Compilation Principles Chapter 3 part3 (Context-free grammar and its syntax tree, ambiguity, bottom-up, top-down, harmful rules and redundant rules)

Context-free grammar and its grammar tree, sentence structure analysis, harmful rules and redundant rules

(1) Context-free grammar

1. Examples:

(2) Normative derivation and normative sentence patterns

1. Definition:

If in any part of the derivation α⇒β, where α and β are sentence patterns, they replace the leftmost (rightmost) nonterminal symbol in α, then this derivation is called the leftmost (rightmost) derivation

2. Note:

①The rightmost derivation is called the normative derivation
②The sentence pattern derived from the norm is called the normative sentence pattern

3. Example: (must write again)

From the example in the figure above:
①The leftmost derivation is to replace the leftmost nonterminal derivation on the right of the production .
②The rightmost derivation is to replace the rightmost nonterminal derivation on the right of the production .

(3) Syntax tree

1. Function:

Intuitively describe the derivation process of context-free grammar.

2. Examples:

3. Definition: (should be useless, just look at it)

(4) Ambiguity of grammar

1. Definition:

       If a sentence in a grammar corresponds to two different grammar trees , then the grammar is said to be ambiguous . Ambiguous grammar exists in a sentence, and it has two different left-most (right) derivations.
       For a programming language, it is hoped that its grammar is unambiguous, because it is hoped that the analysis of each sentence in it is unique.

2. Example:

3. Example 2 (Ambiguous grammar becomes unambiguous grammar)

4. Note:

If the same grammar, the derivation process is different, but the result is two identical grammar trees, it is also unambiguous

(the derivation process is different, but the results are equivalent)

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(5) Analysis of sentence patterns (generalization)

1. Definition:

The process of identifying whether the input symbol string is a grammatically correct program. (Judging whether it conforms to the grammar)

2. Classification: (just take a look)

(6) Top-down analysis method

1. Definition:

       Starting from the beginning symbol of the grammar, we repeatedly use the production of the grammar to find the derivation that matches the symbol string.
       The syntax tree structure: the grammar start symbol number as a syntax tree roots , and gradually establish a syntax tree down, so that the end symbol string syntax tree node is exactly the input symbol string.

2. Example: (feeling to take the test)

3. The main problem of the top-down approach: (is a choice production)

(7) Bottom-up analysis method

1. Definition:

       Starting from the input symbol string, the reduction is carried out step by step , until the reduction to the beginning symbol of the grammar .
       Syntax tree construction: start from the input symbol string and use it as the end node symbol string of the syntax tree to construct the syntax tree from the bottom up

2. Examples:

3. The main problem of bottom-up analysis: (Is to determine the "reducible string")

(8) Harmful rules and redundant rules

1. Definition of harmful rules: U->U, useless, and cause grammatical ambiguity

2. Redundant rule definition: rules that are not used in all sentence derivation

Manifestations:

        Unreachable: non-terminal symbols that do not appear on the right side of any production

        Non-terminal: the non-terminal symbol of the terminal string cannot be deduced

3. Example: (important)

Among them (2) is also non-terminating

4. ε Rule

Definition: A->ε production is allowed in context-free grammar, and A->ε is called the ε rule