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    Compiler Design

    Compiler Design - Bottom-Up Parser, Bottom-up parsing starts from the leaf nodes of a tree and works in upward direction till it reaches the root node. Here, we start from a sentence and then appl

    Compiler Design - Bottom-Up Parser

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    Bottom-up parsing starts from the leaf nodes of a tree and works in upward direction till it reaches the root node. Here, we start from a sentence and then apply production rules in reverse manner in order to reach the start symbol. The image given below depicts the bottom-up parsers available.

    Shift-Reduce Parsing

    Shift-reduce parsing uses two unique steps for bottom-up parsing. These steps are known as shift-step and reduce-step.

    Shift step: The shift step refers to the advancement of the input pointer to the next input symbol, which is called the shifted symbol. This symbol is pushed onto the stack. The shifted symbol is treated as a single node of the parse tree.Reduce step : When the parser finds a complete grammar rule (RHS) and replaces it to (LHS), it is known as reduce-step. This occurs when the top of the stack contains a handle. To reduce, a POP function is performed on the stack which pops off the handle and replaces it with LHS non-terminal symbol.

    LR Parser

    The LR parser is a non-recursive, shift-reduce, bottom-up parser. It uses a wide class of context-free grammar which makes it the most efficient syntax analysis technique. LR parsers are also known as LR(k) parsers, where L stands for left-to-right scanning of the input stream; R stands for the construction of right-most derivation in reverse, and k denotes the number of lookahead symbols to make decisions.

    There are three widely used algorithms available for constructing an LR parser:

    SLR(1) – Simple LR Parser:

    Works on smallest class of grammar

    Few number of states, hence very small table

    Simple and fast construction

    LR(1) – LR Parser:

    Works on complete set of LR(1) Grammar

    Generates large table and large number of states

    Slow construction

    LALR(1) – Look-Ahead LR Parser:

    Works on intermediate size of grammar

    Number of states are same as in SLR(1)

    LR Parsing Algorithm

    Here we describe a skeleton algorithm of an LR parser:

    token = next_token()

    repeat forever s = top of stack

    if action[s, token] = “shift si” then

    PUSH token PUSH si

    token = next_token()

    else if action[s, token] = “reduce A::= β“ then

    POP 2 * |β| symbols s = top of stack PUSH A PUSH goto[s,A]

    else if action[s, token] = “accept” then

    return else error()

    LL vs. LR

    LL LR

    Does a leftmost derivation. Does a rightmost derivation in reverse.

    Starts with the root nonterminal on the stack. Ends with the root nonterminal on the stack.

    Ends when the stack is empty. Starts with an empty stack.

    Uses the stack for designating what is still to be expected. Uses the stack for designating what is already seen.

    Builds the parse tree top-down. Builds the parse tree bottom-up.

    Continuously pops a nonterminal off the stack, and pushes the corresponding right hand side. Tries to recognize a right hand side on the stack, pops it, and pushes the corresponding nonterminal.

    Expands the non-terminals. Reduces the non-terminals.

    Reads the terminals when it pops one off the stack. Reads the terminals while it pushes them on the stack.

    Pre-order traversal of the parse tree. Post-order traversal of the parse tree.

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    स्रोत : www.tutorialspoint.com

    LR parser

    LR parser

    From Wikipedia, the free encyclopedia

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    In computer science, LR parsers are a type of bottom-up parser that analyse deterministic context-free languages in linear time.[1] There are several variants of LR parsers: SLR parsers, LALR parsers, Canonical LR(1) parsers, Minimal LR(1) parsers, and GLR parsers. LR parsers can be generated by a parser generator from a formal grammar defining the syntax of the language to be parsed. They are widely used for the processing of computer languages.

