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It is fitting to wrap up the foregoing developments by summarizing the notion of a formal grammar that appeared to evolve in the present case. For the sake of future reference and the chance of a wider application, it is also useful to try to extract the scheme of a formalization that potentially holds for any formal language. The following presentation of the notion of a formal grammar is adapted, with minor modifications, from the treatment in (DDQ, 60–61).
It is fitting to wrap up the foregoing developments by summarizing the notion of a formal grammar that appeared to evolve in the present case. For the sake of future reference and the chance of a wider application, it is also useful to try to extract the scheme of a formalization that potentially holds for any formal language. The following presentation of the notion of a formal grammar is adapted, with minor modifications, from the treatment in (DDQ, 60–61).
A ''formal grammar'' <math>\mathfrak{G}</math> is given by a four-tuple <math>\mathfrak{G} = ( \, ^{\backprime\backprime} \, S \, ^{\prime\prime}, \, \mathfrak{Q}, \, \mathfrak{A}, \, \mathfrak{K} \, )</math> that takes the following form of description:
<pre>
<pre>
1. "S" is the "initial", "special", "start", or "sentence symbol".
1. "S" is the "initial", "special", "start", or "sentence symbol".
Since the letter "S" serves this function only in a special setting,
Since the letter "S" serves this function only in a special setting,
