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■ft tr 
 
 Report No. 30^ 
 
 "fill tli 
 
 THE GENERATION OF A 
 DETERMINISTIC PARSING ALGORITHM 
 
 fey 
 
 Alan James Beals 
 
 January 6, 1969 
 
The person charging this material is re- 
 sponsible for its return on or before the 
 Latest Date stamped below. 
 
 Theft, mutilation, and underlining of books 
 are reasons for disciplinary action and may 
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 University of Illinois Library 
 
 im ■ m 
 
 MA' L2 
 
Report No. 30U 
 
 THE GENERATION OF A 
 DETERMINISTIC PARSING ALGORITHM* 
 
 by 
 
 Alan James Beals 
 
 January 6, 1969 
 
 Department of Computer Science 
 University of Illinois 
 Urbana, Illinois 6l801 
 
 * This work was supported in part by the Advanced Research Projects 
 Agency as administered by the Rome Air Development Center under 
 Contract No. US AT 30(602^ UlUU and submitted in partial fulfillment 
 of the requirements for the degree of Master of Science in Computer 
 Science, February, 1969. 
 
Ill 
 ACKNOWLEDGEMENT 
 
 The author gratefully acknowledges the aid and encourage- 
 ment of Professor Robert S. Northcote in "both the development of the 
 algorithm herein described and the content of the document. 
 
 Thanks are also due to Mr. Franklin DeRemer and Mr. Jacques 
 LaFrance for their help in developing the algorithm. 
 
 The author would like to express his appreciation of the 
 Department of Computer Science of the University of Illinois and of 
 the ILLTAC IV project for their financial support. 
 
 Special thanks also to Mrs. Mildred Pape for her time and 
 effort in typing the manuscript. 
 
IV 
 
 ABSTRACT 
 
 This paper describes an algorithm for the conversion of a 
 grammar in the form of a set of BNF productions into a deterministic 
 parsing algorithm as described by a set of modified Floyd productions. 
 The algorithm is extended in such a way that it may easily become a 
 part of a complete translator writing system and make use of the 
 information available in the semantic part of such a system. The 
 paper also includes a discussion of the implementation of the extended 
 algorithm and describes potential related research. 
 
TABLE OF CONTENTS 
 
 Page 
 
 1. INTRODUCTION 1 
 
 2. THE ALGORITHM 3 
 
 2.1 Notation 3 
 
 2.2 Label Determination ..... 6 
 
 2 . 3 Descriptor Set Generation 6 
 
 2.4 Descriptor t o FPL Production Mapping 7 
 
 2 • 5 Preclusion and Error Production 8 
 
 2.6 Summary 9 
 
 3- CONTEXTUAL ANALYSIS 10 
 
 3-1 Bar Symbols 11 
 
 3.2 Bar Symbol Removal 12 
 
 3-3 Nta and Ntb Groups 13 
 
 3-4 Ntb. (tt, n) Groups ik 
 
 3 • 5 Summary l6 
 
 h. COMBINED GROUPS 19 
 
 4.1 Ct (m) Groups 19 
 
 4.2 ch (m) Groups 21 
 
 4-3 CNtb (m) Groups 23 
 
 4.4 N* (m) as an Element of (k) 25 
 
 4-5 Initial Revision of BNF Grammar 26 
 
 4.6 Summary 23 
 
vi 
 
 Page 
 
 5. SEMANTICS AND EMPTY BNF PRODUCTIONS 29 
 
 5«1 Semantic Routines 29 
 
 5«2 Semantic Conditions 31 
 
 5-3 Empty BNF Productions 3k 
 
 6. IMPLEMENTATION 36 
 
 6.1 BNF Production Storage 36 
 
 6.2 Grammar Revisions 38 
 
 6 . 3 Label Determination kO 
 
 6.4 Descriptor Set Generation kl 
 
 6.5 Descriptor Set to FPL Production Mapping k2 
 
 6.6 Preclusion Elimination ^3 
 
 6.7 Nta, Ntb (tt, n), CNtb (m) Groups kQ 
 
 7- OPTIMIZATION AND ERROR RECOVERY 51 
 
 7«1 Stack Comparisons 51 
 
 7.2 Variable Lookahead Length 55 
 
 7 • 3 Nonterminal Symbol Expansion 56 
 
 7«4 Pseudo Orders 56 
 
 7 • 5 Error Recovery 57 
 
 8. CONCLUSION 60 
 
 8.1 Precedence Systems 60 
 
 8.2 Right Bounded Context . 62 
 
 8.3 Problems 6k 
 
 8.4 Potential Improvements 6k 
 
 8.5 Research Extensions ..... 66 
 
Vll 
 
 Page 
 APPENDICES 67 
 
 A. THE PSEUDO ORDERS 67 
 
 B. OUTPUT OF THE BNE TO FPL CONVERSION PROGRAM 
 
 ON THE SAMPLE LANGUAGE DEMALGOL 70 
 
 LIST OF REFERENCES 109 
 
1 . INTRODUCTION 
 
 The algorithm which converts Backus Naur Form (BNF) pro- 
 ductions to Floyd Production Language (FPL) productions and its 
 implementation, which are described here, grew from the need for a 
 procedure oriented language for the ILLIAC IV computer "being designed 
 by and built for the University of Illinois. Since the ILLIAC IV 
 is a completely new concept in digital computers, the details of a 
 language best suited to it and to its applications are relatively 
 unknown. For this reason, the use of a compiler-compiler, or 
 translator writing system (TWS) is preferable to writing a specific 
 hard code program for the translation of a fixed language. It is 
 anticipated that the use of a TWS will make the task of changing 
 the language easier for the language designers whenever the need 
 for such changes should appear. It is also hoped that the avail- 
 ability of a TWS will encourage users of the ILLIAC IV to modify 
 this base language and create new languages more nearly suited to 
 specific applications. 
 
 The goals of this TWS are the same as those of any TWS; 
 namely, the building of a translator which is fast, occupies as 
 little space as possible, and is capable of generating efficient 
 code. A TWS must also be able to accept the grammars of a large 
 class of languages. In addition, since we hope to encourage the use 
 of the TWS by applications people who are often not familiar with 
 language specifications, it is important that the language specifi- 
 cation input to the TWS be in as simple a form as possible. 
 
Consideration was given to several different parsing 
 irithms as potential bases of the system. Among these were the 
 algorithms of McKeeman [l], Wirth and Weber [2], Ingerman [3], 
 Erooker and Morris [U], and Trout [5]* Without precluding subsequent 
 incorporation of some of the other methods, it was decided that some 
 version of the production language (FPL) of Floyd [6], Evans [7], 
 and Feldman [8] was potentially most likely to meet the first of 
 the above criteria. The input to such a system is, however, more 
 complex than was desirable. 
 
 Chomsky [9] type two (context free) productions were 
 chosen as the most widely known and easily understood method of 
 language syntax specification. The most commonly used notation for 
 this type of production is the Backus-Naur Form (BNF). Algorithms 
 for conversion of BNF to FPL by Earley [10] and DeRemer[ll] were 
 considered and that of DeRemer chosen as the more promising. 
 
 This thesis is a description of an extension of that 
 algorithm and the subalgorithms used in its implementation. Brief 
 ussions of the properties of both the algorithm and its imple- 
 mentation are included where appropriate. 
 
2. THE ALGORITHM 
 
 The algorithm described in this chapter is that which 
 was proposed by F. L. DeRemer [ll] at the University of Illinois. 
 Subsequent chapters will describe the extensions necessary for its 
 practical implementation. The notation used here will also be 
 used in the following chapters. 
 
 2.1 Notation 
 
 We consider a language L to be defined by a phrase 
 structure grammar 
 
 G = (V T , V N , S, P) 
 
 where 
 
 V = the set of terminal symbols of L which will be 
 represented by lower case Latin letters, 
 
 V = a set of nonterminal symbols which will be repre- 
 sented by upper case Latin letters, 
 
 S e V is the objective symbol 
 
 P = a numbered set of rules defining a language L 
 specified by the user, together with Z -> _[_ S 
 
Strings of symbols will be denoted by Greek letters, "the rules 
 defining L will be Chomsky type two productions and will be written 
 in the form: 
 
 N - a 
 
 Symbol X (X e V = V U V ) is a head symbol of N if 
 
 N = X, or 
 
 N -* X . . . , or 
 
 there exists a subset of P of the form 
 
 N - N . • • 
 
 N l 7 N 2 ' * ' 
 
 N -» X . . • n > 1 
 n — 
 
 The string to be parsed is assumed to be of the form 
 
 i*l 
 
 where a € L(G), the set of strings defined by G, or a e V„, , the 
 set of all strings over V . 
 
 The Chomsky type two productions will be referred to 
 simply as productions, or for ease of notation, BNF productions. 
 
The FPL statements will be referred to as productions (when the 
 context makes clear which type of production is meant) or FPL 
 productions. 
 
