Changes

In this usage, the characterization <math>S_1 :> S_2\!</math> is tantamount to a grammatical license to transform a string of the form <math>Q_1 \cdot q \cdot Q_2</math> into a string of the form <math>Q1 \cdot W \cdot Q2,</math> in effect, replacing the non-terminal symbol <math>q\!</math> with the non-initial string <math>W\!</math> in any selected, preserved, and closely adjoining context of the form <math>Q1 \cdot \underline{~~~} \cdot Q2.</math>  In this application the notation <math>S_1 :> S_2\!</math> can be read to say that <math>S_1\!</math> ''produces'' <math>S_2\!</math> or that <math>S_1\!</math> ''transforms into'' <math>S_2.\!</math>

In this usage, the characterization <math>S_1 :> S_2\!</math> is tantamount to a grammatical license to transform a string of the form <math>Q_1 \cdot q \cdot Q_2</math> into a string of the form <math>Q1 \cdot W \cdot Q2,</math> in effect, replacing the non-terminal symbol <math>q\!</math> with the non-initial string <math>W\!</math> in any selected, preserved, and closely adjoining context of the form <math>Q1 \cdot \underline{~~~} \cdot Q2.</math>  In this application the notation <math>S_1 :> S_2\!</math> can be read to say that <math>S_1\!</math> ''produces'' <math>S_2\!</math> or that <math>S_1\!</math> ''transforms into'' <math>S_2.\!</math>

An ''immediate derivation'' in <math>\mathfrak{G}</math> is an ordered pair <math>(W, W')\!</math> of sentential forms in <math>\mathfrak{G}</math> such that:

An "immediate derivation" in !G! is an ordered pair (W, W')

of sentential forms in !G! such that:

| W  = Q_1 · X · Q_2,

{| align="center" cellpadding="8" width="90%"

| W'  = Q_1 · Y · Q_2,

|

|

| i.e.  X :> Y in !G!.

& (X, Y) \in \mathfrak{K}.

This relation is indicated by saying that W "immediately derives" W',

This relation is indicated by saying that W "immediately derives" W',

that W' is "immediately derived" from W in !G!, and also by writing:

that W' is "immediately derived" from W in !G!, and also by writing: