In computing

Computing

Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...

, recursive ascent parsing is a technique for implementing an LALR parser which uses mutually-recursive functions rather than tables. Thus, the parser is directly encoded in the host language similar to recursive descent. Direct encoding usually yields a parser which is faster than its table-driven equivalent for the same reason that compilation is faster than interpretation. It is also (nominally) possible to hand edit a recursive ascent parser, whereas a tabular implementation is nigh unreadable to the average human.

Recursive ascent was first described by Thomas Penello in his article in 1986. He was not intending to create a hand-editable implementation of an LR parser, but rather a maintainable and efficient parser implemented in assembly language

Assembly language

An assembly language is a low-level programming language for computers, microprocessors, microcontrollers, and other programmable devices. It implements a symbolic representation of the machine codes and other constants needed to program a given CPU architecture...

. The technique was later expounded upon by G.H. Roberts in 1988 as well as in an article by Leermakers, Augusteijn, Kruseman Aretz in 1992 in the journal Theoretical Computer Science. An extremely readable description of the technique was written by Morell and Middleton in 2003. A good exposition can also be found in a TOPLAS article by Sperber and Thiemann.

Recursive ascent has also been merged with recursive descent, yielding a technique known as recursive ascent/descent. This implementation technique is arguably easier to hand-edit due to the reduction in states and fact that some of these states are more intuitively top-down rather than bottom up. It can also yield some minimal performance improvements over conventional recursive ascent.

Summary

Intuitively, recursive ascent is a literal implementation of the LR parsing

LR parser

In computer science, an LR parser is a parser that reads input from Left to right and produces a Rightmost derivation. The term LR parser is also used; where the k refers to the number of unconsumed "look ahead" input symbols that are used in making parsing decisions...

 concept. Each function in the parser represents a single LR automaton

Finite state machine

A finite-state machine or finite-state automaton , or simply a state machine, is a mathematical model used to design computer programs and digital logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states...

 state. Within each function, a multi-branch statement is used to select the appropriate action based on the current token popped off the input stack. Once the token has been identified, action is taken based on the state being encoded. There are two different fundamental actions which may be taken based on the token in question:

• Shift - Encoded as a function call, effectively jumping to a new automaton state.
• Reduce - Encoded differently according to the semantic action routine for the relevant production. The result of this routine is wrapped in an ADT
  Algebraic data type
  In computer programming, particularly functional programming and type theory, an algebraic data type is a datatype each of whose values is data from other datatypes wrapped in one of the constructors of the datatype. Any wrapped datum is an argument to the constructor...
  
   which is returned to the caller. The reduce action must also record the number of tokens which were shifted prior to the reduce, passing this value back to the caller along with the reduce value. This shift counter determines at which point up the call stack the reduce should be handled.

There is also a third LR automaton action which may be taken in a given state, but only after a reduce where the shift counter has decremented to zero (indicating that the current state should handle the result). This is the goto action, which is essentially a special case of shift designed to handle non-terminals in a production. This action must be handled after the multi-branch statement, since this is where any reduction results will "resurface" from farther down the call stack.

Example

Consider the following grammar in bison

GNU bison

GNU bison, commonly known as Bison, is a parser generator that is part of the GNU Project. Bison reads a specification of a context-free language, warns about any parsing ambiguities, and generates a parser which reads sequences of tokens and decides whether the sequence conforms to the syntax...

 syntax:

expr : expr '+' term   { $$ = $1 + $3; }

     | expr '-' term   { $$ = $1 - $3; }

     | term            { $$ = $1; }

     ;



term : '(' expr ')'    { $$ = $2; }

     | num             { $$ = $1; }

     ;



num : '0'              { $$ = 0; }

    | '1'              { $$ = 1; }

    ;

This grammar is LR(0) in that it is left-recursive (in the expr non-terminal) but does not require any lookahead. Recursive ascent is also capable of handling grammars which are LALR(1) in much the same way that table-driven parsers handle such cases (by pre-computing conflict resolutions based on possible lookahead).

The following is a Scala implementation of a recursive ascent parser based on the above grammar:


object ExprParser {
private type Result = (NonTerminal, Int)

private sealed trait NonTerminal {
val v: Int
}

private case class NTexpr(v: Int, in: Stream[Char]) extends NonTerminal
private case class NTterm(v: Int, in: Stream[Char]) extends NonTerminal
private case class NTnum(v: Int, in: Stream[Char]) extends NonTerminal

class ParseException(msg: String) extends RuntimeException(msg) {
def this = this("")

def this(c: Char) = this(c.toString)
}

def parse(in: Stream[Char]) = state0(in)._1.v

/*
* 0 $accept: . expr $end
*
* '(' shift, and go to state 1
* '0' shift, and go to state 2
* '1' shift, and go to state 3
*
* expr go to state 4
* term go to state 5
* num go to state 6
*/
private def state0(in: Stream[Char]) = in match {
case cur #:: tail => {
def loop(tuple: Result): Result = {
val (res, goto) = tuple

if (goto 0) {
loop(res match {
case NTexpr(v, in) => state4(in, v)
case NTterm(v, in) => state5(in, v)
case NTnum(v, in) => state6(in, v)
})
} else (res, goto - 1)
}

