Changes

Grammar&nbsp;6 has the intermediate alphabet <math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, F \, ^{\prime\prime}, \, ^{\backprime\backprime} \, R \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime} \, \},</math> with the production set <math>\mathfrak{K}</math> as listed in the next display.

Grammar&nbsp;6 has the intermediate alphabet <math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, F \, ^{\prime\prime}, \, ^{\backprime\backprime} \, R \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime} \, \},</math> with the production set <math>\mathfrak{K}</math> as listed in the next display.

<pre>

<br>

| !C!(!P!).  Grammar 6

 

|

| !Q! = {"S'", "R", "F", "T"}

| align="left"  style="border-left:1px solid black;"  width="50%" |

|

<math>\mathfrak{C} (\mathfrak{P}) : \text{Grammar 6}\!</math>

| 1. S   :> !e!

| align="right" style="border-right:1px solid black;" width="50%" |

<math>\mathfrak{Q} = \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, F \, ^{\prime\prime}, \, ^{\backprime\backprime} \, R \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime} \, \}</math>

|  2. S   :> S'

|-

| colspan="2" style="border-top:1px solid black; border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black" |

|  3. S' :> R

1.

|  4. S' :> F

& S

& :>

|  5. S' :> S' · S'

|  6. R   :> m_1

2.

& S

|  7. R   :> p_j, for each j in J

& :>

& S'

|  8. R   :> R · R

3.

|  9. F   :> "-()-"

& S'

& :>

| 10. F   :> "-(" · T · ")-"

& R

| 11. T   :> ","

4.

& S'

| 12. T   :> S'

& :>

& F

| 13. T   :> T · ","

5.

| 14. T   :> T · "," · S'

& S'

& :>

& S' \, \cdot \, S'

6.

& R

& :>

& m_1

7.

& R

& :>

& p_j, \, \text{for each} \, j \in J

8.

& R

& :>

& R \, \cdot \, R

9.

& F

& :>

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

10.

& F

& :>

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

11.

& T

& :>

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

12.

& T

& :>

& S'

13.

& T

& :>

& T \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime}

14.

& T

& :>

& T \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, S'

 

The preceding development provides a typical example of how an initially

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.

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

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

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