 An FPL production will be written in the form: 
 
 Ll:pa|y-*N|*Ii 
 
 The label LI may or may not be present. The string (3 Ot is to be com- 
 pared to the top of a stack. If p a is not identical to the top of 
 the stack, processing is transferred to the beginning of the next 
 production in sequence. If 3 a is identical to the top of the stack, 
 the terminal symbol string 7 is compared to the next symbols in the 
 input stream. The lack of a match is treated in the same way as a 
 failure to match the stack. Both 3 and 7 may be empty as will be 
 further explained later. The -> N indicates that a at the top of the 
 stack is to be replaced by the single symbol N. This field may be 
 empty. The * may or may not appear and, if present, indicates that 
 the next input symbol is to be scanned into the top of the stack. 
 The L is the label of the next production to be used. 
 
 A descriptor (tt, n) associates a FPL production with a 
 BNF production in the sense that the a in the FPL production corres- 
 ponds to the first n > 1 symbols on the right hand side (RHS) of 
 BNF production tt. 
 
2.2 label Determination 
 
 The FPL productions are grouped and a label is attached to 
 the first production of each group. The labels are thus associated 
 with an entire group rather than a single production. 
 
 The first step of the algorithm is to determine the labels 
 of all the FPL groups. Let X (tt) be the n-th symbol on the RHS of 
 BNF production tt. There are three rules for determining which 
 labels (groups) must be created. 
 
 For each N € V : 2.2.1 
 
 label Nh exists if 3 tt, n : N = X (tt), n > 1 
 
 ' n 
 
 For each N e V^: 2.2.2 
 
 label Nt exists if 3 TT, n : N = X (tt), n > 
 
 For each t e V : 2.2-3 
 
 label t (tt, n) exists for each ir , n : t = X (tt), n > 1 
 
 2.3 Descriptor Set Generation 
 
 The next step is to determine the set of FPL descriptors, 
 D = ((tt., n.) i = 1, 2, . . . , k} for each FPL group which must 
 exist. The group labels are descriptive in the sense that the three 
 types of labels generate descriptor sets in the following three 
 .'erent ways. 
 
D = {(tt, 1) | X (tt) e V and the left side 2.3.1 
 of ir is a head symbol of N] 
 
 D Nt = {(tt, n) | N = X n (tt), n > 0, all tt) 2.3-2 
 
 D t (tt, n) = <r* n > 2 - 3 - 3 
 
 2.4 Descriptor to FPL Production Mapping 
 
 For each group, the descriptors are then mapped into 
 FPL productions. If a is a string of length n > 1, the three 
 mapping rules are: 
 
 If production tt is M -* ON . . . 2.4.1 
 
 then (tt, n) maps into: 
 a | | * Nh 
 
 If production 7T is M -» at . . . 2.4.2 
 
 then (tt, n) maps into 
 a | | * t (tt, n + 1) 
 
 If production 7T is M -» a 2.4.3 
 
 then (tt, n) maps into 
 a I -> M I Mt 
 
In addition, two special groups must be generated. They 
 
 are: 
 
 START: Eh: | | * Sh 
 
 _ (0, 3): S _ | - £ | Success Exit 
 
 2.5 Preclusion and Error Production 
 
 If, within any group, the stack comparison string <x of 
 one FPL production is such that it may preclude the application of 
 a production with stack comparison string cc which follows it 
 (if a, = 60! or a = 60!-,), a contextual analysis must be done on 
 both productions. That is, the strings (3 of symbols which may pre- 
 cede a and the strings 7 of terminal symbols which may follow a in 
 the particular context (as defined by the descriptor) must be gener- 
 ated to sufficient length for each of the productions so that (3 a J 
 allows only one production of a group to apply for any entry to that 
 group. An error production is added at the end of each group. 
 
2.6 Summary 
 
 The algorithm thus consists of the following five steps: 
 
 1. Read the BEF grammer of L and add the special 
 
 production E -* J S j ; 
 
 2. Determine the labels of the FPL groups required; 
 
 3- Generate descriptor sets for each group; 
 
 k. Map the descriptors into FPL productions and create 
 the two special groups, Eh, and J (0, 3); 
 
 5r Do the necessary contextual analysis to remove 
 
 preclusions and add the FPL error production to 
 each group. 
 
10 
 
 3- CONTEXTUAL ANALYSIS 
 
 The algorithm described in chapter two is complete but 
 cannot be the basis for a TWS parsing algorithm unless a practical 
 method of contextual analysis is available. Initial attempts to 
 actually generate lookback and lookahead symbol strings of suffi- 
 cient length to eliminate preclusion of one FPL production by 
 another proved impractical. The generation of the lookback symbol 
 string, however, is relatively redundant in the sense that it is 
 implicit in the grouping. This chapter introduces an extension of 
 the algorithm which, in most cases, eliminates preclusion of one 
 production by another when the stack comparison strings of the two 
 are of different lengths. This extension also allows a subgrouping 
 of the Nt groups which introduces more implicit lookback. 
 
 The use of the terminal symbol lookahead string remains 
 as described in chapter two. The generation of this string will be 
 described in a later chapter. It is important to note, however, 
 that the generation of these lookahead strings is the most time and 
 space consuming part of an implementation of this algorithm. Even 
 more important is that the translator generated by a TWS based on 
 this algorithm will be slowed down by excessive use of lookahead 
 since all possible lookahead strings must be compared with the 
 input stream if any lookahead is needed. In this way the single 
 FPL production 
 
 a 
 
11 
 
 might became 
 
 a | 7 1 . . . 
 
 a | 7 2 • • • 
 
 a I 7 ... 
 
 1 'm 
 
 For these reasons it is important to limit the need for lookahead 
 as much as possible. 
 
 3.1 Bar Symbols 
 
 The extension mentioned above is the insertion of a special 
 symbol into the stack to mark the beginning of the search for a par- 
 ticular nonterminal symbol. It is called a bar symbol and is 
 denoted by N. Production mapping rule 2.4.1 is therefore modified 
 to: 
 
 If production it is M -> aN . . . 3«1«1 
 
 then (it, n) maps into 
 a I «- N I * Nh 
 
 where *- N means push N onto the stack. 
 
 The use of the bar symbol makes the lookback string f3 the 
 same for all FPL productions, that is, one symbol which may be any 
 bar symbol. As such it will not be noted in FPL productions from 
 this point on. This device differentiates in all but one special 
 
12 
 
 case (associated with the removal of a bar symbol) "between two 
 productions which have stack comparison strings of different lengths. 
 
 3.2 ar Symbol Removal 
 
 The bar symbol N is inserted in the stack when it is known 
 that nonterminal symbol N is a subgoal of the parse, and should, 
 therefore, be removed when N has been recognized. It is implicit 
 that this has just happened upon entry to the Nt group. If, however, 
 N is explicitly left recursive (ELR), that is, there exist ELR BNF 
 productions ir. of the form 
 
 N -> Na 
 
 then the reduction is not complete until the corresponding FPL pro- 
 ductions (i.e., those with descriptors (ir. , l)) have been processed. 
 This type of FPL production will be referred to as ELR. 
 
 The Nt groups thus must be semi-ordered. The ELR produc- 
 tions must come first, followed by a bar symbol removal production, 
 and then the rest of the productions of the group. The bar symbol 
 removal production is of the form 
 
 NN I •* N I 
 
 In this case a = NN, 3 is empty (not any bar symbol), and 
 the lack of a label for transfer indicates that the next production 
 in se<; should be processed. 
 
13 
 
 All productions of an Nt group have N as the last symbol 
 of the stack comparison string. All of the ELR productions have 
 stack comparison strings which are precisely the single symbol N. 
 The bar symbol, which would otherwise prevent the preclusion of 
 the longer strings, may be removed between the processing of the 
 ELR productions and the processing of the non-ELR productions. 
 Therefore, the ELR productions will preclude all other productions 
 of the group. Lookahead strings must be generated for the ELR 
 productions to eliminate this preclusion. 
 
 3-3 Nta and Ntb Groups 
 
 The non-ELR productions of an Nt group fall into two 
 classes: those with descriptors (it, l), called class A; and those 
 with descriptors (it , n) with n > 1, called class B. Just prior to 
 a transfer to the Nt group the stack has N in the top position and 
 a bar symbol in the second position. If the bar symbol is N, it 
 has been put into the stack by a FPL production of the type: 
 
 a I «- N * Nh 
 
 which by mapping rule 3«1«1 comes from the BNF production it of the 
 form 
 
 M -» ON . . • 
 
Ik 
 
 Therefore, the production in the Nt group which must apply (after 
 ELR productions have been processed and the bar symbol removed) has 
 the descriptor (ir , n + l) where n is the length of the non-empty 
 string OL. This production is in class B. If, on the other hand, 
 the bar symbol is not N, then the FPL production which must apply 
 (after ELR processing) comes from a BNF production 7T of the form: 
 
 M -> Na 
 
 and has the descriptor (jr , l). This is a class A production. Thus, 
 the bar symbol in the second position of the stack can be used as 
 the parameter for a dynamic transfer to either a group labelled Nta 
 which consists of the ELR productions and the class A productions, 
 or a group labelled Ntb which consists of the ELR productions, the 
 bar symbol removal production, and the class B productions. 
 