    An LR parser (Left-to-right, Rightmost derivation in reverse) reads input text from left to right without backing up (this is true for most parsers), and produces a rightmost derivation in reverse: it does a bottom-up parse – not a top-down LL parse or ad-hoc parse. The name LR is often followed by a numeric qualifier, as in LR(1) or sometimes LR(). To avoid backtracking or guessing, the LR parser is allowed to peek ahead at lookahead input symbols before deciding how to parse earlier symbols. Typically is 1 and is not mentioned. The name LR is often preceded by other qualifiers, as in SLR and LALR. The LR() notation for a grammar was suggested by Knuth to stand for "translatable from left to right with bound ."[1]

    LR parsers are deterministic; they produce a single correct parse without guesswork or backtracking, in linear time. This is ideal for computer languages, but LR parsers are not suited for human languages which need more flexible but inevitably slower methods. Some methods which can parse arbitrary context-free languages (e.g., Cocke–Younger–Kasami, Earley, GLR) have worst-case performance of O(n3) time. Other methods which backtrack or yield multiple parses may even take exponential time when they guess badly.[2]

    The above properties of L, R, and are actually shared by all shift-reduce parsers, including precedence parsers. But by convention, the LR name stands for the form of parsing invented by Donald Knuth, and excludes the earlier, less powerful precedence methods (for example Operator-precedence parser).[1] LR parsers can handle a larger range of languages and grammars than precedence parsers or top-down LL parsing.[3] This is because the LR parser waits until it has seen an entire instance of some grammar pattern before committing to what it has found. An LL parser has to decide or guess what it is seeing much sooner, when it has only seen the leftmost input symbol of that pattern.

    Contents

    1 Overview

    1.1 Bottom-up parse tree for example A*2 + 1

    1.2 Shift and reduce actions

    1.3 Bottom-up parse stack

    1.4 Bottom-up parse steps for example A*2 + 1

    1.5 LR parse steps for example A*2 + 1

    1.6 Grammar for the example A*2 + 1

    1.7 Parse table for the example grammar

    1.8 LR parser loop

    2 LR generator analysis

    2.1 LR states

    2.2 Finite state machine

    2.3 Lookahead sets

    2.4 Syntax error recovery

    2.5 Variants of LR parsers

    2.6 Theory

    3 Additional example 1+1

    3.1 Action and goto tables

    3.2 Parsing steps 3.3 Walkthrough

    4 Constructing LR(0) parsing tables

    4.1 Items 4.2 Item sets

    4.3 Extension of Item Set by expansion of non-terminals

    4.4 Closure of item sets

    4.5 Augmented grammar

    5 Table construction

    5.1 Finding the reachable item sets and the transitions between them

    5.2 Constructing the action and goto tables

    5.2.1 A note about LR(0) versus SLR and LALR parsing

    5.3 Conflicts in the constructed tables

    6 See also 7 References 8 Further reading 9 External links

    Overview[edit]

    Bottom-up parse tree for example A*2 + 1 [edit]

    Bottom-up parse tree built in numbered steps

    An LR parser scans and parses the input text in one forward pass over the text. The parser builds up the parse tree incrementally, bottom up, and left to right, without guessing or backtracking. At every point in this pass, the parser has accumulated a list of subtrees or phrases of the input text that have been already parsed. Those subtrees are not yet joined together because the parser has not yet reached the right end of the syntax pattern that will combine them.

    At step 6 in an example parse, only "A*2" has been parsed, incompletely. Only the shaded lower-left corner of the parse tree exists. None of the parse tree nodes numbered 7 and above exist yet. Nodes 3, 4, and 6 are the roots of isolated subtrees for variable A, operator *, and number 2, respectively. These three root nodes are temporarily held in a parse stack. The remaining unparsed portion of the input stream is "+ 1".

    Shift and reduce actions[edit]

    As with other shift-reduce parsers, an LR parser works by doing some combination of Shift steps and Reduce steps.

    A Shift step advances in the input stream by one symbol. That shifted symbol becomes a new single-node parse tree.

    A Reduce step applies a completed grammar rule to some of the recent parse trees, joining them together as one tree with a new root symbol.

    If the input has no syntax errors, the parser continues with these steps until all of the input has been consumed and all of the parse trees have been reduced to a single tree representing an entire legal input.

    स्रोत : en.wikipedia.org

    LR Parsers

    LR parsers are used to parse the large class of context free grammars. This technique is called LR(k) parsing.

    Home » Compiler » LR Parsers – Compiler Design

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    LR Parsers – Compiler Design

    By Dinesh Thakur

    LR parsers are used to parse the large class of context free grammars. This technique is called LR(k) parsing.

    • L is left-to-right scanning of the input.

    • R is for constructing a right most derivation in reverse.

    is the number of input symbols of lookahead that are used in making parsing decisions.