loop(cur match {
case '(' => state1(tail)
case '0' => state2(tail)
case '1' => state3(tail)
case c => throw new ParseException(c)
})
}

case Stream => throw new ParseException
}

/*
* 4 term: '(' . expr ')'
*
* '(' shift, and go to state 1
* '0' shift, and go to state 2
* '1' shift, and go to state 3
*
* expr go to state 7
* term go to state 5
* num go to state 6
*/
private def state1(in: Stream[Char]): Result = in match {
case cur #:: tail => {
def loop(tuple: Result): Result = {
val (res, goto) = tuple

if (goto 0) {
loop(res match {
case NTexpr(v, in) => state7(in, v)
case NTterm(v, in) => state5(in, v)
case NTnum(v, in) => state6(in, v)
})
} else (res, goto - 1)
}

loop(cur match {
case '(' => state1(tail)
case '0' => state2(tail)
case '1' => state3(tail)
case c => throw new ParseException(c)
})
}

case Stream => throw new ParseException
}

/*
* 6 num: '0' .
*
* $default reduce using rule 6 (num)
*/
private def state2(in: Stream[Char]) = (NTnum(0, in), 0)

/*
* 7 num: '1' .
*
* $default reduce using rule 7 (num)
*/
private def state3(in: Stream[Char]) = (NTnum(1, in), 0)

/*
* 0 $accept: expr . $end
* 1 expr: expr . '+' term
* 2 | expr . '-' term
*
* $end shift, and go to state 8
* '+' shift, and go to state 9
* '-' shift, and go to state 10
*/
private def state4(in: Stream[Char], arg1: Int): Result = in match {
case cur #:: tail => {
decrement(cur match {
case '+' => state9(tail, arg1)
case '-' => state10(tail, arg1)
case c => throw new ParseException(c)
})
}

case Stream => state8(arg1)
}

/*
* 3 expr: term .
*
* $default reduce using rule 3 (expr)
*/
private def state5(in: Stream[Char], arg1: Int) = (NTexpr(arg1, in), 0)

/*
* 5 term: num .
*
* $default reduce using rule 5 (term)
*/
private def state6(in: Stream[Char], arg1: Int) = (NTterm(arg1, in), 0)

/*
* 1 expr: expr . '+' term
* 2 | expr . '-' term
* 4 term: '(' expr . ')'
*
* '+' shift, and go to state 9
* '-' shift, and go to state 10
* ')' shift, and go to state 11
*/
private def state7(in: Stream[Char], arg1: Int): Result = in match {
case cur #:: tail => {
decrement(cur match {
case '+' => state9(tail, arg1)
case '-' => state10(tail, arg1)
case ')' => state11(tail, arg1)
case c => throw new ParseException(c)
})
}

case Stream => throw new ParseException
}

/*
* 0 $accept: expr $end .
*
* $default accept
*/
private def state8(arg1: Int) = (NTexpr(arg1, Stream), 1)

/*
* 1 expr: expr '+' . term
*
* '(' shift, and go to state 1
* '0' shift, and go to state 2
* '1' shift, and go to state 3
*
* term go to state 12
* num go to state 6
*/
private def state9(in: Stream[Char], arg1: Int) = in match {
case cur #:: tail => {
def loop(tuple: Result): Result = {
val (res, goto) = tuple

if (goto 0) {
loop(res match {
case NTterm(v, in) => state12(in, arg1, v)
case NTnum(v, in) => state6(in, v)
case _ => throw new AssertionError
})
} else (res, goto - 1)
}

loop(cur match {
case '(' => state1(tail)
case '0' => state2(tail)
case '1' => state3(tail)
case c => throw new ParseException(c)
})
}

case Stream => throw new ParseException
}

/*
* 2 expr: expr '-' . term
*
* '(' shift, and go to state 1
* '0' shift, and go to state 2
* '1' shift, and go to state 3
*
* term go to state 13
* num go to state 6
*/
private def state10(in: Stream[Char], arg1: Int) = in match {
case cur #:: tail => {
def loop(tuple: Result): Result = {
val (res, goto) = tuple

if (goto 0) {
loop(res match {
case NTterm(v, in) => state13(in, arg1, v)
case NTnum(v, in) => state6(in, v)
case _ => throw new AssertionError
})
} else (res, goto - 1)
}

loop(cur match {
case '(' => state1(tail)
case '0' => state2(tail)
case '1' => state3(tail)
case c => throw new ParseException(c)
})
}

case Stream => throw new ParseException
}

/*
* 4 term: '(' expr ')' .
*
* $default reduce using rule 4 (term)
*/
private def state11(in: Stream[Char], arg1: Int) = (NTterm(arg1, in), 2)

/*
* 1 expr: expr '+' term .
*
* $default reduce using rule 1 (expr)
*/
private def state12(in: Stream[Char], arg1: Int, arg2: Int) = (NTexpr(arg1 + arg2, in), 2)

/*
* 2 expr: expr '-' term .
*
* $default reduce using rule 2 (expr)
*/
private def state13(in: Stream[Char], arg1: Int, arg2: Int) = (NTexpr(arg1 - arg2, in), 2)

private def decrement(tuple: Result) = {
val (res, goto) = tuple
assert(goto != 0)
(res, goto - 1)
}
}