Left Recursion in Parsing Expression Grammars

Parsing Expression Grammars (PEGs) are a formalism that can describe all deterministic context-free languages through a set of rules that specify a top-down parser for some language. PEGs are easy to use, and there are efficient implementations of PEG libraries in several programming languages. A frequently missed feature of PEGs is left recursion, which is commonly used in Context-Free Grammars (CFGs) to encode left-associative operations. We present a simple conservative extension to the semantics of PEGs that gives useful meaning to direct and indirect left-recursive rules, and show that our extensions make it easy to express left-recursive idioms from CFGs in PEGs, with similar results. We prove the conservativeness of these extensions, and also prove that they work with any left-recursive PEG. PEGs can also be compiled to programs in a low-level parsing machine. We present an extension to the semantics of the operations of this parsing machine that let it interpret left-recursive PEGs, and prove that this extension is correct with regards to our semantics for left-recursive PEGs.Comment: Extended version of the paper "Left Recursion in Parsing Expression Grammars", that was published on 2012 Brazilian Symposium on Programming Language

Pattern matching in compilers

In this thesis we develop tools for effective and flexible pattern matching. We introduce a new pattern matching system called amethyst. Amethyst is not only a generator of parsers of programming languages, but can also serve as an alternative to tools for matching regular expressions. Our framework also produces dynamic parsers. Its intended use is in the context of IDE (accurate syntax highlighting and error detection on the fly). Amethyst offers pattern matching of general data structures. This makes it a useful tool for implementing compiler optimizations such as constant folding, instruction scheduling, and dataflow analysis in general. The parsers produced are essentially top-down parsers. Linear time complexity is obtained by introducing the novel notion of structured grammars and regularized regular expressions. Amethyst uses techniques known from compiler optimizations to produce effective parsers.Comment: master thesi

Stream Processing using Grammars and Regular Expressions

In this dissertation we study regular expression based parsing and the use of grammatical specifications for the synthesis of fast, streaming string-processing programs. In the first part we develop two linear-time algorithms for regular expression based parsing with Perl-style greedy disambiguation. The first algorithm operates in two passes in a semi-streaming fashion, using a constant amount of working memory and an auxiliary tape storage which is written in the first pass and consumed by the second. The second algorithm is a single-pass and optimally streaming algorithm which outputs as much of the parse tree as is semantically possible based on the input prefix read so far, and resorts to buffering as many symbols as is required to resolve the next choice. Optimality is obtained by performing a PSPACE-complete pre-analysis on the regular expression. In the second part we present Kleenex, a language for expressing high-performance streaming string processing programs as regular grammars with embedded semantic actions, and its compilation to streaming string transducers with worst-case linear-time performance. Its underlying theory is based on transducer decomposition into oracle and action machines, and a finite-state specialization of the streaming parsing algorithm presented in the first part. In the second part we also develop a new linear-time streaming parsing algorithm for parsing expression grammars (PEG) which generalizes the regular grammars of Kleenex. The algorithm is based on a bottom-up tabulation algorithm reformulated using least fixed points and evaluated using an instance of the chaotic iteration scheme by Cousot and Cousot

Towards semantic mathematical editing *

Currently, there exists a big gap between formal computer-understandable mathematics and informal mathematics, as written by humans. When looking more closely, there are two important subproblems: making documents written by humans at least syntactically understandable for computers, and the formal verification of the actual mathematics in the documents. In this paper, we will focus on the first problem. For the time being, most authors use T E X, L A T E X, or one of its graphical frontends in order to write documents with many mathematical formulas. In the past decade, we have developed an alternative wysiwyg system GNU T E X MACS , which is not based on T E X. All these systems are only adequate for visual typesetting and do not carry much semantics. Stated in the MathML jargon, they concentrate on presentation markup, not content markup. In recent versions of T E X MACS , we have started to integrate facilities for the semantic editing of formulas. In this paper, we will describe these facilities and expand on the underlying motivation and design choices. To go short, we continue to allow the user to enter formulas in a visually oriented way. In the background, we continuously run a packrat parser, which attempts to convert (potentially incomplete) formulas into content markup. As long as all formulas remain sufficiently correct, the editor can then both operate on a visual or semantic level, independently of the low-level representation being used. An important related topic, which will also be discussed at length, is the automatic correction of syntax errors in existing mathematical documents. In particular, the syntax corrector that we have implemented enables us to upgrade existing documents and test our parsing grammar on various books and papers from different sources. We will provide a detailed analysis of these experiments

