The Syntax of Programmnig Languages-A Survey

ROBERT W. FLOYD

Summary-The syntactic rules for many programming languages of the way quotation marks are used in English, for the have been expressed by formal grammars, generally variants of same purpose, to distinguish phrase-structure grammars. The syntactic analysis essential to translation of programming languages can be done entirely me- The baby can say "one word" chanically for such languages. Major problems remain in rendering analyzers efficient in use of space and time and in finding fully satis- from factory formal grammars for present and future programming lan- guages. The baby can say one word. INTRODUCTION Names of phrase types appearing in the text are hyphen- ated to show explicitly that the separate words of a N RECENT YEARS, few programming languages name need have no individual meaning and that the designed for widespread use have escaped having name as a whole is used as a technical term, without the more orderly part of their formation rules and such connotations as its individual words may suggest. restrictions presented in one of several simple tabular The angular brackets enclosing a name in a grammatical forms, somewhat like the axioms of a formal mathe- rule share this function. A complete set of grammatical matical system. ALGOL, JOVIAL, FORTRAN, rules for a language written in a format equivalent to NELIAC, COBOL, BALGOL, MAC, APT, and their that of the example is a phrase-structure grammar offshoots have all been defined in such a fashion (see (PSG); a language definable by a PSG is a phrase- Sections A and B of the bibliography). For some of structure language (PSL).' these languages, the formalism is easy and natural. For In general, a phrase-structure grammar, taken as a set others, it is not; FORTRAN [A9} suffers needlessly, of definitions, provides a list of alternative constructions bound in the unaccustomed corsetry of her younger in a definition for each syntactic type, where each con- rival's design. Whatever the merits of formal grammars struction is a list of characters and syntactic type names. in general, some languages are best defined in words. A construction represents the set of phrases which can Where formal grammars are appropriate, however, be formed by replacing each syntactic type name with mathematical and linguistic analysis provides compilers a phrase of that type; the phrases of a certain type are of lower cost and high reliability, and theoretical all those represented by some construction in the defi- knowledge about the structure and value of the language nition of that type. There is usually a single syntactic itself. type, called "program" (or "sentence"), which is used PHRASE-STRUCTURE GRAMMARS in the definition of no other type; the set of phrases of this type is the language defined by the grammar. On The most representative and fruitful example of the the one hand, PSG's can define some languages of con- use of a formal grammar in defining a programming siderable complexity; on the other, such simple sets of language is the use of a phrase-structure grammar to strings as that consisting of 'abc,' 'aabbcc,' 'aaabbbccc,' specify most of the syntactic rules of ALGOL 60 [A7], etc., are demonstrably not definable by any phrase [A8], [B1], [B5] The form for grammatical rules used structure grammar [C4]. in the report which officially defines ALGOL 60 is It is evident that a complete definition of a pro- typified [Al] by gramming language may be expressed far more con- (for statement):: = (for clause) (statement) cisely by a PSG than by the corresponding English | statement). sentences and that it is humanly impossible to read or (label): (for write those sentences, with their hundreds of occur- This assertion can be read "A for-statement is defined rences of 'is defined to be,' 'followed by,' and 'or.' If a to be a for-clause followed by a statement, or a label phrase-structure grammar is nearly adequate to define followed by a colon ':' followed by a for-statement." a language, then most of the rules defining the language The symbol ' *: =' stands for 'is defined to be'; ' |' stands for 'or' and is used to separate alternative forms of the I The type of grammar described here is sometimes called a con- text-free phrase-structure grammar, as distinguished from a more gen- definiendum. The angular brackets'( )' are used to en- eral type of grammar, the context-dependent phrase-structure gram- close each name of a phrase type, distinguishing it as a mar. The latter has no known applications to programming languages, the term "phrase-structure" is not necessarily appropriate for a con- name, rather than the thing named. This is the reverse text-dependent grammar, and the term "context-free" has certain misleading implications; we will therefore use the short term "phrase- structure grammar" for what is sometimes also called a context-free Manuscript received Febrary 3, 1964; revised May 4, 1964. phrase-structure grammar [C6], simple phrase structure grammar The author is with Computer Associates, Inc., Wakefield, Mass. [Cl], or Type 2 grammar [C41. 