Bohemia - a Validator for Parser Frameworks
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Derivatives of Parsing Expression Grammars
Derivatives of Parsing Expression Grammars Aaron Moss Cheriton School of Computer Science University of Waterloo Waterloo, Ontario, Canada [email protected] This paper introduces a new derivative parsing algorithm for recognition of parsing expression gram- mars. Derivative parsing is shown to have a polynomial worst-case time bound, an improvement on the exponential bound of the recursive descent algorithm. This work also introduces asymptotic analysis based on inputs with a constant bound on both grammar nesting depth and number of back- tracking choices; derivative and recursive descent parsing are shown to run in linear time and constant space on this useful class of inputs, with both the theoretical bounds and the reasonability of the in- put class validated empirically. This common-case constant memory usage of derivative parsing is an improvement on the linear space required by the packrat algorithm. 1 Introduction Parsing expression grammars (PEGs) are a parsing formalism introduced by Ford [6]. Any LR(k) lan- guage can be represented as a PEG [7], but there are some non-context-free languages that may also be represented as PEGs (e.g. anbncn [7]). Unlike context-free grammars (CFGs), PEGs are unambiguous, admitting no more than one parse tree for any grammar and input. PEGs are a formalization of recursive descent parsers allowing limited backtracking and infinite lookahead; a string in the language of a PEG can be recognized in exponential time and linear space using a recursive descent algorithm, or linear time and space using the memoized packrat algorithm [6]. PEGs are formally defined and these algo- rithms outlined in Section 3. -
CS 432 Fall 2020 Top-Down (LL) Parsing
CS 432 Fall 2020 Mike Lam, Professor Top-Down (LL) Parsing Compilation Current focus "Back end" Source code Tokens Syntax tree Machine code char data[20]; 7f 45 4c 46 01 int main() { 01 01 00 00 00 float x 00 00 00 00 00 = 42.0; ... return 7; } Lexing Parsing Code Generation & Optimization "Front end" Review ● Recognize regular languages with finite automata – Described by regular expressions – Rule-based transitions, no memory required ● Recognize context-free languages with pushdown automata – Described by context-free grammars – Rule-based transitions, MEMORY REQUIRED ● Add a stack! Segue KEY OBSERVATION: Allowing the translator to use memory to track parse state information enables a wider range of automated machine translation. Chomsky Hierarchy of Languages Recursively enumerable Context-sensitive Context-free Most useful Regular for PL https://en.wikipedia.org/wiki/Chomsky_hierarchy Parsing Approaches ● Top-down: begin with start symbol (root of parse tree), and gradually expand non-terminals – Stack contains leaves that still need to be expanded ● Bottom-up: begin with terminals (leaves of parse tree), and gradually connect using non-terminals – Stack contains roots of subtrees that still need to be connected A V = E Top-down a E + E Bottom-up V V b c Top-Down Parsing root = createNode(S) focus = root A → V = E push(null) V → a | b | c token = nextToken() E → E + E loop: | V if (focus is non-terminal): B = chooseRuleAndExpand(focus) for each b in B.reverse(): focus.addChild(createNode(b)) push(b) A focus = pop() else if (token -
Total Parser Combinators
Total Parser Combinators Nils Anders Danielsson School of Computer Science, University of Nottingham, United Kingdom [email protected] Abstract The library has an interface which is very similar to those of A monadic parser combinator library which guarantees termination classical monadic parser combinator libraries. For instance, con- of parsing, while still allowing many forms of left recursion, is sider the following simple, left recursive, expression grammar: described. The library’s interface is similar to those of many other term :: factor term '+' factor parser combinator libraries, with two important differences: one is factor ::D atom j factor '*' atom that the interface clearly specifies which parts of the constructed atom ::D numberj '(' term ')' parsers may be infinite, and which parts have to be finite, using D j dependent types and a combination of induction and coinduction; We can define a parser which accepts strings from this grammar, and the other is that the parser type is unusually informative. and also computes the values of the resulting expressions, as fol- The library comes with a formal semantics, using which it is lows (the combinators are described in Section 4): proved that the parser combinators are as expressive as possible. mutual The implementation is supported by a machine-checked correct- term factor ness proof. D ] term >> λ n j D 1 ! Categories and Subject Descriptors D.1.1 [Programming Tech- tok '+' >> λ D ! niques]: Applicative (Functional) Programming; E.1 [Data Struc- factor >> λ n D 2 ! tures]; F.3.1 [Logics and Meanings of Programs]: Specifying and return .n n / 1 C 2 Verifying and Reasoning about Programs; F.4.2 [Mathematical factor atom Logic and Formal Languages]: Grammars and Other Rewriting D ] factor >> λ n Systems—Grammar types, Parsing 1 j tok '*' >>D λ ! D ! General Terms Languages, theory, verification atom >> λ n2 return .n n / D ! 1 ∗ 2 Keywords Dependent types, mixed induction and coinduction, atom number parser combinators, productivity, termination D tok '(' >> λ j D ! ] term >> λ n 1. -
