPAREN | RPAREN)) |
- ("b" $ (BEGIN | END)) |
("w" $ WHITESPACE)).%
-// Testing
-//============
-
-def time[T](code: => T) = {
- val start = System.nanoTime()
- val result = code
- val end = System.nanoTime()
- println((end - start)/1.0e9)
- result
-}
-
-val r1 = ("a" | "ab") ~ ("bcd" | "c")
-println(lexing(r1, "abcd"))
-
-val r2 = ("" | "a") ~ ("ab" | "b")
-println(lexing(r2, "ab"))
-
// Two Simple While Tests
//========================
-println("prog0 test")
-val prog0 = """read if"""
-println(env(lexing_simp(WHILE_REGS, prog0)))
+println("test: read n")
-println("prog1 test")
+val prog0 = """read n"""
+println(lexing_simp(WHILE_REGS, prog0))
-val prog1 = """read n; write (n)"""
-println(env(lexing_simp(WHILE_REGS, prog1)))
+println("test: read n; write n ")
+
+val prog1 = """read n; write n"""
+println(lexing_simp(WHILE_REGS, prog1))
-// Bigger Test
-//=============
+// Bigger Tests
+//==============
+
+// escapes strings and prints them out as "", "\n" and so on
+def esc(raw: String): String = {
+ import scala.reflect.runtime.universe._
+ Literal(Constant(raw)).toString
+}
+
+def escape(tks: List[(String, String)]) =
+ tks.map{ case (s1, s2) => (s1, esc(s2))}
val prog2 = """
-write "fib";
+write "Fib";
read n;
minus1 := 0;
minus2 := 1;
@@ -278,36 +252,33 @@
minus1 := temp;
n := n - 1
};
-write "result";
-write minus2
-"""
-
-println("Tokens")
-println(env(lexing_simp(WHILE_REGS, prog2)))
-println(env(lexing_simp(WHILE_REGS, prog2)).filterNot{_._1 == "w"}.mkString("\n"))
-
-// some more timing tests with
-// i copies of the program
-
-for (i <- 0 to 20 by 10) {
- print(i.toString + ": ")
- time(lexing_simp(WHILE_REGS, prog2 * i))
-}
-
-
-val fib = """
-write "Fib";
-read n;
-minus1 := 0;
-minus2 := 1;
-while n > 0 do {
-temp := minus2;
-minus2 := minus1 + minus2;
-minus1 := temp;
-n := n - 1
-};
write "Result";
write minus2
"""
-println(env(lexing_simp(WHILE_REGS, prog2)).filterNot{_._1 == "w"})
+println("lexing Fib")
+println(escape(lexing_simp(WHILE_REGS, prog2)).mkString("\n"))
+
+
+
+val prog3 = """
+start := 1000;
+x := start;
+y := start;
+z := start;
+while 0 < x do {
+ while 0 < y do {
+ while 0 < z do {
+ z := z - 1
+ };
+ z := start;
+ y := y - 1
+ };
+ y := start;
+ x := x - 1
+}
+"""
+
+println("lexing Loops")
+println(escape(lexing_simp(WHILE_REGS, prog3)).mkString("\n"))
+