¹ The study of transformations arose out of the attempt to construct a method for analyzing language samples longer than a sentence ; a preliminary list of English transformations is given in Z. Harris, Discourse analysis, Lg. 28.18-23 (1952). Although the present paper was presented at the 1955 meeting of the Linguistic Society in Chicago, some of the details on English transformations have been added since that time, in connection with a project of the National Science Foundation.

From a time when this work was still at an early stage, Noam Chomsky has been carrying out partly related studies of transformations and their position in linguistic analysis : see his dissertation, Transformational analysis (University of Pennsylvania, 1955); and his paper Three models for the description of language, IRE Transactions on Information Theory, IT-2, No. 3, 113-24 (1956); now also his book Syntactic structures (The Hague, 1957), reviewed by Lees in this number of Language. My many conversations with Chomsky have sharpened the work presented here, in addition to being a great pleasure in themselves.

² Notation: Morpheme and word classes: N (noun) and V (verb) as above; A (adjective) includes large, old, extreme, etc.; T (article) includes the, a; P (preposition) includes of, from, to, etc.; C (conjunction) includes and, or, but, etc.; D (adverb) includes very, well, quickly, etc. Classes of affixes (mostly suffixes, some prefixes) : na indicates an affix such that N + na (i.e. the sequence N na) yields an A word (a word substitutable for A morphemes) : papery, cloth-like. Similarly vn after V yields an N word: growth; nn after N yields an N word: growths, childhood; and so on. And v (tense and verb ‘auxiliary’ class, §2.5) includes -ed will, can, etc. S stands for sentence. The equivalence A = B indicates that if sequence A occurs in a sentence, the substitution of B for A also yields a sentence. All these classes apply specifically to English; the analyses and transformations below have been set up for English data, although the principles are general and not limited to any particular language.

³ It might be argued that individual co-occurrence is essentially different from morphological classification simply because it is a direct reflection of the speaker's combinations of meanings, and is therefore not subject at all to investigation for distributional regularities. No doubt the speakers' meanings, or the knowledge and perceptions of the body of speakers, is a major factor in building up the co-occurrence set of each morpheme. But linguistic productivity, and other factors which are determined at least partly by structural and historical factors, also affect co-occurrence: different noun-making suffixes occur in avoidance and evasion for no semantic reason ; killing occurs in a () sense of humor but perhaps not in a () laugh. Furthermore, it frequently happens that morphemes in one of their co-occurrences have idiomatic meanings which cannot reasonably be drawn from the meanings of the component morphemes in any other occurrences, so that one can hardly claim that the occurrence in question was based on the meaning of the morphemes. Nor can one easily predict what combinations will appear: I saw them off but not I noticed them off; There's trouble ahead and There' s trouble afoot; dressed chicken but not undressed chicken. A seed catalog describes a marigold as exceedingly double, though one might not have expected a quantifier before a number word. The observed co-occurrences thus have to be taken as raw data for classification and comparison; they cannot be adequately derived from some nonlinguistic source such as ‘the desired combinations of meanings’.

⁴ It can be readily seen that the statement ‘there is a stateable set of B-co-occurrents for each A_i in the construction A B’ is equivalent to ‘the construction A B is satisfied (i.e. instances of it actually occur) for a stateable set of A_i B_j pairs’. For our present purposes, it will be sufficient to describe a construction thus: a construction is a sentence, or a class sequence such that some construction is defined as a combination of that class sequence plus other class sequences. Thus T A N V is a sentence construction; T A N (a member of the set of N-phrase constructions) and V (a member of the set of V-phrase constructions) are each constructions, since N-phrase plus V-phrase defines a sentence. For all except certain transformational sentences we can replace the words above by these : A construction is a sentence, or an immediate constituent of a construction.