 Since the bar symbol removal production cannot apply in 
 the Nta group, it need not be included and ordering is unnecessary. 
 The Ntb group is identical to the Nt group in every way, except 
 that the class A productions have been deleted. It is possible for 
 only class A or class B non-ELR productions to exist, in which case 
 only Nta or Ntb groups, respectively, need be built. 
 
 Ntb {it , n) Groups 
 
 The Ntb groups can be further split. This is done by 
 associating a descriptor with each bar symbol as it is pushed into 
 the stack. If the FPL production which pushes N into the stack has 
 
15 
 
 the descriptor {it, n) , then the descriptor for the non-ELR Ntb group 
 production which must eventually apply is (it , n + l). Therefore, 
 a separate group, labelled Ntb ("IT, n), is built for each class B 
 production. An Ntb (it, n) group contains the Nt ELR productions, 
 followed by the bar symbol removal production, and the single pro- 
 duction with descriptor (if, n) . 
 
 The splitting of the Nt group into Nta and Ntb (tt, n) 
 groups completely eliminates the need for lookahead to prevent the 
 preclusion of one class B production by another. Even more import- 
 ant is that if an ELR production needs several multisymbol lookahead 
 strings (i.e., 3, Qb, ac, Qd, . . . ) to prevent it from precluding a 
 particular non-ELR production but needs fewer, shorter lookahead 
 strings (i.e., p, a) to prevent preclusion of all other ELR and 
 non-ELR productions, then the larger set of lookaheads is applied 
 only when necessary. 
 
 This splitting of the Nt groups and the associated dynamic 
 transfers make it necessary to change the special START group to 
 make it consistent. It becomes: 
 
 START: Eh: ]_ | «- S (0, 2) | * Sh 
 
 where the special BNF production Z -> ]_ S j is assumed to be number 
 zero. 
 
16 
 
 3-5 Summary 
 
 With the extensions described above the various rules given 
 in chapter two are changed to the following: 
 
 a) Label Determination: 
 
 For each N e V : 3-5-1 
 
 label Nh exists if 3 TT, n : 
 
 N = X (ir), n > 1 
 n 
 
 For each N € V : 3-5-2 
 
 label Nta exists if 3 TT : 
 N = X (ir), ir not ELR 
 
 For each N e V : 3-5-3 
 
 label Ntb (x, n) exists for each ir , n : 
 N = X (ir), n > 1 
 
 For each t £ V : 3-5- 1 * 
 
 label t (tt, n) exists for each ir , n : 
 
 t = X (tt) : n > 1 
 n 
 
17 
 
 b) Descriptor Set Generation: 
 
 D Nh = [(jr > 1) I X l (Tr) € V T 3 " 5 * 5 
 
 and the LHS of .production tt 
 
 is a head symbol of N} 
 
 D Nta = [ijr > D I N = x ! (t)} 3-5.6 
 
 D Ntb (T, n) -«V 1} ' N = X l (7r i^ 3 ' 5 ' 7 
 
 7T is ELR} U 
 
 {bar symbol removal production} U 
 
 {(tt, n)} (with ordering) 
 
 D t (r, n) " {T > n) 3 - 5 - 8 
 
 c) Mapping Descriptors to FPL Productions: 
 (a of length n > 1) 
 
 If production 7T is M -»• aN . . . 3* 5*9 
 
 then (tt, n) maps into 
 a, I ♦- n (tt, n + 1) I *Nh 
 
 If production tt is M -» at . . . 3-5.10 
 
 then (tt, n) maps into 
 a I -* M I *t (ir, n + 1) 
 
18 
 
 If production 7T is M-»a 3* 5*11 
 
 then (ir, n) maps into 
 a | -* M | DMt 
 
 where, if K (ir , n) is the bar symbol at stack level two, then 
 
 K = M => DMt = Mtb (IT , n) 
 
 K * M =^> DMt = Mta 
 
19 
 
 1+. COMBINED GROUPS 
 
 A further extension of the algorithm, which makes it 
 possible to accept a larger class of grammars, is the combination 
 of two or more FPL productions in a group into a single production. 
 Two productions are combined (if possible) when the first precludes 
 the second and the finite lookahead is not sufficient to differen- 
 tiate between the two. Each production which is formed by such a 
 combination creates the need for one or more additional groups. 
 
 k.l Ct (m) Groups 
 
 The simplest combination possible is of two or more FPL 
 productions formed by mapping rule 3* 5*10. If, within a group, 
 the productions 
 
 a 
 
 a 
 
 t (-n^, n) 
 
 I * t (7T k , n) 
 
 should appear, and if a differentiation by lookahead is not possible, 
 then they can be combined into the single production 
 
 a 
 
 *Ct (m) 
 
 U.l.l 
 
20 
 
 where this is the m-th such combination to have been made. 
 Associated with the integer m is the set of labels 
 
 £ Ct(m) = {t (7r i' n) I ± = lf 2 > ' ' '> k] k ' 1 ' 2 
 
 The descriptor set of Ct(m) is defined by: 
 
 d„w n = y D 4.1.3 
 
 ct(m) ^ct(m) q 
 
 Group Ct (m) is then precisely the union of the various groups 
 which could have been transferred to had the combination not been 
 made. 
 
 The Ct (m) group generated above is: 
 
 Ct (m) : at I . . • 
 
 at ... 
 
 error 
 
 As is easily seen, the preclusion has not been eliminated, but simply 
 moved to a different group. This group, however, has one more symbol 
 in the stack comparison field and therefore the maximum length look- 
 ahead c reaches one symbol further into the input. The net 
 effect of a combination of this type is the implicit one symbol 
 
 < nsion of the maximum lookahead capability of an implementation 
 of the algorithm. 
 
21 
 
 k.2 ch (m) Groups 
 
 Another possible combination is of productions formed by 
 mapping rule 3* 5*9 which cause bar symbols of different nonterminals 
 to be pushed into the stack. This cannot be done under a certain 
 condition, but it will be shown later in this chapter how this condi- 
 tion can be eliminated. 
 
 If, within a group, the productions 
 
 a 
 
 a 
 
 | *- N x ( 7 r 1 , n) I * Kjh 
 
 N, (w. , n) * N v h 
 k v k k 
 
 should appear, and if a differentiation by lookahead is not poss- 
 ible, then they can be combined into the single production 
 
 a 
 
 (m) 
 
 ch (m) 
 
 4.2.1 
 
 where this is the m-th such combination to have been made. The symbol 
 (m) is called a metabar symbol and represents the set of bar symbols 
 which could have been pushed into the stack by the various produc- 
 tions which were combined. That is: 
 
 (m) = {^ (tt i , n), . . ., N k (ir k , n)} 
 
 1+.2.2 
 
 The sets represented by the metabar symbols must be avail- 
 able when the FPL productions are used to parse an input string. 
 
22 
 re axe two reasons for this. The bar symbol removal production 
 
 NN | - N | 
 
 must apply when stack level one contains N and stack level two con- 
 tains N, or stack level two is (m) and N e (m) . The second use of 
 these sets is in applying the dynamic transfer, DMt, defined in 
 3.5.11. The definition of DMt remains the same if K (tt, n) is the 
 bar symbol at stack level two. However, if the symbol at stack 
 level two is (m), then DMt is defined as follows: 
 
 M (tt, n) g (m) => DMt = Mtb (it , n) 4.2.3 
 
 M (tt , n) £ (in) => DMt = Mta 
 
 The metabar symbol (m) also satisfies the implicit one symbol look- 
 back for any bar symbol. 
 
 The production formed by a combination of this type indicates 
 a transfer to label ch(m) . This type of group is necessary whenever such 
 a combination is made. Its descriptor is indirectly defined by (m) 
 as follows : 
 
 ch(m) - ■ /— n IJh 
 v ' N e (m) 
 
23 
 
 Again the new group to be built is exactly the union of all the 
 groups which could have been transferred to by the productions 
 which were combined. 
 
 U.3 CNtb (m) Groups 
 
 A third type of combination is of productions formed by 
 mapping rule 3-5*9 where the bar symbols to be pushed into the 
 stack are all for the same nonterminal symbol. If, within a group, 
 the productions 
 
 a 
 
 N (tt., n) * Nh 
 
 a I 4- N (tt, , n) | * Nh 
 
 should appear, and if a differentiation by lookahead is not possible, 
 then they can be combined into the single production 
 
 a 
 
 N * (m) 
 
 * Nh 
 
 U.3-1 
 
 where this is the m-th such combination to have been made. The 
 special bar symbol N * (m) is the same as N in terms of implicit 
 lookback and bar symbol removal. It does, however, call for a 
 further definition of the dynamic transfer, DMt, of 3«5-H and 
 k.2.3- This transfer remains the same under the previously defined 
 
2k 
 
 stack level two conditions, but is extended when stack level two is 
 • (m) as follows: 
 
 K = M => DMt = CMtb (m) U.3.2 
 
 K * M => DMt = Mta 
 
 The label of a group which is built whenever a combination 
 of this type is made is CMtb (m) . Associated with the integer m is 
 the set of labels: 
 
 £ CMtb (m) = {Mtb (7r i' n) | i = 1, 2, . . ., k} U.3-3 
 
 The descriptor set for this new group is then defined by 
 
 >W W - ,e, CMtb I \ 
 
 In this case the productions which were combined each pushed into 
 the stack a bar symbol which defined a dynamic transfer to an 
 Mtb (tt f n) group. This new group which must be formed is the 
 union of those Mtb (tt, n) groups. It must include the bar symbol 
 removal production and be semi-ordered in the same way as a 
 Mtb (tt , n) group. 
 
