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Parsing R code: Freedom of expression is not always a good idea
With my growing interest in R it was inevitable that I would end up writing a parser for it. The fact that the language is relatively small (the add-on packages do the serious work) hastened the event because it did not look like much work; famous last words. I knew about R’s design and implementation being strongly influenced by the world view of functional programming and this should have set alarm bells ringing; this community have a history of willfully ignoring some of the undesirable consequences of their penchant of taking simple ideas and over generalizing them (i.e., I should have expected hidden complications).
While the official R language definition only contains a tiny fraction of the information needed to create a full implementation I decided to use it rather than ‘cheat’ and look at the R project implementation sources. I took as my oracle of correctness the source code of the substantial amount of R in its 3,000+ package library. This approach would help me uncover some of the incorrect preconceived ideas I have about how R source fits together.
I started with a C lexer and chopped and changed (it is difficult to do decent error recovery in automatically generated lexers and I prefer to avoid them). A few surprises cropped up ** is supported as an undocumented form of ^ and by default ]] must be treated as two tokens (e.g., two ] in a[b[c]] but one ]] in d[[e]], an exception to the very commonly used maximal munch rule).
The R grammar is all about expressions with some statement bits and pieces thrown in. R operator precedence follows that of Fortran, except the precedence of unary plus/minus has been increased to be above multiply/divide (instead of below). Easy peasy, cut and paste an existing expression grammar and done by tea time :-). Several tea times later I have a grammar that parses all of the R packages (apart from 80+ real syntax errors contained therein and a hand full of kinky operator combinations I’m not willing to contort the grammar to support). So what happened?
Two factors accounts for most of the difference between my estimate of the work required and the actual work required:
- my belief that a well written grammar has no ambiguities (while zero is a common goal for many projects a handful might be acceptable if the building is on fire and I have to leave). A major advantage of automatic generation of parser tables from a grammar specification is being warned about ambiguities in the grammar (either shift/reduce or reduce/reduce conflicts). At an early stage I was pulling my hair out over having 59 conflicts and decided to relent and look at the R project source and was amazed to find their grammar has 81 ambiguities!
I have managed to get the number of ambiguities down to the mid-30s, not good at all but it will have to do for the time being.
- some of my preconceptions about of how R syntax worked were seriously wrong. In some cases I spotted my mistake quickly because I recognized the behavior from other languages I know, other misconceptions took a lot longer to understand and handle because I did not believe anybody would design expression evaluation to work that way.
The root cause of the difference can more concretely be traced to the approach to specifying language syntax. The R project grammar is written using the form commonly seen in functional language implementations and introductory compiler books. This form has the advantage of being very short and apparently simple; the following is a cut down example in a form of BNF used by many parser generators:
expr : expr op expr | IDENTIFIER ; op : &' | '==' | '>' | '+' | '-' | '*' | '/' | '^' ; |
This specifies a sequence of IDENTIFIERs separated by binary operators and is ambiguous when the expression contains more than two operators, e.g., a + b * c can be parsed in more than one way. Parser generators such as Yacc will complain and flag any ambiguity and pick one of the possibilities as the default behavior for handling a given ambiguity; developers can specify additional grammar information in the file read by Yacc to guide its behavior when deciding how to resolve specific ambiguities. For instance, the relative precedence of operators can be specified and this information would be used by Yacc to decide that the ambiguous expression a + b * c should be parsed as-if it had been written like a + (b * c) rather than like (a + b) * c. The R project grammar is short, highly ambiguous and relies on the information contained in the explicitly specified relative operator precedence and associativity directives to resolve the ambiguities.
An alternative method of specifying the grammar is to have a separate list of grammar rules for each level of precedence (I always use this approach). In this approach there is no ambiguity, the precedence and associativity are implicitly specified by how the grammar is written. Obviously this approach creates much longer grammars, there will be at least two rules for every precedence level (19 in R, many with multiple operators). The following is a cut down example containing just multiple, divide, add and subtract:
... multiplicative_expression: cast_expression | multiplicative_expression '*' cast_expression | multiplicative_expression '/' cast_expression ; additive_expression: multiplicative_expression | additive_expression '+' multiplicative_expression | additive_expression '-' multiplicative_expression ; ... |
The advantages of this approach are that, because there are no ambiguities, the developer can see exactly how the grammar behaves and if an ambiguity is accidentally introduced when editing the source it should be noticed when the parser generator reports a problem where previously there were none (rather than the new ambiguity being hidden in the barrage of existing ones that are ignored because they are so numerous).