346 Floyd: Syntax of Programming Languages 347 can be neatly and compactly listed without explanation, 5) 'John' followed by any verb followed by 'Mary' is conserving space, time, and clarity; attention may be a sentence. concentrated on the few syntactic rules which do not fit d) 'Loves' is a verb. the pattern of phrase definitions. 6) 'John loves Mary' is a sentence. As mentioned above, the rules of a PSG are analogous in a phrase structure has From this point of view, a sentence to axioms. One who somehow obtained a program language is the last line of a derivation from the symbol and an understanding of its structure can use a PSG '(sentence),' provided that no further substitutions are to prove the program is well formed and to demonstrate possible.3 The grammar is regarded not as an axiom the structure to others. The usefulness of a PSG to a sentences but as a device for programmer writing in the language, or to the compiler scheme for validating which translates it into machine language coding, is generating them. When a PSG is considered as a genera- A not us how tive grammar, its rules are commonly called productions. less apparent. grammar does tell to syn- The two viewpoints are substantially equivalent, but a it not us how to thesize specific program; does tell the generative viewpoint, by making explicit the process analyze a particular given program.2 In order to construct programs in a phrase-structure by which sentences are constructed, makes the grammar a A writer of may every rule of its grammar more tractable object of study. programs language, one interpret in a now be thought of as a device to generate as a permit to perform certain acts of substitution. PSL can a to each syntactic type of a grammar, sentences, with choices between alternatives governed, Assigning symbol the let us interpret each rule as allowing the substitution, for example, by the structure of a flow chart of for the definiendum, of any one of the alternative de- program. Not enough is known about linguistic behavior finientes. Applying these substitution rules repeatedly to specify the mechanism of choice in detail. to type A compact representation of a derivation is the syntax the symbol designating the syntactic 'program' for the derivation or 'sentence,' we arrive eventually at a sequence of sym- tree [C3], [Gi]; the syntax tree bols in which no further substitutions can take place; above is: this string is a program or sentence in the language, the process by which it was produced being an abbreviated (sentence) proof of its sentencehood. The symbols designating syn- (noun) (predicate) tactic types, for which substitutions may be made, are called nonterminal characters; those undefined symbols which form sentences are the terminal characters. (v (noun) Take, for instance, the grammar: John loves lary a) (sentence)-*(noun)(predicate) b) (predicate)-*>(verb)(noun) c) (noun)-*John| Mary In general, a syntax tree is like a genealogical tree for a d) (verb)--loves. family whose common ancestor is (sentence), where the immediate descendants (sons) of a symbol form one of Successive substitution, starting with (sentence), the alternatives of the definition of that symbol and gives the sequence where only the terminal characters fail to have de- 1) (sentence) scendants. Such a tree represents a derivation of the 2) (noun)(predicate) sentence formed by its terminal characters. It also 3) John (predicate) illustrates the structure of the sentence; the terminal 4) John (verb)(noun) descendants of any node on the tree form a phrase in 5) John (verb) Mary the sentence, of the type designated by that node. In a 6) John loves Mary. language satisfactorily described by its grammar, the phrases of a sentence are its meaningful units. Some This sequence, a derivation of the sentence "John compilers take advantage of this, creating a syntax tree loves Mary," is an abbreviation of the following proof: as a structured representation of the information con- 1) Any sentence is a sentence. tained in the source program. Suitable processes then a) A noun followed by a predicate is a sentence. translate the tree into a computer program, or a deri- 2) Any noun followed by any predicate is a sentence. vation tree for an equivalent sentence in another lan- c) 'John' is a noun. guage or a related sentence in the same language. 3) 'John' followed by any predicate is a sentence. SYNTAX-DIRECTED ANALYSIS b) A verb followed by a noun is a predicate. 4) 'John' followed by any verb followed by any noun A syntax-directed analyzer might be defined as any is a sentence. procedure capable of constructing a syntax tree for an c) 'Mary' is a noun. arbitrary sentence in an arbitrary PSL. This ideal, how-