25 
 
 4.4 N * (m) as an Element of (k) 
 
 An extension of the devices of sections 4.2 and 4.3 
 allows the combination of any set of productions formed by mapping 
 rule 3- 5 • 9« If the bar symbols to be pushed into the stack by the 
 productions to be combined are mixed, in the sense that some are of 
 different nonterminal symbols and some are of the same nonterminal 
 symbols, then the procedures of the previous two sections do not 
 apply. 
 
 In this ease the procedure of section 4.3 is applied to 
 whichever sets of productions qualify, and the procedure of section 
 4.2 is applied to the resulting set of productions. Two of the 
 rules of section 4.2 must be amended in this case because metabar 
 symbol (k) now defines a set which contains both bar symbols, 
 N (j:, n), and special bar symbols, N * (m) . First, the part of the 
 definition of DMt of 4.2.3 must be changed. It becomes: 
 
 If the symbol at stack level two is (k), then 4.4.1 
 
 M {it , n) e (k) => DMt = Mtb (ir , n) 
 
 M * (m) € (k) => DMt = CMtb (m) 
 
 M (7T, n) <ji (k), M * (m) ^ (k) => DMt = Mta 
 
26 
 
 Rule U.2.4 which defines the descriptor set for ch (k) must also be 
 changed to read as follows : 
 
 D ch 00 - 1 • (k) u D Nh h - h - 2 
 
 N * e (k) 
 
 U.5 Initial Revision of BNF Grammar 
 
 Section U.2 made reference to a condition which prevented 
 
 the combination of productions as described in that section. This 
 
 occurs when the nonterminal symbols associated with the bar symbols 
 
 to be pushed into the stack by two of the productions are such that 
 
 one is a head symbol of the other. That is, when N (tt . , n) and 
 
 1 (tt ., n) would be elements of (m) and N is a head symbol of M. 
 J 
 
 This will always cause a dynamic transfer to Ntb (tt , n) upon 
 recognition of N. This ignores completely the possibility that 
 this particular occurrence of N is the beginning of a substring 
 which will eventually reduce to M (in which case the transfer 
 should be to Nta) . 
 
 The problem can be overcome by a simple revision of the 
 BNF grammar before any BNF production to FPL conversion is done. 
 This involves a search of all the BNF productions for pairs of the 
 form: 
 
 ON 
 
 B ■+ OtX . . . 
 
27 
 
 where A may or may not be the same as B, a is a string of length 
 n > 1, and X e V = V U v, and X is a head symbol of N. This pair 
 is then replaced by 
 
 A -» ON . . . 
 
 B -+ aQ 
 
 (Q is a new nonterminal 
 symbol. ) 
 
 and the production 
 
 Q -> X 
 
 is added to the set of BNF productions. 
 
 This revision of the BNF grammar does not change the 
 language being specified but does keep the previously described 
 condition from occurring and preventing the combination of pro- 
 ductions when necessary. Allowing X to be a terminal symbol in the 
 revision also makes certain that there will never be preclusion 
 involving FPL productions generated by both mapping rule 3«5«9 
 and mapping rule 3«5«10. Thus, the only case where combination 
 of productions cannot be used to overcome preclusion is when one 
 or more of the FPL productions involved has been generated by 
 mapping rule 3«5«H« 
 
28 
 
 U.6 __ 
 
 The total algorithm is now extended to include an initial 
 BNF grammar revision. In addition, preclusions which cannot be 
 resolved by lookahead and do not involve an FPL production which 
 is generated by mapping rule 3« 5*11 may be eliminated by combining 
 productions and creating new groups. These combination procedures 
 use the new special symbols (m) and N * (m) . The definition of the 
 dynamic transfer label, DMt, is extended to: 
 
 If stack level two is K (ir, n) then 4.6.1 
 
 K = M => DMt = Mtb (fr,n) 
 K * M => DMt = Mta 
 
 If stack level two is (m) then 4.6.2 
 
 M (tt, n) e (in) => DMt = Mtb (it, n) 
 M * (k) € (in) => DMt = CMtb (k) 
 M (tt, n) i (in) and M * (k) ^ (m) => 
 
 DMt = Mta 
 
 If stack level two is K * (m) then U.6. 3 
 
 K = M => DMt = CMtb (m) 
 K * M => DMt = Mta 
 
29 
 
 5- SEMANTICS AND EMPTY BNF PRODUCTIONS 
 
 The algorithm described in chapters one through four has 
 been implemented on a Burroughs B5500 computer at the University 
 of Illinois. The input to the program is the grammar of a language 
 in the form of a set of modified BNF productions. The output is a 
 stream of pseudo orders corresponding to the FPL productions gen- 
 erated, and a set of tables, one of which contains the definitions 
 of the metabar symbols. 
 
 5.1 Semantic Routines 
 
 The BNF productions include two different applications of 
 semantics. The semantics are written separately as a set of num- 
 bered routines which are accessible to the parser interpreter which 
 causes the pseudo orders to be executed. The semantic routines 
 are associated with the BNF productions by placing the appropriate 
 number (preceded by #) anywhere on the RHS of a production, except 
 at the beginning. For example: 
 
 1) <A> 
 
 2) <A> 
 
 3) <A> 
 
 = a <B> #1 
 = a #2 <C> 
 = a #3 <D> #1 
 
 would all be valid input productions. Since the total set of FPL 
 productions has at least one production for each possible descriptor, 
 
30 
 
 the semantic routines can be executed precisely when the parse 
 reaches the point indicated in the BNF grammar. This requires an 
 extra field in the FPL productions which applies in the same way 
 for all of the mapping rules. The general FPL production becomes 
 
 Ll:0a|7-+N|m*L 
 
 where m is an integer referring to a semantic routine which is to 
 be called immediately upon recognition of p, a in the stack and 7 
 in the input stream, and before any stack manipulation is done. All 
 other fields of the production are as previously described. The 
 mapping rules are extended to include the setting of this semantic 
 action field when the descriptor being mapped is (ir, n) and # <integer> 
 follows symbol n of production ir . 
 
 Each stack position, in addition to containing a syntactic 
 symbol, also contains a field which the language designer may use 
 (through semantic routines) for information associated with that 
 particular syntactic symbol. The semantic routines are also used 
 for many other things such as building identifier tables and gen- 
 erating object or intermediate language code. 
 
 The use of semantic routines does place one restriction 
 
 on the algorithm. A set of FPL productions which should, accord- 
 
 • to the procedures described in chapter four, be combined, may 
 
 not be combined if they have different semantic actions. This is 
 
31 
 
 because the appropriate semantic routine must be executed before 
 continuing the parse. For example, the <A>h group, from the above 
 BNF productions, would be 
 
 <A>h : a | *. B (l, 2) | * Bh 
 
 a | «- C (1, 2) | 2 * Ch 
 
 a | «- D (l, 2) | 3 * Dh 
 error 
 
 The preclusion involved here must be overcome by lookahead or not 
 at all. This restriction has little practical effect on the capa- 
 bilities of the system since, in actual use of the system, the vast 
 majority of semantic routine designations are at the end of RHS's, 
 (i.e., semantic actions to be performed upon recognition of complete 
 constructs) . 
 
 5»2 Semantic Conditions 
 
 A second use of semantic routines allows the language 
 designer to effect the parse by differentiating, with semantics, 
 between otherwise identical syntactic symbols. Semantic routines 
 used for this purpose are called semantic conditions and are 
 denoted in both BNF and FPL productions by <#m> where m is an 
 integer and refers to semantic routine number m. These semantic 
 conditions are associated with a particular use of a symbol (either 
 terminal or nonterminal) by inserting them into the BNF productions 
 
32 
 
 immediately following that symbol on the appropriate RHS. The 
 system considers the semantic condition as a permanent part of the 
 symbol which precedes it and, in fact, treats that symbol as being 
 syntactically different than the same symbol with a different 
 semantic condition, or with no semantic condition. 
 
 The following example illustrates the use of semantic 
 conditions. Assume the following productions are part of a BNF 
 "rammar . 
 
 <A> -* a <#1> 
 <A> -> a <#2> 
 <A> - a 
 
 The Ah group then would be 
 
 Ah : a <#1> | -* A | DAt 
 
 a <#2> | -v A | DAt 
 
 a | -> A | DAt 
 error 
 
 No preclusion exists since the three single symbol stack comparison 
 B are considered by the system as being different symbols. 
 