Abstract Syntax Trees & Top-Down Parsing
Abstract Syntax Trees & Top-Down Parsing Review of Parsing • Given a language L(G), a parser consumes a sequence of tokens s and produces a parse tree • Issues: – How do we recognize that s ∈ L(G) ? – A parse tree of s describes how s ∈ L(G) – Ambiguity: more than one parse tree (possible interpretation) for some string s – Error: no parse tree for some string s – How do we construct the parse tree? Compiler Design 1 (2011) 2 Abstract Syntax Trees • So far, a parser traces the derivation of a sequence of tokens • The rest of the compiler needs a structural representation of the program • Abstract syntax trees – Like parse trees but ignore some details – Abbreviated as AST Compiler Design 1 (2011) 3 Abstract Syntax Trees (Cont.) • Consider the grammar E → int | ( E ) | E + E • And the string 5 + (2 + 3) • After lexical analysis (a list of tokens) int5 ‘+’ ‘(‘ int2 ‘+’ int3 ‘)’ • During parsing we build a parse tree … Compiler Design 1 (2011) 4 Example of Parse Tree E • Traces the operation of the parser E + E • Captures the nesting structure • But too much info int5 ( E ) – Parentheses – Single-successor nodes + E E int 2 int3 Compiler Design 1 (2011) 5 Example of Abstract Syntax Tree PLUS PLUS 5 2 3 • Also captures the nesting structure • But abstracts from the concrete syntax a more compact and easier to use • An important data structure in a compiler Compiler Design 1 (2011) 6 Semantic Actions • This is what we’ll use to construct ASTs • Each grammar symbol may have attributes – An attribute is a property of a programming language construct -
Staged Parser Combinators for Efficient Data Processing
Staged Parser Combinators for Efficient Data Processing Manohar Jonnalagedda∗ Thierry Coppeyz Sandro Stucki∗ Tiark Rompf y∗ Martin Odersky∗ ∗LAMP zDATA, EPFL {first.last}@epfl.ch yOracle Labs: {first.last}@oracle.com Abstract use the language’s abstraction capabilities to enable compo- Parsers are ubiquitous in computing, and many applications sition. As a result, a parser written with such a library can depend on their performance for decoding data efficiently. look like formal grammar descriptions, and is also readily Parser combinators are an intuitive tool for writing parsers: executable: by construction, it is well-structured, and eas- tight integration with the host language enables grammar ily maintainable. Moreover, since combinators are just func- specifications to be interleaved with processing of parse re- tions in the host language, it is easy to combine them into sults. Unfortunately, parser combinators are typically slow larger, more powerful combinators. due to the high overhead of the host language abstraction However, parser combinators suffer from extremely poor mechanisms that enable composition. performance (see Section 5) inherent to their implementa- We present a technique for eliminating such overhead. We tion. There is a heavy penalty to be paid for the expres- use staging, a form of runtime code generation, to dissoci- sivity that they allow. A grammar description is, despite its ate input parsing from parser composition, and eliminate in- declarative appearance, operationally interleaved with input termediate data structures and computations associated with handling, such that parts of the grammar description are re- parser composition at staging time. A key challenge is to built over and over again while input is processed. -
AST Indexing: a Near-Constant Time Solution to the Get-Descendants-By-Type Problem Samuel Livingston Kelly Dickinson College
Dickinson College Dickinson Scholar Student Honors Theses By Year Student Honors Theses 5-18-2014 AST Indexing: A Near-Constant Time Solution to the Get-Descendants-by-Type Problem Samuel Livingston Kelly Dickinson College Follow this and additional works at: http://scholar.dickinson.edu/student_honors Part of the Software Engineering Commons Recommended Citation Kelly, Samuel Livingston, "AST Indexing: A Near-Constant Time Solution to the Get-Descendants-by-Type Problem" (2014). Dickinson College Honors Theses. Paper 147. This Honors Thesis is brought to you for free and open access by Dickinson Scholar. It has been accepted for inclusion by an authorized administrator. For more information, please contact [email protected]. AST Indexing: A Near-Constant Time Solution to the Get-Descendants-by-Type Problem by Sam Kelly Submitted in partial fulfillment of Honors Requirements for the Computer Science Major Dickinson College, 2014 Associate Professor Tim Wahls, Supervisor Associate Professor John MacCormick, Reader Part-Time Instructor Rebecca Wells, Reader April 22, 2014 The Department of Mathematics and Computer Science at Dickinson College hereby accepts this senior honors thesis by Sam Kelly, and awards departmental honors in Computer Science. Tim Wahls (Advisor) Date John MacCormick (Committee Member) Date Rebecca Wells (Committee Member) Date Richard Forrester (Department Chair) Date Department of Mathematics and Computer Science Dickinson College April 2014 ii Abstract AST Indexing: A Near-Constant Time Solution to the Get- Descendants-by-Type Problem by Sam Kelly In this paper we present two novel abstract syntax tree (AST) indexing algorithms that solve the get-descendants-by-type problem in near constant time. -