I See Chomsky, [C31, p. 48. 3 See Chomsky, [C31, ch. 4. 348 IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS August ever, is rarely achieved; most syntax-directed analyzers 'a.' 53 covers 'a,' reports success. S2 reports success. are restricted to languages whose grammars satisfy cer- SI appoints 84 to find 'c.' S4 sees 'b' in the sentence, re- tain special conditions. Let us consider a typical pro- ports failure. Si fires S4 and tells S2 to try again. S2 tells cedure for syntax-directed analysis. 83 to try again. S3 uncovers 'a,' reports failure. S2 fires Because the analyzer makes use of a complicated S3, then appoints S3 to find a Z. S3 appoints S4 to find hierarchy of subordinate goals in seeking its principal 'a.' S4 covers 'a,' reports success. S3 appoints S5 to find goal, we will introduce it with a metaphor. Suppose a 'b.' S5 covers 'b,' reports success. S3 reports success. S2 man is assigned the goal of analyzing a sentence in a reports success. Si appoints S6 to find 'c.' S6 covers 'c,' PSL of known grammar. He has the power to hire sub- reports success. Si reports success. The organization ordinates, assign them tasks, and fire them if they fail; chart of Si and his subordinates, they in turn have the same power. The convention will be adhered to that each man will be told only once Si "try to find a G" where G is a symbol of the language, S2 S6 and may thereafter be repeatedly told "try again" if the particular instance of a G which he finds proves un- S3 satisfactory to his superiors. Depending on the form of the definition of G, each subordinate (e.g., S) should S4 S5 adopt an appropriate strategy: when labeled with goals rather than names, gives the 1) If G is a terminal character, and if it is the next syntax tree character of the sentence, S must cover the character, and report success to his superior. If it is not the next x character of the sentence, S must report failure. After Y c success, if told by his superior to try again, S must report failure and uncover the character. z 2) If G--G1, S must appoint a subordinate S1 with the command, "Try to find a G1." S repeats SI's report to a b his superior, firing SI on a report of failure. If told to of the sentence 'abc.' try again, S must tell Si to try again, again transmitting This metaphor conceals certain difficulties by rele- the report to his superior and firing Si on failure. gating bookkeeping tasks to imaginary men who are 3) If G- G1G2 - - G,,C S must appoint successively assumed to automatically appear when hired, disappear one subordinate Si for each G,, with the command, when fired, remember the names of their subordinates "Try to find a G,." If Si succeeds, i is increased by one, and superiors, and so on. It is not difficult, however, by a new subordinate hired and the process repeated until the use of a stack (pushdown list) to simulate the i>n, when S reports success. If Si fails Si is fired, i is process on a computer, making the entire process ex- decreased by one and if i > 0, the new S, (predecessor of plicit. As a convenience for the analyzer, let each de- he who failed) told to try again. If i =0, S reports failure, finiens of the grammar be followed by the additional having exhausted all ways of finding a G. If after suc- symbols "|I - ," so that "A ->B CD" would be rewritten cess, S is told to try again, he sets i = n, tells Si to try "A ->B CD H ." Each subordinate in the metaphor is again, and proceeds as before on Si's report. represented by an element Sx of a stack, and contains 4) If G--G1 G2 . G,C S must appoint successively five fields: goal),, the fixed goal given to Sx by this su- one subordinate Si for each Gi, with the command, "Try perior; ix, the place in the definition of goal at which Sx to find a Gi." If Si fails he is fired, i is increased by one, a is reading in the grammar; supx, the name -of S,'s new subordinate hired, and the process repeated until superior (i.e., his location in the stack); sub?, the name i>n, when S reports failure. If Si succeeds, S