Ambiguity detection tools try to statically track down ambiguities in context-free grammars. Current ambiguity detection tools, however, either are too slow for large real- istic cases, or produce incomprehensible ambiguity reports. AmbiDexter is the ambiguity tool to have your cake and eat it too

Basten, H.J.S. (Bas)

Storm, T. (Tijs) van der

English

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AMBIDEXTER: Practical Ambiguity DetectionTool DemonstrationBas BastenCentrum Wiskunde & Informaticabasten@cwi.nlTijs van der StormCentrum Wiskunde & InformaticaUniversiteit van Amsterdamstorm@cwi.nlAbstractAmbiguity detection tools try to statically track downambiguities in context-free grammars. Current ambiguitydetection tools, however, either are too slow for large real-istic cases, or produce incomprehensible ambiguity reports.AMBIDEXTER is the ambiguity tool to have your cake andeat it too.1. IntroductionContext-free grammars are an important form of sourcecode, both for the development of source code analysis andmanipulation tools, and for prototyping (domain specific)languages [7]. A common requirement is that a grammaris not ambiguous,—i.e. does not allow multiple derivationsfor the same string. If a grammar is ambiguous this often in-dicates a grammar bug that needs to be fixed. It is, however,very hard to establish whether a grammar is ambiguous ornot.Ambiguity detection tools are used to statically try andfind ambiguities. To be practical, such tools should (1) pro-vide feedback that is comprehensible to the grammar de-veloper, and (2) come up with an answer within reasonabletime. In this tool demo we present AMBIDEXTER, a tool forpractical ambiguity detection. It combines two approachesto ambiguity detection: exhaustive searching and approxi-mative searching. As a result, AMBIDEXTER benefits fromeach technique’s strengths, while avoiding their respectivedrawbacks.2. Ambiguity DetectionA context-free grammar is ambiguous if it allows multiplederivations for the same string. A well-known example ofan ambiguous grammar is the following one, describing if-then-else statements:Stm → "if" Exp StmStm → "if" Exp Stm "else" StmIf this grammar is used to parse the string “if x if y ...else ...” then it is unclear whether the else-branch be-longs to the inner-most if-statement or to the outer-most if-statement. In other words, there are two valid derivationtrees for this snippet of source code. Both trees are shownin Figure 1."if" Exp Stmx"if" Exp Stm"else" Stmy ... ..."if" Exp Stm"else" Stmx "if" Exp Stmy ......Figure 1. The “dangling else” ambiguityThe goal of ambiguity detection is to statically analyze agrammar and to uncover ambiguities such as the one in Fig-ure 1. Unfortunately, ambiguity of context-free grammarsis undecidable in the general case. Nevertheless, there aresemi-decision techniques to approach the problem.Ambiguity detection techniques can be divided over twocategories:1. Exhaustive searching: start generating all sentences inthe language of a grammar and check if they have mul-tiple parse trees [9, 1].2. Approximative searching: the grammar is approxi-mated into an alternative form that that can be analyzedin finite time [8, 4].An advantage of exhaustive searching is that if an ambigu-ous sentence is found, the productions involved in the ambi-guity can be derived from the parse trees (cf. Figure 1). Thisis valuable information for the grammar developer. Unfor-tunately, generating strings of increasing length is of expo-nential complexity and will not terminate if the grammar isunambiguous.On the other hand, approximative searching techniquesalways terminate, but this comes at the expense of preci-sion. If no ambiguities are found, the grammar is unambigu-ous. However, if ambiguities are found, they might includefalse positives. As a result, they require manual inspection.Finally, unlike in exhaustive approaches, the ambiguity re-ports of these tools tend to be hard to understand.3. AMBIDEXTERAMBIDEXTER combines exhaustive and approximativesearching to benefit from both their strengths. The goal isto produce precise and