From 495dce5d6c68f5b5973c167e5e2287777038a012 Mon Sep 17 00:00:00 2001 From: ceriel Date: Thu, 10 Jul 1997 07:55:35 +0000 Subject: [PATCH] Added LLgen_NCER.n --- doc/LLgen/LLgen_NCER.n | 2712 ++++++++++++++++++++++++++++++++++++++++ doc/LLgen/Makefile | 10 +- doc/LLgen/proto.make | 6 + 3 files changed, 2726 insertions(+), 2 deletions(-) create mode 100644 doc/LLgen/LLgen_NCER.n diff --git a/doc/LLgen/LLgen_NCER.n b/doc/LLgen/LLgen_NCER.n new file mode 100644 index 000000000..3693a1525 --- /dev/null +++ b/doc/LLgen/LLgen_NCER.n @@ -0,0 +1,2712 @@ +.RP +.TL + + + +Top-down Non-Correcting Error Recovery + in LLgen +.AU +Arthur van Deudekom +Peter Kooiman +.AI +Department of Mathematics and Computer Science +Vrije Universiteit +Amsterdam + + + + + +Supervised by +.AU +dr. D. Grune +.AI +Department of Mathematics and Computer Science +Vrije Universiteit +Amsterdam + +.AB +This paper describes the design and implementation of a parser +generator with non-correcting error recovery based on the extended LL(1) +parser generator LLgen. It describes a top-down algorithm for implementing +this error recovery technique that can handle left-recursive grammars. +The parser generator has been tested with several existing ACK-compilers, +among which C and Modula-2. Various optimizations have been tried and are +discussed in this paper. +.AE +.LP +.nr PS 12 +.nr VS 14 + +.NH +Introduction +.EQ +delim $$ +.EN + +.nr PS 10 +.nr VS 12 +.RS +.LP +One of the trickier problems in constructing parser-generators is what +to do when the input to the generated parser is not well formed. Several +approaches are known, most of which are `correcting', meaning that they +modify the input to make it correct. However, in most cases there are +several possible corrections, and often the one chosen will turn out +to be the wrong one. As a result of such an incorrect choice, spurious error +messages can occur. Every programmer knows from experience how the omission +of a single `)' can on occasion lead to pages of error messages. + +.LP +A radically different approach is to just discard all the input up to +and including the offending token, and start with a clean slate at the +token following the offending one. [RICHTER] describes how +this idea can be used to construct a non-correcting error recovery system +that will never introduce spurious error messages. It is, however, +possible that errors are overlooked. + +.LP +In this paper we describe the incorporation of this non-correcting error +recovery into LLgen, an existing LL(1) parser generator. +In this introduction, we will describe in detail this non-correcting error +recovery technique, give an overview of LLgen and how it handles +errors, and finally describe how we have incorporated noncorrecting +error recovery in LLgen. +.RE + +.NH 2 +Non-correcting syntax error recovery + +.LP +Richter describes how syntax error recovery can be done +without making any corrections to the input text. Richter gives three +reasons why recovery without correction is desirable: + +.IP 1 +In most cases there are many possible corrections, the choice among which +will severely influence the further processing of the input. Thus, the +probability of selecting the right correction is not high. + +.IP 2 +The harm done by selecting the wrong correction is often unlimited. + +.IP 3 +The loss of information to the user of a non-correcting recovery technique +need not be grave. + +.LP +The non-correcting technique described by Richter can be summarized as +follows: When a syntax-error has occurred, the input up to and including the +erroneous symbol is discarded; the remainder of the +input is processed by a substring parser of the input +language, that is a parser that recognizes any substring of a string in the input +language. When the substring parser detects a syntax error, the offending +symbol is reported as another error, and the input up to and including the +erroneous symbol is discarded. The process is then repeated with the remaining input, possibly +finding other syntax errors, until all the input is scanned. +This process yields what Richter calls a +.I +suffix analysis +.R +of an input string. Formally, given an input string +.I x +, suffix analysis produces a set of strings $w sub k$ and a set of symbols +$ a sub k$ such that +.br + +.IP +$x~ =~ w sub 0 a sub 0 w sub 1 a sub 1~...w sub n-1 a sub n-1 w sub n$ +.LP +and such that: +.br +.IP + $w sub 0$ is the longest prefix of $x$ that is a prefix of +a string in the input language L, formally: there is a string $y$ such that +$w sub 0 y$ is in L, but there is no string $z$ such that $w sub 0 a sub 0 z$ +is in L; +.IP +For $0 < k < n$, $w sub k$ is a longest substring of $x$ that is also a +substring of a string in L, formally there are strings $u$ and $v$ such that +$u w sub k v$ is in L, but there are no strings $y$ en $z$ such that +$y w sub k a sub k z$ is in L; +.IP +$w sub n$ is a substring of $x$ +that is a substring of a string in L, formally: +there exist $u$ and $v$, such that $u w sub n v$ is in L. Note that +$w sub n$ need not be a suffix of a string in L, if $x$ represents incomplete +input $w sub n$ is not a suffix of a string in L. + +.LP +Now, the $a sub k$ indicate points at which an error is detected. The +"real" error need not be at $a sub k$, it can have occurred anywhere +within $w sub k a sub k$. +In his paper, Richter shows that, although this method may miss errors, it +will never introduce spurious errors. + +.LP +For implementing the technique, a parser that recognizes any +substring of the input language is needed. If we confine ourselves to +syntactical analysis, it is sufficient to construct a substring +recognizer. Richter himself does not give a practical construction, but +[CORMACK] describes how a LR substring parser can be constructed +that handles BC-LR(1,1) grammars. In this paper, we describe the construction +of a LL substring recognizer that can handle any grammar. Furthermore, +our recognizer is actually a suffix-recognizer, that is, a recognizer that +recognizes any suffix of a string in the input language. Our suffix recognizer has the +correct-prefix property, +meaning that it detects the first syntax error as early as possible +in a left-to-right scan of the input. Specifically, if the input language +is L and the invalid input is $x$ , it finds a string $w$ and an input symbol +$a$ such that $x = way$ , there is a string $z$ such that $wz$ +is in L, and there is no string $z$ such that $waz$ is in L. +Because the suffix parser has this correct-prefix property, it can be +used as a substring parser, because it will detect the first input symbol that +is not part of a substring of the language. Because it is a suffix-recognizer, +it additionally will detect incomplete input, because in that case +at the end of the input the parser will not be in an accepting state. + +.NH 2 +Overview of LLgen + +.LP +LLgen is an extended LL(1) parser generator. For a complete description, +see [GRUNE]. +LLgen can actually handle grammars that are not LL(1), because it allows +the use of conflict-resolvers. In case of an LL(1) conflict, these resolvers +are used to statically or dynamically decide which rule to use. As we will see +later, this feature makes it necessary for the suffix-recognizer to +handle grammars that are not LL(1). Semantic actions can occur anywhere +in the grammar rules, and they are executed when their position is +reached during parsing. A typical LLgen rule looks like +.br +.IP +S: A { +.I action +} B +.LP +where the action is a piece of C-code, that will be executed +when the parser is using the rule for S and has recognized A. + +.LP +LLgen-generated parsers use correcting syntax error recovery, based on a +scheme designed by R\*:ohrich [ROEHRICH], inserting or deleting symbols at the point of error detection +until correct input results. This means that actions in the parser will +always be executed in an order that could also have resulted from +syntactically correct input, and most importantly, once a grammar-rule +is started it is guaranteed to be completed. This means that syntactic +errors can never result in inconsistencies for the actions. Actions +only have to deal with syntactically correct input. In a nutshell, the +error recovery in LLgen-parsers works as follows: Suppose the parser is +presented with correct input that breaks off before the end. The error +recovery mechanism now provides a continuation path, chosen in such a +way that all active rules are left as soon as possible. Effectively, the +continuation path is the `shortest way out'. The symbols on this path are +called `acceptable', and end-of-file is also `acceptable'. Furthermore, at +each point along this `shortest path' there can be other terminals that +would be correct; these are `acceptable' as well. Now, when an +error occurs, all symbols that are not acceptable are discarded, until +an acceptable symbol appears in the input. The tokens on the path up to +but not including the acceptable input symbol are inserted. +From then on, normal parsing resumes. + +.NH 2 +Incorporation of non-correcting error recovery in LLgen + +.LP +An important consideration in incorporating the non-correcting recovery +in LLgen was that correct programs should suffer as little as possible +in what regards compilation speed. Furthermore, the existing error +recovery method has the highly desirable property that rules that are +started will be finished too, thus ensuring that errors in the +input text will not cause inconsistencies in the semantic actions. We have +implemented the non-correcting error recovery in such a way that this +property is preserved. + +.LP +The way we have achieved these goals is by actually including +the suffix recognizer as a `second recognizer' in the generated parser. +Correct programs are handled in the usual way by the parser, but if an error +occurs the following happens: instead of going to the standard error +recovery routine, the parser starts executing the non-correcting error +handler. This process continues, reporting all errors, until the +end of the input text is reached. Then, control is handed back to +the standard error recovery routine. This routine will now think +there is no more input, and thus start inserting tokens so as to construct +a `shortest way out'. This ensures that all rules that were started are +also finished, and no inconsistencies can occur in the semantic actions. +However, this method does require some modifications to the error reporting +routine. Normally, if the generated parser inserts a token, it reports +this to the user, but in this case this is undesirable. The insertions only +serve to maintain consistency in the semantic actions +and do not signify errors, so reporting of insertions should be suppressed. +.bp +.nr PS 12 +.nr VS 14 +.PS +boxwid = boxwid / 1.5 +boxht = boxht / 1.5 +arcrad = arcrad / 1.5 +movewid = movewid / 1.5 +moveht = moveht / 1.5 +arrowwid = arrowwid / 1.5 +arrowht = arrowht / 1.5 +arrowhead = arrowhead / 1.5 +linewid = linewid / 1.5 +lineht = lineht / 1.5 +.PE +.NH +The LL suffix parser + +.nr PS 10 +.nr VS 12 +.RS +.LP +In this chapter, we describe the construction of the LL suffix parser. +The described parser is not restricted to LL(1) grammars, because the +presence of conflict resolvers in LLgen allows for more general grammars, +that may even be left-recursive. We start this chapter with a discussion +of the implications of conflict resolvers, and continue with descriptions +of the parser algorithm, the used data-structures, +the handling of left- and right recursion, and some possible optimizations. +.RE + +.NH 2 +LLgen conflict resolvers and their implications + +.LP +In grammars that are nearly but not completely LL(1), conflicts +will arise in the two places where parsing decisions are made: the choice +of which alternative to start (`alternation conflicts') and the decision +to stop or continue a repeated item (`repetition conflicts'). In order to +allow LLgen to handle this type of grammar, the user can +specify conflict resolvers in those places where conflicts arise. +These resolvers are Boolean expressions labeling an alternative, +and are evaluated when a conflict arises during parsing. If the +expression evaluates to `true' the labeled alternative will be taken. +The Boolean expressions are expressions