Syntactic Analysis, Or Parsing, Is the Second Phase of Compilation: the Token File Is Converted to an Abstract Syntax Tree
Syntactic Analysis Syntactic analysis, or parsing, is the second phase of compilation: The token file is converted to an abstract syntax tree. Analysis Synthesis Compiler Passes of input program of output program (front -end) (back -end) character stream Intermediate Lexical Analysis Code Generation token intermediate stream form Syntactic Analysis Optimization abstract intermediate syntax tree form Semantic Analysis Code Generation annotated target AST language 1 Syntactic Analysis / Parsing • Goal: Convert token stream to abstract syntax tree • Abstract syntax tree (AST): – Captures the structural features of the program – Primary data structure for remainder of analysis • Three Part Plan – Study how context-free grammars specify syntax – Study algorithms for parsing / building ASTs – Study the miniJava Implementation Context-free Grammars • Compromise between – REs, which can’t nest or specify recursive structure – General grammars, too powerful, undecidable • Context-free grammars are a sweet spot – Powerful enough to describe nesting, recursion – Easy to parse; but also allow restrictions for speed • Not perfect – Cannot capture semantics, as in, “variable must be declared,” requiring later semantic pass – Can be ambiguous • EBNF, Extended Backus Naur Form, is popular notation 2 CFG Terminology • Terminals -- alphabet of language defined by CFG • Nonterminals -- symbols defined in terms of terminals and nonterminals • Productions -- rules for how a nonterminal (lhs) is defined in terms of a (possibly empty) sequence of terminals -
Lecture 3: Recursive Descent Limitations, Precedence Climbing
Lecture 3: Recursive descent limitations, precedence climbing David Hovemeyer September 9, 2020 601.428/628 Compilers and Interpreters Today I Limitations of recursive descent I Precedence climbing I Abstract syntax trees I Supporting parenthesized expressions Before we begin... Assume a context-free struct Node *Parser::parse_A() { grammar has the struct Node *next_tok = lexer_peek(m_lexer); following productions on if (!next_tok) { the nonterminal A: error("Unexpected end of input"); } A → b C A → d E struct Node *a = node_build0(NODE_A); int tag = node_get_tag(next_tok); (A, C, E are if (tag == TOK_b) { nonterminals; b, d are node_add_kid(a, expect(TOK_b)); node_add_kid(a, parse_C()); terminals) } else if (tag == TOK_d) { What is the problem node_add_kid(a, expect(TOK_d)); node_add_kid(a, parse_E()); with the parse function } shown on the right? return a; } Limitations of recursive descent Recall: a better infix expression grammar Grammar (start symbol is A): A → i = A T → T*F A → E T → T/F E → E + T T → F E → E-T F → i E → T F → n Precedence levels: Nonterminal Precedence Meaning Operators Associativity A lowest Assignment = right E Expression + - left T Term * / left F highest Factor No Parsing infix expressions Can we write a recursive descent parser for infix expressions using this grammar? Parsing infix expressions Can we write a recursive descent parser for infix expressions using this grammar? No Left recursion Left-associative operators want to have left-recursive productions, but recursive descent parsers can’t handle left recursion -
Understanding Source Code Evolution Using Abstract Syntax Tree Matching
Understanding Source Code Evolution Using Abstract Syntax Tree Matching Iulian Neamtiu Jeffrey S. Foster Michael Hicks [email protected] [email protected] [email protected] Department of Computer Science University of Maryland at College Park ABSTRACT so understanding how the type structure of real programs Mining software repositories at the source code level can pro- changes over time can be invaluable for weighing the merits vide a greater understanding of how software evolves. We of DSU implementation choices. Second, we are interested in present a tool for quickly comparing the source code of dif- a kind of “release digest” for explaining changes in a software ferent versions of a C program. The approach is based on release: what functions or variables have changed, where the partial abstract syntax tree matching, and can track sim- hot spots are, whether or not the changes affect certain com- ple changes to global variables, types and functions. These ponents, etc. Typical release notes can be too high level for changes can characterize aspects of software evolution use- developers, and output from diff can be too low level. ful for answering higher level questions. In particular, we To answer these and other software evolution questions, consider how they could be used to inform the design of a we have developed a tool that can quickly tabulate and sum- dynamic software updating system. We report results based marize simple changes to successive versions of C programs on measurements of various versions of popular open source by partially matching their abstract syntax trees. The tool programs, including BIND, OpenSSH, Apache, Vsftpd and identifies the changes, additions, and deletions of global vari- the Linux kernel. -
