Changes

Achieving a grammar that respects this convention typically requires a more detailed account of the initial setting of a type, both with regard to the type of context that incites its appearance and also with respect to the minimal strings that arise under the type in question.  In order to find covering productions that satisfy the intermediate significance condition, one must be prepared to consider a wider variety of calling contexts or inciting situations that can be noted to surround each recognized type, and also to enumerate a larger number of the smallest cases that can be observed to fall under each significant type.

Achieving a grammar that respects this convention typically requires a more detailed account of the initial setting of a type, both with regard to the type of context that incites its appearance and also with respect to the minimal strings that arise under the type in question.  In order to find covering productions that satisfy the intermediate significance condition, one must be prepared to consider a wider variety of calling contexts or inciting situations that can be noted to surround each recognized type, and also to enumerate a larger number of the smallest cases that can be observed to fall under each significant type.

With the foregoing array of considerations in mind, one is gradually led to a grammar for <math>\mathfrak{L} = \mathfrak{C} (\mathfrak{P})</math> in which all of the covering productions have either one of the following two forms:

With the array of foregoing considerations in mind,

one is gradually led to a grammar for !L! = !C!(!P!)

in which all of the covering productions have either

one of the following two forms:

| S  :>  !e!

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

|

|

| q :>   W, with q in {"S"} |_| !Q!,  and W in (!Q! |_| !A!)^+

q

& :>

& W,

& \text{with} \ q \in \{ \, ^{\backprime\backprime} \, S \, ^{\prime\prime} \, \} \cup \mathfrak{Q} \ \text{and} \ W \in (\mathfrak{Q} \cup \mathfrak{A})^+

A grammar that fits into this mold is called a "context-free" grammar.

A grammar that fits into this mold is called a "context-free" grammar.

The first type of rewrite rule is referred to as a "special production",

The first type of rewrite rule is referred to as a "special production",