My first big misconception about R syntax was to think that R had statements, it doesn’t. What other languages would treat as statements R always treats as expressions. The if, for and while constructs have values (e.g., 2*(if (x == y) 2 else 4)). No problem, I used Algol 68 as an undergraduate, which supports this kind of usage. I assumed that when an if appeared as an operand in an expression it would have to be bracketed using () or {} to avoid creating a substantial number of parsing ambiguities; WRONG. No brackets need be specified, the R expression if (x == y) 2 else 4+1 is ambiguous (it could be treated as-if it had been written if (x == y) 2 else (4+1) or (if (x == y) 2 else 4)+1) and the R project grammar relies on its precedence specification to resolve the conflict (in favor of the first possibility listed above).
My next big surprise came from the handling of unary operators. Most modern languages give all unary operators the same precedence, generally higher than any binary operator. Following Fortran the R unary operators have a variety of different precedence levels; however R did not adopt the restrictions Fortran places on where unary operators can occur.
I assumed that R had adopted the restrictions used by other languages containing unary operators at different precedence levels, e.g., not allowing a unary operator token to follow a binary operator token (i.e., there has to be an intervening opening parenthesis); WRONG. R allows me to write 1 == !1 < 0, while Fortran (and Ada, etc) require that a parenthesis be inserted between the operands == ! (hopefully resulting in the intent being clearer).
I had to think a bit to come up with an explicit set of grammar rules to handle R unary operator's freedom of expression (without creating any ambiguities).
Stepping back from the details. My view is that programming language syntax should be designed to reduce the number of mistakes developers make. Requiring that brackets appear in certain contexts helps prevent mistakes by the original author and subsequent readers of the code.
Claims that R (or any other language) syntax is 'natural' is clearly spurious and really no more than a statement of preference by the speaker. Our DNA has not yet been found to equip us to handle one programming language better than another.
Over the coming months I hope to have the time to analyse R source looking for faults that might not have occurred had brackets been used. Also how much code might be broken if R started to require brackets in certain contexts?
An example of the difference that brackets can make is provided by the handling of the unary ! operator in R and C/C++/Java/etc. Take the expression !x > y, which R parses as-if written !(x > y) and C/C++/Java/etc as if written (!x) > y. I would not claim that either is better than the other from the point of view of developers getting the behavior right, I know that some C programmers get it wrong and I suspect that some R programmers do too.
By increasing the precedence of unary plus/minus the R designers ensured that 8/-2/2 was parsed like (8/-2)/2 rather than 8/(-2/2).
Parsing Fortran 95
I have been looking at doing some dimensional analysis of the Climategate code and so needed a Fortran parser.
The last time I used Fortran in anger the modern compilers were claiming conformance to the 1977 standard and since then we have had Fortran 90 (with a minor revision in 95) and Fortran 03. I decided to take the opportunity to learn something about the new features by writing a Fortran parser that did not require a symbol table.
The Eli project had a Fortran 90 grammar that was close to having a form acceptable to bison and a few hours editing and debugging got me a grammar containing 6 shift/reduce conflicts and 1 reduce/reduce conflict. These conflicts looked like they could all be handled using glr parsing. The grammar contained 922 productions, somewhat large, but I was only interested in actively making use of parts of it.
For my lexer I planned to cut and paste an existing C/C++/Java lexer I have used for many projects. Now this sounds like a fundamental mistake, these languages treat whitespace as being significant while Fortran does not. This important difference is illustrated by the well known situation where a Fortran lexer needs to lookahead in the character stream to decide whether the next token is the keyword do or the identifier do5i (if 1 is followed by a comma it must be a keyword):
do 5 i = 1 , 10 do 5 i = 1 . 10 ! assign 1.10 to do5i 5 continue |
In my experience developers don’t break up literals or identifier names with whitespace, and so I planned to mostly ignore the whitespace issue (it would simplify things if some adjacent keywords were merged to create a single keyword).
In Fortran the I/O is specified in the language syntax, while in C like languages it is a runtime library call involving a string whose contents are interpreted at runtime. I decided to ignore I/O statements by skipping to the end of line (Fortran is line oriented).
Then the number of keywords hit me, around 190. Even with the simplifications, I had made writing a Fortran lexer look like it would be a lot of work; some of the keywords only had this status when followed by a = and I kept uncovering new issues. Cutting and pasting somebody else’s lexer would probably also involve a lot of work.
I went back and looked at some of the Fortran front ends I had found on the Internet. The GNU Fortran front-end was a huge beast and would need serious cutting back to be of use. moware was written in Fortran and used the traditional six character abbreviated names seen in ‘old-style’ Fortran source and not a lot of commenting. The Eli project seemed a lot more interested in the formalism side of things, and Fortran was just one of the languages they claimed to support.
The Open Fortran Parser looked very interesting. It was designed to be used as a parsing skeleton that could be used to produce tools that processed source, and already contained hooks that output diagnostic output when each language production was reduced during a parse. Tests showed that it did a good job of parsing the source I had, although there was one vendor extension used quite often (and not documented in their manual). The tool source, in Java, looked straightforward to follow, and it was obvious where my code needed to be added. This tool was exactly what I needed 🙂
GLR parsing is the future
Traditionally parser generators have required that their input grammar be LALR(1) or some close variant (I would include LL(1) in this set). Back when 64k was an unimaginably large amount of memory being able to squeeze parser tables in a few kilobytes was very important; people received PhDs on parser table compression.