 The semantic routines which are used as semantic conditions 
 may do anything that any other semantic routine may do. They must, 
 however, also set a fixed boolean variable in the skeleton program 
 
33 
 
 either true or false. The symbol X <#m> in the stack comparison 
 string of an FPL production is processed by first comparing the 
 symbol X with the stack in the normal manner and then executing 
 semantic routine number m. If the value returned is true, then 
 the symbol is considered to have matched the stack and processing 
 of that production continues. If it is false, the stack compar- 
 ison has failed and processing is transferred to the beginning of 
 the next production in sequence. 
 
 The use of semantic conditions increases drastically the 
 capabilities of the system in that they can be used in conjunction 
 with normal semantic routines to refer back to every step of the 
 parse which has preceded their execution. They must be used with 
 great care, however, since 
 
 a <#n> 
 
 is a preclusion which is not recognized by the system. In addition, 
 
 <#n> 
 
 <#m> 
 
 may also be a preclusion not recognized by the system if the user has 
 failed to effectively differentiate between the two cases. 
 
3U 
 
 5.3 Empty BNF Prod-actions 
 
 An empty BNF production is 
 
 N - \ 
 
 where X is the null string. The use of the empty production is 
 unnecessary in specifying a language. It is, however, useful in 
 that it can make the specification of a grammar easier for the 
 language designer. Since this is one of the primary goals of this 
 system, it is allowed. 
 
 The algorithm, as described, does not handle the empty 
 production, so an initial pass is made which completely removes 
 all empty productions by a straight- forward back substitution. 
 (It is possible to completely remove them because of the form of 
 the production E ■+ J_ S J_. ) This may affect semantic routines, as 
 in the following example : 
 
 A -*• aBc #1 
 
 B -> \ 
 
 B - b 
 
35 
 
 which becomes 
 
 A -* aBc #1 
 
 A -* ac #1 
 
 B -* t> 
 
 Semantic routine number one may refer to stack level three expecting 
 that it is the level of symbol a. Whenever such an effect is poss- 
 ible (i.e., whenever the number of symbols preceding a semantic 
 routine call is reduced) a message is printed to that effect and 
 processing is continued with the assumption that the semantic routine 
 is not affected. It becomes the user's responsibility to rewrite the 
 semantic routine if necessary. This is not a serious problem since, 
 in most cases, the syntactic part of the language is written and 
 processed prior to the actual writing of the semantics. 
 
36 
 
 6. IMPLEMENTATION 
 
 This chapter will describe the more interesting features 
 of the implementation. Emphasis will be given to those parts of 
 the algorithm l) which this implementation may modify slightly, 
 or 2) for which the method of implementation is not relatively 
 obvious . 
 
 6.1 BNF Production Storage 
 
 The BNF productions are first converted into a numerical 
 form and the RHS's are stored in a logical one dimensional array 
 called PR0TAB. Each RHS symbol uses one word of the array with an 
 extra word for semantic conditions. Each word is broken into sev- 
 eral fields which contain the following information: 
 
 1) a two part numerical representation of 
 the symbol 
 
 2) which (if any) semantic routine call 
 follows this symbol 
 
 3) the number of words to the beginning 
 of the next RHS 
 
 U) whether this symbol is semantically 
 conditioned 
 
37 
 5) whether this is the leftmost symbol of 
 
 and ELR production 
 
 6) the nonterminal symbol which is the left 
 side of this production. 
 
 All of the symbols used in the algorithm are separated 
 into the following types: 
 
 nonterminal symbols 
 terminal symbols 
 bar symbols 
 metabar symbols 
 special bar symbols 
 semantic conditions 
 identifiers 
 numbers 
 strings 
 
 The semantic conditions are not actually symbols but 
 the implementation, in many ways, treats them as if they are. 
 Identifiers, numbers, and strings are specified in the BMF grammar 
 by <*I>, <*N>, and <*S>, respectively. These are considered by the 
 system to be three different terminal symbols. These nine differ- 
 ent classes of symbols are each given a unique type number. 
 
 The second part of the numerical representation of the 
 first six classes of symbols is a number corresponding to a 
 
38 
 
 particular symbol or semantic routine within that class. Identifiers, 
 numbers, and strings have no such entries. The scan procedure of the 
 skeleton program recognizes these as entities and uses the entry- 
 field in the stack as a pointer to the address in the ECD symbol 
 table of the particular identifier, number, or string recognized. 
 This pointer then can be used by the semantic routines. Special 
 (or reserved) words of the language are specified in the syntax as 
 alphanumeric character strings (i.e., #BEGIN) and each is given a 
 separate entry number within the class of terminal symbols. One 
 of the tables output by the conversion program is a list of these 
 special words and their associated entry numbers for use by the 
 scan procedure. 
 
 The above described method of storing the BNF productions 
 allows the conversion routine almost immediate access to most of 
 the information it needs, while at the same time using as little 
 space as possible. During the course of this conversion certain 
 checks are made of the syntax. Among these are tests that all non- 
 terminal symbols (except Z) appear on both right and left sides of 
 BNF productions, and a check that there is at least one string of 
 terminal symbols which will reduce to each nonterminal symbol. 
 
 ■-•jnmar Revisions 
 
 During the course of the BNF production storage, the non- 
 terminal symbols which occur on the left side of empty productions 
 are stored. This information is used to eliminate all empty produc- 
 tions in the manner described in section 5 -3- 
 
39 
 
 At this point, two dimensional boolean arrays which mark 
 the nonterminal head symbols (NTHS), the terminal head symbols (THS), 
 and the nonterminal tail symbols (NTTS, defined analogously to head 
 symbols) of each nonterminal are filled. For entry into the THS 
 array the special terminal symbols identifier, number, and string 
 are put at the end of the other terminal symbols. These tables 
 are initialized as follows: 
 
 If g a production M -+ N . . . 
 
 then NTHS [M, N] = true else false 
 
 If g a production M -*■ t . . . 
 
 then THS [M, t] = true else false 
 
 If g a production M -»■ . . .N 
 
 then NTTS [M, N] = true else false 
 
 where a symbol used as a subscript refers to the entry field for 
 that symbol (except identifier, number and string). The tables 
 are then filled by iteratively applying the principal that if X 
 is a head (tail) symbol of N and N is a head (tail) symbol of M, 
 then X is a head (tail) symbol of M. These tables are completed 
 by setting NTHS [N, N] and NTTS [N, N] equal true for all non- 
 terminal symbols N. 
 
 At this point the RHS's are compared in pairs and all 
 necessary grammar revisions are made as described in section k.^. 
 
Uo 
 
 The BNF grammar is now in a form acceptable to the conversion 
 algorithm and the NTHS and NTTS tables are available for use 
 when applicable. 
 
 Before conversion actually begins, a table of pointers 
 to each RHS occurrence of each nonterminal symbol, and a table of 
 pointers to RHS beginnings corresponding to the use of each non- 
 terminal symbol as a left side are constructed. These are used 
 to eliminate excessive scanning of the entire array of RHS symbols. 
 
 6.3 *abel Determination 
 
 Very little is necessary for label determination. All 
 nonterminal symbols require an Nt group which is separated into 
 Nta and Ntb (ir, n) groups in a manner which will be further dis- 
 cussed later. A single scan through the BNF production table 
 (PRjfcAB) is sufficient to determine which Nh groups are necessary. 
 No label determination is done for the t (?r, n) groups. Instead, 
 when the conversion of an FPL production to pseudo orders reaches 
 a label for transfer to a t (tt, n) group, the single FPL produc- 
 tion of that group is generated and the pseudo orders for it are 
 placed directly into the pseudo order stream. This saves unnec- 
 cessary transfers when the pseudo orders are processed. The last 
 production in a sequence of su< "rations is followed by the 
 error pseudo order. 
 
 As the FPL productions are generated in the Nta, 
 (tt, n), and Nh groups the need for Ct ("ir, n) , ch (m), and 
 (m) groups arises. Whenever such a need occurs the name 
 
Ul 
 
 of the group needed is simply inserted into a list, along with a 
 pointer to the information necessary to build the group. These 
 groups are created one at a time after the Nta, Ntb (ir, n), and 
 Nh groups have been built. The generation of a combined group 
 may add to the list of combined groups which are needed. 
 
 6.U Descriptor Set Generation 
 
 A descriptor will continue to be denoted by (ir, n) . It 
 is, however, actually a single number which points at a word in 
 PRj^TAB. The descriptor set for a Nt group is then precisely the 
 entries for N in the table of pointers to RHS occurrences. 
 
 The descriptor set for a Nh group is generated by using 
 information available in each word to step through the first symbol 
 of each RHS in PRj^TAB. If this first symbol X is a terminal symbol 
 and if the left side M of this production is such that NTHS [N, M] = 
 true, then the pointer to that first symbol is a descriptor in the 
 Nh group. The descriptor sets for the Nh groups are saved, even 
 after the groups have been built. 
 