⁵ An example of indirect use of these considerations. Since the classes A and N in English contain in general different morphemes and words, the A-co-occurrence of N_i in A N_i and the N-co-occurrence of N_i in N_i of N will be different sets. But many A words contain N morphemes (having been formed by N + na: wooden, glassy); and for these N na N_i constructions (a subset of A N_i) we find that the N-co-occurrents are partially similar to the N-co-occurrents of N_i in N_i of N (wooden table, table of wood, glassy surface, surface of glass, but only glassy stare). This suggests that the status of N_i relative to () of N is similar to the status of N_i relative to N na (), and hence relative to A (), since N na is just a subset of A. (Note that the difference of meaning between glassy surface and surface of glass is not relevant here.)

⁶ Same subscript means same member of the class : the second appearance of N₁ indicates the same morpheme as the first N₁.

⁷ This requirement excludes, among others, the cases of small classes whose members have the same immediate neighbors but different co-occurrents elsewhere in the sentence, e.g. and, or.

⁸ Examples of all these will be given in a later paper, describing how transformations are actually set up for a language.

⁹ These are examples of two major types of environmental effect. In the first, the absent combinations (e.g. book whom) do not occur in ordinary use of the language. In the second, the absent combinations (e.g. The letter was returned # They must have been misaddressed) can be found, but usually with different textual environment, often with different intonation, and in any case not as the statistically checked experimental result of asking the informant to substitute The letter for The letters.

¹⁰ Further analyses will become possible in §2.2 when we add the consideration of individual co-occurrence; while the further step of setting up transformations (§§3.0 ff.) is based on the added consideration of identical co-occurrences (§1.3).

¹¹ Two constructions of the same n classes may also be distinguished by their n-tuples, as two morphemes of the same phonemes are distinguished here. For example, if P N (at this time etc.) occurs in various sentence positions, we merely consider it the same construction but in different positions. If, however, the particular pairs of P and N are partly different in different positions (say at sentence beginning and medially), we define two separate P N constructions.

¹² There are many special eases, homonymities, etc. which must be left for a later discussion.

¹³ There is a minor special case of N₁ P N₂ in which the two N have both parallel and P N = A characteristics, e.g. in crushed against the wall of the building or heard the paddle of the canoe. Internally the N P N is of the P N = A type. But in relation to the preceding V, each N occurs in similar sentence environments as object N of that V. That is, N₁ and N₂ occur in same sentence environments after this V, even though they do not otherwise, and in respect to this they are parallel.

¹⁴ The P N = A type of N₁ P₃ N₂ also often occurs in reverse order, N₂ P₄ N₁, but with different sentence environment, usually different P, and with a change of headship: The name of the lists is ‘Soldiers killed in battle‘. Since the environment is not held constant, there is little interest in this unless some particular relations can be stated, e.g. between the P₃ and P₄ choices.

¹⁵ Where X (or Y) in the given environment participates in a discontinuous morpheme extending to another construction, we find this participation on both X and Y of X C Y: He reads, He reads and writes. Certain C may be defined as participating in such an extending morpheme even where their X or Y alone would not : in N_i and N_j V, the V generally shows the plural morpheme even when N_i V or N_j V alone does not (A man and woman are here but A man is here).

¹⁶ By Noam Chomsky.

¹⁷ This zero morpheme meets the requirements for a zero—of being determined by observable conditions (namely I, you, and plurals as subject) ; and it satisfies the meaning of V + zero, which is not just V in general but V in the present tense. The -s ‘third person singular’ can now be considered an alternant of this zero, occurring with the remaining subjects.

¹⁸ For convenience, we will henceforth consider the -ed and zero (and -s) suffixes to be members of the auxiliary class v; this requires us to view could, should, etc. as independent members of v rather than as can, shall, etc. + -ed. Alternatively we can regard the suffixes as a separate class, and could as can + -ed, etc. But should, would often occur in environments where -ed does not otherwise occur (e.g. I would, if he will too). Furthermore, we would have to note that can etc. occur with -ed (to make could) but not with -s (He can, but He sees). Note in the whole analysis the departure of structural considerations from historical antecedents.

