Changes

The preceding development provides a typical example of how an initially effective and conceptually succinct description of a formal language, but one that is terse to the point of allowing its prospective interpreter to waste exorbitant amounts of energy in trying to unravel its implications, can be converted into a form that is more efficient from the operational point of view, even if slightly more ungainly in regard to its elegance.

The preceding development provides a typical example of how an initially effective and conceptually succinct description of a formal language, but one that is terse to the point of allowing its prospective interpreter to waste exorbitant amounts of energy in trying to unravel its implications, can be converted into a form that is more efficient from the operational point of view, even if slightly more ungainly in regard to its elegance.

The basic idea behind all of this machinery remains the same:  Besides the select body of formulas that are introduced as boundary conditions, it merely institutes the following general rule:

The basic idea behind all of this machinery remains the same:  Besides

the select body of formulas that are introduced as boundary conditions,

it merely institutes the following general rule:

| If   the strings S_1, ..., S_k are sentences,

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

|

| then  their concatenation in the form

| <math>\operatorname{If}</math>

|

| the strings <math>S_1, \ldots, S_k\!</math> are sentences,

|       Conc^k_j S_j = S_1 · ... · S_k

|-

|

|       is a sentence,

| their concatenation in the form

|

|-

| and  their surcatenation in the form

| &nbsp;

|

| <math>\operatorname{Conc}_{j=1}^k S_j \ = \ S_1 \, \cdot \, \ldots \, \cdot \, S_k</math>

|       Surc^k_j S_j = "-(" · S_1 · "," · ... · "," · S_k · ")-"

|-

|

|       is a sentence.

| is a sentence,

|-

| their surcatenation in the form

|-

| <math>\operatorname{Surc}_{j=1}^k S_j \ = \ ^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, S_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, \ldots \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, S_k \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}</math>

|-

| &nbsp;

| is a sentence.

==Generalities About Formal Grammars==

==Generalities About Formal Grammars==