- A Syntax-directed translation scheme is an extension of a context free grammar that describes the process of translating input strings into output strings.
- The scheme associates to each production rule of the source context free
language a production rule of the target context free language.
- $\alpha $ is called the source element of the rule
- $\beta $ is called the translation elementof the rule
- There is 1-1 correspondence between the nonterminal symbols of $\alpha $ and $\beta $

- A translation form is a pair $\left(u,v\right)$
where
- $u$ is a sentential form of the underlying grammar
- $v$ is the translation resulted by the derivation of $u$

E $\to $ E + T, T E + $\to $ T, T T $\to $ T * F, F T * $\to $ F, F F $\to $ a , a E,E $\Rightarrow $ E + T, T E + $\Rightarrow $ T + T, T T + $\Rightarrow $ F + T, T F + $\Rightarrow $ ${a}_{1}$ + T, T ${a}_{1}$ + $\Rightarrow $ ${a}_{1}$ + T * F, F T * ${a}_{1}$ + $\Rightarrow $ ${a}_{1}$ + F * F, F F * ${a}_{1}$ + $\Rightarrow $ ${a}_{1}$ + ${a}_{2}$ * F, F ${a}_{2}$ * ${a}_{1}$ + $\Rightarrow $ ${a}_{1}$ + ${a}_{2}$ * ${a}_{3}$, ${a}_{3}$ ${a}_{2}$ * ${a}_{1}$ + - Note that the parse trees of the source and target strings relate the
same way to the nonterminal symbols, up to permutations in their
orderings.