Protecting Systems From Exploits Using Language-Theoretic Security

Any computer program processing input from the user or network must validate the input. Input-handling vulnerabilities occur in programs when the software component responsible for filtering malicious input---the parser---does not perform validation adequately. Consequently, parsers are among the most targeted components since they defend the rest of the program from malicious input. This thesis adopts the Language-Theoretic Security (LangSec) principle to understand what tools and research are needed to prevent exploits that target parsers. LangSec proposes specifying the syntactic structure of the input format as a formal grammar. We then build a recognizer for this formal grammar to validate any input before the rest of the program acts on it. To ensure that these recognizers represent the data format, programmers often rely on parser generators or parser combinators tools to build the parsers. This thesis propels several sub-fields in LangSec by proposing new techniques to find bugs in implementations, novel categorizations of vulnerabilities, and new parsing algorithms and tools to handle practical data formats. To this end, this thesis comprises five parts that tackle various tenets of LangSec. First, I categorize various input-handling vulnerabilities and exploits using two frameworks. First, I use the mismorphisms framework to reason about vulnerabilities. This framework helps us reason about the root causes leading to various vulnerabilities. Next, we built a categorization framework using various LangSec anti-patterns, such as parser differentials and insufficient input validation. Finally, we built a catalog of more than 30 popular vulnerabilities to demonstrate the categorization frameworks. Second, I built parsers for various Internet of Things and power grid network protocols and the iccMAX file format using parser combinator libraries. The parsers I built for power grid protocols were deployed and tested on power grid substation networks as an intrusion detection tool. The parser I built for the iccMAX file format led to several corrections and modifications to the iccMAX specifications and reference implementations. Third, I present SPARTA, a novel tool I built that generates Rust code that type checks Portable Data Format (PDF) files. The type checker I helped build strictly enforces the constraints in the PDF specification to find deviations. Our checker has contributed to at least four significant clarifications and corrections to the PDF 2.0 specification and various open-source PDF tools. In addition to our checker, we also built a practical tool, PDFFixer, to dynamically patch type errors in PDF files. Fourth, I present ParseSmith, a tool to build verified parsers for real-world data formats. Most parsing tools available for data formats are insufficient to handle practical formats or have not been verified for their correctness. I built a verified parsing tool in Dafny that builds on ideas from attribute grammars, data-dependent grammars, and parsing expression grammars to tackle various constructs commonly seen in network formats. I prove that our parsers run in linear time and always terminate for well-formed grammars. Finally, I provide the earliest systematic comparison of various data description languages (DDLs) and their parser generation tools. DDLs are used to describe and parse commonly used data formats, such as image formats. Next, I conducted an expert elicitation qualitative study to derive various metrics that I use to compare the DDLs. I also systematically compare these DDLs based on sample data descriptions available with the DDLs---checking for correctness and resilience

flap: A Deterministic Parser with Fused Lexing

Lexers and parsers are typically defined separately and connected by a token stream. This separate definition is important for modularity and reduces the potential for parsing ambiguity. However, materializing tokens as data structures and case-switching on tokens comes with a cost. We show how to fuse separately-defined lexers and parsers, drastically improving performance without compromising modularity or increasing ambiguity. We propose a deterministic variant of Greibach Normal Form that ensures deterministic parsing with a single token of lookahead and makes fusion strikingly simple, and prove that normalizing context free expressions into the deterministic normal form is semantics-preserving. Our staged parser combinator library, flap, provides a standard interface, but generates specialized token-free code that runs two to six times faster than ocamlyacc on a range of benchmarks.Comment: PLDI 2023 with appendi