Outline. Parser overview Contextfree grammars (CFG s) Derivations SyntaxDirected Translation


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1 Outline Introduction to Parsing (adapted from CS 164 at Berkeley) Parser overview Contextfree grammars (CFG s) Derivations SyntaxDirected ranslation he Functionality of the Parser Input: sequence of tokens from lexer Output: abstract syntax tree of the program Onepass compiler: directly generate assembly code his is what you will do in the first assignment Bali SaM code xample Pyth: if x == y: z =1 else: z = 2 Parser input: IF ID == ID : ID = IN LS : ID = IN Parser output (abstract syntax tree): IFHNLS == = = ID ID ID IN ID IN 1
2 Why A ree? ach stage of the compiler has two purposes: Detect and filter out some class of errors Compute some new information or translate the representation of the program to make things easier for later stages Recursive structure of tree suits recursive structure of language definition With tree, later stages can easily find the else clause, e.g., rather than having to scan through tokens to find it. Notation for Programming Languages Grammars: ( ) We can view these rules as rewrite rules We start with and replace occurrences of with some righthand side ( ) ( ) ( ) ContextFree Grammars A CFG consists of A set of nonterminals N By convention, written with capital letter in these notes A set of terminals By convention, either lower case names or punctuation A start symbol S (a nonterminal) A set of productions Assuming N, or Y 1 Y 2... Y n where Y i N xamples of CFGs Simple arithmetic expressions: ( ) One nonterminal: Several terminals:,,, (, ) Called terminals because they are never replaced By convention the nonterminal for the first production is the start one 2
3 Key Idea 1. Begin with a string consisting of the start symbol 2. Replace any nonterminal X in the string by a righthand side of some production X Y 1 Y n 3. Repeat (2) until there are only terminals in the string 4. he successive strings created in this way are called sentential forms. he Language of a CFG (Cont.) Write X 1 X n Y 1 Y m if X 1 X n Y 1 Y m in 0 or more steps he Language of a CFG Let G be a contextfree grammar with start symbol S. hen the language of G is: L(G) = { a 1 a n S a 1 a n and every a i is a terminal } xamples: S 0 also written as S 0 1 S 1 Generates the language { 0, 1 } What about S 1 A A 0 1 What about S 1 A A 0 1 A What about S ( S ) 3
4 Derivations and Parse rees A derivation is a sequence of sentential forms resulting from the application of a sequence of productions S Parse tree: summary of derivation w/o specifying completely the order in which rules were applied Start symbol is the tree s root For a production X Y 1 Y n add children Y 1,, Y n to node X Derivation xample Grammar () String Derivation in Detail (1) Derivation in Detail (2) 4
5 Derivation in Detail (3) Derivation in Detail (4) Derivation in Detail (5) Derivation in Detail (6) 5
6 Notes on Derivations A parse tree has erminals at the leaves Nonterminals at the erior nodes A leftright traversal of the leaves is the original input he parse tree shows the association of operations, the input string does not! here may be multiple ways to match the input Derivations (and parse trees) choose one AS vs. Parse ree AS is condensed form of a parse tree operators appear at ernal nodes, not at leaves. "Chains" of single productions are collapsed. Lists are "flattened". Syntactic details are omitted e.g., parentheses, commas, semicolons AS is a better structure for later compiler stages omits details having to do with the source language, only contains information about the essential structure of the program. xample: 2 (4 5) Parse tree vs. AS Summary of Derivations F (2) ( F (4) F ) F (5) We are not just erested in whether s L(G) Also need derivation (or parse tree) and AS. Parse trees slavishly reflect the grammar. Abstract syntax trees abstract from the grammar, cutting out detail that erferes with later stages. A derivation defines a parse tree But one parse tree may have many derivations Derivations drive translation (to ASs, etc.) Leftmost and rightmost derivations most important in parser implementation 6
7 Ambiguity Grammar ( ) Ambiguity. xample he string has two parse trees Strings is leftassociative Ambiguity. xample he string has two parse trees has higher precedence than Ambiguity (Cont.) A grammar is ambiguous if it has more than one parse tree for some string quivalently, there is more than one rightmost or leftmost derivation for some string Ambiguity is bad Leaves meaning of some programs illdefined Ambiguity is common in programming languages Arithmetic expressions IFHNLS 7
8 Dealing with Ambiguity here are several ways to handle ambiguity Ambiguity. xample he has only one parse tree now Most direct method is to rewrite the grammar unambiguously ( ) nforces precedence of over nforces leftassociativity of and Ambiguity Associativity Declarations Impossible to convert automatically an ambiguous grammar to an unambiguous one Used with care, ambiguity can simplify the grammar Sometimes allows more natural definitions But we need disambiguation mechanisms Instead of rewriting the grammar Use the more natural (ambiguous) grammar Along with disambiguating declarations Most tools allow precedence and associativity declarations to disambiguate grammars xamples Consider the grammar Ambiguous: two parse trees of Leftassociativity declaration: %left 8
9 Summary Grammar is specified using a contextfree language (CFL) Derivation: starting from start symbol, use grammar rules as rewrite rules to derive input string Leftmost and rightmost derivations Parse trees and abstract syntax trees Ambiguous grammars Ambiguity should be eliminated by modifying grammar, by specifying precedence rules etc. depending on how ambiguity arises in the grammar Remaining question: how do we find the derivation for a given input string? 9
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