¹⁹ These are only combinations that constitute verb structures. To each of these can be added be -en just before the V, forming the passive of that construction; but this involves also a certain rearrangement of the sentence environment (§4.11). A few other combinations occur, as in He has had stolen from him two invaluable manuscripts, which seems to contain v + have -en + have -en + V. But the constituent analysis here is not he (subject N) + has had stolen (V) + P N + object N-phrase, for these cannot be rearranged like other N, V, P N, or replaced here by other N, V, P N. This sentence has to be analyzed as a transformation; even without that the stolen would be taken with from him, not with has had. Note the alternative form He has had two invaluable manuscripts stolen from him.

²⁰ The N being subject of the V. If which follows N P N, either of the N may be the one with similar co-occurrents : I was watching the wall of books which ().

²¹ In English the antecedent is almost always in a different sentence structure from the pro-morpheme, though both sentence structures may be within the same sentence.(Sentence structure is used here to mean any sequence which is a transform of a sentence, such as which had cracked in The wall which had cracked finally collapsed.) An exception is pronoun + self, whose antecedent is almost always the subject : Carl saw himself, Carl went by himself, Carl himself saw it. This can perhaps be analyzed as not a pronoun but just a morpheme self (different from the self), with the subject having a discontinuous repetition (in pronoun form) before this self. However, pronoun + 's (which is a member of A) occurs freely in the same clause as its antecedent N : He took his books.

²² The total co-occurrence range of a free he equals the total co-occurrence ranges of all bound he. A marginal case is such pronoun occurrences as unstressed you're, we're, one's in () only young once, which can perhaps be replaced by all members of N, or perhaps only by a new subclass of N (people, Jim, etc. ; whereas one can otherwise be substituted by any N). In contrast, the it of It's raining is not a pro-morpheme at all: almost no other morpheme can substitute for it here, so that this it is just a member of N.

²³ We also find some as a member of T (article class) in some person. Many words are members of more than one class.

²⁴ The s of ours, yours, etc. and the n of mine are also pro-N : I'll take my book and you take yours.

²⁵ The following analysis will show who to contain the morpheme wh- even though it lacks the phonemic /hw/.

²⁶ Various additional considerations show that these morphemes belong to the classes missing in the sentence structure that follows them. For example, P occurs in general only before N, but it also occurs before whom, which, what (to whom, from which, etc.). Throughout §2.62 N indicates N-phrase: the wh- words replace a full N-phrase and do not have T or A before them; and V will be used for V-phrase. Whenever S is written here directly after wh- it is understood that some part of this S is occupied by the post-wh- morpheme, e.g. ... who went is wh- S, the -o being the subject N ; whom I saw is wh- S, the -om being the object N.

²⁷ We find that in place of who, whom, which, and a zero morpheme in place of whom, which, when no P precedes these: a flower that had dropped, the place I mentioned. We regard that or zero as variants of wh-, with the -o, -om, -ich appearing after it in a zero variant. In the first S₁ wh- S₂ type below, that or a zero morpheme replaces the wh-, with the post-wh- morpheme appearing in full in S₂: I know who came, I know that he came. Justification for these analyses becomes apparent when all the constructions are compared.

²⁸ It is impossible to give here all the co-occurrence characteristics which justify these analyses, but as an example note that in sentences like I found what you lost the two verbs are always such as have some nouns (not merely pronouns) which are common to both their object ranges. We would hardly find, for example, I bit what you extrapolated.

²⁹ Among minor occurrences of wh- note these : wh- S constituting an independent subject N-phrase, primarily in N is N sentences and passives (Who did it is a question, Who did it can no longer be discovered) ; wh-ever S as independent N-phrase (Whoever did it was a fool) ; the construction What a clean job !; while as a C. Sentences like I know where may be analyzed as I know where S with the S present in a zero pro-morpheme; the antecedent S is usually present in the neighborhood.

³⁰ After constructions like I am going, I have gone, the second part is but he isn't, but he hasn't, not but he doesn't. The is and has operate like members of v. After I will be going the second part is and so will you be or and so will you, with the be repeated like a member of v or zeroed like a V. A similar situation occurs in N is N sentences : He's a fool but she isn't, He'll be late but she won't be or but she won't. And the case is similar for Y to Y and V Ying sequences : I'll try to catch it if you will or if you try.