Parsing with Earley Virtual Machines
Communication papers of the Federated Conference on DOI: 10.15439/2017F162 Computer Science and Information Systems, pp. 165–173 ISSN 2300-5963 ACSIS, Vol. 13 Parsing with Earley Virtual Machines Audrius Saikˇ unas¯ Institute of Mathematics and Informatics Akademijos 4, LT-08663 Vilnius, Lithuania Email: [email protected] Abstract—Earley parser is a well-known parsing method used EVM is capable of parsing context-free languages with data- to analyse context-free grammars. While being less efficient in dependant constraints. The core idea behind of EVM is to practical contexts than other generalized context-free parsing have two different grammar representations: one is user- algorithms, such as GLR, it is also more general. As such it can be used as a foundation to build more complex parsing algorithms. friendly and used to define grammars, while the other is used We present a new, virtual machine based approach to parsing, internally during parsing. Therefore, we end up with grammars heavily based on the original Earley parser. We present several that specify the languages in a user-friendly way, which are variations of the Earley Virtual Machine, each with increasing then compiled into grammar programs that are executed or feature set. The final version of the Earley Virtual Machine is interpreted by the EVM to match various input sequences. capable of parsing context-free grammars with data-dependant constraints and support grammars with regular right hand sides We present several iterations of EVM: and regular lookahead. • EVM0 that is equivalent to the original Earley parser in We show how to translate grammars into virtual machine it’s capabilities. -
To an Abstract Syntax Tree
School of Computing Science @ Simon Fraser University Parsing Lecture 09: Data Abstraction ++ ➡ Parsing A parser transforms a source program (in concrete • Parsing is the process of translating a sequence of characters (a string) into syntax) toana abstractn abs syntaxtract tree.syn tax tree (AST): program AST −−−−−−→ Parser −−−→ Processor text • Compilers (and some interpreters) analyse abstract syntax trees. • Compilers very well understood • In fact, there exist “compiler compilers” • Example: YACC (yet another compiler compiler) http://dinosaur.compilertools.net/ An Abstraction for Inductive Data Types – p.34/43 Copyright © Bill Havens 1 School of Computing Science @ Simon Fraser University Expression Syntax Extended • An abstract syntax expresses the structure of the concrete syntax without the details. • Example: extended syntax for Scheme expressions • Includes literals (constant numbers) <exp> ::= <number> | <symbol> | (lambda (<symbol>) <exp>) | (<exp> <exp>) • We would define an abstract datatype for this grammar as follows: (define-datatype expression expression? (lit-exp (datum number?)) (var-exp (id symbol?)) (lambda-exp (id symbol?) (body expression?)) (app-exp (rator expression?) (rand expression?))) • Now lets parse sentences in the language specified by the BNF grammar into abstract syntax trees Copyright © Bill Havens 2 School of Computing Science @ Simon Fraser University Parser for Extended Expressions • Here is an example parser for the lambda expression language above: (define parse-expression (lambda (datum) (cond ((number? -
CSCI 742 - Compiler Construction
CSCI 742 - Compiler Construction Lecture 12 Recursive-Descent Parsers Instructor: Hossein Hojjat February 12, 2018 Recap: Predictive Parsers • Predictive Parser: Top-down parser that looks at the next few tokens and predicts which production to use • Efficient: no need for backtracking, linear parsing time • Predictive parsers accept LL(k) grammars • L means “left-to-right” scan of input • L means leftmost derivation • k means predict based on k tokens of lookahead 1 Implementations Analogous to lexing: Recursive descent parser (manual) • Each non-terminal parsed by a procedure • Call other procedures to parse sub-nonterminals recursively • Typically implemented manually Table-driven parser (automatic) • Push-down automata: essentially a table driven FSA, plus stack to do recursive calls • Typically generated by a tool from a grammar specification 2 Making Grammar LL • Recall the left-recursive grammar: S ! S + E j E E ! num j (E) • Grammar is not LL(k) for any number of k • Left-recursion elimination: rewrite left-recursive productions to right-recursive ones S ! EE0 S ! S + E j E E0 ! +EE0 j E ! num j (E) E ! num j (E) 3 Making Grammar LL • Recall the grammar: S ! E + E j E E ! num j (E) • Grammar is not LL(k) for any number of k • Left-factoring: Factor common prefix E, add new non-terminal E0 for what follows that prefix S ! EE0 S ! E + E j E E0 ! +E j E ! num j (E) E ! num j (E) 4 Parsing with new grammar S ! EE0 E0 ! +E j E ! num j (E) Partly-derived String Lookahead parsed part unparsed part S ( (num)+num ) E E0 ( (num)+num ) (E)