Changes

|}

|}

In order to transform these recursive definitions into grammar rules, one introduces a new pair of intermediate symbols, <math>\operatorname{Conc}</math> and <math>\operatorname{Surc},</math> corresponding to the operations that share the same names but ignoring the inflexions of their individual parameters <math>j\!</math> and <math>k.\!</math> Recognizing the

In order to transform these recursive definitions into grammar rules,

type of a sentence by means of the initial symbol <math>S\!</math> and interpreting <math>\operatorname{Conc}</math> and <math>\operatorname{Surc}</math> as names for the types of strings that are generated by concatenation and by surcatenation, respectively, one arrives at the following transformation of the ruling operator definitions into the form of covering grammar rules:

one introduces a new pair of intermediate symbols, "Conc" and "Surc",

corresponding to the operations that share the same names but ignoring

the inflexions of their individual parameters j and k.  Recognizing the

type of a sentence by means of the initial symbol "S", and interpreting

"Conc" and "Surc" as names for the types of strings that are generated

by concatenation and by surcatenation, respectively, one arrives at

the following transformation of the ruling operator definitions

into the form of covering grammar rules:

1. Conc :> "".

 

    Conc :> Conc · S.

 

1.

2. Surc :> "-()-".

& \operatorname{Conc}

 

& :>

    Surc :> "-(" · S · ")-".

 

    Surc :> Surc ")-"^(-1) · "," · S · ")-".

& \operatorname{Conc}

& :>

& \operatorname{Conc} \cdot S

2.

& \operatorname{Surc}

& :>

& ^{\backprime\backprime} \, \operatorname{()} \, ^{\prime\prime}

& \operatorname{Surc}

& :>

& ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, S \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}

& \operatorname{Surc}

& :>

& \operatorname{Surc} \, \cdot \, ( \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime} \, )^{-1} \, \cdot \, ^{\backprime\backprime} \operatorname{,} ^{\prime\prime} \, \cdot \, S \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}

As given, this particular fragment of the intended grammar

As given, this particular fragment of the intended grammar

contains a couple of features that are desirable to amend.

contains a couple of features that are desirable to amend.