**1. Grammar symbols: Used cross reference.**

Reference of each grammar's symbol used within each rule's productions. The index uses the tripple: rule name, its subrule no, and the symbol's position within the symbol string.

**2. NS_rules_phrase_th::TH_rules_phrase_th::**

Rphrase 1.3

**3. NULL thread:.**

Rphrase 2.3

**4. Rphrase:.**

Rrules_phrase 1.1

**5. rules-phrase:.**

Rphrase 1.2

**6.** |?|::.

Rphrase 2.2 Rphrase 3.1

**7.** ||!:.

Rphrase 1.1 Rphrase 2.1

**8. Grammar Rules's First Sets.**

**9.** _Rrules_phrase_ **# in set: 2.**

1?|| ||

**10.** _Rphrase_ **# in set: 2.**

1?|| ||

**11.** **LR State Network.**

List of productions with their derived LR state lists. Their subrule number and symbol string indicates the specific production being derived. The "p" symbol indicates the production's list of derived states from its closured state. Multiple lists within a production indicate 1 of 2 things:

1) derived string that could not be merged due to a lr(1) conflict

2) partially derived string merged into another derived lr states

A partially derived string is indicated by the "merged into" symbol \(\nearrow\)used as a superscript along with the merged into state number.

**12.** **Rrules_phrase.**

1 Rphrase

\(\triangleright\) 1 6

**13.** **Rphrase.**

1 ||  rules-phrase NS_rules_phrase_th::TH_rules_phrase_th

\(\triangleright\) 1 3 5

2 || || || NULL

\(\triangleright\) 1 3 4

3 |?|

\(\triangleright\) 1 2

**14.** **List of reducing states.**

The following legend indicates the type of reducing state.

Points 2-4 are states that must meet the lr(1) condition:

1) r -- only 1 production reducing

2) r\({}^{2}\) -- 2 or more reducing productions

3) s/r -- shift and 1 reducing production

4) s/\(r^{2}\) -- shift and multiple reducing productions

\(\subset\) 2\({}^{r}\)\(4^{r}\)\(5^{r}\)\(6^{r}\)

**15.** **Lr1 State's Follow sets and reducing lookahead sets.**

Notes on Follow set expressions:

1) The "follow set" for rule uses its literal name and tags its grammar rule rank number as a superscript.

Due to space limitations, part of the follow set information uses the rule's literal name while the follow set expressions refers to the rule's rank number. This \(<\) rule name, rule rank number \(>\) tuple allows you the reader to decifer the expressions. Transitions are represented by S\({}_{x}\)R\({}_{z}\) whereby S is the LR1 state identified by its "x" subscript where other transient calculations occur within the LR1 state network. R indicates the follow set rule with the subscript "z" as its grammar rank number that contributes to the follow set.

The \(\nearrow\)\({}^{x}\) symbol indicates that a merge into state "x" has taken place. That is, the reduced subrule that depends on this follow set finds its follow set in 2 places: its birthing state that generated the sequence up to the merged into state, and the birthing state that generated the "merged into" state. So the rule's "follow set" calculation must also continue its calculation within the birth state generating the "x merged into" state.

\begin{tabular}{l l l l} State: & 1 & Follow Set contributors, merges, and transitions \\ \(\leftarrow\) & Follow set Rule & \(\rightarrow\leftarrow\) & follow set symbols contributors & \(\rightarrow\) \\ Rules\_phrase1 & & & & \\ Local follow set yield: & & & & \\ \(\leftarrow\) & Follow set Rule & \(\rightarrow\leftarrow\) & follow set symbols contributors & \(\rightarrow\) \\ Rphrase2 & & R\({}_{1\mbox{-}1\mbox{-}1}\) S\({}_{1}R_{1}\) & & & \\ Local follow set yield: & & & & \\ \end{tabular}

Common Follow sets.
* 17 LA set: 1. eolr.

**18.** **Index.**

R\({}_{1}\) **---** **Rrules_phrase: 12.**

R\({}_{2}\) **---** **Rphrase: 13.**

_Rphrase_: 10.**

_Rrules_phrase_: 9.**