³¹ In He came, and fast, we satisfy the property of C of always occurring between identical constructions, by saying that a zero pro-S of he came occurs before fast. This is supported by the fact that the D word in the position of fast will always be in the D-co-occurrence of the verb of the preceding section (came).

³² There are many subtypes. For example, there is no The scare made the girVs scream. Note the general similarities to the constructions of §2.8.

³³ Some first V have a P before the second V: insist on going, insist on you going, succeed in taking, stop noticing, stop him from noticing, stop him noticing.

³⁴ It will be noted later that for each such construction V N₁ N₂ the same morphemes also occur in the construction VN₂ P N₁: give a book to the fellow, ask a question of him. But this is a transformational criterion, such as we are skirting here : the constructional status here is to be determined only by grammar and co-occurrence ranges. Some additional transformational properties characterize only this structure: the transformation of replacing the second N by its pro-N generally involves interchange of the two N (give it to the fellow) but not so for the first N (give him a book); there are two passive transformations, one of which shows the P N character of the first N (A book was given to the fellow, The fellow was given a book).

³⁵ Similarly in N Vⁿ N : They are honorary members. The shambles above does not conflict since it is preceded by the singular a and is hence singular like its first N barn.

³⁶ This construction is thus seen to have some similarities to the N₁ V₁ (N₂ V₂) of §2.7 (We heard it flow etc.), although the V₁ there is not in the V^b subclass. When transformations are considered, these two will be found to be special cases of the same transformation.

³⁷ Furthermore, V has restricted co-occurrence relations to P (i.e. there are specific V P pairs) in such forms as He took the project over, but V does not seem to have specific pairs with the second N of V N N. A different analysis of this and of forms like threw the door open is proposed by Noam Chomsky.

³⁸ There may be small differences in meaning, and large differences in style; this does not affect the fact (but only the interpretation) of the co-occurrence equivalences discussed above or the transformational equivalences discussed below.

³⁹ There is also a minor type of question-assertion sequence, as in Did you go to Rome, or to Paris?, Did you, or she, do it?. These have two like constituents joined by or, with a rising intonation on the first and a falling intonation at sentence-end. (It is distinct from the yes-no question Did you or she do it? with one rising intonation.) The assertion here is I went to Rome or To Rome (and She or She did or She did it). The two or more constituents joined by or function like the post-wh- morpheme of that status (to Rome, or to Paris functions like where; the pro-morpheme equals a disjunction of members of its class). That is, the assertion always contains a constituent of that constructional status (e.g. To Rome, or perhaps Neither, just to Marseilles) and repetitions, pro-morphemes, or zeros of the rest of the question as above.

⁴⁰ From this it follows, incidentally, that two matched sentences do not occur in identical environments even if their introducers seem to be identical: they really appear in two different positions in respect to their one discontinuous matching introducer: people are cynical occurs in position ()₁ and people are not cynical occurs in position ()₂ of the environment Some ()₁ Some ()₂.

⁴¹ Some of these C occur also with a different transformation, in which the subject N is zeroed and the V has -ing instead of a tense or auxiliary v: The sailors got the raise while (still) organizing for it. When the reconstructed secondary would be N is N, N is A, or N is P N, this transformation may treat is as a V or may drop the is, when the subject N is zeroed: The sailors got the raise while being on duty or while on duty. In this transformation the secondary sentence (C + S₂) often appears first : While walking home, we found this stone. In Walking home, we found this stone we can say there is a zero member of C. With zero and certain other C, the zeroed subject N is followed by to V in the place of v V: To get there we must rush; They rushed so as to get there on time.

⁴² Certain occurrences of and and or cannot be regarded as deriving in this way from two sentences; e.g. Sugar and water make syrup (compare Sugar with water makes syrup), They argued back and forth, a black and white drawing, She and I disagreed. It is generally possible to characterize these cases. Certain specific combinations of specific morphemes + and fall in this category, e.g. between N and N (I lost it somewhere between Fifth and Sixth). In the case of N and N V each other (Electrons and positrons repel each other) we do not directly expand the N and N because of the pro-N-pair each other.

⁴³ The distinctions have to be drawn carefully. Coordinating conjunctions do not necessarily have reversible order : The goldfish ate too much and died.

