Sentential Forms, And Parse Tree

Sentential Forms:

For a grammar G, with start symbol S, any string a such that
S?* a is called a sentential form.
Let G = (V, T, P, S) be a CFG, and ? ? (V U T)*. If S?(??* )? then ? is a sentential form.
A sentential form that can be obtained by a rightmost derivation from the start symbol is a right-sentential form of the grammar (and similarly with leftmost derivations)
If S?(??rm )? then ? is a left-sentential form, and if S?(??rm )? then ? is a right-sentential form.
Note: L(G) is those sentential forms that are in T*.

Example 5: Recall G1:
E ? I | E + E | E * E | (E)
I ? a | b | Ia | Ib | I0 | I1

1? Then E * (I + E) is a sentential form since
E ?E * E ? E * (E) ? E * (E + E) ? E*(I + E)
This derivation is neither leftmost, nor right-most.
2? a * E left-sentential form, since

E ? E * E ? I * E ?a * E
3? E * (E + E) is a right-sentential form since
E ? E *E ? E * (E) ?E * (E + E)

4. Parse Trees.:

Graphical representations of derivations. The leaves of a parse tree for a fully filled out tree is a sentence.
Every derivation can be represented by a parse tree. The tree shows the symbols of a terminal string are grouped into substrings, each of which belongs to the language of one of the variables of the grammar.
In a derivation tree, the root is the start variable, all internal nodes are labeled with variables, while all leaves are labeled with terminals. The children of an internal node are labeled from left to right with the right-hand side of the production used.