Left factoring serves as a method in compiler design that involves eliminating common prefixes from production rules within a context-free language. This practice enhances the comprehensibility of the grammar and boosts parsing efficiency.
Grammar in the format below is considered to have been left factored -
S ⇒aX | aY | aZ
A serves as a terminal symbol, whereas S, X, Y, and Z are non-terminal symbols. Thus, a left-factored grammar is characterized by multiple productions that possess a common prefix or commence with the same symbol. In this specific instance, the three distinct productions - S aX, S aY, and S aZ, exhibit a common non-terminal symbol on the left side and share the identical prefix 'a'. Consequently, the provided grammar is considered to be left-factored.
Left-factored grammar issues
Understanding and translating programming code becomes challenging with the presence of left factoring. This technique complicates the translation process by introducing phrases that initiate similarly but diverge in direction.
When applying left-factoring in grammar, top-down parsers face ambiguity due to multiple productions sharing a common prefix. This shared prefix makes it challenging for the parser to determine which production to use in deriving the specified string, leading to ambiguity in the top-down parsing process.
To address this issue, it is necessary to convert the left-factored language into a corresponding grammar where no productions have common prefixes. Left factoring is a technique employed in compiler design to achieve this goal.
Compiler Design using Left Factoring
Left factoring is employed to convert a left-factored language into a grammar that is equivalent, aiming to remove ambiguity for the top-down parser. This process involves isolating shared prefixes from the production rules during left factoring.
Apply the algorithm below to execute left factoring in the given grammar:
Let's say the grammar is in the following format:
A ⇒ αβ1 | αβ2 | αβ3 | …… | αβn | γ
The common prefix can be found when A is a non-terminal.
After splitting those expressions with a shared beginning, we will introduce a fresh rule where the recently included non-terminal will derive the expressions that were formerly divided by a shared beginning.
A ⇒ αA'
A' ⇒ β1 | β2 | β3 | …… | βn
This programming language can be easily parsed using a top-down parser to generate a specified string. Therefore, left factoring is performed on the provided grammar in compiler design in this way.
Advantages of using left factoring in compiler design
There are several advantages of using left factoring in compiler design. Some advantages of left factoring are as follows:
- Error detection: Left factoring makes it simpler to discover errors since it makes it easier to pinpoint the prefix in the input string that was the source of the parsing problem.
- Grammar Consistency: Because left factoring adheres to predetermined norms, it helps ensure grammar consistency. It guarantees that the grammar is predictable and specified.
- The complexity of rules is reduced: As we factor out the common prefix, the complexity of complex and larger rules with common prefixes is reduced. As a result, the rules are easier to understand, and the grammar is more understandable.
Challenges of the Left Factor in Compiler Design:
When doing left factoring in the grammar, there are numerous difficulties. The following are some difficulties:
- Ambiguity is introduced: Left factoring in grammar often introduces ambiguity since it introduces additional rules that allow the parser to parse a string in different ways.
- Lower Parsing Efficiency: Numerous additional production rules are established by factoring away the common prefix in left factoring. Additionally, we add new non-terminals . It becomes increasingly sophisticated as a result of the grammar's size expansion.
- Common prefix identification: If the grammar is already very big, finding common prefixes might occasionally be challenging.
Left factoring implementation
The use of left factoring using a practical case.
A ⇒aB | aC | aD is the production rule stated.
B ⇒ b
C ⇒ c
D ⇒ d
When contrasting with a, b, c, and d, which serve as terminals, A, B, C, and D are classified as non-terminals.
Productions sharing a common prefix will be segmented. For instance, these productions include A aB, A aC, and A aC. The shared prefix is utilized to produce a fresh non-terminal denoted as A'.
A is equal to aA', where A' represents the newly generated non-terminal.
The recent non-terminal we added will generate those productions sharing a common prefix in accordance with a newly introduced production rule.
A` ⇒ B | C | D
The final grammar would be as follows:
A ⇒aA`
A` ⇒ B | C | D
B ⇒ b
C ⇒ c
D ⇒ d
This language is simple to parse by the top-down parser to produce a given string. Thus, left factoring on a given grammar is carried out in compiler design in this manner.