 The descriptor denoted (ir, n + l) is (ir, n) + 1 if the 
 
 symbol at (ir, n) is not semantically conditioned. It is (tt, n) + 2 
 
 if the symbol at (ir, n) is semantically conditioned. The single 
 
 descriptor for the t (tt, n) group is available when the need for 
 
 that group arises. The descriptor sets for Ct (tt, n) , ch (m), and 
 
 CNtb (m) groups are generated by a straight forward application of 
 
 U.1.3, k.2.k, and k.3.k. The label sets £_. , N and £___. , N are 
 ' ' Ct (m) CNt (m) 
 
 the information associated with names, as discussed in section 6-3« 
 
k2 
 
 6.5 Descriptor Set to FPL production Mapping 
 
 The mapping of descriptors to FPL productions is very 
 simple. The descriptor is first increased by one if the symbol 
 pointed at is semantically conditioned. The stack comparison field 
 of the FPL production is thirty-two (32) words long and is filled, 
 right justified, directly from PR0TAB using the descriptor. The 
 next word is the semantic routine to be called and is filled from 
 the appropriate field of the last word in the stack comparison. 
 The next word is minus one, one, or zero corresponding to «-, ->•, 
 or blank, respectively. The following word is the bar symbol to 
 be pushed, the nonterminal which the stack is to be reduced to, 
 or zero. The next word is one or zero for scan or no scan, respec- 
 tively. This is followed by the two part numerical label name. 
 These labels are formed similarly to the symbols in that there are 
 five classes or types. The entry fields are filled as follows: 
 
 Type Entry 
 
 Ct (m) m 
 
 ch (m) m 
 
 Nh N 
 
 t (n, n) (n, n) 
 DNt N 
 
h3 
 
 The last word of a numerical FPL production is the revised descriptor 
 from which it came. Much of the information in the production is 
 redundant. This format is used because it simplifies the conver- 
 sion into pseudo orders, a list of which is given in Appendix A. 
 
 6.6 Preclusion Elimination 
 
 The splitting and ordering of the Nt group is more easily 
 described if the elimination of preclusions is explained first. 
 Assume for this explanation that no ordering or splitting is 
 necessary. 
 
 All of the numerical FPL productions for a particular 
 group are generated and placed, one per line, into a table for 
 processing. The first production is compared, one at a time, with 
 the productions which follow it. If the stack comparison string 
 for the two productions is identical, then a preclusion exists and 
 lookahead generation is necessary. The two productions are asso- 
 ciated with two identical buffers. Each line of these buffers has 
 two words of control information plus n additional words, where n 
 is the maximum number of symbols of lookahead. 
 
 The two productions are expanded into the first lines of 
 the two buffers as follows : 
 
 word one: the entry part of the left side of the 
 BNF production which formed this FPL 
 production. 
 
kk 
 
 word two: zero 
 
 the rest of the line is filled, left justified, 
 by the symbols of this RHS which are not in 
 the stack comparison field (as many as will 
 fit). 
 
 Figure 1 is the flow chart for the generation of look- 
 ahead with the variables used defined as follows: 
 
 I, J, K are loop indices 
 
 LK1 is the buffer associated with the 
 
 first FPL production 
 LK2 is the buffer associated with the 
 
 second FPL production 
 LL is the maximum lookahead length 
 LK1PT is a pointer to the first empty line 
 
 of LK1 (initially equal two) 
 LK2PT is a pointer to the first empty line 
 
 of LK2 (initially equal two) 
 
 The procedure GETSYM extends the string in line I (J) of 
 buffer LK1 (LK2) with pointer LK1PT (LK2PT) by finding all PRjfrTAB 
 urrences of nonterminal symbols which are not the last symbols 
 
h5 
 
 ( START V 
 
 !•— 1 
 
 ©- 
 
 £> 
 
 YES 
 
 J*— 1 
 
 K«— 3 
 
 YES 
 
 YES 
 
 YES 
 
 EXIT 
 
 EXIT 
 
 GETSYM 
 (LM.LKIPT.I) 
 
 J 
 
 GETSYM 
 <LK2,LK2PT,J) 
 
 NT2T 
 (LKl.LKlPT.l) 
 
 1 
 
 NT2T 
 (LK2,LK2PT,J) 
 
 ©- 
 
 j>" — j*i 
 
 LK1[I,2]«- 
 K-2 
 
 «•• K+l 
 
 © 
 
 <D 
 
 i- — i+i 
 
 Figure 1. Flow Chart for Lookahead Generation 
 
1+6 
 
 of a RHS, and which are marked in array NTTS as having the terminal 
 symbol of LK1 [l,l] as a tail symbol. Each such occurrence is used 
 to create a new line in LK1 as follows: 
 
 word one: the left side symbol of the occurrence; 
 
 words three through K-l: identical to row I; 
 
 words K through LL + 2: the symbols which follow 
 the occurrence in that RHS (left justified). 
 
 The procedure NT2T expands the nonterminal symbol at LK1 [I, K] 
 (LK2 [J, K]) by replacing it with each RHS which has it as a left 
 side. Each such RHS creates a new line as follows: 
 
 words one through K-l: identical to row I; 
 
 starting at word K: the symbols of the RHS 
 
 (symbols which would fill the line beyond 
 LL + 2 are ignored); 
 
 ese words through word LL + 2 (if free words 
 lable) : the words of line I starting at 
 we- 1. 
 
hi 
 
 For both GETSYM and NT2T, line I is saved at the end of 
 the buffer. Each new line created is compared with all lines pre- 
 viously processed (lines one through 1-1 and the lines at the end 
 of the buffer). If the new line (except word two) is identical to 
 any of these it is ignored. The first new line not ignored is put 
 at Line I and the rest are placed starting at LK1PT (which is 
 incremented by one for each such line) . If all new lines created 
 by GETSYM or NT2T while processing line I of LK1 are ignored, 
 then LK1PT is decremented by one, line LK1PT is moved to line I, 
 and control is transferred to point C in the flow chart. If this 
 occurs while processing line J of LK2, then LK2PT is decremented 
 by one, line LK2PT is moved to line J, and control is transferred 
 
 to D. 
 
 Exit A is taken when sufficient lookahead has been gener- 
 ated for the first FPL production to prevent it from precluding the 
 second. Comparison with the rest of the FPL productions is then 
 continued. If further preclusions occur the precluded production 
 is expanded into LK2, LK2PT is set equal to two, and the procedure 
 outlined by Figure 1 is repeated. The lookahead already generated 
 may prove sufficient, or an extension of it may be generated. If 
 Exit A is taken and no further preclusion exists, then lookahead 
 generation is complete for this FPL production. Each line of LK1 
 represents a different lookahead string and word two indicates how 
 many of the symbols are meaningful. The entire process is then 
 repeated for the next FPL production of the group. 
 
kQ 
 
 Exit B is taken when the two FPL productions cannot be 
 differentiated by lookahead. In this case the second is combined 
 with the first to form a new production which replaces the first 
 in the table. The second production is also removed. The com- 
 
 .ed production then is compared to the following productions 
 just as any other production would be. The only difference is that 
 an expansion of it into LKL creates one line for each of the orig- 
 inal productions which were combined to create it. For this 
 reason, the descriptors of those productions must be retained until 
 the processing of the new production is complete. 
 
 If the group being created is not an Nta or Ntb (tt , n) 
 group, then the production is converted into pseudo orders as soon 
 as this processing is complete. 
 
 Nta, Ntb (ir, n), CNtb (m) Groups 
 
 The building of CNtb (m) groups is similar to that described 
 in section 6.6 but has the following difference. The table of FPL 
 productions must be semi-ordered with the ELR productions first. 
 The ELR productions preclude the non-ELR productions even though 
 the stack comparison strings are not identical. ELR and non-ELR 
 productions may not be combined. Lastly, pseudo orders for the bar 
 ..ibol removal production must be generated after processing of the 
 ELR productions and before processing of the non-ELR productions. 
 
k 9 
 
 The Nta and Ntb (tt, n) groups are created by first building 
 an FPL production table which contains only the ELR productions. 
 This table is then processed exactly as described in section 6.6. 
 Upon completion of the processing of one of these productions, the 
 production and all non-empty lines of LK1 are saved in a separate 
 buffer. 
 
 A FPL production table which contains the non-ELR class A 
 productions, is then built. The ELR productions, and the partial 
 lookaheads associated with them, are then compared with each of 
 these productions just as if the class A productions had followed 
 them in the FPL production table originally. Combination of ELR 
 and non-ELR productions is allowed in this case. When each of the 
 ELR productions has been processed it is converted to pseudo orders. 
 The remaining class A productions are then processed and converted 
 to pseudo orders in the normal manner. This completes the construc- 
 tion of Nta group. 
 
 To build each of the Ntb (ir, n) groups a FPL production 
 table is built which contains the single appropriate class B non-ELR 
 production. The procedure then followed is the same as for the Nta 
 group with the following exceptions. The ELR productions preclude 
 the non-ELR production even though the stack comparison strings are 
 not identical. Combination of ELR and non-ELR productions is not 
 allowed. Pseudo orders for the bar symbol removal production must 
 be generated before they are generated for the non-ELR production. 
 
50 
 
 A list of the pseudo orders that may be generated is given 
 in Appendix A. Appendix B gives a complete listing of the output 
 from the B5500 syntax preprocessor program SYNPROF/TWS for a BKF 
 specification of a grammar for the language DEMALGL, a subset of 
 ALGOL. 
 
