Changes

<ol style="list-style-type:decimal">

<ol style="list-style-type:decimal">

<li>The ''concatenation'' <math>\operatorname{Conc}_{j=1}^k</math> of the sequence of <math>k\!</math> strings <math>(s_j)_{j = 1}^k</math> is defined recursively as follows:</li>

<li>The ''concatenation'' <math>\operatorname{Conc}_{j=1}^k</math> of the sequence of <math>k\!</math> strings <math>(s_j)_{j=1}^k</math> is defined recursively as follows:</li>

<ol style="list-style-type:lower-alpha">

<ol style="list-style-type:lower-alpha">

<li><math>\operatorname{Conc}_{j = 1}^1 (s_j)_{j = 1}^k \ = \ s_1.</math></li>

<li><math>\operatorname{Conc}_{j=1}^1 s_j \ = \ s_1.</math></li>

<li>

<li>

<p>For <math>\ell > 1,\!</math></p>

<p>For <math>\ell > 1,\!</math></p>

<p><math>\operatorname{Conc}_{j=1}^\ell (s_j)_{j = 1}^k \ = \ (\operatorname{Conc}_{j=1}^{\ell - 1} (s_j)_{j = 1}^k) \, \cdot \, s_\ell.</math></p></li>

<p><math>\operatorname{Conc}_{j=1}^\ell s_j \ = \ \operatorname{Conc}_{j=1}^{\ell - 1} s_j \, \cdot \, s_\ell.</math></p></li>

</ol>

</ol>

<li>The ''surcatenation'' <math>\operatorname{Surc}_{j=1}^k</math> of the sequence of <math>k\!</math> strings <math>(s_j)_{j = 1}^k</math> is defined recursively as follows:</li>

<li>The ''surcatenation'' <math>\operatorname{Surc}_{j=1}^k</math> of the sequence of <math>k\!</math> strings <math>(s_j)_{j=1}^k</math> is defined recursively as follows:</li>

<ol style="list-style-type:lower-alpha">

<ol style="list-style-type:lower-alpha">

<li><math>\operatorname{Surc}_{j=1}^1 (s_j)_{j = 1}^k \ = \ ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></li>

<li><math>\operatorname{Surc}_{j=1}^1 s_j \ = \ ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></li>

<li>

<li>

<p>For <math>\ell > 1,\!</math></p>

<p>For <math>\ell > 1,\!</math></p>

<p><math>\operatorname{Surc}_{j=1}^\ell (s_j)_{j = 1}^k \ = \ (\operatorname{Surc}_{j=1}^{\ell - 1} (s_j)_{j = 1}^k) \, \cdot \, ( \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime} \, )^{-1} \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_\ell \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></p></li>

<p><math>\operatorname{Surc}_{j=1}^\ell s_j \ = \ \operatorname{Surc}_{j=1}^{\ell - 1} s_j \, \cdot \, ( \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime} \, )^{-1} \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_\ell \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></p></li>

</ol></ol>

</ol></ol>

'''NB.'''  The notation in this next section needs fixing.

'''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 by making a few additional conventions and auxiliary definitions.

<ol style="list-style-type:decimal">

<ol style="list-style-type:decimal">