¹ This article was written while I was a member of the Mechanical Translation Group, Research Laboratory of Electronics, Massachusetts Institute of Technology. The work was supported in part by the National Science Foundation, and in part by the U. S. Army Signal Corps, the Air Force Office of Scientific Research, and the Office of Naval Research. I am indebted to Victor Yngve for suggestions which greatly improved the argument presented here.

² The phrase-structure grammar allows for ‘discontinuous constituents’. The type of grammar is like that described in Yngve, ‘A model and an hypothesis for language structure’, Proceedings of the American Philosophical Society 104.444–66 (1960). The grammar is described in detail in §5 of this paper. The transformational grammar is to be found in Noam Chomsky, ‘A transformational approach to syntax’, Third Texas conference on problems of linguistic analysis in English 138–44 (1958; published 1962).

³ Chomsky, op.cit. 124–58; Syntactic structures² (The Hague, 1962), especially Chapter 5; ‘Explanatory models in linguistics’, Proceedings of the 1960 International Congress on Logic, Methodology, and Philosophy of Science, ed. Suppes, Nagel, and Tarski (Stanford, 1962); ‘The logical basis of linguistic theory’, Preprints of papers for the Ninth International Congress of Linguists 509–74 (Cambridge, Mass., 1962); R. B. Lees, review of Syntactic structures in Lg. 33.375–407 (1957); The grammar of English nominalizations (Bloomington, 1960).

⁴ ‘The logical basis of linguistic theory’.

⁵ Syntactic structures 11.

⁶ Ibid. Cf. Chomsky, ‘On the notion rule of grammar’, Structure of language and its mathematical aspects, ed. Jakobson, Proceedings of symposia in applied mathematics 12.6 (Providence, 1961) : 'By a “grammar of the language L” I will mean a device of some sort (that is, a set of rules) that provides, at least, a complete specification of an infinite set of grammatical sentences of L and their structural descriptions. In addition to making precise the notion “structural description”, the theory of grammar should meet requirements of the following kind. It should make available:

1. (1) (a)

   (1) (a) a class of possible grammars G₁, G₂, …,

2. (b)

   (b) a class of possible sentences S₁, S₂, …,

3. (c)

   (c) a function f such that f(i,j) is the set of structural descriptions of the sentence s_i that are provided by the grammar G_j.

4. (d)

   (d) a function m(i) which evaluates G_i,

5. (e)

   (e) a function g such that g(i,n) is the description of a finite automaton that takes sentences of (b) as input and gives structural descriptions assigned to these sentences by G_i (i.e. various, perhaps all, members of f (i,j)) as output, where η is a parameter determining the capacity of the automaton.'

⁷ ‘The logical basis of linguistic theory’ 514.

⁸ Formally, this motivation will ideally be provided by the function m(i) mentioned in footnote 6. The use of the evaluation function m(i) is explained further in ‘On the notion rule of grammar’ 7: 'That is, m may be a measure of complexity that leads to choice among alternative proposed grammars that are compatible with given data.' (This is also discussed in almost all the references in footnote 3.) A choice of one grammar over another which accounts for the same data (generates the same sentences) will be motivated if and only if the selected grammar has a higher value (according to the function m) than the other grammar. Note that in practice it will probably be impossible to give an exact specification of m. For example, Lees has noted that 'no natural science can claim … a true evaluation procedure' (review of Chomsky 380). This is an important point, as will appear in what follows.

⁹ Syntactic structures 26. Various names have been given to the theory of grammar for which a formal model is sought: Formal structural linguistics, IC analysis, traditional notion of parsing (Chomsky, ‘A transformational approach to syntax’ 124) ; taxonomic model applied to syntax (Chomsky, ‘Logical basis of linguistic theory’ 510) ; constituent structure, immediate-constituent analysis (Chomsky, ‘On the notion rule of grammar’ 9, 15); phrase structure, bracketing, immediate-constituent analysis (Lees, review of Chomsky 385).

¹⁰ Syntactic structures 29.

¹¹ ‘On the notion rule of grammar’ 8–9. See also Chomsky, ‘On certain formal properties of grammars’, Information and control, No. 2 (1959).

¹² These diagrams are explained in Syntactic structures, Chapter 4.

¹⁴ 'The extreme example of this difficulty is the case of true coordination, e.g., “the man was old, tired, tall, …, but friendly.” The only correct P-Marker [i.e. 'phrase marker'] would assign no internal structure at all within the sequence of coordinated items. But a constituent structure grammar can accommodate this possibility only with an infinite number of rules; that is, it must necessarily impose further structure in quite an arbitrary way.'—Chomsky, 'On the notion rule of grammar' 15.

¹⁵ I am not sure that this criticism of phrase structure has ever been explicitly made, though it is as valid as the preceding. The more usual criticism is that a description which reveals the active-passive relationship cannot be motivated, which appears to be the criticism that constituent structure fails to reach the level of explanatory adequacy. However, one reason why such a description cannot be motivated is that the description cannot occur in a constituent structure grammar as Chomsky has defined it, e.g. Syntactic structures 88–91.

¹⁶ Chomsky, op.cit. 88.

¹⁷ Loc.cit.

¹⁸ More details in Chomsky, Syntactic structures, Chapters 5–8, especially Chapter 8, ‘The explanatory value of linguistic theory’. Cf. ‘The logical basis of linguistic theory’ 517–24.

¹⁹ 'The motivation for adding transformational rules to the grammar is quite clear …'— 'On the notion rule of grammar' 17.

²⁰ See the passage quoted above, at footnote 11.

²¹ A standard example is They are (flying planes) as compared with They (are flying) planes.

²² 529–30.

²³ Yngve, ‘A model and an hypothesis for language structure’.

²⁴ Paul M. Postal, Constituent structure: A study of contemporary models of syntactic description (to appear).

²⁵ 41–2, footnote 6.

²⁶ This is Yngve's rule, which I also accept in the grammars given below.

²⁷ ‘A model and an hypothesis for language structure’.

²⁸ More formally: In the string X + C + Y (where X and Y are strings of constituents) ‘expand’ constituent C if and only if (a) there is a rule with C on the left side and (b) there is not a constituent B included in the string X so that there is a rule with B on the left side.

²⁹ The subscript notation suggested here is based on that in the computer language comit, which is particularly suited for use in writing generative grammars. See V. H. Yngve, Introduction to COMIT programming and COMIT programmers' Reference Manual (Cambridge, Mass., 1962).

³⁰ We could even forget that the abbreviated form abbreviates anything and take it to be basic.

³¹ These are of course only rough suggestions. There is no reason why exact specification of such description must be given before a fairly large grammar has been written. A detailed treatment of these issues appears in David Allen Dinneen, A left-to-right generative grammar of French (Cambridge, Mass., 1962). Dinneen's distinction between the ‘grammar of specifiers’ and the ‘grammar of sentences’ is a much more sophisticated distinction than mine between ‘restriction rules’ and ‘expansion rules’.

³² ‘A model and an hypothesis for language structure’.

³³ Other grammars of this form have been written at MIT and elsewhere for English, German, French, Finnish, and Arabic. Many of these grammars are in the form of computer programs for generating actual sentences. An example is Arnold C. Satterthwait, Parallel sentence-construction qrammars of Arabic and English (Cambridge, Mass., 1962).