51 
 
 7- OPTIMIZATION AMD ERROR RECOVERY 
 
 There are a number of ways in which both the algorithm 
 and its implementation may be optimized. Some of these have already 
 been described in chapter six. That is to say, the minor changes 
 of the algorithm necessary for its implementation may be considered 
 optimizations. 
 
 7-1 Stack Comparisons 
 
 The first optimization to be described is the one which 
 most effects the speed and efficiency of a translator based on the 
 FPL productions generated by this algorithm. It is recognition of 
 the fact that immediately after a scan, no stack comparison need 
 be done except of the top symbol of the stack. To see this, it is 
 necessary to consider the situation upon entry to each of the six 
 types of groups. 
 
 The BNF production which causes generation of a t (ir, n) 
 group is of the form N -* cut . . . . The FPL production which calls 
 for a transfer to this t (tt, n) group is 
 
 a | | * t (tt, n) 
 
 and the single production in the group is 
 
 at 
 
52 
 
 The test for a preceding bar symbol and a stack comparison for the 
 string a is obviously unnecessary because if these tests were to fail, 
 the transfer to t (tt, n) would never have been made. 
 
 The Ct (m) group is similar, except that it arises from 
 a set of BNF productions : 
 
 N -> at 
 
 N p -* Oft . . . 
 
 N, -+ at . . . 
 k 
 
 The transferring FPL production is: 
 
 a I * Ct (m) 
 
 The Ct (m) group contains the PFL productions 
 
 at 
 at 
 
 at 
 
 or combinations thereof. A^ain, only a check of the top of the 
 :'or the symbol t is necessary. 
 
53 
 
 All transfers to Nh or ch (ra) groups are made from FPL 
 productions of the form: 
 
 a | ••- Q | * L 
 
 where Q is N (if , n) , (m), or N* (m) and L is Nh or ch (m) . 
 Therefore, stack level two must contain a bar symbol upon entry 
 
 to an Nh or ch (m) group. Since all the FPL productions in these 
 groups are of the form 
 
 the implicit lookback for a bar symbol is unnecessary. 
 
 All transfers to Nta groups are made from FPL productions 
 of the form: 
 
 a | -* N | DNt 
 
 After this reduction stack level two is some bar symbol and stack 
 level one is N. All FPL productions of an Nta group are of the form: 
 
 N 
 
 Thus no stack comparison is necessary and lookahead alone determines 
 which FPL production applies. Using the implementation described 
 
5** 
 
 in chapter six, the last production of an Nta group will have no 
 lookahead and must apply. Therefore, no error production is 
 necessary after this group. 
 
 The configuration of the stack upon entry to a Ntb (ir, n) 
 or CNtb (m) group is the same as upon entry to a Nta group. These 
 groups begin with the ELR productions of the form: 
 
 N 
 
 which requires no stack comparison. The dynamic transfer DNt is 
 defined in such a way that the bar symbol removal production must 
 apply if the transfer is to a Ntb (ir , n) or CNt (m) group, so no 
 stack comparison is necessary for it. This leaves only the non-ELR 
 production(s) . If the bar symbol is N or N * or (m) where 
 N or N * e (m), then it was pushed into the stack by 
 
 a | 4- N pr N * | * Nh 
 
 or a | «■ (m) * ch (m) 
 
 In either case, this came from a BNF production of the form 
 
 M -* r /ll . . . (and possibly others of the form M -> OK . . ., where 
 
 : N). The transfer DNt, in each case, is to Ntb (tt, n) or CNtb (m) 
 which has as on -ELR product ion( s) : 
 
 cm 
 
55 
 
 which applies with no stack comparison. Again, only lookahead 
 differentiates between the productions and no error production is 
 necessary. 
 
 7.2 Variable Lookahead Length 
 
 The lookahead generation was described in section 6.6 as 
 being done once for a given maximum lookahead length. A vast 
 majority of groups for any reasonable grammar (based on actual use 
 of a translator using this algorithm) can be built with a look- 
 ahead of zero or one symbols. All of the nontrivial grammars which 
 have been input to the TWS have had a few groups which needed up 
 to three symbols of lookahead. A one symbol lookahead generation, 
 which assumes a possible maxijmum of three symbols, is very ineffi- 
 cient since extra (unnecessary) symbols must be retained at each 
 step. 
 
 To overcome this inefficiency the algorithm without com- 
 bination of productions is first applied with an assumed maximum 
 lookahead length of one. The names of groups which cannot be built 
 in this first pass are stored in a table. The algorithm with com- 
 bination of productions and a maximum lookahead length specified by 
 the language designer (up to fifteen, with default of three) is then 
 applied. This two pass approach has proved, in practice, to signif- 
 icantly increase efficiency. 
 
56 
 
 7»3 . . ■ rminal Symbol Expansion 
 
 The flow chart for lookahead generation (Figure l) indi- 
 cates a looping on the procedure NT2T. The purpose of this looping 
 is to ret all n (or less) symbol expansions which begin with a 
 terminal symbol of a particular nonterminal. In this case n is the 
 number of symbols which, beginning at word K, would fill line I 
 of LK1. Such expansion of a nonterminal symbol may occur several 
 times in the building of the various groups. 
 
 A special procedure has been added which uses the princi- 
 ple of the loop through NT2T to generate the desired expansion and 
 save the results, or simply returns the strings directly if the 
 expansion has been done previously. 
 
 The use of this procedure replaces the two loops in 
 re 1. This also significantly improves efficiency. 
 
 J .k >seudo Orders 
 
 The generation of pseudo orders will not be discussed in 
 any detail since it is relatively obvious what orders are necessary. 
 Three things, however, should be noted. 
 
 First, two different tests for terminal symbols in the 
 stack or lookahead must exist. One, for identifiers, numbers, and 
 strings, tests only the type, and another tests both type and entry. 
 
 It was shown in section 7-1 that the entire stack compar- 
 ison is unnecessary. It is, however, necessary, for productions of 
 the form: 
 
 a I -* N I DNt 
 
57 
 
 to retain the length of the string a, because that is the number of 
 symbols which must be replaced by N at the top of the stack. 
 
 A relatively complex set of pseudo orders combined with 
 proper ordering of the lookahead strings for a given FPL production 
 can reduce the number of symbols which must actually be compared. 
 A simple example is the following. Assume the lookahead strings 
 for a production are : 
 
 a b c 
 e f g 
 a b d 
 
 If these are reordered to 
 
 a b c 
 a b d 
 e f g 
 
 it is easily seen that two separate tests for ab are unnecessary. 
 
 7-5 Error Recovery 
 
 Section 7*1 shows that the bar symbols are not necessary 
 for lookback. They continue, however, to serve two very useful 
 functions. The first, which has already been discussed, is to act 
 as the parameter for the dynamic transfer, DNt. Their second, and 
 
58 
 
 equally important, function is their use in error recovery. Error 
 recovery is not a necessary part of the algorithm, but a translator 
 based on the algorithm must have same form of error recovery if it 
 is to be practically useful. 
 
 One of the tables output by the TWS for the skeleton 
 program is a set of lists of all terminal symbols which may follow 
 each nonterminal symbol. These lists are generated by properly 
 initializing LK1 and then initiating a one symbol lookahead 
 .eration. 
 
 A syntactic error is found in the input string by execu- 
 tion of the error production at the end of same group. When this 
 occurs, the stack is searched for the uppermost bar symbol. If 
 this symbol is N or N *, the input stream is scanned until one of 
 the terminal symbols t which may follow N is found. The symbols 
 between the N or N * in the stack and the t in the input stream 
 are deleted. The nonterminal symbol N is then pushed into the 
 stack and the dynamic transfer to DNt is made. 
 
 If the uppermost bar symbol is (m), then the input stream 
 is scanned for a terminal symbol t which may follow any of the non- 
 terminal symbols M which are such that M e (m) or M * e (m). If t 
 may follow only one of these, the procedure described above is 
 applied. If it may follow several, then one is chosen arbitrarily 
 and the procedure is appli( 
 
 This error recovery can be extremely effective or extremely 
 ineffective depending on the state of the parse when an error is 
 
59 
 
 encountered. The worst case occurs when the uppermost bar symbol 
 is S. If S is not recursive this causes the entire input string to 
 be deleted. Experience indicates, however, that the error recovery 
 just described is, in general, about as effective as that of many 
 hand coded compilers, particularly for languages, such as ALGOL, 
 which are specified recursively. 
 
6o 
 
 8. CONCLUSION 
 
 A TWS based on the algorithm described in the preceding 
 chapters has been fully implemented. In general, it satisfies the 
 goals set for it in chapter 1. This chapter briefly compares it to 
 other parsing algorithms and discusses the subclass of grammars 
 which it will accept. There are also brief discussions of problems 
 yet to be solved, of potential improvements, and of areas of further 
 research. 
 
