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'''NB.''' The notation in this next section needs fixing.
The definitions of these syntactic operations can now be organized in a slightly better fashion, for both conceptual and computational purposes, by making a few additional conventions and auxiliary definitions.
The definitions of these syntactic operations can now be organized in a slightly better fashion, for both conceptual and computational purposes, by making a few additional conventions and auxiliary definitions.
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Notice that the expressions <math>\operatorname{Conc}^0_j s_j</math> and <math>\operatorname{Surc}^0_j s_j</math> are defined in such a way that the respective operators
Notice that the expressions Conc^0_j z_j and Surc^0_j z_j
<math>\operatorname{Conc}^0</math> and <math>\operatorname{Surc}^0</math> basically "ignore", in the manner of constants, whatever sequences of strings <math>s_j\!</math> may be listed as their ostensible arguments.
are defined in such a way that the respective operators
Conc^0 and Surc^0 basically "ignore", in the manner of
constants, whatever sequences of strings z_j may be
listed as their ostensible arguments.
Having defined the basic operations of concatenation and surcatenation
Having defined the basic operations of concatenation and surcatenation on arbitrary strings, in effect, giving them operational meaning for the all-inclusive language <math>\mathfrak{L} = \mathfrak{A}^*,</math> it is time to adjoin the notion of a more discriminating grammaticality, in other words, a more properly restrictive concept of a sentence.
on arbitrary strings, in effect, giving them operational meaning for
the all-inclusive language !L! = !A!*, it is time to adjoin the
notion of a more discriminating grammaticality, in other words,
a more properly restrictive concept of a sentence.
<pre>
If !L! is an arbitrary formal language over an alphabet of the sort that
If !L! is an arbitrary formal language over an alphabet of the sort that
we are talking about, that is, an alphabet of the form !A! = !M! |_| !P!,
we are talking about, that is, an alphabet of the form !A! = !M! |_| !P!,