A Typed, Algebraic Approach to Parsing
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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. -
Adaptive LL(*) Parsing: the Power of Dynamic Analysis
Adaptive LL(*) Parsing: The Power of Dynamic Analysis Terence Parr Sam Harwell Kathleen Fisher University of San Francisco University of Texas at Austin Tufts University [email protected] [email protected] kfi[email protected] Abstract PEGs are unambiguous by definition but have a quirk where Despite the advances made by modern parsing strategies such rule A ! a j ab (meaning “A matches either a or ab”) can never as PEG, LL(*), GLR, and GLL, parsing is not a solved prob- match ab since PEGs choose the first alternative that matches lem. Existing approaches suffer from a number of weaknesses, a prefix of the remaining input. Nested backtracking makes de- including difficulties supporting side-effecting embedded ac- bugging PEGs difficult. tions, slow and/or unpredictable performance, and counter- Second, side-effecting programmer-supplied actions (muta- intuitive matching strategies. This paper introduces the ALL(*) tors) like print statements should be avoided in any strategy that parsing strategy that combines the simplicity, efficiency, and continuously speculates (PEG) or supports multiple interpreta- predictability of conventional top-down LL(k) parsers with the tions of the input (GLL and GLR) because such actions may power of a GLR-like mechanism to make parsing decisions. never really take place [17]. (Though DParser [24] supports The critical innovation is to move grammar analysis to parse- “final” actions when the programmer is certain a reduction is time, which lets ALL(*) handle any non-left-recursive context- part of an unambiguous final parse.) Without side effects, ac- free grammar. ALL(*) is O(n4) in theory but consistently per- tions must buffer data for all interpretations in immutable data forms linearly on grammars used in practice, outperforming structures or provide undo actions. -
Efficient Recursive Parsing
Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1976 Efficient Recursive Parsing Christoph M. Hoffmann Purdue University, [email protected] Report Number: 77-215 Hoffmann, Christoph M., "Efficient Recursive Parsing" (1976). Department of Computer Science Technical Reports. Paper 155. https://docs.lib.purdue.edu/cstech/155 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. EFFICIENT RECURSIVE PARSING Christoph M. Hoffmann Computer Science Department Purdue University West Lafayette, Indiana 47907 CSD-TR 215 December 1976 Efficient Recursive Parsing Christoph M. Hoffmann Computer Science Department Purdue University- Abstract Algorithms are developed which construct from a given LL(l) grammar a recursive descent parser with as much, recursion resolved by iteration as is possible without introducing auxiliary memory. Unlike other proposed methods in the literature designed to arrive at parsers of this kind, the algorithms do not require extensions of the notational formalism nor alter the grammar in any way. The algorithms constructing the parsers operate in 0(k«s) steps, where s is the size of the grammar, i.e. the sum of the lengths of all productions, and k is a grammar - dependent constant. A speedup of the algorithm is possible which improves the bound to 0(s) for all LL(l) grammars, and constructs smaller parsers with some auxiliary memory in form of parameters -
Conflict Resolution in a Recursive Descent Compiler Generator
LL(1) Conflict Resolution in a Recursive Descent Compiler Generator Albrecht Wöß, Markus Löberbauer, Hanspeter Mössenböck Johannes Kepler University Linz, Institute of Practical Computer Science, Altenbergerstr. 69, 4040 Linz, Austria {woess,loeberbauer,moessenboeck}@ssw.uni-linz.ac.at Abstract. Recursive descent parsing is restricted to languages whose grammars are LL(1), i.e., which can be parsed top-down with a single lookahead symbol. Unfortunately, many languages such as Java, C++, or C# are not LL(1). There- fore recursive descent parsing cannot be used or the parser has to make its deci- sions based on semantic information or a multi-symbol lookahead. In this paper we suggest a systematic technique for resolving LL(1) conflicts in recursive descent parsing and show how to integrate it into a compiler gen- erator (Coco/R). The idea is to evaluate user-defined boolean expressions, in order to allow the parser to make its parsing decisions where a one symbol loo- kahead does not suffice. Using our extended compiler generator we implemented a compiler front end for C# that can be used as a framework for implementing a variety of tools. 1 Introduction Recursive descent parsing [16] is a popular top-down parsing technique that is sim- ple, efficient, and convenient for integrating semantic processing. However, it re- quires the grammar of the parsed language to be LL(1), which means that the parser must always be able to select between alternatives with a single symbol lookahead. Unfortunately, many languages such as Java, C++ or C# are not LL(1) so that one either has to resort to bottom-up LALR(1) parsing [5, 1], which is more powerful but less convenient for semantic processing, or the parser has to resolve the LL(1) con- flicts using semantic information or a multi-symbol lookahead. -
