Разработка транслятора с языка PROST на язык С++. Часть 2., страница 5

n₁₅ = n₁₄ u {op_if | op_if → if (<const> < <const>) then end else end Є p, if (<const> < <const>) then end else end Є (n14 u t)}

= {unop, binop, condition, expression, op_input, op_outputs, op_label, op_goto, operators, EX, op_assignment, op_outputn, op_while, ELSE, op_if}

n₁₆ = n₁₅ U {operator → label <identifer> ; Є p, label <identifer> ; Є (n15 U T)}

= {unop, binop, condition, expression, op_input, op_outputs, op_label, op_goto, operators, EX, op_assignment, op_outputn, op_while, ELSE, op_if, operator}

n₁₇ = n₁₆ U {code | code → code end Є p, code end Є (n16 u t)}

= {unop, binop, condition, expression, op_input, op_outputs, op_label, op_goto, operators, EX, op_assignment, op_outputn, op_while, ELSE, op_if, operator, code}

Безполезными являются символы: op_DIM

2.1.3.7 Устранение цепных правил

N₀ = operator

n₁ = {op_assignment | operator → op_assignment Є p, operator Є n0} U n₀

= {operator, op_assignment}

n₂ = {op_while | operator → op_while Є p, operator Є n1} U n₁

   = {operator, op_assignment, op_while}

n₃ ={op_input | operator → op_input Є p, operator Є n2} U n₂

   = {operator, op_assignment, op_while, op_input}

n₄ = {op_outputn | operator → op_outputn Є p, operator Є n3} U n₃

   = {operator, op_assignment, op_while, op_input, op_outputn}

n₅ = {op_outputs | operator → op_outputs Є p, operator Є n4} U n₄

   = {operator, op_assignment, op_while, op_input, op_outputn, op_outputs}

n₆ = {op_GOTO | operator → op_GOTO Є p, operator Є n5} U n₅

   = {operator, op_assignment, op_while, op_input, op_outputn, op_outputs, op_GOTO}

n₇ = {OP_LABEL | operator → OP_LABEL Є p, operator Є n6} U n₆

   = {operator, op_assignment, op_while, op_input, op_outputn, op_outputs, op_GOTO, OP_LABEL}

n8 = {OP_IF | operator → OP_IF Є p, operator Є n7} U n₇

= {operator, op_assignment, op_while, op_input, op_outputn, op_outputs, op_GOTO, OP_LABEL, OP_IF}

n_operator = {operator, op_assignment, op_while, op_input, op_outputn, op_outputs, op_GOTO, OP_LABEL, OP_IF}

N0 = expression

N1 = {ex | expression → ex Є p, expression Є n0} U n0

= {expression, ex}

N_expression = {expression, ex}

P’ = { operator → <identifer> := expression; |

while ( expression condition expression ) do operators |

input <identifer> ;|

outputn expression ; |

outputs <strc> ; |

goto <identifer> ; |

label <identifer> ; |

if ( expression condition expression ) then operators ELSE

expression → <const>|

- expression |

expression binop expression |

<identifer>|

(expression) }

2.1.3.8 Устранение левой рекурсии

P = { expression → <const> |

- expression |

expression binop expression |

<identifer> |

(expression) }

P’ = { EXPRESSION → <const>  EXPRESSION’|

- expression EXPRESSION’ |

<identifer> EXPRESSION’ |

(expression) EXPRESSION’

EXPRESSION’ → binop expression EXPRESSION’ | λ }

2.1.3.9 Грамматика языка в нормальной форме Грейбах

Преобразовав грамматику, таким образом, мы получаем грамматику без левой рекурсии, без цепных правил, без бесполезных и недостижимых символов:

TYPE → integer | float | label

vardef → <identifer> as type ;

vardefs → vardef vardefs | end

defs → vars vardefs

binop → + | - | * | /

condition → < | > | = | <> | <= | >=

EXPRESSION → <const>  EXPRESSION’|

- expression EXPRESSION’ |

<identifer> EXPRESSION’ |

(expression) EXPRESSION’

EXPRESSION’ → binop expression EXPRESSION’ | λ

ELSE → else operators | λ

operator → <identifer> := expression; |

while ( expression condition expression ) do operators |

input <identifer> ; | outputn expression ; |

outputs <strc> ; |

goto <identifer> ; |

label <identifer> ; |

if ( expression condition expression ) then operators ELSE

operators → operator operators | end

code → code operators

program → defs code ;

2.1.3.10 Разработка МП-автомата.