in C, and can consult +any information available at the point they occur. +However, if a syntactic error has occurred in the input, and the non-correcting +error recovery starts, we can no longer rely on the conflict resolvers to +guide parsing decisions. The suffix recognizer is only concerned with +syntax, and will not execute any semantic actions. It recognizes suffices +of correct input, but does not know or care what prefix would make +the suffix a correct program; as a result, the information that conflict +resolvers could use is not available, because the semantic actions +that would build this information have not been executed. +Therefore, the information used by the conflict resolvers is no longer +reliable, and the suffix parser needs to be able to handle the underlying +grammar without their help. In particular, it has to be able to handle +left-recursive grammars. + +.NH 2 +The suffix parser algorithm + +.LP +Our algorithm needs easy access to the grammar rules; in the description +we assume there is an efficient way to access the grammar rules. In +the next chapter we will describe the details of the actual implementation. +For the moment, we will only consider grammars that are not left- or +right-recursive. In the next section, we will discuss how the algorithm has to be adapted +to handle left- and right recursion. + +.LP +Suppose the grammar is G, and the input to the suffix recognizer is +$a sub 0 a sub 1 ... a sub n-1 a sub n$. Remember that parsing is +always started by the `normal' LLgen generated parser. It's only after +a syntactic error has occurred that the suffix recognizer will be started. +The input to the suffix recognizer thus is the `tail' of the input, starting +at the first symbol after the position where the first syntax error was +found. + +.LP +Now, in order to get parsing going again, the parser scans the grammar +for rules which contain symbol $a sub 0$ in the right hand side: +.br + + A: $alpha ~ a sub 0 ~ beta$ +.br + +.LP +where $alpha$ and $beta$ represent a string of terminals and non-terminals, +possible empty. Now, for each of these rules found, and for any string +$b sub 0 b sub 1$...$ b sub m$ that can be generated by $beta$ it holds that +$a sub 0 b sub o b sub 1$...$b sub m$ is a substring of some string in L. +This can be shown as follows, supposing that the start symbol is S and +S $-> sup * gamma$ A $delta$: +.br + +S $-> sup * gamma$ A $delta$ $-> sup * gamma ~ alpha ~ a sub 0 beta ~ delta +-> sup * gamma ~ alpha ~ a sub 0 b sub 0 b sub 1$...$b sub m delta$ + +.br +Of course, there may very well be more than one such string +$b sub 1 b sub 2$..$b sub m$, and one of these strings can be empty as well, if +$beta$ can produce empty. Now, in what we will call the +.I +predicting phase +.R +the algorithm will +produce all possible symbols $b sub 0$. Then, in what we will call the +.I +accepting phase +.R +these symbols are matched against +the input, and those not matching are discarded. Then, entering the next +predicting phase, the algorithm will produce +all symbols $b sub 1$, and match them against the next input symbol in +the subsequent accepting phase, +etc. In case one of the strings $b sub 0$...$b sub m$ is empty, or +the end of one of the strings is reached, some way to continue is +needed; we will discuss this later. First let's see how the +algorithm produces the strings $b sub 0$...$b sub m$ . + +.LP +For each rule in the grammar of the form +.br + + A: $alpha a sub 0 W sub 1 W sub 2$...$W sub p$ +.br + +with each $W sub k$ a terminal or nonterminal, a +.I +prediction graph +.R +is created that looks like this: + +.PS +down; box "$a sub 0$"; arrow; box "$W sub 1$"; arrow +box "$W sub 2$"; arrow dashed; box "$W sub p$" +arrow; box "END" "$[A]$" +.PE + +.LP +The bottom element of these prediction graphs is an end-marker containing the +left-hand side of the rule used. All these graphs have $a sub 0$ on top, and +this $a sub 0$ is matched against the $a sub 0$ in the input in the +accepting phase that follows, removing the +$a sub 0$ from the graph. If the prediction graph is now empty, we have to find a way +to continue; this case is treated later. First we will consider what to do if +the prediction graph is not empty. There are two possibilities: either $W sub 1$ is a +terminal, or it is a nonterminal. If it is a terminal, we are finished for +the moment; if not, the algorithm scans for rules of the form +.br + + $W sub 1$: $U sub 1 U sub 2$...$U sub i$ +.br + +.LP +with each $U sub k$ a terminal or nonterminal. Now, the algorithm substitutes +the top of the prediction graph with the right-hand sides +of all the rules found. Because there can be more than one rule, the +prediction graph can now become a DAG (Directed Acyclic Graph). +Supposing there are two rules with $W sub 1$ in the LHS: + +.br + + $W sub 1$: $U sub 1 U sub 2$...$U sub i$ +.br + $W sub 1$: $V sub 1 V sub 2$...$V sub j$ + +.LP +the prediction graph will now look like this: + +.PS +B1: box "$U sub 1$" +move +B2: box "$V sub 1$" +arrow dashed down from bottom of B1 +B3: box "$U sub i$" +arrow dashed down from bottom of B2 +B4:box "$V sub j$" +move to 0.5 +down;move +B5:box "$[W sub 1 ]$" +arrow dashed; +box "$W sub p$" +arrow; +box "END" "$[A]$" +arrow from B3.bottom to B5.top +arrow from B4.bottom to B5.top +.PE + +.LP +The graph element representing $W sub 1$ is left in the stack, the +notation $[W sub 1 ]$ indicates it has been substituted. These substituted +element will from now on be ignored by the algorithm. The elements +$U sub 1$ and $V sub 1$ are now `on top' of the prediction graph. + +.LP +If $W sub 1$ can also produce empty, its successor in the prediction graph +has to be processed +as well; the algorithm walks down the graph to this successor, and +there the process is repeated; if it is a terminal we are finished, else we +substitute it with the right hand sides of its grammar rule. +However, the element that we want to substitute now, say $W sub k$, cannot +be marked `substituted' just like that, because it can be on another +path, on which it cannot be substituted yet. Therefore, a copy of element +$W sub k$ is made, it is marked $[W sub k ]$, and an edge is created +from $[W sub k ]$ to the successor of $W sub k$. This produces graphs like +this: +.br +.PS +B1: box "$U sub 1$" +move +B2: box "$V sub 1$" +move +X1:box "$X sub 1$" +arrow dashed down from bottom of B1 +B3: box "$U sub m$" +arrow dashed down from bottom of B2 +B4:box "$V sub j$" +arrow dashed down from bottom of X1 +Xj: box "$X sub j$" +move to 0.5 +down;move +B5:box "$[W sub 1 ]$" +arrow dashed; +B6: box "$W sub k$" +arrow +Wk1:box "$W sub k+1$" +arrow dashed +box "$W sub n$" +arrow; +box "END" "$[A]$" +arrow from B3.bottom to B5.top +arrow from B4.bottom to B5.top +move down from Xj.top;move;move;move +Wk: box "$[W sub k ]$" +arrow from Xj.bottom to Wk.top +arrow from Wk.bottom to Wk1.top +.PE + +.LP +This process of substituting is repeated with all nonterminals that are +now on top of the prediction graph, until there are only terminals on top of +the graph. +This completes the prediction phase of the algorithm, not taking into account +what to do if an END marker appears on top of the graph. +Now, the algorithm enters its accepting phase, in which +the terminals on top are compared with the next symbol in the input. +If a terminal in the graph matches the input, its element is deleted +from the graph, and the substitution process will continue with its +successors, in the next prediction phase. +If a terminal on top of the graph does not +match the input, the path it is on represents a `dead-end', which +does not need to be processed any further. The terminal is no longer +a `top', and the algorithm will not visit it again. + +.LP +There is one tricky situation: consider again this graph: + +.PS +B1: box "$U$" +move +B2: box "$a$" +move to 0.5 +down;move +B5:box "$W sub 1 $" +arrow dashed; +box "$W sub n$" +arrow; +box "END" "$[A]$" +arrow from B1.bottom to B5.top +arrow from B2.bottom to B5.top +.PE + +.LP +Here, the algorithm is processing $W sub 1$ in the predicting phase, and +using some rule it has produced $a$ on top; there is another rule with +$W sub 1$ in its LHS which has produced nonterminal $U$ on top. +Now, suppose $U$ is a nonterminal that can +produce empty. Now, the algorithm starts substituting $U$, and walks +down $W sub 1$. What we definitely do not want +is the algorithm to start substituting $W sub 1$ again, because then we +would loop forever. Therefore, if the algorithm starts processing +element $W sub 1$ it should make it $[W sub 1 ]$ before it does +anything else. On entering the element +for the second time in the prediction phase , it sees that it is already substituted, +so there is nothing to do. +It then just walks to the successor of $W sub 1$ and +starts substituting it. This is correct, since the fact that the algorithm +enters an element for the second time in a prediction phase means that the element +indirectly can produce the empty string, and thus its successor must +be substituted as well in the prediction phase. + +.LP +It is easy to see that the substitution process will stop: the algorithm can +only loop if it starts processing an element for the second time in a +prediction phase, +or if the processing of an element eventually yields a graph with that +same element on top. +The first case cannot occur because the algorithm marks elements it is +processing as `substituted' before it does anything else, meaning that those elements will not +be processed again; the second case can only occur if the grammar is +left-recursive, which we assumed it was not. + +.LP +The algorithm simulates +left-most derivations of strings $a sub 0 b sub 0 b sub 1$..$b sub n$ +starting from $a sub 0 W sub 1$..$W sub p$; as we showed before, if +the algorithm recognizes a string $a sub 0 b sub 0$..$b sub n$ that +string is a substring of some string in L. Conversely, because the +algorithm start out by using all rules of the form +A: $alpha a sub 0 beta$, and then proceeds to simulate all +possible left-most derivations, it will recognize all input +$a sub 0 b sub 0$... $b sub n$ that can be produced starting from +$a sub 0 beta$. + +.LP +Now we will discuss what has to be done if an END marker appears as +top of the prediction graph. +When this happens, it means that starting from some rule +.br + + A: $alpha a sub 0 beta$ + +.br +the algorithm has produced a leftmost-derivation of a string +$a sub 0 b sub 1 .. b sub n$ starting from $a sub 0 beta$, or that $beta$ can produce +empty and the string so far is just $a sub 0$. The next step is to assume +that the have recognized A and that that some string produced by $alpha$ +is part of the prefix that makes the suffix we are recognizing a +correct string in L. Remember that in the END marker we kept record of +the LHS of the rule that has started the graph, and we will now use this +LHS to continue recognizing. What the algorithm does is scan for all +rules of the form: +.br + + B: $gamma$ A $delta$ +.br + +with $gamma$ and $delta$ possibly empty strings of terminals and nonterminals. +The algorithm now starts a new component in the prediction graph, and if $delta$ is +$W sub 1 W sub 2$...$W sub n$ it looks like this: + +.PS +down;box "$W sub 1$"; arrow +box "$W sub 2$"; line dashed; box "$W sub n$" +arrow; box "END" "$[B]$" +.PE + +.LP +Note that the END marker now contains B, because we have started to match +a rule for B. If the $delta$ in the rule for B was empty, this just produces +and END marker with B in it; in this case, the process is just repeated +with all rules of the form: +.br + + C: $zeta$ B $eta$ +.br + +.LP +etc, until we have a prediction graph with a nonterminal or terminal on top. +Now, the substitution algorithm is again applied over all nonterminals on +top, until every top contains a terminal. It is possible that during +substitution again an END marker will turn up; if this happens +we again scan for rules to continue with etc. +This `continuation algorithm' can only loop if, when +trying to build a new prediction graph for matched symbol A, it produces an empty +graph with again matched symbol A. If this happens, the grammar was +(directly or indirectly) right-recursive, and we assumed that it was not. +Therefore, the algorithm will terminate. The terminals on top of the +new graph after applying this `continuation' algorithm are exactly those +that could follow the string $A sub 0 b sub 0$..