A Parsing Machine for Pegs
A Parsing Machine for PEGs ∗ Sérgio Medeiros Roberto Ierusalimschy [email protected] [email protected] Department of Computer Science PUC-Rio, Rio de Janeiro, Brazil ABSTRACT parsing approaches. The PEG formalism gives a convenient Parsing Expression Grammar (PEG) is a recognition-based syntax for describing top-down parsers for unambiguous lan- foundation for describing syntax that renewed interest in guages. The parsers it describes can parse strings in linear top-down parsing approaches. Generally, the implementa- time, despite backtracking, by using a memoizing algorithm tion of PEGs is based on a recursive-descent parser, or uses called Packrat [1]. Although Packrat has guaranteed worst- a memoization algorithm. case linear time complexity, it also has linear space com- We present a new approach for implementing PEGs, based plexity, with a rather large constant. This makes Packrat on a virtual parsing machine, which is more suitable for impractical for parsing large amounts of data. pattern matching. Each PEG has a corresponding program LPEG [7, 11] is a pattern-matching tool for Lua, a dy- that is executed by the parsing machine, and new programs namically typed scripting language [6, 8]. LPEG uses PEGs are dynamically created and composed. The virtual machine to describe patterns instead of the more popular Perl-like is embedded in a scripting language and used by a pattern- "regular expressions" (regexes). Regexes are a more ad-hoc matching tool. way of describing patterns; writing a complex regex is more We give an operational semantics of PEGs used for pat- a trial and error than a systematic process, and their per- tern matching, then describe our parsing machine and its formance is very unpredictable. -
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 -
Parser Generation Bottom-Up Parsing LR Parsing Constructing LR Parser
CS421 COMPILERS AND INTERPRETERS CS421 COMPILERS AND INTERPRETERS Parser Generation Bottom-Up Parsing • Main Problem: given a grammar G, how to build a top-down parser or a • Construct parse tree “bottom-up” --- from leaves to the root bottom-up parser for it ? • Bottom-up parsing always constructs right-most derivation • parser : a program that, given a sentence, reconstructs a derivation for that • Important parsing algorithms: shift-reduce, LR parsing sentence ---- if done sucessfully, it “recognize” the sentence • LR parser components: input, stack (strings of grammar symbols and states), • all parsers read their input left-to-right, but construct parse tree differently. driver routine, parsing tables. • bottom-up parsers --- construct the tree from leaves to root input: a1 a2 a3 a4 ...... an $ shift-reduce, LR, SLR, LALR, operator precedence stack s m LR Parsing output • top-down parsers --- construct the tree from root to leaves Xm .. recursive descent, predictive parsing, LL(1) s1 X1 s0 parsing Copyright 1994 - 2015 Zhong Shao, Yale University Parser Generation: Page 1 of 27 Copyright 1994 - 2015 Zhong Shao, Yale University Parser Generation: Page 2 of 27 CS421 COMPILERS AND INTERPRETERS CS421 COMPILERS AND INTERPRETERS LR Parsing Constructing LR Parser How to construct the parsing table and ? • A sequence of new state symbols s0,s1,s2,..., sm ----- each state ACTION GOTO sumarize the information contained in the stack below it. • basic idea: first construct DFA to recognize handles, then use DFA to construct the parsing tables ! different parsing table yield different LR parsers SLR(1), • Parsing configurations: (stack, remaining input) written as LR(1), or LALR(1) (s0X1s1X2s2...Xmsm , aiai+1ai+2...an$) • augmented grammar for context-free grammar G = G(T,N,P,S) is defined as G’ next “move” is determined by sm and ai = G’(T, N { S’}, P { S’ -> S}, S’) ------ adding non-terminal S’ and the • Parsing tables: ACTION[s,a] and GOTO[s,X] production S’ -> S, and S’ is the new start symbol. -
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) -
1 Top-Down Parsing