comprehensible ambiguity reports asfast as possible. We use approximative filtering to narrowdown the search space for an exhaustive checker. This alsoallows us to detect both ambiguity and unambiguity.The tool operates in two stages:1. Harmless production filtering: harmless productionsare productions that cannot be involved in ambigu-ity. Using an extension of the approximative tech-nique of [8] such productions are identified and re-moved from the grammar.2. Derivation generator: for the productions that are notidentified as harmless, an exhaustive derivation gener-ator is applied to detect remaining ambiguities.As a result, AMBIDEXTER leverages the strengths ofboth approaches to ambiguity detection:• Unambiguity is detected if all productions are identi-fied as harmless.• Comprehensible ambiguity reports are produced as aconsequence of employing a derivation generator.• Performance is improved because the production filter-ing reduces the derivation generator’s search space.The filtering technique is described in more detail in [2].It has been empirically validated on a collection of real-lifeprogramming language grammars [3]. We were able to fil-ter between 12–78% of the productions rules of the variousgrammars. It turns out this improved the performance ofderivation generation substantially, sometimes by orders ofmagnitude. For instance, on a C grammar with a “danglingelse” ambiguity like the one in Figure 1, we witnessed aspeedup of AMBER [9] of almost 4000x, after filtering 21%of the production rules.Our current derivation generator was not included in [3],but early results show it is on average twice as fast asAMBER. Furthermore, we have parallelized it in order toexploit present-day multicore machines for even better per-formance.AMBIDEXTER accepts input grammars in YACC [6]and SDF [5] format, and takes into account their disam-biguation constructs like priorities and follow restrictions.It is available for download at http://homepages.cwi.nl/~basten/ambiguity/.4. ConclusionContext-free grammars are important software engineeringartifacts. They are used for the development of sourcecode analysis and manipulation tools and for prototypingcomputer languages. In this tool demo we have presentedAMBIDEXTER, a tool for practical ambiguity detection.By combining exhaustive and approximative approachesAMBIDEXTER produces comprehensible ambiguity reportsin a much faster time.References[1] R. Axelsson, K. Heljanko, and M. Lange. Analyzing context-free grammars using an incremental SAT solver. In Pro-ceedings of the 35th International Colloquium on Automata,Languages, and Programming (ICALP’08), volume 5126 ofLNCS, 2008.[2] H. J. S. Basten. Tracking down the origins of ambiguity incontext-free grammars. In Proceedings of the Seventh In-ternational Colloquium on Theoretical Aspects of Computing(ICTAC 2010). Springer, 2010. To appear.[3] H. J. S. Basten and J. J. Vinju. Faster ambiguity detection bygrammar filtering. In Proceedings of the Tenth Workshop onLanguage Descriptions, Tools and Applications (LDTA 2010).ACM, 2010. To appear.[4] C. Brabrand, R. Giegerich, and A. Møller. Analyzing am-biguity of context-free grammars. Sci. Comput. Program.,75(3):176–191, 2010.[5] J. Heering, P. R. H. Hendriks, P. Klint, and J. Rekers. The syn-tax definition formalism SDF - reference manual. SIGPLANNotices, 24(11):43–75, 1989.[6] S. C. Johnson. Yacc: Yet Another Compiler-Compiler. AT&TBell Laboratories. http://dinosaur.compilertools.net/yacc/.[7] P. Klint, R. Lämmel, and C. Verhoef. Toward an engineeringdiscipline for grammarware. ACM Transactions on SoftwareEngineering Methodology, 14(3):331–380, 2005.[8] S. Schmitz. Conservative ambiguity detection in context-freegrammars. In L. Arge, C. Cachin, T. Jurdzin´ski, and A. Tar-lecki, editors, ICALP’07: 34th International Colloquium onAutomata, Languages and Programming, volume 4596 ofLNCS, 2007.[9] F. W. Schröer. AMBER, an ambiguity checker for context-free grammars. Technical report, compilertools.net, 2001. Seehttp://accent.compilertools.net/Amber.html.

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