$b sub n$ in a substring +of a string in L. +To see this, suppose we have `recognized' the rule +.br + + A: $alpha a sub 0 beta$ + +.br +and $a sub 0 b sub 0 b sub 1$...$b sub n$ is the string produced from +$a sub 0 beta$ by the algorithm. Now, using rule: +.br + + B: $gamma$ A $delta$ + +.br +and supposing that S $->$ $zeta$ B $eta$ we get +.br + + S $->$ $zeta$ B $eta$ $->$ $zeta gamma$ A $delta$ $eta$ $->$ $zeta gamma a sub 0 b sub 0 b sub 1$ ... $b sub n$ $delta$ $eta$ + +.br +.LP +and thus any string produced by a derivation starting from +$delta$ can come right after $a sub 0 b sub 0$...$b sub n$ in a substring +of some string in L. The algorithm will proceed to generate all these +strings starting from $delta$. If $delta$ produces empty, the above +is just repeated. Because in the `continuation' part +all possible rules are considered, the whole algorithm will recognize +all substrings of any string in L. In order to determine if we +have actually recognized a suffix of some string in L, we need to +remember if within a predicting phase the `continuation' part of the algorithm has been run +on an END marker containing the start-symbol S; +if this is the case, then the input seen until now is a suffix of some string in L. +Formally, it means that there is a derivation starting from start symbol +$S$ such that if the +input seen until now is $a sub 0 a sub 1$..$a sub n$, then: +.br + + S $-> sup * alpha beta$ $-> sup * alpha a sub 0 a sub 1$..$a sub n$ +.br + +.LP +where $alpha$ can be empty, $beta$ is not empty. + +.NH 2 +The prediction graph data structure + +.LP +The graphs that are produced by the suffix recognizer may grow extremely +large; to facilitate an efficient +implementation we have devised a way of keeping the size of the +data structure under control, in a way that is very similar to +the way described in [TOMITA]. + +.LP +The basic idea is, that in a prediction phase of the algorithm, it is not +necessary to explicitly substitute each nonterminal every time it +turns up as a `top'; it is sufficient to do it once, because the +second substitution will produce exactly the same subgraph starting at +the substituted nonterminal. Here is an example: + +.PS +down;box "$a$";arrow;box "A";arrow dashed;box "[B]";arrow +box "C";arrow dashed;box "END" "[X]" +move right from last box.e; +box "END" "[Y]"; +arrow <- dashed up from last box.top; +box "D";arrow <- up from last box.top +box "B" +.PE + +.LP +Here, in the left component of the graph, nonterminal B has been +substituted. Now, in the same prediction phase, the algorithm again runs into +B, now in the right component. There is no need to compute again +what the substitution will produce, it is exactly the part on top +of B in the left component. Therefore, all that is needed is: + +.PS +down;box "$a$";arrow;box "A";arrow dashed; +B1: box "[B]";arrow +box "C";arrow dashed;box "END" "[X]" +move right from last box.e; +box "END" "[Y]"; +arrow <- dashed up from last box.top; +box "D" +arrow from B1.bottom to last box.top +.PE + +So, when, in a prediction phase of the algorithm, a nonterminal is substituted, +the nonterminal is placed on a list, together with a pointer to +the substituted nonterminal. If in the same prediction phase a nonterminal that +is on the list becomes a top, all we need to do is place an edge +between the already substituted one and the successor of the top we are currently +processing. When a prediction phase is finished, the list is cleared. +There is one catch: if we consider again the last picture, +note that if nonterminal B can (directly or indirectly) produce empty, +it is also necessary to substitute D. However, it is not difficult to +determine if a nonterminal can produce empty. LLgen already computes +this information for each nonterminal. + +.LP +Without this `joining together' of graph components, each +element in the graph has exactly one successor, except the END marker, +which has none. +Now that components get joined as described, an element can have any +number of successors. The recognizer algorithm now has to consider all +successors of a graph element instead of one. + +.NH 2 +Handling right recursion + +.LP +The only problem right-recursive grammars cause in the algorithm is in the +`continuation' part; they can cause this part of the algorithm to loop +forever. As an example, consider: +.br + + A: $alpha$ B +.br + B: $beta$ C +.br + C: $gamma$ A + +.LP +Now suppose the `substitution' part of the algorithm has turned up +an END marker with nonterminal A in it. The continuation algorithm will +now produce: + +.PS +box "END" "[A]";move;box "END" "[C]";move;box "END" "[B]";move +box "END" "[A]";move;box "END" "[C]" +.PE + +.LP +etc. etc. However, a slight modification to the algorithm suffices +to eliminate this problem; within each prediction phase of the algorithm, we +simply maintain a list of nonterminals that have turned up in an +END marker. As soon as an END marker turns up whose nonterminal is +already in the list, we stop the `continuation' algorithm; the part +of the graph that would be produced by it already has been generated +by an earlier invocation of the algorithm in the same prediction phase. +At the end +of a prediction phase, when all heads are terminals, we clear the list. +This way, no looping can occur; even if the right recursion is +indirect, for instance if in the above example the rule for A had been +.br + + A: $alpha$ B $delta$ +.br +.LP +where $delta$ can produce empty, the algorithm still works; the substitution +of $delta$ will yield an END marker on top, and when trying to find +a continuation for LHS A the algorithm notices A is already on the list. + + +.NH 2 +Handling left recursion + +.LP +Left-recursion is, unfortunately, a much tougher problem than +right-recursion. The result of left-recursive grammar rules is that +the substitution algorithm never stops, because it can keep on building +the graph with the same set of rules without ever turning up a terminal. +One course of action would be to pre-process the grammar rules to +eliminate left-recursion; there are algorithms that eliminate direct +and indirect left-recursion. However, we have taken another course; by +allowing the produced graphs to contain loops, we can handle left +recursion without any modifications to the grammar. As soon as +we come to the point that we want to substitute a nonterminal +which was already substituted earlier on the same path and in +the same prediction phase, we can +make a link from the `older' nonterminal to the successor of +the `new' nonterminal. In this way we have constructed a loop +in the graph. As an example, suppose we have the following rules: +.br + +D: A + +A: B a + +B: A | x + +.br +Suppose also that we have nonterminal `D' on top of a stack. We +now start substituting `D': + +.PS +A: box "A" +move +X: box "x" +move to 0.5 +down +move +B: box "[B]" +arrow +box "a" +arrow +box "[A]" +arrow +box "[D]" +arrow dashed +box "END" "[S]" + +arrow from A.s to B.n +arrow from X.s to B.n + +.PE + +.LP +We now have an `A' on top of of the stack which was already +substituted on the same path and also in the same prediction phase. To avoid +never ending substitution we make a loop as follows: + +.PS +A: box "A" dashed +move +X: box "x" +move to 0.5 +down +move +B: box "[B]" +arrow +box "a" +arrow +A2: box "[A]" +arrow +box "[D]" +arrow dashed +box "END" "[S]" + +arrow dashed from A.s to B.n +arrow from X.s to B.n +arc <- from B.w to A2.w +.PE + +.LP +The dashed box with `A' in it means that it can be deleted, because +there is already an occurrence of it in the loop. + +.LP +The most beautiful result of loops in graphs is +that the original parsing algorithm needs only one minor change. +When the algorithm visits an element which has more than one +outgoing edge the algorithm starts tracking down both paths, +just like before, only now there may be one or more backedges among +these edges, but the algorithm needs not to be aware of this fact. +The only difficulty with loops is that the algorithm might go into +a loop; it continues searching for terminals but it might happen +that there are no valid terminals in the loop. The solution to this +problem is not very difficult; just set a flag at all elements we +visit. When we reach an element which has this flag turned on, we +don't have to search any further. At the end of the prediction phase, when we +have found all possible new heads, all flags are cleared. +Even if there are no loops in the +prediction graph, setting flags may be used as an optimization: +it is possible that two paths come together at one point. In that situation +it is useless to scan for the second time the part of the graph which +both paths have in common. + +.NH 2 +Some optimizations using reference counts + +.LP +As explained in section 2.2, it is sometimes necessary to copy a +prediction graph element before substituting it. In order to determine +if a certain element has to be copied, it is convenient to maintain +a reference count in each graph element. This reference count keeps +track of the number of edges that enter an element. Now, when we want +to substitute an element with reference count not 0, we need to +copy it, because there is another path in the prediction graph that +contains the element we want to substitute, and on this other path +the element cannot be substituted yet. + +.LP +Maintaining reference counts also enables us to perform another +optimization: remember that if, in a prediction phase, a terminal +is predicted that does not match the current inputsymbol, we from +then on just ignore the path in the graph starting at the terminal. +However, we can safely delete the terminal from the graph; furthermore, +all its successors in the prediction graph that have reference count +0 can be deleted as well, as can their successors with reference +count 0, etc. This way, we delete from the prediction graph +most elements that are no longer accessible, but not all of them; as will +be explained in the next section, loops in the prediction graph +can cause problems. + +.NH 2 +The algorithm to delete inaccessible loops + +.LP +Deleting graph elements which are no longer reachable is not as easy +as it looks when there are loops in the graph, introduced by +the extension to the algorithm that handles left recursive grammars. +Suppose for example that we have a very simple loop as in the left +picture below: + +.PS +down +X: box "x" "(0)" +arrow +box "[B]" "(2)" +arrow +box "a" "(1)" +arrow +box "[A]" "(1)" +arrow +box "[D]" "(1)" +arc <- from 2nd box.w to 2nd last box.w + +move right from X.ne +move +move +move +move +move +move +down +box "x" "(0)" dashed +arrow dashed +B: box "[B]" "(1)" +arrow +box "a" "(1)" +arrow +box "[A]" "(1)" +arrow +box "[D]" "(1)" +arc <- from B.w to 2nd last box.w +.PE + +.LP +The number below each symbol indicates the reference count of that element. +Suppose now that we delete `x', then we have the situation depicted in the +picture on the right. The loop consisting of `[B]', `a' and `[A]' is now +unreachable, so all these elements can be deallocated. +The reference count of `[B]' is 1, so it will not be deleted. To be precise +all elements in the loop have their reference counts on 1, and +consequently none of these will be deleted. But we stated earlier +that all elements of the loop cannot be reached anymore and that the +loop had to be deleted! In this example the reference counts of the +loop elements are all 1, but in more complex situations it is also +possible that some of the elements have a reference count of more +than 1. + +.LP +To solve this problem we present an algorithm, devised by E. Wattel, that +determines whether a loop can be deleted or not. +The algorithm consists of two parts. The first part of the algorithm goes as +follows: it presumes that all elements of the loop will indeed be +deleted. Every time it deletes an element it decreases the reference +count of all the successors of the element that are also member of the same +loop. How the algorithm knows which elements belong to the loop and which +do not will be explained later. The situation of the example above will now +look like this: + +.PS +down +box "[B]" "(0)" +arrow +box "a" "(0)" +arrow +box "[A]" "(0)" +arrow +box "[D]" "(1)" +arc <- from 1st box.w to 2nd last box.w +.PE + +.LP +The number below each symbol indicates again the reference count +after we have applied the first part of the algorithm. + +.LP +The second part of the algorithm checks and restores the +reference counts of all members of the loop . When it finds +out that one or more reference counts are not 0, it concludes +that it is still possible to enter the loop in some way, and +that it cannot be +deleted yet. In the other case it reports that the loop can be +deleted, which is also true in our example. + +.LP +We will now formally describe the first part of the algorithm +that finds all directed circuits from a given vertex, and determines if +the vertices on those circuits can be deleted. +The algorithm works on prediction-graphs in which every edge that +is in a circuit is marked. Note that a marked edge may be in more than one circuit. +We will call this mark `C'. +The input to the algorithm is such a prediction graph, and a start vertex, +say A. The first part of the algorithm is: + +.IP 1 +Put the start vertex A on a list L; mark all edges `unused' +.IP 2 +If L is empty, stop +.IP 3 +For each vertex in list L, check if there are edges marked both C' and +`unused'. For each edge found, mark it `used', and traverse it to its +other endpoint; put this endpoint on a new list M, initially empty +.IP 4 +Decrease the reference count of all vertices on M by 1 +.IP 5 +L := M; go to 2 + +.LP +It is clear that the algorithm will terminate: each edge is only traversed once, +and the number of edges is finite. We will now prove some properties of this +part of the algorithm. + +.LP +.I +An edge is traversed by the algorithm if and only if it is on some +directed circuit $A ->$...