--- a/progs/token.scala Sun Jul 28 14:24:46 2019 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,313 +0,0 @@
-// A Simple Tokenizer according to Sulzmann & Lu
-
-import scala.language.implicitConversions
-import scala.language.reflectiveCalls
-
-abstract class Rexp
-case object ZERO extends Rexp
-case object ONE extends Rexp
-case class CHAR(c: Char) extends Rexp
-case class ALT(r1: Rexp, r2: Rexp) extends Rexp
-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
-
-abstract class Val
-case object Empty extends Val
-case class Chr(c: Char) extends Val
-case class Sequ(v1: Val, v2: Val) extends Val
-case class Left(v: Val) extends Val
-case class Right(v: Val) extends Val
-case class Stars(vs: List[Val]) extends Val
-case class Rec(x: String, v: Val) extends Val
-
-// some convenience for typing in regular expressions
-def charlist2rexp(s : List[Char]): Rexp = s match {
- case Nil => ONE
- case c::Nil => CHAR(c)
- case c::s => SEQ(CHAR(c), charlist2rexp(s))
-}
-implicit def string2rexp(s : String) : Rexp =
- charlist2rexp(s.toList)
-
-implicit def RexpOps(r: Rexp) = new {
- def | (s: Rexp) = ALT(r, s)
- def % = STAR(r)
- def ~ (s: Rexp) = SEQ(r, s)
-}
-
-implicit def stringOps(s: String) = new {
- def | (r: Rexp) = ALT(s, r)
- def | (r: String) = ALT(s, r)
- def % = STAR(s)
- def ~ (r: Rexp) = SEQ(s, r)
- def ~ (r: String) = SEQ(s, r)
- 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 {
- case ZERO => false
- case ONE => true
- case CHAR(_) => false
- case ALT(r1, r2) => nullable(r1) || nullable(r2)
- case SEQ(r1, r2) => nullable(r1) && nullable(r2)
- case STAR(_) => true
- 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 {
- case ZERO => ZERO
- case ONE => ZERO
- case CHAR(d) => if (c == d) ONE else ZERO
- case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
- case SEQ(r1, r2) =>
- if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
- else SEQ(der(c, r1), r2)
- case STAR(r) => SEQ(der(c, r), STAR(r))
- 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 {
- case Empty => ""
- case Chr(c) => c.toString
- case Left(v) => flatten(v)
- case Right(v) => flatten(v)
- case Sequ(v1, v2) => flatten(v1) + flatten(v2)
- case Stars(vs) => vs.map(flatten).mkString
- case Rec(_, v) => flatten(v)
-}
-
-// extracts an environment from a value;
-// used for tokenise a string
-def env(v: Val) : List[(String, String)] = v match {
- case Empty => Nil
- case Chr(c) => Nil
- case Left(v) => env(v)
- case Right(v) => env(v)
- case Sequ(v1, v2) => env(v1) ::: env(v2)
- case Stars(vs) => vs.flatMap(env)
- case Rec(x, v) => (x, flatten(v))::env(v)
-}
-
-// The Injection Part of the Tokeniser
-
-// 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) =>
- if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
- case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
- case STAR(r) => Stars(Nil)
- 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)
- case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
- case (SEQ(r1, r2), Right(v2)) => Sequ(mkeps(r1), inj(r2, c, v2))
- case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
- case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
- case (CHAR(d), Empty) => Chr(c)
- 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))
-def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))
-def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
- case Right(v) => Right(f2(v))
- case Left(v) => Left(f1(v))
-}
-def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
- case Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
-}
-def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) =
- (v:Val) => Sequ(f1(Empty), f2(v))
-def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) =
- (v:Val) => Sequ(f1(v), f2(Empty))
-def F_RECD(f: Val => Val) = (v:Val) => v match {
- case Rec(x, v) => Rec(x, f(v))
-}
-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)
- val (r2s, f2s) = simp(r2)
- (r1s, r2s) match {
- case (ZERO, _) => (r2s, F_RIGHT(f2s))
- case (_, ZERO) => (r1s, F_LEFT(f1s))
- case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
- else (ALT (r1s, r2s), F_ALT(f1s, f2s))
- }
- }
- case SEQ(r1, r2) => {
- val (r1s, f1s) = simp(r1)
- val (r2s, f2s) = simp(r2)
- (r1s, r2s) match {
- case (ZERO, _) => (ZERO, F_ERROR)
- case (_, ZERO) => (ZERO, F_ERROR)
- case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
- case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))
- case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
- }
- }
- case RECD(x, r1) => {
- val (r1s, f1s) = simp(r1)
- (RECD(x, r1s), F_RECD(f1s))
- }
- case r => (r, F_ID)
-}
-
-// 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 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)
-
-lexing_simp(("a" | "ab") ~ ("b" | ""), "ab")
-
-// The Lexing Rules for a Small While 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"
-val ID = SYM ~ (SYM | DIGIT).%
-val NUM = PLUS(DIGIT)
-val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
-val SEMI: Rexp = ";"
-val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
-val WHITESPACE = PLUS(" " | "\n" | "\t")
-val RPAREN: Rexp = ")"
-val LPAREN: Rexp = "("
-val BEGIN: Rexp = "{"
-val END: Rexp = "}"
-val STRING: Rexp = "\"" ~ SYM.% ~ "\""
-
-
-val WHILE_REGS = (("k" $ KEYWORD) |
- ("i" $ ID) |
- ("o" $ OP) |
- ("n" $ NUM) |
- ("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("prog1 test")
-
-val prog1 = """read n; write (n)"""
-println(env(lexing_simp(WHILE_REGS, prog1)))
-
-
-// Bigger Test
-//=============
-
-val prog2 = """
-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("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"})