Grammatical improvements (elimination of left recursion)

In the last grammar there is a case of left recursion, which will affect the future use of the syntax analysis, so the need to eliminate left recursion, so that the use of grammatical analysis.

< programs >→< external declarations > < programs > '

< programs > ' →< programs > | Ε

< external declarations >→< function Definitions > | < definition >

< function definition >→< function declaration > < function body >

< function declaration >→< function return type > < function header >

< function return type >→< return type > | < return type > < pointer >

< function head >→ (< parameters >) | ( )

< function Body >→{< declaration statement > < executable statement part >}

< return type >→void | int | char | float | Double

< hands >→* | * < hands >

< parameters >→< Identifier types > < identifiers > | < identifier types > < identifiers >, < parameters >

< identifier type >→int | char | Double | float | < marker type > < pointer >

< identifiers (variables) >→< Letters > | _ | < identifiers > < numbers > | < identifiers > < letters >

< identifiers (variables) >→< Letters > | _ | < identifiers (variables) > '

< identifiers (variables) > ' →< numbers > | < letters >

< Letter >→a | B | C |......| x | y | Z

< Digital >→0 | 1|......| 8 | 9

< declaration statements >→< Identifier types > < identifiers >; | < identifier type > < identifier >; < declaration statements >

< executable statement parts >→< Statements > | < executable statement Parts > < statements >

< statements >→< Expression Statements > | < conditional statements > | < looping statements > | < jump statements >

< loop statement >→<while (expression statement) {executable Statement part}> | <for (expression; expression; expression) {executable Statement part}> | do{executable Statement Part}while (expression statement);

< conditional statements >→< IF statements > | <if-else Statement > | <switch Statement >

< if statement >→<if (expression statement) {executable statement part}>

<if-else Statement >→<if (expression statement) {executable statement part} else {executable statement part}>

<switch statement >→<switch (variable) {SWITCH statement block}>

<switch statement block >→< case constant: Executable Statement part > | < default: executable statement part > | < Case constants: Executable statement section > <switch statement block >

< constants >→< numbers > | < go 0 numbers > < constants >

< go 0 Digital >→1 | 2 | 3 |......| 8 | 9

< jump statement >→continue; | break; | return; | return expression; |return

< expression statements >→< Assignment Expressions > | < logical Expressions > | < arithmetic expression e>

< Assignment expressions >→< variables > = < arithmetic expressions >

< logical Expressions >→ (< expressions > | < numbers >) < logical operators > (< expressions > | < numbers >)

E→t|te '

E ' → (+t|-t) e ' |ε

T→f| FT '

T ' → (*f|/F) T ' |ε

F→PF '

F ' → (↑p |ε) F '

P (E) | < Constants > | < identifiers >

< logical operators >→> | < |! = | <= | >= | = = | ? | : | ! | || | &&

Grammatical improvements (elimination of left recursion)