$->A$. +.R +.br + +The if-part is easy; if an edge $e$ connecting vertices $W$ and $V$ is on some directed circuit starting in +$A$, then there is a path $A ->$...$-> W -> V$; let $A ->$...$-> W -> V$ be a path +of minimum length from $A$ to $V$. If the length of the path from $A$ to +$W$ is $k$, then after turn $k$ of the algorithm $W$ will be on list L. To see +that this is the case, suppose that $W$ is not on list L after turn $k$; +this means that the edge entering $W$ was already marked used in a +previous turn, but then there would be a shorter path from $A$ +to $W$, contradicting the assumption that the path is of +minimum length. The edge +$e$ is marked `C', because it is in a circuit; it is marked `unused', for if +it were marked used, there would be a shorter path from $A$ to $V$. So, +in turn $k + 1$, the edge $e$ will be traversed. + +.LP +On the other hand, suppose that an edge $e$ is traversed by the algorithm; +we will show by induction on the number of turns the algorithm has made +that $e$ is on a directed circuit $A->$..$->A$. In the first turn, all +edges from $A$ that are marked `C' are traversed, and clearly, if an edge +from $A$ is part of a circuit then that edge is part of a circuit from $A$ to $A$. +Now suppose that in turn $n+1$ an edge $e$ connecting vertices $W$ and +$V$ is traversed. This means the edge is +marked `C', so it is part of some circuit. If there is a path from $V$ to $A$, +we can simply trace a circuit +$A->$...$-> W -> V -> $...$-> A$, and clearly $e$ is on a circuit from +$A$ to $A$. Now, suppose there is no path from $V$ to +$A$. We can always trace a circuit $W -> V ->$...$-> W$ because the +edge from $W$ to $V$ is part of a circuit; and by the +induction hypothesis there is a circuit $A ->$...$-> W ->$...$-> A$. We can +now make a `detour' at $W$, yielding a circuit $A->$...$-> W -> V$... +$-> W ->$...$-> A$. This case is shown in the picture below. +So in either case $e$ is on a circuit from $A$ to $A$. + +.PS +down; +B1: box "A"; +arrow dashed; +B3: box dashed; +arrow dashed; +B2: box "W"; +arrow dashed; box dashed; +arc <- from B1.w to last box.w +arrow right "$e$" "C" from B2.e +box "V"; arrow dashed; box dashed; +arrow dashed -> from last box.n to B3.e +.PE + +.LP +.I +A vertex appears on list L if and only if it is on some directed +circuit from $A$ to $A$. +.R +.br + +.LP +If a vertex is in such a circuit, there is an edge that enters it, which +is part of a circuit form $A$ to $A$; we already showed that this edge +is traversed by the algorithm, and thus the vertex will appear on list +L. Conversely, if a vertex appears on list L, then an edge entering +that vertex has been traversed by the algorithm; we showed that this +edge is part of a circuit from $A$ to $A$, and thus the vertex is +part of a circuit from $A$ to $A$. + +.LP +.I +When the algorithm is finished, each vertex that is part of some +directed circuit from $A$ to $A$ has its reference count decreased by exactly +the number of edges entering it that are part of a directed circuit from $A$ to $A$. +.R +.br + +.LP +Each edge that is part of some circuit from $A$ to $A$ is traversed +exactly once; the reference count of the endpoint is decreased +by one after an edge has been traversed. Thus, if a vertex is endpoint +of $k$ such vertices, its reference count is decreased by $k$. + +.LP +.I +If the reference count of each of the vertices visited by the algorithm +is 0 after the algorithm has finised, all these vertices can be deleted; +if the reference count is not zero for one or more of the visited +vertices, then none of them can be deleted. +.R +.br + +.LP +Suppose all visited vertices have reference count 0; this means that +each of the vertices is only entered by edges that are on a circuit +from $A$ to $A$. Therefore, it holds that any path leading to any +of the visited vertices has to start in one of the visited vertices; there +is no path starting in an unvisited vertex to a visited one. Thus, +all the visited vertices are unreachable. +Conversely, if one of the visited vertices has reference count not zero, +then there is a path from an unvisited vertex to this vertex. Because from +the vertex with reference count non zero, we can get to $A$, and from $A$ +we can get to any of the other vertices, all visited vertices are +reachable. + +.LP +The second part of the algorithm now checks if all reference counts are +zero, and if they are, it deletes all visited vertices. + + +.NH 2 +Marking loop elements + +.LP +One point we have omitted so far is how the edges in the prediction +graph that are part of a loop get marked. +Basically, a loop can be detected: + + a. when it is made; +.br + b. when we want to know about it. + +.LP +The first approach checks if a loop is constructed +as soon as we join two paths in the graph, and if so, marks all +edges of the loop. The other approach does not do any checking when two +paths are joined together; it starts looking for loops when we want +to delete an element with reference count not 0, marking all edges +belonging to the loops it discovers. In practice it turns out that +we very often encounter elements that we would like to delete, but that have +reference count not 0, whereas the joining of paths occurs relatively +infrequently. We therefore have chosen to check if a loop is created +when two paths in a prediction graph are joined. + +.LP +Now the question arises how to find and mark all edges of +the loop. For this problem we devised also an algorithm. +Because we already know that there is an edge from the element on which +the new path is connected to the successor of the joined element, the +algorithm only has to find a path from this last element back to the first one. +This can be done by a backtracking depth first search; to find a path from +one element to another we have to find a possible empty path +from one of the successors of the first element to the last element. As +soon as we have found a path, we can mark all the edges on the path and also +the backedge as loop edges. In case that there is more than one path +back to the first element it is necessary that the algorithm continues +searching after it has found one path. + +.LP +To avoid looping of this algorithm we have to set a flag at the elements +which are on the path already. When the algorithm is backtracking it can +clear the flags at the elements it is leaving. + +.LP +To speed up the searching process we can set flags at the edges we have already +visited but did not lead back to the first element. When the algorithm +encounters such an edge it already knows that this edge is not worth +searching again and can be skipped. At the end of the algorithm these +flags have to be cleared again. + +.LP +One might propose another optimization: as soon as +we reach an edge that is already marked as a loop edge, we +can stop searching for other loop edges. There is, however, +a case in which this can go wrong. Imagine the following situation: + +.PS +down +E: box "[E]" +arrow " C" ljust +D: box "[D]" +arrow " C" ljust +C: box "c" +arrow " C" ljust +box "b" +arrow " C" ljust +A: box "[A]" +arrow +box "a" + +move right from D +move right +J: box "[J]" +down +arrow from J.s " C" ljust +I: box "i" +arrow " C" ljust +H: box "[H]" +arrow from H.s to A.e + +arc <- from E.w to A.w +move left from C +move left +"C" +arc -> from H.e to J.e +move right from I +move right +"C" + +arrow dashed from E.s to J.n + + +.PE + +What we have here is a prediction graph with two loops; all edges that belong +to a loop are again marked with an `C'. Note that the edge between `[H]' +and `[A]' is not a loop edge. Suppose that `[J]' is not yet +completely substituted, i.e. there is another production rule for +J: +.br + +J: E + +.br +The `E' on top of the right path is now joined with the `[E]' +on the left path, which is depicted by the dashed arrow +between `[E]' and `[J]'. When we take a good look at the graph +we see that the two loops are merged into one. But that is not +the most important observation we have to make: not only the +edge between `[E]' and `[J]' must be marked as a loop edge, but +also the edge between `[H]' and `[A]'! So it is not possible +to stop searching for loop edges as soon as we have found an +edge which was already marked as a loop edge. We have to continue +until we reach the element at which we started: `[E]'. So the +optimization proposed above is incorrect. + + +.NH 2 +Optimizations using FIRST and FOLLOW sets + +.LP +In the algorithm as we have described it, every nonterminal on top of the graph +is substituted until only terminals remain on top; these terminals are +then matched against the current input symbol. However, by using +FIRST sets, we can save considerably on the number of computations +necessary. Suppose one of the top elements of the graph is nonterminal A, +and the current inputsymbol is $a$. Then, it is of no use to substitute +A if terminal $a$ is not in FIRST(A), because then substituting A will +never produce $a$ on top of the graph. So, before substituting a +nonterminal we check if the current inputsymbol is in its FIRST set; if +it is not, we can declare the path the nonterminal is on a dead end, and +delete it, without having to perform the actual substitution. Of course, if +A can produce empty, we still have to consider its successor in the graph. + +.LP +Similarly, when we have an END marker on top, with nonterminal B in +it, and we consider using rule +.br + + D: $alpha$ B C $gamma$ + +.br +We first check if the current inputsymbol is in FIRST(C); if this is +not the case, there is no need to start a graph component with this +rule, because it will never produce the next inputsymbol on top. +Again, if C produces empty, we still have to evaluate the part of the +rule following C. + +.LP +To circumvent the problems caused in the FIRST set optimization by +nonterminal that produce empty, we can also make use of FOLLOW-sets. +When substituting, if we encounter a nonterminal whose FIRST set does +not contain the current inputsymbol but which can produce empty, +we check if the current inputsymbol is in its FOLLOW set. If it is not, +there is no need to process its successor. Similarly, in case we +are processing an END marker as explained above, there is no need +to process the part of the rule following C if FIRST(C) does not +contain the input symbol, or C produces empty but the inputsymbol +is not in FOLLOW(C). +.bp +.nr PS 12 +.nr VS 14 + +.NH +Test results + +.nr PS 10 +.nr VS 12 +.RS + +.LP +In this chapter, we discuss some test results that were obtained +by recompiling existing ACK compilers with the modified LLgen. +We tried several combinations of possible optimizations, including +`dumb' ones, like no optimization at all, not even deleting unreachable +prediction graph elements. +The incorporation of LLgen with non-correcting error recovery went +smoothly; only minor modifications to the Make-files were necessary. +Specifically, these modifications consisted of passing an extra +flag to LLgen, and including the new generated C-file Lncor.c in +the list of generated C-files. Also, the LLmessage error reporting +routine had to be adapted. We successfully recompiled the C, Modula-2 +and Occam compilers; in the next sections, we discuss some test results +that were obtained with the Modula-2 and C compilers. + +.RE +.LP +.NH 2 +Performance + +.LP +We will now present and discuss, with the aid of some +diagrams, time and space measurements on the non-correcting error +recovery. We have measured the effect of various optimizations. +These optimizations include the first-set optimization and the follow-set +optimization. We also measured the effect of leaving out the loop-deletion +algorithm, regarding both time and space. We performed out measurements using +C- and Modula-2-programs of three different sizes; one of approximately +750 tokens, one of appr. 5000 tokens and one of appr. 15000 tokens. We have +chosen to represent the sizes of programs in the number of tokens instead of +number of lines, because the number of tokens more realistically +reflects the load the programs put on the error recovery mechanism. Also we give +our time measurements in usertime instead of realtime, because realtime +depends heavily on the load of the system, which usertime does not. +Our space measurements are based on the size of the prediction graphs. +Note that all files are entirely recognized by the non-correcting error +recovery technique. We achieved this by putting a `1' at the beginning +of each file; because then each file starts with a syntax error LLgen +is forced to continue with the non-correcting error recovery. + +.NH 3 +Time and space measurements on the effect of the first-set optimization + +.LP +In the diagram below we show our time measurements we got from recognizing +the C-programs both with and without first-set optimization. + +.G1 +coord x 0, 17000 y 0, 65 +ticks bot out at 750, 5000, 15000 +label bot "Number of tokens" +label left "User Time" "(sec)" left .3 +draw no_opt dashed +draw first_opt dashed + +copy thru X + times size +2 at $1, $2 + times size +2 at $1, $3 + next no_opt at $1, $2 + next first_opt at $1, $3 +X until "XXX" + +742 2.5 .9 +5010 16.3 5.8 +14308 54.2 16.8 +XXX + +copy thru X "$1 $2" size -2 at 11000, $3 X until "XXX" +No optimization 55 +First-set optimization 20 +XXX +.G2 + +.I +.ce +Time measurements of three C-programs with and without first-set optimization +.R + +.LP +Notice the considerable time savings we +get when the first-set optimization is turned on; a factor of slightly more than +3. Obviously this is an extremely useful optimization. On the other hand +we found there were no measurable time savings when using the follow-set +optimization; for that reason we did not chart the result of this optimization. +It seems that the time savings gained by the optimization are +waisted again by the extra processing time needed. We conclude that +this optimization is of little or no use when we want to save on time. + +.LP +In the following picture the time measurements of three Modula-2 programs +are given, again with and without first-set optimization. + +.G1 +coord x 0, 17000 y 0, 65 +ticks bot out at 750, 5000, 15000 +label bot "Number of tokens" +label left "User Time" "(sec)" left .3 +draw no_opt dashed +draw first_opt dashed +copy thru X + times size +2 at $1, $2 + times size +2 at $1, $3 + next no_opt at $1, $2 + next first_opt at $1, $3 +X until "XXX" + +823 1.3 .6 +4290 7.6 3.5 +16530 30.5 14.3 +XXX + +copy thru X "$1 $2" size -2 at 13000, $3 X until "XXX" +No optimization 30 +First-set optimization 15 +XXX +.G2 + +.I +.ce +Time measurements of three Modula-2-programs with and without first-set optimization +.R + +.LP +From this picture we can conclude mainly the same as above; considerable +time savings when we use the first-set optimization; +the factor is somewhat less, but still more than 2. Again we have omitted +the results of the follow-set optimization, for the same reason as before. + +.LP +There is however one remarkable difference between the two languages: parsing +C-programs needs almost twice the time as parsing programs of comparable +sizes written in Modula-2. This can be explained by the fact that the +C-grammar is far more complicated than that of Modula-2, and also the +production rules are longer in C, so building, deleting and definitely +traversing the graph will consume more time. + +.LP +Now we come to the space measurements of both C- and Modula-2 programs. +In the picture below we present the maximum sizes of the prediction graphs, +during the recognition of the three C-programs. + +.G1 +coord x 0, 17000 y 0, 18000 +ticks bot out at 750, 5000, 15000 +label bot "Number of tokens" +label left "Maximum size of" "the prediction graph" "(bytes)"left .3 +draw no_opt dashed +draw first_opt dashed +copy thru X + times size +2 at $1, $2 + times size +2 at $1, $3 + next no_opt at $1, $2 + next first_opt at $1, $3 +X until "XXX" + +742 5568 10444 +5010 7668 12664 +14308 13636 17308 +XXX + +copy thru X "$1 $2" size -2 at 8000, $3 X until "XXX" +No optimization 16000 +First-set optimization 7000 +XXX +.G2 + +.I +.ce +Maximum sizes of the prediction graphs when recognizing three C-programs +.R + +.LP +From this diagram we see that, although the prediction graphs +are smaller when the first-set optimization is used, the space savings are +not as spectacular as the time savings achieved by this optimization. + +.LP +In Modula-2 the first-set optimization also causes a decrease in memory +usage. The savings are less than in C, but still about 1.5 Kb. Again +this can be explained by the fact that the rules of the Modula-2 grammar +are shorter than that of C. + +.G1 +coord x 0, 17000 y 0, 12000 +ticks bot out at 750, 5000, 15000 +label bot "Number of tokens" +label left "Maximum size of" "the prediction graph" "(bytes)" left .3 +draw no_opt dashed +draw first_opt dashed +copy thru X + times size +2 at $1, $2 + times size +2 at $1, $3 + next no_opt at $1, $2 + next first_opt at $1, $3 +X until "XXX" + +823 5056 3292 +4290 6420 4664 +16530 11388 9632 +XXX + +copy thru X "$1 $2" size -2 at 8000, $3 X until "XXX" +No optimization 10000 +First-set optimization 4000 +XXX +.G2 + +.I +.ce +Maximum sizes of the prediction graphs when recognizing three Modula-2-programs +.R + +.NH 3 +Input that is recognized in quadratic time + +.LP +The measurements presented may suggest that the time required to +recognize input depends linearly on the length of the input; however, +this is not always the case. When there are recursive rules in the +grammar, the time needed to recognize input that is produced by this +rules can become proportional to the square of the input length. +Consider this set of grammar rules: +.br +.nf + + S: '{' A '}' + A: 'a' A | $epsilon$ + +.fi +.LP +When the input is `{aaa....', the algorithm will produce the following +prediction graphs: + +.PS +up; B1: box "END" "S"; arrow <- ;box "}";arrow <- ;box "A";arrow <- ;box "{"; +move right from B1.se; move +up; B2: box "END" "S"; arrow <-; box "}"; arrow <-; box "[A]"; +arrow <-; box "A"; arrow <-; box "a"; +move right from B2.se; move +up; B3: box "END" "S"; arrow <-; box "}"; arrow <-; box "[A]"; +arrow <-; box "[A]"; arrow <-; box "A"; arrow <-; box "a"; +move right from B3.se;move +up; B4: box "END" "S"; arrow <-; box "}"; arrow <-; box "[A]"; +arrow <-; box "[A]"; arrow <-; box "[A]"; arrow <- ; box "A"; arrow <-;box "a"; +.PE + +.LP +In each prediction phase, a new [A] appears on the prediction graph. However, +since A also produces empty, the prediction algorithm has to traverse all the +elements [A] until it finds the element `}'. In the first prediction phase, +there is one element [A], in the second there are two, etc, so in all +1 + 2 + 3 + ... + k = $k(k+1) over 2$ elements have to be traversed if +there are k prediction phases, making this proportional to the square +of the input length. We constructed a parser with this simple input grammar +and measured the processing time the error recovery mechanism used. +In the following diagram the dashed line shows the processing time needed; +the dotted line is the curve $t = 13 n sup 2$. Clearly the processing time +is proportional to the square of the number of tokens. + +.G1 +coord x 0, 2100 y 0, 60 +ticks bot out at 500, 1000, 1500, 2000 +label bot "Number of tokens" +label left "User Time" "(sec)" left .3 +draw quad dashed + +copy thru X + times size +2 at $1, $2 + next quad at $1, $2 +X until "XXX" + +500 3.0 +1000 12.4 +1500 28.6 +2000 51.4 +XXX + +draw dotted +for i from 0 to 2100 by 25 do { next at i, 0.000013 * i * i } +.G2 + +.LP +In the grammar used for the C compiler, array initializations are handled by a recursive +rule, so we would expect that the error recovery mechanism needs quadratic +processing time to recognize such an initialization; we made measurements on +the processing time and indeed, the +processing time needed grows proportionally to the square of the size of the input, as the +next figure shows. Here, the processing times are about half of those in +the previous example; this is so because the recursion appears after two +tokens are recognized. Note that the algorithm only takes quadratic time +when it is recognizing input that is generated by a recursive grammar rule. +Other input is still recognized in linear time, regardless of the fact that +there are recursive grammar rules. + +.G1 +coord x 0, 5000 y 0, 85 +ticks bot out at 1150, 2400, 3600, 4800 +label bot "Number of tokens" +label left "User Time" "(sec)" left .3 +draw quad dashed + +copy thru X + times size +2 at $1, $2 + next quad at $1, $2 +X until "XXX" + +1150 5.1 +2400 20.3 +3600 43.7 +4800 78.6 +XXX +.G2 + +.LP +Unfortunately, there is no easy way to speed up the recognition of these +recursively defined language elements; they are caused by the substituted +tokens that are left in the prediction graph, and we cannot just delete those +`dummies' from the graph during a prediction phase because the `join' part of the +prediction algorithm depends on them. One could traverse the graph after +a prediction phase to delete the dummies, but then the processing +time needed to recognize non-recursively defined language elements would +increase dramatically. However, we feel that in practice things +like large array initializations will not occur in hand-made programs; when +they occur, it is probably in computer-generated programs, which normally +will be correct anyway, meaning that the error recovery never sees them. +When testing such generated programs, one is likely +to use small test-cases, which are handled well by the error recovery. + +.NH 3 +Time measurements on the effect of leaving out the loop-deletion algorithm + +.LP +We now show what effect the loop-deletion algorithm has on processing time. +To put it another way: how much time can be saved when we turn off the +loop-deletion algorithm. In the diagram below we give the measurements of +the three C-programs; note that we do use the first-set optimization. + +.G1 +coord x 0, 17000 y 0, 22 +ticks bot out at 750, 5000, 15000 +label bot "Number of tokens" +label left "User Time" "(sec)" left .3 +draw no_loop dashed +draw loop dashed +copy thru X + times size +2 at $1, $2 + times size +2 at $1, $3 + next no_loop at $1, $2 + next loop at $1, $3 +X until "XXX" + +742 .9 .4 +5010 5.8 6.8 +14308 16.8 20.5 +XXX + +copy thru X "$1 $2" size -2 at 11300, $3 X until "XXX" +With loop-deletion 20 +Without loop-deletion 9 +XXX +.G2 + +.I +.ce +Time measurements on processing three C-programs with and without the loop-deletion algorithm +.R + +The diagram shows that the loop-deletion algorithm +does not dramatically slow down the recognizing process. There is, however, +a measurable time loss of \(+-25%. As we will see later, the loop-deletion +algorithm will turn out to be extremely useful in efficient use of memory +when there are many loops