Syntactic description of a sentence may be carried out in accordance with ‘immediate constituent analysis’ (Chomsky 1957). In keeping with this type of analysis, words of a sentence are arranged into phrases, which can be divided into smaller constituent phrases and so forth, until the ultimate constituents (words or morphemes) are reached. Those phrases can afterwards be categorized as noun phrases (NP), verb phrases (VP), etc. A constituent structure of a sentence is its phrase structure and the rules of the phrase structure grammar, in their simple form, may be illustrated as follows:

fig3

Fig. 3 Simple phrase structure grammar rules (Chomsky 1957:26)
Each of the rules (i) – (vi) in the above diagram has the form of X → Y, where X is a single element, Y is a string consisting of one or more elements, and the arrow suggests that the element to its left be replaced (rewritten) with the string of elements to its right. Considering what follows:
fig4
Fig. 4 Derivation of the sentence “the man hit the ball” (Chomsky 1957:27)
one shall assume the above diagram as a derivation of the sentence “the man hit the ball”. The numbers to the right of each derivation line stand for the rule of the grammar presented in Fig. 3, which rule was applied to create that line from the preceding one. Thus, line two in Fig. 4 is formed from the first line by substituting Sentence with NP + VP with reference to the rule (i) in Fig. 3, line three in Fig. 4 is formed from the second line by substituting NP with T + N with reference to the rule (ii) in Fig. 3, line four in Fig. 4 is formed from the third line by substituting VP with Verb + NP with reference to the rule (iii) in Fig. 3, and so on. The derivation of the sentence “the man hit the ball” can be demonstrated more clearly by means of a tree diagram (also known as phrase-marker) as presented below:
fig5
Fig. 5 Tree diagram (Chomsky 1957:27)
It must be, though, stated that the tree diagram reveals less information than the derivation in Fig. 4 due to the fact that it fails to show the order, in which the rules were applied in Fig. 4. Only by means of the derivation in Fig. 4 can one construct the tree diagram in Fig. 5, but not reversely, for it is possible to construct a derivation that reduces to the tree diagram in Fig. 5 with a different order of application of the rules. With the use of the tree diagram in Fig. 5 one can notice what is crucial in Fig. 4 in order to determine the phrase structure (constituent analysis) of the derived sentence “the man hit the ball”. Provided that the sequence of words of this sentence can be tracked back to a single point of origin in the tree diagram in Fig. 5, then a sequence of words of this sentence is a constituent of type Z, and its points of origin are labeled Z. Therefore, “hit the ball” can be tracked back to VP in Fig. 5 and as such it is a VP of the derived sentence. However, “man hit” cannot be tracked back to a single point of origin in Fig. 5, and as such it is not a constituent at all.
If two derivations reduce to the same diagram of the form presented in Fig. 5, they are equivalent. If a grammar constructs nonequivalent derivations of the same sentence, it is a case of ‘constructional homonymity’ (structural ambiguity) and, provided that the grammar is correct, this sentence of the language should be ambiguous, thus analyzable in more than one way. For instance, the sentence “flying planes can be dangerous” may be classified as ambiguous since ‘planes’ might be either the object of ‘flying’ or the subject of ‘can’ (Chomsky 1957).
It is now essential to generalize on the rules of the simple phrase structure grammar presented in the diagram in Fig. 3. It is important to be able to limit application of a rule to a certain context. Hence, T may be rewritten a on condition that the subsequent noun is singular (but not plural), analogously, Verb can be rewritten “hits” on condition that the preceding noun is man (but not men). In order to limit the rewriting of X as Y to the context Z – W, one ought to formulate the following rule: Z + X + W → Z + Y + W. For instance, considering singular and plural verbs, instead of creating an additional rule Verb → hits in the diagram of Fig. 3, we ought to have NP sing + Verb → NP sing + hits demonstrating that Verb is rewritten hits only in the context of NP sing . Similarly, the rule (ii) of the diagram in Fig. 3 will have to be reformulated so as to account for NP sing and NP pl. Therefore, the rule (ii) of the grammar of the type presented in Fig. 3 could be replaced by a rule such as:
fig6
Fig. 6 NP sing / NP pl rule (Chomsky 1957:29)
where Ø stands for the morpheme singular for nouns and plural for verbs (e.g. “boy”, “come”), and S stands for the morpheme singular for verbs and plural for nouns (e.g. “comes”, “boys”). However, there is one feature of the grammar of Fig. 3, which must be retained, namely only a single element can be rewritten in any single rule (Chomsky 1957).
One point of generalization that may now be made is that each grammar based on constituent analysis is defined by a finite set Σ of initial strings as well as the finite set F of rules of the form X → Y. Although X does not have to be a single symbol, only a single symbol of X may be rewritten in formulation of Y. Analyzing the grammar of Fig. 3, it is possible to state that the single symbol Sentence was the only member of the set Σ of the initial strings, and F comprised of the rules (i) – (vi), however, one could modify Σ so as it would account for Declarative Sentence or Interrogative Sentence as additional symbols. Within the framework of the grammar [ Σ, F ], one can now define derivation as “a finite sequence of strings, beginning with an initial string of Σ, and with each string in the sequence being derived from the preceding string by application of one of the instruction formulas of F” (Chomsky 1957:29). It is now essential to introduce the term ‘terminated derivation’, that is a derivation whose last string cannot be further rewritten by the rules F. Consequently, the last string of a terminated derivation is its ‘terminal string’, and the set of terminal strings of the grammar [Σ, F] is a ‘terminal language’. The phrase structure of each sentence, which is a terminal string, can be reconstructed by means of associated diagrams, which may also define the grammatical relations in the terminal languages.
Providing that it is possible to generate all the grammatical sequences of morphemes of a language by means of the grammar [Σ, F], the very grammar should hence be completed by a phonemic structure of these morphemes in order for it to produce the grammatical phoneme sequences of the language. This might be achieved by creating a set of rules of the form X → Y, for instance, for English, in a form similar to the kind presented:
fig7