⁴⁴ He is richer than you is not He is rich + you are rich but He is rich + -er than + you are rich. Cf. Edward Sapir, Grading: A study in semantics, Philosophy of science 11.93-116 (1944).

⁴⁵ The first sentence may have an object, as in I phoned him to learn what was going on, transformed from N₁ V₁ N₂ and N₁ V₂. Superficially this can be confused with the next case below (N₁ V₁ N₂ and N₂ V₂) until the various co-occurrence ranges are checked, as also the substitutability of C (I phoned him in order to ...). When both N₁ and N₂ are in the subject range for V₂, the sentence is ambiguous, and both analyses (and both meanings) are possible. (Such homonymities appear wherever a single resultant structure is obtained from different transformations and underlying sentences.) Example: We saw him up there from We saw him + We were up there or from We saw him + He was up there.

⁴⁶ Another transformation for two sentences with the same object will be seen in §3.8. The shared words, like the zeros of the parallel sentences (§§3.3-5) and bound pro-morphemes in general, are not merely two independent occurrences of the same morpheme. Rather, the morpheme in question extends into the shared, zero, or pro-morphemed position in the next sentence. Hence the meaning of the underlying sentences is not merely that I bought a house and that he built a house, but that the house that I bought and the one that he built are the same.

⁴⁷ This formulation overlooks the fact that certain sentences containing N_i may not co-occur with some particular N_i is () sentences. The more exact statement therefore is: Any sentence S₁ which contains an N_i-phrase (provided the N_i-phrase is a transform of an N_i is [ ] sentence) can be analyzed as a shared-word combination of S₁ with N_i in place of the N_i-phrase + the corresponding N_i is sentence.

⁴⁸ Cf. the end of §2.62.

⁴⁹ But other V + P N do not have this transformation : there is no passive of The flowers grew near the wall. Nor does the passive occur with N is N sentences: They became refugees, We are at peace. In N is N sentences the long morphemes -s ‘plural’ etc. extend over both N ; the position of the second N can be occupied by any N-phrase, PN-phrase, or A-phrase (including Ving, or Ven from the passive) ; and a certain subclass of V including become, remain, etc. occurs in the position of is.

⁵⁰ The V P mentioned above operates like the first X position. All these examples have shown the passive of a primary S₁ which includes a secondary S₂ in one of its N positions. The secondary S₂ could be transformed into a passive without affecting the primary : Many thousands watched the daredevils race the cars, Many thousands watched the cars being raced by the daredevils. Or both primary and secondary can be transformed: The cars being raced by the daredevils were watched by many thousands. In the shared-word sequence (§3.6), the primary sentence can be transformed, but the secondary only if the result fits with the restrictions on word-sharing. In contrast, there is no passive of V to V constructions because these do not constitute a single sentence structure composed out of S₁ and S₂ but two parallel structures (§3.5) : I phoned to meet him.

⁵¹ The by which is a member of P has restrictions of co-occurrence; that is, it occurs between certain V_i and N_j and not between others. The by of the passive occurs between any V_i and N_j which satisfy N_j V_i.

⁵² Among the many details omitted here are the characterizations of such exceptions which do not transform as It caught fire. There is a partial transformation with -able in the position of -en: The milk is drinkable by the children. But there are various restrictions on the occurrence of this -able, so that it can only be considered a quasi-transformation (§4.5). Note that there is a semantic addition in -able such as we do not have in the -en passive.

⁵³ There are many other introducers, with the constructional status of D, P N, or N V that, which occur with almost any sentence: perhaps, certainly, in general, It is probable that, etc. We could propose transformations, for example: S ⟷ It is probable that S ; or N v V D ⟷ How D N v V! (How quickly he came!). Since there may be some S with which these do not occur, we have to consider them quasi-transformations (§4.5) ; note that they contribute more specific semantic additions than do the transformations.