reports of Sx's most recently-appointed subordinate; and success. If after success S is told to try again, he tells S5 predx,, the predcesesor of Sx among the subordinates of (who succeeded) to try again, and proceeds as before on his superior. For each field, a zero specifies the absence Si9s report. of a value. The chief executive of the process, Si, is set 5) All more complicated definitions can be regarded initially to have a goal of '(sentence)' with all other as built up from the first four types. fields set to zero. The index X signifies the subordinate As an example, take the sentence 'abc' and the S), who is currently active; the index v signifies the first grammar element of the stack to which no goal is currently as- first X -> Yc signed. The indexj signifies the uncovered character of the input string. The grammar is represented by the Y->a z vector gram, of which each character either belongs to Z -> ab the language defined or is one of (-*>, 1, H). All occur- rences of S, goal, i, sup, sub, and pred, unless otherwise in which X represents (sentence). Si is appointed to find indexed, are implicitly indexed with X. an X. Si appoints S2 to find a Y. S2 appoints S3 to find When the algorithm terminates successfully, the con- 1964 Floyd: Syntax of Programming Languages 349 tents of the stack represent a syntax tree for the sen- of your goal. His superior is you, his tence taken from the input string. Each word in the predecessor your previously junior sub- stack represents a node in the tree, where goal repre- ordinate. Remember only your most recent sents the label of the node, i is the index in gram of subordinate, protect him from other assign- the following the rule of the grammar applied at that ments, and await his report. node, sup designates the parent node, sub designates M= Report success to your superior, who pro- the rightmost son of the node, and pred designates ceeds through the definition of his goal. the sibling immediately to the left of the node. Only N= Report failure to your superior, who will goal, sub, and pred are needed in order to construct the take your predecessor as his junior sub- tree. Thus the tree ordinate and fire you. A 0 = When told to try again, determine again whether your local is terminal or not. B 'C P = If terminal, uncover the input character you previously covered, and report failure. D E F Q, R = If goal is nonterminal, tell your junior sub- ordinate to try again. x y z S, T= If you have no junior subordinate, you have would be represented by the stack: exhausted an alternative; try the next one. Goal i sup sub pred 1 A ? 0 4 0 2 B ? 1 3 0 3 x 0 2 0 0 4 C ? 1 9 2 5 D ? 4 6 0

6 y 0 5 0 0 7 E ? 4 8 5 8 z 0 7 0 0 9 F ? 4 10 7 10 0 9 0 0

Fig. 1 is a flowchart for this process. There follows M an item-by-item explanation of the flowchart. SUCCESS~ _ x sup i I 1 A =Chief executive SI is appointed to find a sentence. S2 awaits employment. B = You are a newly appointed subordinate (SX); determine whether your goal is a non- terminal (defined) character, or terminal. C, D = If the first character of the input sentence is your goal, cover it and report success to your superior; otherwise report failure and

await temporary unemployment. = Sx (9oaIx, ij , SUpx , sub, pred.) E = Find the beginning of the definition of your goal. by means not described here. Prepare Fig. 1-Flowchart for syntax-directed analysis. to read that definition. F, G, H= If you have reached a '|' in the definition The serious and intrinsic flaw of the algorithm is that of your goal, report success unless you are it fails for grammars whose rules contain certain types the chief executive, in which case you have of cyclic formations. If the definition of A contains an analyzed the sentence. alternative beginning with A, or if one of the alterna- I, J, K = If you have exhausted all alternatives in the tives for A begins with B, one of those for B begins with definition of your goal, report failure unless C, and one of these for C begins with A, e.g., then certain you are the chief executive, in which case choices of input string lead the procedure into an infinite the input is not a sentence. loop. A grammar containing such formations is called L = Otherwise, appoint a subordinate whose left-recursive [G3]. It is possible, at some cost to the goal is the next character in the definition explanatory power of a grammar, to reformulate it ex- 350 IEEE TRANSACTIONS ON ELECTRONIC COMPUTERS August cluding left-recursive definition [C1i]. This has been separated by at most one phrase, then there is some successfully done for several programming languages