Fig. 7 Morphophonemic rules (Chomsky 1957:32)
and incorporating it into the phrase structure derivations. One should, however, bear in mind that it is no longer required that only a single symbol be rewritten in each rule of the set of morphophonemic rules illustrated above. Given the above, the application of Fig. 7 to the phrase structure derivations, will produce a unified process of generating phoneme sequences from the initial string Sentence, thus making it possible to generate the grammatical phoneme sequences of the language.
The phrase structure grammar based on the immediate constituent analysis has been so far proved to be more adequate than a model based on the finite state processes. However, attempting to consider sentences beyond the scope of the simplest type of phrase structure grammar, one finds the process extremely difficult and complicated. In order to examine the limitations of phrase structure grammar, some examples depicting improvements that ought to be made over the grammar of the form [ Σ, F ] should be presented.
It is well known that, among many other processes, sentences may be created by means of conjunction. Given the two sentences of the form Z + X + W as well as Z + Y + W, where X and Y are constituents of these sentences, it is possible to create a new sentence of the form Z – X + and + Y – W. Considering the following:
fig8
Fig. 8 Sample sentences / conjunction (Chomsky 1957:35)
one should see that sentence (21) can be formed from sentences (20a-b). However, when X and Y are not constituents (or are constituents but of different kinds in a sense that each of them has a single point of origin in a tree diagram, though this origin is labeled differently), we cannot use the above form to create sentences of the type considered. For instance, we cannot form (25) from (24a-b).
fig9
Fig. 9 Sample sentences / conjunction (Chomsky 1957:36)
The description of conjunction may be simplified by setting up constituents so that the rule presented below will apply.
fig10
Fig. 10 Conjunction rule (Chomsky 1957:36)
Although it is much simpler to account for conjunction by means of the above rule rather than without such a rule, we are, at this point, prone to encounter difficulty arising from the fact that due to certain limitations of a grammar [Σ, F] of phrase structure, and the like, it is impossible to incorporate the rule of Fig. 10 is such grammars. The basic feature of the rule of Fig. 10 is that one ought to know both the form of S1 and S2 as well as their constituent structure prior to the application of the rule to sentences S1 and S2, form which a new sentence S3 is to be formed. In this respect, it is clear that the very rule fails to apply to phrase structure grammar since it does not allow such double reference.
Another example can illustrate improvements that ought to be made over the grammar of the form [Σ, F]. Fig. 3 accounts only for one way of analyzing the element Verb as hit. It is obvious that the verb may take a number of other forms, for instance, some of the forms of the verb take are: takes, has + taken, will + take, has + been + taken, is + being + taken. Equally obvious is the fact that analysis of the aforementioned auxiliary verbs is an important process in the development of the English grammar. However, once attempted to include these phrases into a [Σ, F] grammar, one discovers that the description appears to be rather complex. In order for the grammar of the type presented in Fig. 3 to account for the occurrence of auxiliary verbs in, say, declarative sentences, it should include the following rules:
fig11
Fig. 11 Auxiliary verb phrase rule (Chomsky 1957:39)
The interpretation of the rule (28iii) is as follows: “we must choose the element C, and we may choose zero or more of the parenthesized elements in the given order. In (29i) we may develop C into any of three morphemes, observing the contextual restrictions given” (Chomsky 1957:39). Not reiterating the initial steps, the following derivation of the type of Fig. 4 may be constructed so that it illustrates the application of the rules of Fig. 11.
fig12
Fig. 12 Derivation of the sentence “the man has been reading the book” (Chomsky 1957:39-40)
Every auxiliary verb phrase can be generated in a similar way, perhaps with a necessity for adding additional rules that would ensure grammaticality of the sequences to be generated.
However, in order to apply the rule (29i) in the derivation of Fig. 11, one had to make reference to previously conducted derivations to be able to state the constituent analysis of the NP sing the + man, and as already seen in case of the rule of Fig. 10, such double reference collides with the requirements of the grammar of the type [ Σ, F ].
Yet another example illustrating improvements that ought to be made over the grammar of the form [Σ, F] concerns active and passive sentences. In forming passive sentences one makes use of the element be + en of the rule (28iii), though there are certain restrictions that have to be accounted for before the element be + en can be selected, namely the Verb that follows needs to be transitive, Verb cannot be followed by a noun phrase, if Verb is transitive and is followed by the prepositional phrase by + NP, then it is crucial to apply be + en before the string V + by + NP thus inverting the order of the adjacent noun phrases. Hence, in order to extend the grammar of the Fig. 3, it would be necessary to pose many restrictions on the element Verb so that this grammar would produce only grammatical sentences. Those restrictions, on both the elements Verb and be + en, might be excluded provided that one reintroduces passives from the phrase structure grammar by means of the following rule:
fig13
Fig. 13 Passive rule (Chomsky 1957:43)
Although the above rule significantly simplifies the grammar, it is well beyond the scope of the grammar [Σ, F] in that it is necessary to make reference to the constituent structure of the string to which it is to apply and it imposes an inversion on this string.