in the graph. + +The effect of the loop-detecion algorithm on parsing Modula-2 programs +is even less than with C-programs; in fact there is no measurable +time loss: + +.G1 +coord x 0, 17000 y 0, 15 +ticks bot out at 750, 5000, 15000 +label bot "Number of tokens" +label left "User Time" "(sec)" left .3 +draw no_loop dashed +draw loop dashed +copy thru X + times size +2 at $1, $2 + times size +2 at $1, $3 + next no_loop at $1, $2 + next loop at $1, $3 +X until "XXX" + +823 .6 .6 +4290 3.5 3.8 +16530 14.3 14.3 +XXX + +copy thru X "$1 $2" size -2 at 11800, $3 X until "XXX" +With loop-deletion 13 +Without loop-deletion 7 +XXX +.G2 + +.I +.ce +Time measurements on processing three Modula-2-programs with and without a loop-deletion algorithm +.R + +There are at least two reasons for this; both result from the relative +simplicity of the Modula-2 grammar. The distance from a head to an +end of stack marker is shorter than in C, and secondly Modula-2 +causes fewer joins to occur than C, meaning that the loop marking algorithm +is run less often and when it is run it has fewer paths to search. + + +.NH 3 +Space measurements on the effect of leaving out the loop-deletion algorithm + +.LP +Clearly, to make any measurements on the space-usage effects of leaving out +the loop-deletion algorithm we need a program that causes the prediction +graph to contain loops; however, we have not been able to devise a C +or Modula-2 program that does this. In order to be able to make measurements, +we added an extra alternative to a rule of the C compiler grammar, making +it directly left-recursive. To make LLgen accept this new grammar, we +put a `%if' directive in the rule. + +.LP +We have input our standard C test program consisting of 800 tokens to +the error recovery routine for this `doctored' C compiler, +and compared the storage needed for the prediction graphs with the +loop deletion algorithm enabled with the storage needed when the +algorithm is disabled. With the loop-deletion algorithm enabled, the +maximum size of the prediction graph was 5576 bytes. When the loop +algorithm was disabled, the maximum size of the prediction graph +grew to 12676 bytes; furthermore, 12676 bytes of heap were allocated +for the prediction graph, but not deallocated again, because they were +in use by graph elements that were in inaccessible loops. The user-time +the program needed decreased only slightly, from 0.9 to 1.0 seconds. Given the +relatively small input program, this data suggests that when loops +are actually being made, the loop deletion algorithm is definitely +worth the extra overhead it costs, considering the space +that would otherwise be occupied by inaccessible loops. To verify this, +we input the C program consisting of 15000 tokens to the compiler; +execution time increased from 17.3 to 21.1 seconds after enabling +the loop deletion algorithm, while the maximum size of the prediction graph +shrunk from 328664 to 13664 bytes. With the loop-deletion algorithm +disabled, 326720 bytes allocated for the graph were not deallocated again. +Again, given the relatively small increase in execution time and the +large reduction of memory usage, we feel that the loop-deletion +algorithm is useful enough to justify the overhead it creates. + +.NH 2 +Problems encountered + +.LP +In this section we describe some of the problems we encountered +while testing the non-correcting error recovery. + +.NH 3 +The LLgen error reporting mechanism. + +.LP +The parsers generated by LLgen call a user-supplied error reporting +routine, usually called LLmessage. This routine is called with an +integer parameter that is positive, zero or negative. When the parameter +is positive the parser has just inserted a token, whose +number is equal to the parameter; if it is zero, the parser +has deleted a token whose number is in a global variable called LLsymb; if +it is negative, it means that LLgen expected end-of-file, but did not +find it. The routine LLmessage is supposed to print an error message, +and when a token is inserted, it should set all necessary attributes. + +.LP +However, when non-correcting error recovery is used, the situation becomes slightly +different; when the parser inserts a token, it is only to keep the +semantic actions consistent, and does no longer signify an error. +However, the LLmessage routine still has to be called because the +attributes of the inserted token need to be set. Therefore, when +non-correcting error recovery is used, the LLmessage routine should not +print an error message when the parameter is positive, or else it will +print highly confusing error messages indeed. Furthermore, the +LLmessage routine will usually print a message like `token ... deleted' when +it is called with parameter equal to zero; however, when the non-correcting +error recovery is used, it is more appropriate to report something +like `token ... illegal', as the non-correcting error recovery does +not delete tokens. Finally, when an unexpected end-of-file is encountered, +LLgen normally just inserts the missing tokens and calls +LLmessage with the parameter equal to the token number; +when non-correcting error recovery is used we need a way to +actually report we have encountered an unexpected end-of-file. The +way we achieved this is by calling LLgen with parameter 0 and the +global variable LLsymb set to EOFILE when this situation occurs; the +routine LLmessage should print something like `unexpected end of file' +when it is called with parameter 0 and LLsymb is EOFILE. To facilitate +switching between correcting and non-correcting error recovery, the +file Lpars.h contains a statement `#define LLNONCORR' if non-correcting +error recovery is used. + + +.NH 3 +Parsers being started in semantic actions + +.LP +LLgen allows the programmer to define more than one nonterminal as the +start symbol of the input grammar; it will generate a parsing routine +for each of the start symbols. However, the error recovery code +is generated only once; it is shared by all parsers. +The programmer is free to call any +of the generated parsers whenever he wants; for instance, in the C-compiler +a separate parser for expressions in #if and #elsif statements is used. Whenever +the lexical analyzer encounters such a statement, it calls the expression +parser. It is also possible to call a parser in a semantic action of +another parser; in the MODULA-2 compiler a separate parser for +definition modules is used. When the main parser encounters a +FROM defmod IMPORT statement a semantic +actions opens the definition module defmod and starts the parser for +definition modules. + +.LP +The fact that subparsers can be started just about anywhere causes +problems when non-correcting error recovery is used. +Suppose a parser calls another parser in a semantic action +to parse a separate input file. In the Modula-2 compiler, after +seeing the FROM defmod IMPORT statement a semantic action opens +defmod and parses it; now, if a syntax error occurred before the +FROM IMPORT statement, the non-correcting error recovery will not +execute the action that opens and parses the definition module, but +it will not report an error either, because the statement +FROM defmod IMPORT is part of the input language of the main parser. +However, suppose that during the parsing of a definition module +an error occurs; then, some semantic actions that would normally +be executed during parsing of the definition module will not have +taken place. When normal parsing is now resumed by the main parser, +after the non-correcting error recovery has finished with the +definition module, a lot of spurious semantic errors are likely to be +reported, because the semantic actions that would normally have been +executed during the definition module parsing have not been executed +by the error recovery. Therefore, it is desirable that the main parser +does not resume normal parsing, but instead continues with the non-correcting +error recovery as well. Any syntactic errors in the main program will +still be reported, but no spurious semantic errors will be reported +that way. + +.LP +When the lexical analyzer calls other parsers, as is the case in +the ACK C compiler, recursive invocations of the non-correcting error +recovery routine can occur. This will happen if a parser starts the +error recovery, the error recovery calls the lexical analyzer, which +starts another parser that finds a syntax error and calls the +error recovery again. This is not really a problem, but is has +consequences for the implementation of the error recovery routine. + +.LP +The worst case +occurs when two parsers are involved in parsing one input file, and +the secondary parser (e.g. an inline assembly parser) is called in a semantic +action of the main parser. Suppose now that the input text contains +a syntax error; after detecting this error, the parser starts the +non-correcting error recovery. This recovery does not execute any +semantic actions; therefore it will not start the subparser at those points +where the original LLgen generated parser would. As a result, parts +of the program that would be accepted by the subparser will now probably +be rejected as illegal, because the error recovery does not know it +should use another grammar to check these parts. This is a serious +problem, and we have devised and implemented two ways to solve it. + +.LP +The first solution is based on the assumption that whenever a semantic +action occurs in the grammar, another parser can be started at that +point. Obviously, we have no way of knowing which semantic actions start +a parser and which don't, so we assume the worst. +Now, assume that in the grammar there are k symbols defined as +start symbols, say $W sub 1 , W sub 2 , ..., W sub k$. Each of these symbols +will cause LLgen to generate a parser that can be called in any +of the semantic actions of the grammar. We now introduce a new +symbol $X$, and a new grammar rule $X -> W sub 1 X | W sub 2 X | ... | +W sub k X | +epsilon$. +In the grammar the error recovery algorithm uses, we insert this symbol +X at all positions where there are semantic actions in the original grammar, +so a rule $A -> alpha$ { action } $beta$ becomes $A -> alpha X beta$. As a +result, at each position in a grammar rule where a semantic action +occurs, we now accept any input that would be accepted by any of the +parsers. Clearly, this solution is somewhat of a kludge, as it will +accept a lot of input that is not accepted by the original parser. +However, it is guaranteed to never give spurious error messages, because +whenever a parser would be started by the original parser, there now +is an $X$ in the grammar that produces all the strings that would be +accepted by that parser. We have implemented this solution, and found +it to be extremely slow, which of course was to be expected given the +number of semantic actions in the average grammar. Furthermore, +because each time a semantic action occurs in the grammar +a string accepted by any of the generated parsers is accepted, including +strings recognized by the currently running parser, error messages +become hard to interpret. As an example, consider the following +C program: +.br +.nf + + + main() + { + int i, j; + + while (i < j + j++; + + i = 1; + j = 2; + + } + + +.fi +.LP +Clearly, there is a `)' missing in the while-statement; +however, if this program is input to the error recovery it will complain +"} illegal", since after recognizing the +expression controlling the while the original parser starts a +semantic action, so the non-correcting recovery will accept a valid +C program at that point; after recognizing the three statements +following the while-statement as a separate program the +recognizer expects the missing `)', but gets `}' instead. + +.LP +Our second solution is based on the observation that if we knew +which semantic actions can start other parsers, we would only +have to introduce the new symbol $X$ at those places where parsers +can get started. We have therefore extended LLgen with a new directive +%substart, which is used to indicate to the parser generator that +another parser may be started. The %substart is followed by the +startsymbols that will produce the parsers that can be called, +so %substart A, B, C; indicates that in the semantic action +following the directive the parsers