in phrase to which the multiplication sign and any phrase the Compass compiler [D5], [D15]. A second type of adjacent to it belong, but not containing the left paren- syntax-directed analyzer, which is free of the left- thesis. The relation is symbolized, '(<.X,' where the recursion problem, constructs the syntax tree not from sign '< ' is read 'yields precedence to.' Similarly, if 'X' the top down, but from the bottom up [Cii], [D2], is followed by '+' with at most one phrase between, [D5], [D8], [G4]; it is, however, as presently formu- some phrase contains the multiplication sign and any lated, subject to other restrictions. All syntax-directed phrases adjacent to it, but not the plus sign. This rela- analyzers currently known are further restricted in tion is symbolized 'X-> +,' where '->' is read 'takes practice to nonpathological languages; if a sentence is precedence over.' We may deduce that whenever chosen at random from the grammar S >AIB occurs in an ALGOL program, and a and b are arbitrary A-(A) (B)jx phrases, then 'aXb' is a phrase. A third relation, '(_),' B (A] (B]|y, applies to characters of equal precedence. While analysis based on precedence relations does not yield a complete analysis will require a time which increases exponen- derivation of a sentence, it determines the phrases of tially with the length of the sentence, if read from left the sentence and the operators connecting them, which to right. At each character of the first half of the sen- is normally sufficient information for use by a compiler. tence, choice must be made between two alternatives. Not every grammar is amenable to precedence analy- Not until the second half of the sentence is read is any sis. Yet, like phrase-structure grammars, matrices repre- information gained about the correctness of these senting precedence relations are generally adequate for choices. Typical processes will back up and try again the description of the structure of programs in standard many times before hitting on the right pattern. A re- programming languages. Because a precedence matrix lated grammar may be designed to exhaust the patience can be derived from a grammar, and applied to syn- of all known syntax-directed analyzers, whether their tactic analysis, by a completely mechanical process, prejudices be left, right, or center. precedence analysis offers much the same flexibility and It is not known whether a method of syntactic analy- universality as does syntax-directed analysis. sis is possible for which the time required for analysis Neither syntax-directed nor syntax-controlled ana- does not increase exponentially with the length of the lyzers are capable, by themselves, of dealing with non- sentence, even for pathological languages. Known sentences. Syntax-directed analyzers are usually in- methods of full generality, such as the systematic genera- capacitated by syntactic errors in their input sentences tion of all sentences until a match is found, would be [D5], [D9]. Precedence methods are more flexible, but unacceptably slow even for short sentences. The proper- still require explicit specification of error recovery ties of programming languages which make them legible policies. Chomsky has proposed that an adequate to human readers, however, allow them to be analyzed grammar for a natural language must account for our by simple and efficient methods. A case in point is ability to interpret ungrammatical sentences [G3]. Such COBOL, for which a syntax-directed analyzer is greatly grammars are doubly necessary for programming lan- simplified because each choice among alternative con- guages, at least to the extent of localizing the effects of structions can be decided by examining the first char- programming errors. acter or word of that construction [D6]. ADEQUACY SYNTAX-CONTROLLED ANALYSIS The phrase-structure grammar, though developed as An alternative approach to syntactic analysis of a model for natural language, is generally considered in- phrase structure languages, sometimes called syntax- adequate to represent either the structure or the con- controlled analysis, entails a preliminary processing of straints imposed on sentences in most natural languages a grammar during which matrices, tables, and lists are [C3], [C5]. Nor is the PSG sufficient to fully describe constructed describing in some sense the possible con- the formation rules of most programming languages. structions of the grammar. Analysis of sentences then Most require, for example, that the arithmetic type of makes use of these tabulations, and may even dispense each variable be declared before using it