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While compilers for high-level programming languages are large complex software systems, they have particular characteristics that differentiate them from other software systems.​ Their functionality is almost completely well-defined – ideally there exist complete precise.
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The top-down parser will then refine ifs prediction by selecting one of the alternatives of this nonteminal.

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The top- down parser will then compare this with the next input symbol. If they agree, another symbol of the prediction is confirmed. They attempt to discover the syntactic structure of longer and longer prefixes of the input program. They attempt to replace occurrences of right sides of productions by their left-side nonterminals. Such a replacement is called a reduction. Since these are the only two actions, a bottom-up parser is also called shift-reduce parser. The analysis terminates successfully when the parser has reduced the input program by a sequence of shift and reduce steps to the start symbol of the grammar.

The Treatment of Syntax Errors Most programs that are submitted to a compiler are erroneous. Many contain syntax errors.

The compiler should, therefore, treat the normal case, namely the erroneous program, adequately. Lexical errors are rather local. Syntax errors, for instance in the parenthesis structure of a program, are often more difficult to diagnose. This chapter covers required and possible reactions to syntax errors by the parser.

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There are essentially four nonexclusive reactions to syntax errors that are desirable: 1. The error is localized and reported; 2. The error is diagnozed; 3. The error is corrected; 4. The parser gets back into a state in which it can possibly detect further errors. Later stages of the compiler assume that they receive syntactically correct programs in the form of syntax trees. And given that there are en'ors in the program, the programmer better be informed about them.

Second, since the parser only gets suspicious when it gets stuck, the parser will, in general, only detect error symptoms, not errors themselves. Example 3. Each of the three corrections leads to a program with different meaning. We have explained above that, in general, the parser only discovers error symptoms, not errors themselves. Still, we will speak of errors in the following. In this sense, the discussed parsers perform the first two listed actions: they report and try to diagnose errors.

The parser can only attempt a diagnosis of the error symptom. For the third listed action, the correction of an error, the parser would need to guess the intention of the programmer. This is, in general, difficult. Slightly more realistic is to search for an error correction that is globally optimal.

The parser is given the capability to insert or delete symbols in the input word. The globally optimal error correction for an erroneous input word lu is a word w' that is obtained from w by a minimal number of such insertions and deletions. Such methods have been proposed in the literature, but have not been used in practice due to the tremendous effort that is required.

Instead, most parsers perform only local corrections to have the parser move from the error configuration to a new configuration in which it can at least read the 46 3 Syntactic Analysis next input symbol. This prevents the parser from going into an endless loop while trying to repair an error. The Structure of this Chapter Section 3. A special nonde termini Stic pushdown automaton for a context-free grammar is introduced that recognizes the language defined by the grammar.

Deterministic top-down and bottom-up parser for the grammar are derived from this pushdown automaton. Sections 3. The corresponding grammar classes are characterized and methods for generating corresponding parsers are presented. Techniques for error handling are described in detail for both top-down and bottom-up parsers. In Sects. Readers familiar with these notions can skip them and go directly to Sect. In Sect. As for regular expressions, the metacharacter is used to combine several alternatives, here for possible right sides for one nonterminal. These statements always start with the keyword if, followed by an expression in parentheses, and a statement.

This statement may be followed by the keyword else and another statement. Further productions describe how while- and do-while-statements and expressions are constructed. For expressions, only a few alternatives are explicitly given. Examples for such symbols are reserved keywords of the language, or symbol classes such as identifiers which comprise a set of symbols. The nonterminals of the grammar denote sets of words that can be produced from them by means of the production rules of the grammar.

A bottom-up parser, on the other hand, interprets the production A, a as a replacement of the right side a by the left side A. Capital latin letters from the beginning of the alphabet, e. Small latin letters from the beginning of the alphabet, e. The relation P is seen as a set of production rules.

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The relation de- G G notes the reflexive and transitive closure of. The syntactic structure of a program, as it results from syntactic analysis, is the syntax tree or parse tree we will use these two notions synonymously. The parse tree provides a canonical representation of derivations. Within a compiler, the parse tree serves as the interface to the subsequent compiler phases. Most approaches to the evaluation of semantic attributes, as they are described in Chap.

A parse or syntax tree t is an ordered tree where the inner nodes and leaf 50 3 Syntactic Analysis Fig. Moreover, the label B of each inner node n of t together with the sequence of labels Xi, If the root of t is labeled with nonterminal symbol A, and if the concatenation of the leaf labels yields the terminal word w we call t a parse tree for nonterminal A and word w according to grammar G.

If the root is labeled with S, the start symbol of the grammar, we just call t a parse tree for w. A word of the language is called ambiguous if there exists more than one parse tree for it. Correspondingly, the grammar G is called ambiguous if L G contains at least one ambiguous word. The grammar Go, on the other hand, is unambiguous. To each derivation for a word x corresponds a parse tree for x.

On the other hand, to each parse tree for a word X corresponds at least one derivation for x. Any such derivation can be easily read off the parse tree. Two different derivations result depending on the order in which the 3. This results from the different possibilities to choose a nonterminal in a sentential form for the next application of a production. The corresponding uniquely determined derivations are called leftmost and rightmost derivations, respectively. A sentential form that occurs in a leftmost derivation rightmost derivation is called left sentential form right sentential form.

To each parse tree for S there exists exactly one leftmost derivation and exactly one rightmost derivation. Thus, there is exactly one leftmost and one rightmost derivation for each unambiguous word in a language.

The questions is, can one find sentential forms in both derivations that correspond to each other in the following way: in both derivations will, in the next step, the same occurrence of a nonterminal be replaced? The following lemma establishes such a relation. Lemma 3. If this is the case, then there exist exactly one parse tree, one leftmost and one rightmost derivation for each syntactically correct program.

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Eliminating them reduces the size of the grammar, but does not change the language. All nonterminals not having these properties, together with all productions using such nonterminals can be removed. The resulting grammars are called then reduced.


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The first required property of useful nonterminals is productivity. The nonterminal Z, on the other hand, is not productive since the only production for Z contains an occurrence of Z on its right side. Property 1 describes the dependence of the information for Z on the information about symbols on the right side of the production for Z; property 2 indicates how to combine the information obtained from the different alternatives for Z.

When the counter of a production p is decreased to 0 all nonterminals on the right side must be productive. Therefore, also the left side of p is productive through p. To maintain the productions whose counter has been decreased to 0 the algorithm uses a worklist W. Further, for each nonterminal X a list occ[A"] is maintained which consists of all productions where X occurs in the right sides. This concludes the initialization.

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The main iteration processes the productions in W one by one. The counter count[r] is decremented for each production r in this list. The initialization phase essentially runs once over the grammar and does a constant amount of work for each symbol.