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Set Theory

More abstract view of abstract syntax.

• Non-terminal names set of phrases specified by corresponding BNF rule.

  Expression, Op, Numeral

• Rules replaced by syntax builder operations, one for each form of the rule.

  numeral-exp: Numeral -> Expression
  compound-exp: Expression × Op × Expression -> Expression
  bracket-exp: Expression -> Expression

• Terminal words replaced by constants

  plus: Op
  zero: Numeral
  ...

World of words and derivation trees replaced by world of sets and operations.