in a formula entirely with the original grammar. or that dimensions of an array be specified before re- As an example, let us consider precedence analysis ferring to one of its elements. Rules of this type cannot [E2], which is a formalization and extension of methods be incorporated in a PSG [C7]; nor can the rules for of analysis which were used in compilers even before writing DO-loops in FORTRAN [A9]. Any rule re- formal grammars were employed in defining program- quiring that two or more constituent phrases of a con- ming languages. From the grammar of ALGOL it is struction be identical (or different) is almost certainly possible to deduce that in any ALGOL program if a left beyond the scope of phrase-structure definition, as is the parenthesis '(' is followed by a multiplication sign 'X,' indication of scope of nested loops by indentation. 1964 Floyd: Syntax of Programming Languages 351 The PSG is nonetheless a valuable tool for describing [C5], [C14]. Chomsky [C4] and Bar-Hillel, Perles, and languages, both natural and artificial. Chomsky has Shamir [Ci] are important original papers on the described it as the only theory of grammar with any general theory of PSG's; Chomsky [C5] is a thorough linguistic motivation that is sufficiently simple to per- survey of known results about PSG's and related mit serious abstract study. Most published PSG's for language-generating devices. programming languages, while not serving as complete definitions, define languages which include the pro- UNSOLVED PROBLEMS gramming languages as subsets satisfying simple re- Many questions of practical importance in the design strictions, and correctly account for the structure of of programming languages and their compilers are un- programs. answered; some have not, to the writer's knowledge, in It EXTENSIONS been stated print. is not known, for example, how to synthesize a phrase-structure grammar for a program- The use of curly brackets around a part of a rule in ming language, given the precedence relations of its a PSG is sometimes used to signify an arbitrary number, operators. Such a synthesis method would have pre- possibly zero, of occurrences of the form described with- vented the costly ambiguities originally present in in the brackets. As a refinement, super- and subscripts on ALGOL 60. For a given language, it is not known how the closing bracket, if present, signify upper and lower to synthesize a grammar which best displays the struc- limits on the number. A variant uses square brackets to ture of its sentences, best accommodates a particular signify an optional single occurrence of the form de- method of syntactic analysis, or best accounts for the scribed within the brackets. The COBOL syntax uses a structure of sentences containing slight syntactic errors. two-dimensional display of alternatives and options. It is not known whether an analyzer is possible which While none of these operators extends the generative would not consume excessive space and time, even for power of PSG's, they all increase the convenience and pathological languages. Some of these questions are explanatory power. For example, a phrase-structure capable of precise formulation, but even rule-of-thumb description of the functionf(a, b, c, d), if general enough solutions for any of them would be valuable. to deal with functions of arbitrarily many variables, leads to such absurdities as assertions that 'a, b' is a BIBLIOGRAPHY phrase but 'c, d' is not. A definition using curly brackets, The bibliography which follows includes subjects (function)-- (function name) ((expression) related to the syntax of programming languages in-

{(expression), }) sofar as they illuminate the problems of analysis and synthesis of formally defined programming languages. avoids designating as phrases any parts of the function The bibliography is arranged by subjects, alphabetically except those which serve as names or have values. by author within each subject. Particularly recom- An extension to permit specification that two com- mended as introductions to their subjects are [A7 ], ponent phrases of a construction must be identical [A12], [B1], [Ci], [C3], [C4], [C5], [D5], [D12], increases the generative power of PSG's. Such a [E2], [E4], [FiG], [Gi], [G3] (subjects are desig- mechanism is used in Input Language (Siberian nated by letter, individual papers by number). ALGOL) [A5 ], to permit programs to contain relations like "Alpha1 < . . programming language for real-time for minimal linear grammars," Inf. and Control, vol. 6, pp. 119- command systems," in "Annual Review in Automatic Program- 125; June, 