produced by startsymbols +A, B, en C can be started. In the grammar used by the error +recovery, a new symbol $X$ will be introduced at this point, +along with a new rule $X -> AX | BX | CX | epsilon$. Of course, this +solution can still accept input that would not have been accepted +by original parser, for instance if a parser is started +conditionally, based on other semantic information. However, it +is a big improvement over the first solution, both in performance +and the input it accepts. + +.NH 3 +Syntactic errors being handled in semantic actions + +.LP +A programmer may decide to handle certain syntactic errors +in semantic actions, for instance because he is not satisfied with +the standard error recovery. However, since the non-correcting error +recovery does not execute semantic actions, this may cause errors +to remain undetected. We encountered the following example in the ACK +Modula-2 compiler, in the grammar rule for assignment statement: +.br +.nf + + + Assignment_statement: lvalue + [ + '=' + { + error(":= expected"); + } + + | + + ':=' + ] + expression + ; + +.fi +.LP +This works well in the original LLgen; however, statements like +`j=9' are not treated as syntactic, but as semantic errors. +The original LLgen generated parser +will print the (semantic) error message, but the non-correcting recovery +will not execute the semantic action and therefore the erroneous +input will be accepted. + +.LP +To facilitate the incorporation of non-correcting error recovery in parsers +that use this kind of `trick', we extended LLgen with the %erroneous +directive. The directive indicates to the non-correcting recovery +mechanism that the token following it is not really part of the grammar. +When recognizing input, the error recovery will ignore tokens in the +grammar that have %erroneous in front of them. If in the example above, +the '=' is replaced with %erroneous '=', the non-correcting mechanism will +report an error when it sees a statement like 'j = 9'. See appendix B +for details about the implementation of the %erroneous directive. + +.LP +Another example is in the ACK C compiler. For some reason, the +grammar accepts function definitions without `()', so according +to the syntax a function definition can look like: +.br +.nf + + int func + { + .... + } +.fi + +.LP +The absence of the `()', however, causes `func' to be entered in the +symbol table as non-function, and when the parser encounters the body +a semantic action will complain with the error message "Making function body +for non-function". This again will cause the non-correcting error +recovery to miss errors. Consider this piece of code: +.br +.nf + +int i int j = 1; +{} + +.fi + +.LP +where apparently there's a `;' missing between the declarations +of i and j. The original LLgen-generated parser only gives semantic errors: +.br +.nf +"Making function body for non-function" +"j is not in parameter list" +"Illegal initialization of formal parameter, ignored" +.fi +.LP +As a result, the non-correcting error recovery will not report +any errors in this piece of code, because it does not execute the +semantic actions that recognize and report the error. Unfortunately, +due to the way the C-grammar is written, it is not possible to solve +this problem using a %erroneous directive; the part of the grammar +that deals with declaratons would have to be rewritten so as to +syntactically reject functions without `()'. + +.NH 3 +Semantic actions that read input + +.LP +There are no restrictions on what a semantic action can do; +there is nothing to stop the programmer from writing a parser in such +a way that some of the input to the parser is processed by semantic +actions. Obviously, because the non-correcting error recovery does not +execute semantic actions, this kind of parser will not work at all +with the new error recovery. Ironically, LLgen itself is written in +such a fashion; {}-enclosed C-code in its input is processed by +a semantic action in the LLgen grammar. We feel that it is bad +practice to write parsers this way; the `eating' of parts of +the input should be done in the lexical analyzer, not in the parser. +After all, in the case of LLgen, one can regard a semantic action +in the input as one token, and thus it should be handled by +the lexical analyzer as such. + +.NH 2 +Examples of error recovery + +.LP +We will now give some examples that compare non-correcting error +recovery with the correcting error recovery used by parsers generated +by `standard' LLgen. + +Consider the next C program, where there is a `)' missing in the +header of function `test'. +.br +.nf + + 1 int test(a,b + 2 + 3 int a,b; + 4 + 5 { + 6 if (a < b) + 7 return(1); + 8 else + 9 return(0); + 10 } +.fi + +.LP +This small error derails the `standard' parser; it produces the +following error messages, where we have left out 7 messages reporting +semantic errors: +.br +.nf + + line 3: , missing before type_identifier + line 3: , missing before identifier + line 3: ) missing before ; + line 5: { deleted + line 6: if deleted + line 6: < deleted + line 6: ) missing before identifier + line 6: ) deleted + line 7: identifier missing before return + line 7: ; missing before return + line 7: { missing before return + line 8: else deleted + +.fi +.LP +In contrast, the parser using non-correcting error recovery produces +only one error message: +.br + + line 3: type_identifier illegal + +This error message correctly pin-points the error: there should +have been a `)' at the position where type-identifier `int' is. + +.LP +Now, an example with Modula-2; consider this program: +.br +.nf + + 1 MODULE test; + 2 + 3 TYPES + 4 ElementRecordType = RECORD + 5 Element: ElementType; + 6 Next, + 7 Prior: ElementPointerType; + 8 END; + 9 + 10 VARS a,b,c: ElementRecordType; + 11 + 12 + 13 BEGIN + 14 + 15 a := b; + 16 + 17 END test. + +.fi +.LP +There are two syntactic errors in this program; on line 3, TYPES should be TYPE, and +on line 10, VARS should be VAR. We have left out the type declarations of +ElementType and ElementPointerType; clearly this will generate semantic +errors, but we are only interested in syntactic errors anyway. +The correcting error recovery parser +again derails on this program; it produces the following syntactic error messages: +.br +.nf + + line 3: CONST missing before identifier + line 4: '=' missing before identifier + line 4: RECORD deleted + line 5: ':' deleted + line 5: ';' missing before identifier + line 5: '=' missing before ';' + line 5: number missing before ';' + line 6: ',' deleted + line 7: '=' missing before identifier + line 7: ':' deleted + line 7: ';' missing before identifier + line 7: '=' missing before ';' + line 7: number missing before ';' + line 8: ';' deleted + line 10: identifier deleted + line 10: ',' deleted + line 10: identifier deleted + line 10: ',' deleted + line 10: identifier deleted + line 10: ':' deleted + line 10: identifier deleted + line 10: ';' deleted + line 13: BEGIN deleted + line 15: identifier deleted + line 15: := deleted + line 15: identifier deleted + line 15: ';' deleted + line 17: END deleted + line 17: identifier deleted + +.fi +.LP +The error correction mechanism clearly makes the wrong guess by inserting +CONST on line 3; as a result, all that follows is rejected as incorrect. +In contrast, the non-correcting error recovery mechanism only produces +two error messages: +.br +.nf + + line 3: identifier illegal + line 10: identifier illegal + +.fi +.LP +This again exactly pin-points the errors: the identifiers TYPES and +VARS constitute the only errors in the program. Note that the +presence of more than one error does not cause any problems to the +non-correcting recovery mechanism. + +.bp +.nr PS 12 +.nr VS 14 + +.NH +Conclusion + +.nr PS 10 +.nr VS 12 + +.LP +After implementing and testing a non-correcting error recovery mechanism +we have come to the conclusion that it indeed is superior to correcting +mechanisms in what regards the error messages it produces; +the examples we have given clearly show this. However, there is a +clear loss of performance when errors are present in a program, +although we have found this performance +degradation to be acceptable. We feel that the benefits of +better error messages outweigh the loss of performance. In any case, +correct programs do not suffer at all from the incorporation +of a non-correcting recovery mechanism. +The error recovery mechanism we implemented does not make +unreasonable demands on resources; the size of the prediction +graphs stays within reasonable limits. + +.LP +The main problems we encountered had to do with recognizing +`languages within languages', and semantic actions that did +unreasonable things like eating input. The more `well-behaved' a +parser is, the better the results the non-correcting error recovery +mechanism gives. This is also true for the input grammars: with a +language like Modula-2, whose syntax has been designed with parser +generators in mind, the performance of the non-correcting mechanism +is better than with C, whose syntax is extremely hard, if not +impossible to describe with a LL(1) grammar. + +.bp +.nr PS 12 +.nr VS 14 + +.NH +Bibliography + +.nr PS 10 +.nr VS 12 + +.IP [CORMACK] 12 +Gordon V. Cormack, `An LR substring parser for noncorrecting syntax error +recovery', ACM SIGPLAN Notices, vol. 24, no. 7, p. 161-169, July 1989 + +.IP [GRUNE] 12 +Dick Grune, Ceriel J.H. Jacobs, `A programmer friendly LL(1) parser +generator', Softw. Pract. Exper., vol. 18, no. 1, p. 29-38, Jan 1988 + +.IP [RICHTER] 12 +Helmut Richter, `Noncorrecting syntax error recovery', ACM Trans. Prog. Lang. +Sys., vol.7, no.3, p. 478-489, July 1985 + +.IP [ROEHRICH] 12 +Johannes R\*:ohrich, `Methods for the automatic construction of error +correcting parsers', Acta Inform., vol. 13, no. 2, p. 115-139, Feb 1980 + +.IP [TOMITA] 12 +Masaru Tomita, Efficient parsing for natural language, Kluwer Academic +Publishers, Boston, p.210, 1986 +.bp +.SH +Appendix A: Implementation Issues + +.nr PS 10 +.nr VS 12 +.RS +.LP +In this appendix we will describe some implementation issues; +the data structure used to store the grammar during non-correcting +error recovery, postponing deletions of graph elements until after +the prediction phase, and the implementation of the %substart directive . +.RE + +.SH +A.1 The grammar data structure + +.LP +The grammar data structure used by the non-correcting error recovery technique has +to meet two conditions: easy access to a rule as a whole to make +substituting nonterminals efficient and easy access to each symbol in the RHS +of a rule to make starting error recovery and finding continuations +efficient. To fulfill these conditions we decided to construct the +storage of the grammar as follows. + +.LP +A rule in the grammar is divided in two +parts: a LHS and a RHS. The LHS is represented by a struct `lhs' and +for each symbol in the RHS a struct 'symbol' is constructed. +A struct `lhs' contains the number of the +nonterminal forming the LHS of the rule, a pointer to the RHS, the +first- and follow-sets of the nonterminal and a flag 'empty' which +indicates whether the nonterminal produces empty or not. A struct +`symbol' contains a field indicating the type of the symbol, i.e. +a terminal or a nonterminal, the number of the symbol, a `link' pointer +to a struct `symbol' that represents the same symbol, a `next' pointer +to the rest of the RHS and a pointer back to the LHS. + +.LP +A special struct `symbol' is added to the end of the RHS to indicate +the end of a rule. The type of this struct is LLEORULE, the number +is set to -1 and the pointers 'link' and `next' are nil. + +.LP +In case that there is more than one RHS for a LHS, all the RHS's +are put after each other and separated by another special struct +`symbol'. The type of this struct is LLALT, the number is set to +-1 and the 'link' pointer is nil. After the last RHS a `LLEORULE'-struct +marker is added. + +.LP +Finally, to make searching efficient there are two arrays: `terminals' +and `nonterminals'. `terminals' is indexed by the number of a terminal +and contains for each terminal a struct containing a 'link' pointer +to a symbol, representing this terminal, in the RHS of a rule. Because +this symbol has again a 'link' pointer to another symbol representing +the terminal, it is possible by following this chain