    There are three widely used algorithms available for constructing an LR parser:

    • SLR(l) – Simple LR

    o Works on smallest class of grammar.

    o Few number of states, hence very small table.

    o Simple and fast construction.

    • LR( 1) – LR parser

    o Also called as Canonical LR parser.

    o Works on complete set of LR(l) Grammar.

    o Generates large table and large number of states.

    o Slow construction.

    • LALR(l) – Look ahead LR parser

    o Works on intermediate size of grammar.

    o Number of states are same as in SLR(l).

    Reasons for attractiveness of LR parser

    • LR parsers can handle a large class of context-free grammars.

    • The LR parsing method is a most general non-back tracking shift-reduce parsing method.

    • An LR parser can detect the syntax errors as soon as they can occur.

    • LR grammars can describe more languages than LL grammars.

    Drawbacks of LR parsers

    • It is too much work to construct LR parser by hand. It needs an automated parser generator.

    • If the grammar contains ambiguities or other constructs then it is difficult to parse in a left-to-right scan of the input.

    We’ll be covering the following topics in this tutorial:

    Model of LR Parser

    LR parser consists of an input, an output, a stack, a driver program and a parsing table that has two functions

    1. Action 2. Goto

    The driver program is same for all LR parsers. Only the parsing table changes from one parser to another.

    The parsing program reads character from an input buffer one at a time, where a shift reduces parser would shift a symbol; an LR parser shifts a state. Each state summarizes the information contained in the stack.

    The stack holds a sequence of states, s1, · ·· , where is on the top.

    Action This function takes as arguments a state and a terminal (or $, the input end marker). The value of ACTION [i, can have one of the four forms:

    i) Shift where is a state.

    ii) Reduce by a grammar production A—>

    iii) Accept. iv) Error.

    Goto This function takes a state and grammar symbol as arguments and produces a state.

    If GOTO [Ii ,A] = Ij, the GOTO also maps a state and non terminal A to state

    Behavior of the LR parser

    1. If ACTION[sm, = shift The parser executes the shift move, it shifts the next state onto the stack, entering the configuration

    a) the state on top of the stack.

    b) the current input symbol.

    2. If ACTION[sm, =reduce A—> βthen the parser executes a reduce move, entering the configuration

    ai+l …

    a) where is the length of and s= A].

    b) First popped state symbols off the stack, exposing state

    c) Then pushed the entry for A], onto the stack.

    3. If ACTION[sm, = accept, parsing is completed.

    4. If ACTION[sm, = error, the parser has discovered an error and calls an error recovery routine.

    LR Parsing Algorithm

    Algorithm LR Parsing Algorithm.Input   Input string w,

    LR-Parsing table with functions ACTION and

    GOTO for a grammar G

    Output If w is in L(G), the reduction steps of a

    bottom-up parse for w,

    otherwise, an error indication.

    Method Initially, the parser has So on its stack,

    where So is the initial state, and w $ in the

    input buffer.

    let a be the first symbol of w $

    while(l) { //repeat forever

    let s be the state on top of the stack;

    if(ACTION[s, a] =shift t {

    push t onto the stack;

    let a be the next input symbol;

    } else if (ACTION [s, a] = reduce A—> ) {

    pop symbols off the stack;

    let state t now be on top of the stack;

    push GOTO[t, A] onto the stack;

    output the production A—>

    } else if (ACTION [s, a] accept) break;

    //parsing is done

    else call error-recovery routine;

    }

    LR(O) Items

    An LR(O) item of a grammar G is a production of G with a dot at some position of the body.

    (eg.) A —> •XYZ A —> XeYZ A —> XYeZ A —> XYZ•

    One collection of set of LR(O) items, called the canonical LR(O) collection, provides finite automaton that is used to make parsing decisions. Such an automaton is called an LR(O) automaton.

    LR(O) Parser SLR(1) Parser

    An LR(O)parser is a shift-reduce parser that uses zero tokens of lookahead to determine what action to take (hence the 0). This means that in any configuration of the parser, the parser must have an unambiguous action to choose-either it shifts a specific symbol or applies a specific reduction. If there are ever two or more choices to make, the parser fails and the grammar is not LR(O).

    स्रोत : ecomputernotes.com

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