1963. ming," Pergamon Press, The Macmillan, Co., New York, N. Y., [11] S. A. Greibach, "Inverses of phrase structure generators," vol. 3, pp. 53-119; 1963. Ph.D. dissertation, Harvard University, Cambridge, Mass.; [121 W. Taylor, L. Turner, and R. Waychoff, "A syntactical chart June, 1963. of ALGOL 60," Comm. ACM, vol. 4, p. 393; September, 1961. [12] P. S. Landweber, "Three theorems on phrase structure gram- (See [A7].) mars of type 1," Inf. and Control, vol. 6, pp. 131-136; June, 1963. [13] N. Wirth, "A generalization of ALGOL," Comm. A CM, vol. 6, [13] G. H. Matthews, "Discontinuity and asymmetry in phrase pp. 547-554; September, 1963. structure grammars," Inf. and Control, vol. 6, 137-146; June, [14] W. W. Youden, "An analysis of ALGOL 60 syntax," Data Proc. 1963. Systems Div., Nat. Bureau of Standards, Washington, D. C.; [14] R. J. Parikh, "Language-generating devices," Res. Lab. of Elec- August 15, 1961. (See [A7].) tronics, MIT, Cambridge, Mass., Quarterly Progress Rept., [15] "Index to ALGOL 60 syntactical chart," Training and Educa- No. 60, pp. 199-212; January 15, 1961. tion Dept., E.D.P., RCA, Camden, N. J.; October 20, 1961. [15] M. P. Schiitzenberger, "On context-free languages and push- (See [A12].) down automata," Inf. and Control, vol. 6, pp. 246-264; Septem- [16] "COBOL 61, revised specifications for a common business- ber, 1963. oriented language," U. S. Govt. Printing Office, Washington, [16] See also [E2], [G3], [G4]. D. C., 0-598941; 1961. D. Syntax-Directed Analysis B. Expositions of Languages Defined [1] M. P. Barnett and R. P. Futrelle, "Syntactic analysis by digital by Formal Grammars computer," Comm. ACM, vol. 5, pp. 515-526; October, 1962. [2] A. L. Bastian, Jr., "A phrase-structure language translator," [1] H. Bottenbruch, "Structure and use of ALGOL 60," J. ACM, Air Force Cambridge Res. Labs., Hanscom Field, Mass., Rept. vol. 9, pp. 161-221; April, 1962. No. AFCRL-69-549; August, 1962. [2] E. W. Dijkstra, "A primer of ALGOL 60 programming," Aca- [3] R. A. Brooker and D. Morris, "A general translation program demic Press, New York, N. Y.; 1962. for phrase-structure languages," J. A CM, vol. 9, pp. 1-10; [3] H. D. Huskey, M. H. Halstead, and R. McArthur, "Neliac- January, 1962. a dialect of ALGOL, " Comm. A CM, vol. 3, pp. 463-468; August, [4] R. A. Brooker and D. Morris, "A compiler for a self-defining 1960. phrase structure language," Univ. of Manchester, England [4] D. E. Knuth and J. N. Merner, "ALGOL 60 confidential," (undated). Comm. A CM, vol. 4, pp. 268-272; June, 1961. [5] T. E. Cheatham, Jr., and K. Sattley, "Syntax-directed compil- [5] D. D. McCracken, "A Guide to ALGOL Programming," John ing," Proc. Spring Joint Computer Conf., Spartan Books, Balti- Wiley and Sons, Inc., New York, N. Y.; 1962. more, Md., vol. 25, pp. 31-57; 1964. [6] D. D. McCracken, "A Guide to COBOL Programming," John [6] M. E. Conway, "Design of a separable transition-diagram com- Wiley and Sons, Inc., New York, N. Y.; 1963. piler," Comm. A CM, vol. 6, pp. 396-408; July, 1963. [7] P. Naur, "A Course of ALGOL 60 Programming," Regnecen- [7] P. Z. Ingerman, "A syntax oriented compiler... " Moore tralen, Copenhagen, Denmark; 1961. School of Elec. Engineering, Univ. of Penn., Philadelphia; [8] D. T. Ross, "The design and use of the APT language for auto- April, 1963. matic programming of numerically controlled machine tools," [8] E. T. Irons, "A syntax directed compiler for ALGOL 60," Comm. Proc. Computer Applications Symposium, ITT Res. Inst., A CM, vol. 4, pp. 51-55; January, 1961. (See also reference Chicago, Ill., pp. 80-99; 1959. [D13].) [9] J. E. Sammet, "Basic elements of COBOL 61," Comm. ACM, [9] E. T. Irons, "An error-correcting parse algorithm," Comm. A CM, vol. 5, pp. 237-253; May, 1962. vol. 6, pp. 669-673; November, 1963. [10] J. E. Sammet, "Detailed description of COBOL," in "Annual [10] E. T. Irons, "The structure and use of the syntax-directed Review in Automatic Programming," Pergamon Press, The compiler," in "Annual Review in Automatic Programming," Macmillan Co., New York, N. Y., vol. 2, pp. 197-230; 1961. Pergamon Press, The Macmillan Company, New York, N. Y., [11] H. Schwarz, "An Introduction to ALGOL," Comm. ACM, vol. vol. 3, pp. 207-227; 1963. 5, pp. 82-95; February, 1962. [11] R. S. Ledley and J. B. Wilson, "Automatic-programming-lan- [12] Reference Manual, 709/7090 FORTRAN Programming System, guage translation through syntactical analysis," Comm. ACM, IBM Form No. C28-6054-2. vol. 5, pp. 145-155; March, 1962. [13] L. Bolliet, N. Gastinel, and P. J. Laurent, "Un Nouveau Lan- [12] P. 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