- Tokenization: The input string is tokenized to create a series of tokens. Tokens represent the parsing language's smallest meaningful units. Utilizing scanf routines or a more complex lexer, you can tokenize the input in your C program.
- Parser Functions: Create a new parser function to handle each type of non-terminal in your language. These operations might be equivalent to the non-terminals in the context of left factoring once the common prefixes have been eliminated.
- Recursive Descent Parsing: Use a recursive descent parsing strategy in which each non-terminal function relates to a production in the grammar. The precise restrictions for that non-terminal should be handled within these routines.
- Matching and Error Handling: Use matching and error-handling routines to match the anticipated tokens by the grammar rules. Proceed if a token matches the anticipated one; if not, issue an error.
Example:
Let's consider a program to grasp the application of left factoring in the C programming language.
#include<stdio.h>
#include<string.h>
int main()
{
char gram[20],part_1[20],part_2[20],modified_Gram[20],new_Gram[20],temp_Gram[20];
int i,j=0,k=0,l=0,pos;
printf("Enter the Production : A->");
gets(gram);
for(i=0;gram[i]!='|';i++,j++)
part_1[j]=gram[i];
part_1[j]='\0';
for(j=++i,i=0;gram[j]!='\0';j++,i++)
part_2[i]=gram[j];
part_2[i]='\0';
for(i=0;i<strlen(part_1)||i<strlen(part_2);i++){
if(part_1[i]==part_2[i]){
modified_Gram[k]=part_1[i];
k++;
pos=i+1;
}
}
for(i=pos,j=0;part_1[i]!='\0';i++,j++){
new_Gram[j]=part_1[i];
}
new_Gram[j++]='|';
for(i=pos;part_2[i]!='\0';i++,j++){
new_Gram[j]=part_2[i];
}
modified_Gram[k]='X';
modified_Gram[++k]='\0';
new_Gram[j]='\0';
printf("\nGrammar Without Left Factoring is: \n");
printf(" A->%s",modified_Gram);
printf("\n X->%s\n",new_Gram);
}
Output:
Enter the Production: A->bE+acF|bE+f
Grammar Without Left Factoring is:
A->bE+X
X->acF|f
Explanation:
- In this example, first, we are taking a few variables to use them later. Along the road, you will acquire them. When it happens, we are just taking the output.
- In this case, we are dividing the output and storing it in a different variable. As well as finishing off each string with null letters . The string will carry some junk values if a null character is not added at the end of it, producing an error output.
- We are using a for loop and an if statement to store the common prefix in the modified_Gram variable . Additionally, we take the common prefix's most recent place and advance the character by one.
- We are taking the rest of the production in the position we take, utilizing that and the for loop .
Productions within a left-factored grammar typically share a common prefix, such as in the grammar pattern S aX | aY | aZ. On the other hand, a left recursive grammar involves a production rule where a non-terminal symbol generates itself as the initial symbol on the right-hand side. This rule is structured as S Sa | Ab | cb, with S representing the non-terminal symbol.
Comparison with alternative parsing methods
- LL Parsing algorithm: LL is one of the top-down parsing algorithms used in this process. As it parses a string, this method keeps a stack, a parser , and a parsing table for the grammar that is provided. It assesses whether the given grammar/parsing table can create the required string. Errors occur if it is impossible to manufacture. LL parsing algorithms can run more quickly thanks to left factoring in compiler architecture.
- CYK algorithm: "CYK algorithm", an elementary context-free grammar (CFG) parsing algorithm is CYK (Chomsky Normal Form) . This algorithm determines the ability to parse a string using a specified syntax. The size of the parsing table is decreased via left factoring , which boosts the effectiveness of the parsing process.
- LR Parsing algorithm: A bottom-up parsing method for context-free language is LR Parsing . The right-most derivation is created after the input string has been parsed from left to right. As it is constructed from the leaves, it reduces top-level grammar production . Left factoring reduces the number of states in the LR parsing table to maximize effectiveness.