diff -r e66bd5c563eb -r b5b5583a3a08 progs/lexer.scala --- a/progs/lexer.scala Mon Jul 27 11:02:48 2020 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,280 +0,0 @@ -// 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 -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 - -// values -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) -} - -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) -} - -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) -} - - -// 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 lexer - -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)) -} - -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)) -} - -// 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") - -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 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("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) = - env(lex_simp(r, s.toList)) - - -// The Lexing Rules for the Fun Language - -def PLUS(r: Rexp) = r ~ r.% - -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" -val SEMI: Rexp = ";" -val OP: Rexp = ":=" | "=" | "-" | "+" | "*" | "!=" | "<" | ">" -val WHITESPACE = PLUS(" " | "\n" | "\t") -val RPAREN: Rexp = "{" -val LPAREN: Rexp = "}" -val STRING: Rexp = "\"" ~ SYM.% ~ "\"" - - -val WHILE_REGS = (("k" $ KEYWORD) | - ("i" $ ID) | - ("o" $ OP) | - ("n" $ NUM) | - ("s" $ SEMI) | - ("str" $ STRING) | - ("p" $ (LPAREN | RPAREN)) | - ("w" $ WHITESPACE)).% - - -// Two Simple While Tests -//======================== - -println("test: read n") - -val prog0 = """read n""" -println(lexing_simp(WHILE_REGS, prog0)) - -println("test: read n; write n ") - -val prog1 = """read n; write n""" -println(lexing_simp(WHILE_REGS, prog1)) - - -// 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"; -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("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")) -