of pointers +to find all rules containing such a terminal. In a similar way `nonterminals' +is indexed by the number of a nonterminal and contains for each +nonterminal a struct. This struct not only contains a 'link' pointer +linking all rules with this nonterminal, but also contains a 'rule' +pointer. This pointer points to the RHS or RHS's of the rules of which +the nonterminal forms the LHS. + +.LP +As an example, consider the following grammar: + +.br +A: a B +.br +B: a | $epsilon$ +.br + +This will result in the picture below. Note that `pointer' fields +without an arrow indicate nil pointers. + +.PS +dx = 0.05 + +down +A_a: box ht boxht/2 "link" +box invis "a" ljust with .e at A_a.w + +move to A_a.s +move +move + +A: box "link" "rule" +B: box "link" "rule" +line dashed from A.w to A.e +line dashed from B.w to B.e +box invis "A" ljust with .e at A.w +box invis "B" ljust with .e at B.w + +move to A.ne +right +move +move +down + +LHS_A: box wid 1.2 * boxwid ht 2.5 * boxht "`A'" "rhs" "first" "follow" "empty 0" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +move to LHS_A.ne + (1,0) + +RHS_a1: box wid 2.0 * boxwid ht 2.5 * boxht "LLTERM" "`a'" "link" "next" "lhs" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +move to RHS_a1.ne + (1,0) + +RHS_B: box wid 2.0 * boxwid ht 2.5 * boxht "LLNONTERM" "`B'" "link" "next" "lhs" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +move to RHS_B.ne + (1,0) + +RHS_END1: box wid 2.0 * boxwid ht 2.5 *boxht "LLEORULE" "-1" "link" "next" "lhs" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + + +move to LHS_A.s - (0,1) + +LHS_B: box wid 1.2 * boxwid ht 2.5 * boxht "`B'" "rhs" "first" "follow" "empty 1" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +move to LHS_B.ne + (1,0) + +RHS_a2: box wid 2.0 * boxwid ht 2.5 * boxht "LLTERM" "`a'" "link" "next" "lhs" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +move to RHS_a2.ne + (1,0) + +RHS_ALT: box wid 2.0 * boxwid ht 2.5 * boxht "LLALT" "-1" "link" "next" "lhs" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +move to RHS_ALT.ne + (1,0) + +RHS_END2: box wid 2.0 * boxwid ht 2.5 *boxht "LLEORULE" "-1" "link" "next" "lhs" +line dashed from 0.2 to 0.2 +line dashed from 0.4 to 0.4 +line dashed from 0.6 to 0.6 +line dashed from 0.8 to 0.8 + +# Next pointers upper row +.ps 30 +circle radius .01 at 0.75 - (dx, 0) +circle radius .01 at 0.3 - (dx, 0) +circle radius .01 at 0.7 - (dx, 0) +circle radius .01 at 0.7 - (dx, 0) +.ps 10 + +arrow from 0.75 - (dx, 0) to 0.3 +arrow from 0.3 - (dx, 0) to 0.3 +arrow from 0.7 - (dx, 0) to 0.7 +arrow from 0.7 - (dx, 0) to 0.7 + + +# Next pointers lower row +.ps 30 +circle radius .01 at 0.75 - (dx, 0) +circle radius .01 at 0.3 - (dx, 0) +circle radius .01 at 0.7 - (dx, 0) +circle radius .01 at 0.7 - (dx, 0) +.ps 10 + +arrow from 0.75 - (dx, 0) to 0.3 +arrow from 0.3 - (dx, 0) to 0.3 +arrow from 0.7 - (dx, 0) to 0.7 +arrow from 0.7 - (dx, 0) to 0.7 + + +# Link pointers +.ps 30 +circle radius .01 at 0.5 - (2*dx, 0) +circle radius .01 at 0.5 - (dx, 0) +circle radius .01 at 0.25 - (dx, 0) +.ps 10 + +arrow dashed from 0.5 - (2*dx, 0) to RHS_a2.ne - (2*dx,0) +line dashed from 0.5 - (dx, 0) right 4.0 * boxwid then to RHS_a1.ne - (2*dx, 0) -> +line dashed from 0.25 - (dx, 0) right then up .75 then right 7.0 * boxwid then to RHS_B.ne - (2*dx, 0) -> + + +# LHS pointers upper row +.ps 30 +circle radius .01 at 0.9 - (3*dx, 0) +circle radius .01 at 0.9 - (3*dx, 0) +circle radius .01 at 0.9 - (3*dx, 0) +.ps 10 + +line from 0.9 - (3*dx, 0) down -> +line from 0.9 - (3*dx, 0) down -> +line from 0.9 - (3*dx, 0) down then left 8.0 * boxwid then to LHS_A.se -> + + +# LHS pointers lower row +.ps 30 +circle radius .01 at 0.9 - (3*dx, 0) +circle radius .01 at 0.9 - (3*dx, 0) +circle radius .01 at 0.9 - (3*dx, 0) +.ps 10 + +line from 0.9 - (3*dx, 0) down -> +line from 0.9 - (3*dx, 0) down -> +line from 0.9 - (3*dx, 0) down then left 8.0 * boxwid then to LHS_B.se -> + + +# Text above structs +box invis ht boxht/2 "terminals" with .s at A_a.n +box invis ht boxht/2 "nonterminals" with .s at A.n +box invis ht boxht/2 "lhs" with .s at LHS_A.n +box invis ht boxht/2 "lhs" with .s at LHS_B.n +box invis ht boxht/2 "symbol" with .s at RHS_a1.n +box invis ht boxht/2 "symbol" with .s at RHS_B.n +box invis ht boxht/2 "symbol" with .s at RHS_END1.n +box invis ht boxht/2 "symbol" with .s at RHS_a2.n +box invis ht boxht/2 "symbol" with .s at RHS_ALT.n +box invis ht boxht/2 "symbol" with .s at RHS_END2.n +.PE + +.LP +Note that the empty alternative for `B' is represented in the +data structure by the `LLEORULE-struct' immediately following +the `LLALT'-struct. When there are still other alternatives +the `LLEORULE'-struct is replaced by a `LLALT'-struct followed +by the other alternatives and a `LLEORULE'-struct. +Finally, when the empty rule is the only rule for a +nonterminal the RHS will consist only of a `LLEORULE'-struct. + +.SH +A.2 Delayed deletes + +.LP +We encountered a problem with deleting elements during the +prediction phase. Imagine that we have a nonterminal `B' on top of +the graph, and `B' has two alternatives. Now suppose that we +apply the first alternative and we find out that this alternative leads +to a `dead end', i.e. a head that does not match the input symbol, so we want +to get rid of it. When we delete it immediately the deletion algorithm +will also deallocate `[B]' and possibly some elements below `[B]'. +However, there was another alternative for `[B]' which was not yet +developed and maybe this alternative leads to a head which is legal. +But `[B]' has already been deleted and thus cannot be used anymore. A similar +situation can occur when we want to delete a joined element; +the substitution of a nonterminal +that only produces empty and thus has no element above it in the graph +can also lead to such a situation. We therefore decided to put `dead ends' +on a list, `cleanup_arr[]', and after the prediction phase has +finished we delete all elements on this list, and all their descendants +that become unreachable of course. + +.SH +A.3 Clearing flags + +.LP +We implemented two different ways to clear the flags set by the prediction +phase of the algorithm; the first recursively tracks down the whole graph +following the flags, the second puts all elements visited by +the prediction phase +on a list; after the prediction phase has finished the algorithm walks +through this list clearing the flags of all elements on it. We took measurements +on both algorithms and found out that with small programs the times +did not differ much but large programs were processed faster by the +second algorithm. Therefore we decided to use the second algorithm. + +.LP +To speed up the algorithm even more, we do not deallocate the list +after a prediction phase has finished. We just set the number of +elements on the list to 0. This saves considerably on the number +of `Malloc'-calls. + +.SH +A.4 Implementation of %erroneous directive + +.LP +As explained in chapter 3, the user can put a %erroneous directive +in front of a terminal, making the non-correcting error recovery +mechanism ignore that terminal. However, implementing this directive +was not entirely straightforward; consider, for example, the rule +.br +.nf + + A: 'a' | %erroneous 'b' | 'c'; + +.fi +.LP +Just leaving out terminal 'b' will not do, because then nonterminal +A produces empty all of a sudden, which it did not before. +The rule should become +.br +.nf + + A: 'a' | 'c'; + +.fi +but this is hard to implement in LLgen. We took a different approach: +we introduce a new terminal 'ERRONEOUS', and substitute it for all +terminals with an %erroneous directive in front of them. Thus, the +example rule becomes +.br +.nf + + A: 'a' | ERRONEOUS | 'c'; + +.fi +.LP +Since the terminal ERRONEOUS will never be in the input to the parser, +this has exactly the desired effect; when a predicting phase produces +ERRONEOUS as head of a prediction graph this head will never match the +input. In particular, it will not match the terminal that was +originally there (in this case 'b') so that terminal is no longer +regarded as part of the input language at that point. +.bp +.SH +Appendix B: Using the non-correcting error recovery + +.LP +To use the new non-correcting error recovery mechanism, LLgen has to +be called with the new flag -n. LLgen will then create an extra file +called `Lncor.c' which contains the code for the non-correcting recovery +mechanism. This file has to be compiled and linked with the rest +of the program, just like the file `Lpars.c'. + +.LP +The user-supplied error reporting routine `LLmessage' will have to be +modified slightly; when it is called with a positive parameter, it +should only set the attributes of the inserted token, but not report an +error. Note that the lexical analyzer still must return the same token +as it did the last time it was called. When LLmessage is called with +parameter 0, it should report that the token in global variable LLsymb +is illegal; if the value of LLsymb is `EOFILE', the routine should +report an unexpected End-of-file. When LLmessage is called with parameter +-1, it should report that end-of-file was expected. To facilitate +switching between correcting and non-correcting error recovery, +the file Lpars.h contains a statement `#define LLNONCORR' +which indicates that the non-correcting +mechanism is enabled. +Here is a +skeleton for the modified LLmessage routine: +.nr PS 8 +.nr VS 10 +.LP +.br +.nf + + #include "Lpars.h" + extern int LLsymb; + + LLmessage(flag) + int flag; + { + if (flag < 0) + { + /* Error message "end-of-file expected" */; + } + else if (flag) + { + /* flag equals the number of the inserted token */ +#ifndef LLNONCORR + + /* Error message "token inserted" */; +#endif + + /* Code to set attributes for inserted token */ + /* Code to make lexical analyzer return same token as before */ + + else + { + /* The number of the illegal or deleted token is in LLsymb */ +#ifndef LLNONCORR + + /* Error message "token deleted" */; +#else + + if (LLsymb == EOFILE) + { + /* Error message "unexpected end of file" */ + } + else + { + /* Error message "token illegal" */; + } +#endif + + } + + } + +.fi +.nr PS 10 +.nr VS 12 + +.LP +For best results, one should check if the parser calls other parsers +in semantic actions; if this is the case, and the called parser +processes the same input file as the calling parser, then a %substart +should be put in front of the semantic action that starts a parser. +If a semantic action calls parsers defined by startsymbols say +A and B, then `%substart A, B;' should be put in front of the action. +As an alternative, one can use the -s flag of LLgen; this has the +same effect as putting `%substart X, Y, ....;' in front of all +semantic actions, where X, Y, .... are the startsymbols of the grammar. +Clearly, it is preferable to analyze the grammar and put %substart +directives only where appropriate. + +Finally, beware of syntactic errors being handled in semantic +actions; eg, one could have a rule like +.nr PS 8 +.nr VS 10 +.LP +.br +.nf + + Assignment_statement: lvalue + [ + '=' + { + error(":= expected"); + } + + | + + ':=' + ] + expression + ; +.fi + +.nr PS 10 +.nr VS 12 +.LP +To ensure that the non-correcting mechanism will recognize the +`=' as a syntactic error, a `%erroneous' directive should be +put in front of it. diff --git a/doc/LLgen/Makefile b/doc/LLgen/Makefile index f38ff697d..058e6f111 100644 --- a/doc/LLgen/Makefile +++ b/doc/LLgen/Makefile @@ -1,9 +1,15 @@ # $Id$ +GRAP=grap +PIC=pic EQN=eqn REFER=refer TBL=tbl -TARGET=-Tlp + +all: ../LLgen.doc ../LLgen_NCER.doc ../LLgen.doc: LLgen.n LLgen.refs - $(REFER) -sA+T -p LLgen.refs LLgen.n | $(EQN) $(TARGET) | $(TBL) > $@ + $(REFER) -sA+T -p LLgen.refs LLgen.n | $(EQN) | $(TBL) > $@ + +../LLgen_NCER.doc: LLgen_NCER.n + $(GRAP) LLgen_NCER.n | pic | eqn > $@ diff --git a/doc/LLgen/proto.make b/doc/LLgen/proto.make index 0dc63b8b2..efe1efc18 100644 --- a/doc/LLgen/proto.make +++ b/doc/LLgen/proto.make @@ -4,9 +4,15 @@ SRC_DIR = $(SRC_HOME)/doc/LLgen +GRAP=grap +PIC=pic EQN=eqn REFER=refer TBL=tbl $(TARGET_HOME)/doc/LLgen.doc: $(SRC_DIR)/LLgen.n $(SRC_DIR)/LLgen.refs $(REFER) -sA+T -p $(SRC_DIR)/LLgen.refs $(SRC_DIR)/LLgen.n | $(EQN) | $(TBL) > $@ + +$(TARGET_HOME)/doc/LLgen_NCER.doc: $(SRC_DIR)/LLgen_NCER.n + $(GRAP) $(SRC_DIR)/LLgen_NCER.n | pic | eqn > $@ + -- 2.34.1