Section - Top-Down Parsings: 1 Top-Down Parsing 1 Top-Down Parsing ❍ Top-down vs. bottom-up ● less powerful ● more complicated to generate intermediate code or perform semantic routines ● easier to implement, especially recursive descent ❍ Top-down parser ● builds the parse tree from the root down ● follows leftmost derivation; herefore, it is called LL(k) ● we always expand the topmost symbol on the stack (leftmost in derivation) ❍ Top-down procedure (k=1 lookahead) ● utilize stack memory ● start with pushing initial nonterminal S ● at any moment ❍ if a terminal is on the top of the stack ■ if it matches the incoming token, the terminal is popped and the token is con- sumed ■ error otherwise ❍ if a nonterminal is on the top of the stack ■ we need to replace it by one of its productions ■ must predict the correct one in a predictive parser (if more than one alternative) ■ errors possible in a predictive parser if none predicted ● successful termination ❍ empty stack and EOFtk incoming ❍ empty styacj is an error otherwise ❍ Some other properties ● actual program tokens are never on the stack ● the stack contains predicted tokens expected on input ● we must make correct predictions for efficiently solving alternatives 2003 Cezary Z Janikow 1 Section - Top-Down Parsings: 2 Left Recursion Example 1.1 Use the unambiguous expression grammar to top-down parse id+id*id. ❍ Problems to handle in top-down parsing ● left recursive productions (direct or indirect) ❍ infinite stack growth ❍ can always be handled ● non-deterministic productions (more than one production for a nonterminal) ❍ may be handled, or not, by left-factorization ❍ verified by First and Follow sets 2 Left Recursion ❍ Top-down parsers cannot handle left-recursion ● any direct left-recursion can be removed with equivalent grammar ● indirect left-recursions can be replaced by direct, which subsequently can be removed ❍ Removing direct left recursion: ● separate all left recursive from the other productions for each nonterminal ● A → Aα | Aβ | .. -
Top-Down Parsing
CS 4120 Introduction to Compilers Andrew Myers Cornell University Lecture 5: Top-down parsing 5 Feb 2016 Outline • More on writing CFGs • Top-down parsing • LL(1) grammars • Transforming a grammar into LL form • Recursive-descent parsing - parsing made simple CS 4120 Introduction to Compilers 2 Where we are Source code (character stream) Lexical analysis Token stream if ( b == 0 ) a = b ; Syntactic Analysis if Parsing/build AST == = ; Abstract syntax tree (AST) b 0 a b Semantic Analysis CS 4120 Introduction to Compilers 3 Review of CFGs • Context-free grammars can describe programming-language syntax • Power of CFG needed to handle common PL constructs (e.g., parens) • String is in language of a grammar if derivation from start symbol to string • Ambiguous grammars a problem CS 4120 Introduction to Compilers 4 Top-down Parsing • Grammars for top-down parsing • Implementing a top-down parser (recursive descent parser) • Generating an abstract syntax tree CS 4120 Introduction to Compilers 5 Parsing Top-down S → E + S | E E → num | ( S ) Goal: construct a leftmost derivation of string while reading in token stream Partly-derived String Lookahead parsed part unparsed part S ( (1+2+(3+4))+5 → E+S ( (1+2+(3+4))+5 → (S) +S 1 (1+2+(3+4))+5 → (E+S)+S 1 (1+2+(3+4))+5 → (1+S)+S 2 (1+2+(3+4))+5 → (1+E+S)+S 2 (1+2+(3+4))+5 → (1+2+S)+S 2 (1+2+(3+4))+5 → (1+2+E)+S ( (1+2+(3+4))+5 → (1+2+(S))+S 3 (1+2+(3+4))+5 → (1+2+(E+S))+S 3 (1+2+(3+4))+5 6 Problem S → E + S | E E → num | ( S ) • Want to decide which production to apply based on next symbol (1) S -
Part 1: Introduction
Part 1: Introduction By: Morteza Zakeri PhD Student Iran University of Science and Technology Winter 2020 Agenda • What is ANTLR? • History • Motivation • What is New in ANTLR v4? • ANTLR Components: How it Works? • Getting Started with ANTLR v4 February 2020 Introduction to ANTLR – Morteza Zakeri 2 What is ANTLR? • ANTLR (pronounced Antler), or Another Tool For Language Recognition, is a parser generator that uses LL(*) for parsing. • ANTLR takes as input a grammar that specifies a language and generates as output source code for a recognizer for that language. • Supported generating code in Java, C#, JavaScript, Python2 and Python3. • ANTLR is recursive descent parser Generator! (See Appendix) February 2020 Introduction to ANTLR – Morteza Zakeri 3 Runtime Libraries and Code Generation Targets • There is no language specific code generators • There is only one tool, written in Java, which is able to generate Lexer and Parser code for all targets, through command line options. • The available targets are the following (2020): • Java, C#, C++, Swift, Python (2 and 3), Go, PHP, and JavaScript. • Read more: • https://github.com/antlr/antlr4/blob/master/doc/targets.md 11 February 2020 Introduction to ANTLR – Morteza Zakeri Runtime Libraries and Code Generation Targets • $ java -jar antlr4-4.8.jar -Dlanguage=CSharp MyGrammar.g4 • https://github.com/antlr/antlr4/tree/master/runtime/CSharp • https://github.com/tunnelvisionlabs/antlr4cs • $ java -jar antlr4-4.8.jar -Dlanguage=Cpp MyGrammar.g4 • https://github.com/antlr/antlr4/blob/master/doc/cpp-target.md • $ java -jar antlr4-4.8.jar -Dlanguage=Python3 MyGrammar.g4 • https://github.com/antlr/antlr4/blob/master/doc/python- target.md 11 February 2020 Introduction to ANTLR – Morteza Zakeri History • Initial release: • February 1992; 24 years ago.