There is still a market for compact, fast parsers. Formal language grammars abound in communication protocols and vendors of communications hardware are very interested in keeping down costs by using minimizing the storage needed by their devices.
The trouble with LALR(1) is that value 1. It means that the parser only looks ahead one token in the input stream. This often means that a grammar is flagged as being ambiguous (i.e., it contains shift/reduce or reduce/reduce conflicts) when it is actually just locally ambiguous, i.e., reading tokens further head on the input stream would provide sufficient context to unambiguously specify the appropriate grammar production.
Restructuring a grammar to make it LALR(1) requires a lot of thought and skill and inexperienced users often give up. I once spent a month trying to remove the conflicts in the SQL/2 grammar specified by the SQL ISO standard; I managed to get the number down from over 1,000 to a small number that I decided I could live with.
It has taken a long time for parser generators to break out of the 64k mentality, but over the last few years it has started to happen. There have been two main approaches: 1) LR(n) provides a mechanism to look further ahead than one token, ie,
I think that GLR parsing is the future for two reasons:
- It is supported by the most widely used parser generator, bison.
- It enables working parsers to be created with much less thought and effort than a LALR(1) parser. (I don’t know how it compares against LR(n)).
GLR parsers resolve any language ambiguities by effectively delaying decisions until runtime in the hope that reading enough tokens will resolve local ambiguities. If an ambiguity in the token stream cannot be resolved a runtime error occurs (this is the one big downside of a GLR parser, the parser generated by a LALR(1) parser generator may produce lots of build time warnings but never produces errors when the parser is executed).
One example of a truly ambiguous construct (discussed here a while ago) is:
x * y; |
which in C/C++ could be a declaration of y to be a pointer to x, or an expression that multiplies x and y.
Tools that can detect these global ambiguities in a grammar are starting to appear, e.g., DTWA is a bison extension.
I reviewed an early draft of the new O’Reilly book “flex & bison” and tried to get the author to be more upbeat on GLR support in bison; I think I got him to be a bit less cautious.
Parsing without a symbol table
When processing C/C++ source for the first time through a compiler or static analysis tool there are invariably errors caused by missing header files (often because the search path has not been set) or incorrectly defined, or not defined, macro names. One solution to this configuration problem is to be able to process source without handling preprocessing directives (e.g., skipping them, such as not reading the contents of header files or working out which arm of a conditional directive is applicable). Developers can do it, why not machines?
A few years ago GLR support was added to Bison, enabling it to process ambiguous grammars, and I decided to create a C parser that simply skipped all preprocessing directives. I knew that at least one reasonably common usage would generate a syntax error:
func_call(a, #if SOME_FLAG b_1); #else b_2); #endif |
c);
and wanted to minimize its consequences (i.e., cascading syntax errors to the end of the file). The solution chosen was to parse the source a single statement or declaration at a time, so any syntax error would be localized to a single statement or declaration.
Systems for parsing ambiguous grammars work on the basis that while the input may be locally ambiguous, once enough tokens have been seen the number of possible parses will be reduced to one. In C (and even more so in C++) there are some situations where it is impossible to resolve which of several possible parses apply without declaration information on one or more of the identifiers involved (a traditional parser would maintain a symbol table where this information could be obtained when needed). For instance, x * y; could be a declaration of the identifier y to have type x or an expression statement that multiplies x and y. My parser did not have a symbol table and even if it did the lack of header file processing meant that its contents would only contain a partial set of the declared identifiers. The ambiguity resolution strategy I adopted was to pick the most likely case, which in the example is the declaration parse.
Other constructs where the common case (chosen by me and I have yet to get around to actually verifying via measurement) was used to resolve an ambiguity deadlock included:
f(p); // Very common, // confidently picked function call as the common case (m)*p; // Not rare, // confidently picked multiplication as the common case (s) - t; // Quiet rare, // picked binary operator as the common case (r) + (s) - t; // Very rare, //an iteration on the case above |
At the moment I am using the parser to measure language usage, so less than 100% correctness can be tolerated. Some of the constructs that cause a syntax error to be generated every few hundred statement/declarations include:
offsetof(struct tag, field_name) // Declarators cannot be //function arguments int f(p, q) int p; // Tries to reduce this as a declaration without handling char q; // it as part of an old style function definition { MACRO(+); // Preprocessing expands to something meaningful |
Some of these can be handled by extensions to the grammar, while others could be handled by an error recovery mechanism that recognized likely macro usage and inserted something appropriate (e.g., a dummy expression in the MACRO(x) case).
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