⁵⁴ Certain dependent order changes may be mentioned here, though they can be regarded as part of the sentence-elements with which they occur. Most of these are limited to S₂ position (after particular combining elements). The order change N v → v N is usual with the question intonation, and always with the element wh-? ; the inversion of tenses with not can be expressed by assuming not to occur before v and adding not v → v not; and the bringing of the pro-morphemed section to the beginning of the sentence occurs always after wh-.

⁵⁵ Here and in the other transformations it is only the v proper (auxiliary or tense) that is dropped. The expansions of v (be -ing, have -en) remain, and the -ing is added to the first of them (except that the sequence being Ving is avoided) : He has read → His having read, He has been reading → His having been reading.

⁵⁶ After -s the parenthesized of always occurs. More restrictedly, as a quasi-transformation, we have in the position of Ving (of) N₂: your play-readings. Another quasi-transformation is N₁ is a Ver of N₂, Ń₁ is a , and (dropping the N₁) : He is a play-reader, etc.

⁵⁷ In a quoted-sentence object of N₁ said to N₂, I is a pronoun of N₁, you is a pronoun of N₂. The position of the quote marker can be occupied by that (or zero), in which case the special pronoun relations above do not hold, and certain changes occur in the v.

⁵⁸ The case where the set of n-tuples that satisfy one construction is included in the set of n-tuples that satisfy another construction (rather than being identical with that other set) is a one-directional transformation (e.g. §4.11), but does not have to be regarded as a quasi-transformation.

⁵⁹ In general, a given structure may be subject to several transformations, e.g. N v V N, or the object N (or any N) position in a primary sentence. And a given transformation may occur in more than one structure, e.g. zero recurrence, or N v inversion. It may be possible to characterize for a given language what types of transformations occur in what types of structures.

⁶⁰ If two transformations occur in complementary products, so that they do not both occur in the same position, we can call them positional variants of each other, and say that they are the same transformation (but with the observed different values in the different positions).

⁶¹ The set of all sentences is closed with respect to transformations. If homonymous sentences can be suitably distinguished or marked, the set of all transformations (all the occurring products of the elementary transformations) yields a partition of the set of sentences. The set of transformations is thus a quotient set of the set of sentences. If we now map the set of sentences into the set of transformations (so that each sentence is associated with the particular product of transformations that is present in it), then those sentences which are carried into the identity transformation are the kernel of the set of sentences with respect to this mapping. These kernel sentences are precisely the underlying elementary sentences mentioned above.

⁶² But V ! is an N v V kernel sentence with zero variant of you, plus exclamatory intonation. Note that only sequential sentences, or sentences with internal evidence of zeros (as in the case of V!), are built up to full sentence structure. The traditional Fire! is left as it stands; we cannot know with what words to fill it out.

⁶³ Most cases of Ving will occur under V (either from is -ing, as an expansion of v, + V; or else from various transforms of V). But some cases are members of A; these appear in co-occurrences which are not the same as those of the corresponding V. Example : unyielding, and understanding in He has a very understanding manner.

⁶⁴ The sentences of a kernel are therefore maximally independent of each other; one can say that they give the least possible information about each other. (In contrast, transforms obviously contain information about each other, as do sequential sentences.) Nevertheless, some kinds of dependences between sentences cannot be removed by the methods mentioned here, and remain in the kernel. Such are for example dependences among loose and unspecifiable subclasses, e.g. the partitive adjectives of a particular noun: the occurrence of one of them in a kernel sentence tells us that a partly similar sentence with another partitive adjective of that noun also exists in the kernel.

⁶⁵ Both types of problems are discussed in detail and provided with a theoretical framework in Noam Chomsky's dissertation, Transformational analysis.

⁶⁶ Such added flexibilities are often attained when a transformation gives the sentence the form of a different structure which has that flexibility, in this case the similarity between the passive and an N V P N sentence with omittable P N.

⁶⁷ This has been shown by Noam Chomsky, in the reference given in fn. 1.

⁶⁸ There are also possible applications in translation, for many languages are more similar in their kernel sentences than in their total structure (the transformations, and especially the details of the transformations, being more different). Translational equivalences can be established for the kernel combinations of words, and if necessary even for the elementary transformations as such. There is also some reason to think that the kernels may function differently in memory and thought from the transformations.