 8.1 Precedence Systems 
 
 The parsing algorithm can be compared to the precedence 
 systems of McKeeman [1], and Wirth and Weber [2] in the sense that 
 
 of three stack actions is specified by each FPL production. The 
 first of these is to do nothing, which is equivalent to a precedence 
 relation of = . The second is to push a bar symbol into the stack. 
 This is done when a precedence relation of <• exists and occurs at 
 the top of the stack, rather than down in the stack as in the tech- 
 niques of McKeeman, and Wirth and Weber, but effectively serves the 
 same function. The third stack action is to make a reduction, which 
 equivalent to a precedence relation of •> at the top of the stack. 
 
 One advantage of the conversion algorithm (and, hence, of 
 FPL rec< :: produced) is that, with one exception, it is able 
 to make use of more context than is employed in precedence relations 
 in determining the bounds of a substring to be reduced. 
 
61 
 
 In determining the existence of a <• relation both prece- 
 dence schemes consider one symbol below it in the stack. McKeeman 
 makes use of two symbols above it and Wirth and Weber one symbol. 
 The conversion algorithm uses a minimum of one symbol below it in 
 the stack plus further information, which may be implicit in the 
 grouping, and a lookahead (corresponds to symbols above it in the 
 stack) of n symbols, where n is usually greater than two, to decide 
 when it is necessary to push a bar symbol into the stack. 
 
 In determining the existence of a •> relation at the top 
 of the stack, both precedence schemes use a one symbol lookahead 
 while the conversion algorithm uses n (n > l) symbols. Wirth and 
 Weber's system looks one symbol into the stack to determine this 
 relation, while McKeeman' s system looks at two symbols. One symbol 
 is the minimum used explicitly by the conversion algorithm and the 
 information available in the second symbol is, except in a Nta group, 
 implicit in the grouping. 
 
 Another advantage of the generated FPL recognizers over 
 the precedence schemes is that they do not allow two BNF productions 
 with identical RHS's. This is particularly important if several peo- 
 ple are involved in the design of a language, or if the BNF grammar 
 is to be used descriptively, as in the ALGOL report. 
 
62 
 
 8.2 Right Bounded Context 
 Let 
 
 a = x, . . . x • . .x, , x. € V u v. 
 
 1 m tint 
 
 Define (n, p) to be a handle of a if (for k > 0) N -» x, . . .x is 
 the p-th production and x^ . . .x is the leftmost substring of a 
 which appears as a RHS of a production and a reduction to S could 
 begin with a reduction of this substring to N. Floyd [12] defines 
 a grammar as right bounded context (m, n), denoted LR (m, n), if any 
 handle is always uniquely determined by the m stack symbols to its 
 left and the n input symbols to its right. 
 
 The conversion algorithm clearly accepts all grammars which 
 are LR (o, n), where n is the maximum lookahead length. It does 
 accept grammars beyond this. The following grammar 
 
 ir 
 
 1 S - a c N t 
 
 2 S - b c M 
 
 3 N - d 
 
 k M - d t 
 
 LR (2, 0), since in the strings acdt and bcdt, a decision as to 
 ther the substring d is a handle (and should be reduced to N) can 
 made only by looking two symbols to its left for an a or b. 
 
63 
 This problem does not occur in the FPL recognizer since the Sh group 
 
 Sh: a| | *c (l, 2) 
 b| | *c (2, 2) 
 
 effectively separates the two cases. This example can be extended 
 to LR (rtij o) by replacing the c in the first two BNF productions with 
 identical terminal symbol strings m - 1 symbols long. 
 The grammar 
 
 TV 
 
 
 1 
 
 S -> a N c 
 
 2 
 
 S -> b M 
 
 3 
 
 N - K 
 
 h 
 
 M - K c 
 
 5 
 
 K - d 
 
 which is LR (l, 0), cannot be converted to a (deterministic) FPL 
 recognizer by the algorithm because of the preclusion in the Kta 
 group 
 
 Kta: K| - N I DNt 
 
 K| I *c (h, 2) 
 
 which can only be resolved by a one symbol lookback. 
 
6U 
 
 In general, the subclass of Chomsky type two grammars 
 accepted by the BNF to FPL conversion algorithm does not fit any 
 known classification scheme. 
 
 8«3 Problems 
 
 The present implementation of the conversion algorithm 
 described in chapters 2 through 5 has two drawbacks. The first is 
 that its execution consumes relatively large amounts of computer 
 time. The second, and probably more serious, is that when a large 
 grammar is not accepted by the algorithm, it is often difficult to 
 see what changes should be made in the grammar which will make it 
 acceptable without altering the language being defined. 
 
 These two problems tend to emphasize each other in the 
 sense that the time factor makes it impractical to make several runs 
 with tentatively changed grammars in an attempt to find an accept- 
 able one. For this reason it is important that the language designer 
 be relatively certain that his grammatical changes are sufficient 
 on the first attempt at correction. This, unfortunately, is pre- 
 cisely what it is difficult to do. 
 
 8.U Potential Improvements 
 
 One improvement which is being implemented is a rewriting 
 the program with more efficient coding in an attempt to signifi- 
 cantly decrease the execution time. There is reason to believe that 
 <rts will meet with at least some success. 
 
65 
 
 In the near future efforts will be made to give the language 
 designer sufficient diagnostic information to enable him more easily 
 to make the grammatical changes necessary for acceptance by the algo- 
 rithm. How well this can be done is unknown since it is not yet clear 
 exactly what information is needed. 
 
 In general, the speed of compilers built by a TWS based on 
 this algorithm will depend to a great degree on the time taken by the 
 semantic routines. It is important, however, to make the parsing as 
 fast as possible. 
 
 Three things are presently being done in an attempt to in- 
 crease the parsing speed. As can be seen in the appendices the stream 
 of pseudo orders is similar to a sequence of procedure calls. A pro- 
 gram is being written which will convert the pseudo order stream into 
 a block of Burrough's B5500 ALGOL code which, when compiled, should 
 execute faster than the interpretive method now in use. 
 
 A program to convert the initial BWF grammar into one with 
 less productions and less nonterminal symbols is also being written. 
 This will be achieved by back- substitution for a nonterminal symbol 
 which appears as the left side of only one BNF production. For 
 example : 
 
 A->aBp 
 
 B -> 7 
 becomes 
 
66 
 
 This would speed up the parse by cutting down the number of 
 reductions, and associated stack manipulations, necessary at parse 
 time. 
 
 A third improvement is to keep the bar symbols in a separate 
 stack and thus eliminate the stack manipulation necessary for bar 
 symbol removal. This is possible since, as shown in chapter 7> the 
 bar symbols are not actually used for lookback. 
 
 Another potential improvement is the definition of a richer 
 meta- syntactic language. As presently envisioned this would be some- 
 thing similar to the regular expression of a Chomsky type three 
 grammar as the RHS of productions. This would then be mechanically 
 converted to BNF productions by a prepass. It is believed that this 
 would make writing the syntax easier for the language designer. 
 
 The final improvement presently being considered is a rela- 
 tively complex combination of ideas to improve the automatic error 
 recovery of compilers built by a TWS based on this parsing algorithm. 
 
 8. 5 Research Extensions 
 
 Three interesting areas of research appear worthy of pursuit. 
 The first is a new method of subclassification of Chomsky type two 
 grammars which would clarify the properties which make a grammar un- 
 acceptable to this conversion algorithm. 
 
 The second is the investigation of the similarity of the 
 FPL groups to the states of a finite state machine. This area is 
 presently being investigated by F. L. DeRemer at MIT. 
 
 The final area is the application of the principles of this 
 algorithm to Chomsky type one and type zero grammars. 
 
67 
 
 APPENDIX A 
 THE PSEUDO ORDERS 
 
 Njfy0P 
 
 dummy placeholder for array row ends 
 
 updating pointers 
 LLVL 
 ILVL 
 
 initialize lookahead test pointer 
 increment stack pointer 
 
 stack symbol tests 
 
 XSBT (T, A) 
 
 XSBE (E, A) 
 
 XSIT (T) 
 
 XSIE (E) 
 
 test stop stack symbol type-field for 
 value T, false => branch to A 
 
 test top stack symbol entry- field for 
 value E, false => branch to A 
 
 test top stack stymbol type-field for 
 value T, false => print error message 
 and insert correct symbol 
 
 test top stack symbol entry-field for 
 value E, false => print error message 
 and insert correct symbol 
 
 lookahead symbol tests 
 XLAT (T, A) 
 
 XLAE (E, A) 
 
 XLBT (T, A) 
 
 XLBE (E, A) 
 
 test lookahead symbol type- field for 
 value T, true => branch to A 
 
 test lookahead symbol entry- field for 
 value E, true => branch to A 
 
 test lookahead symbol type-field for 
 value T, false => branch to A 
 
 test lookahead symbol entry-field for 
 value E, false => branch to A 
 
68 
 
 XLLT (T) 
 
 XLLE (E) 
 
 test lookahead symbol type-field for 
 value T, false => branch to next 
 production 
 
 test lookahead symbol entry- field for 
 value E, false => branch to next 
 production 
 
 stack manipulation 
 TPSH 
 
 NP0P (N) 
 RED1 (S) 
 REDN (N, S) 
 
 push next terminal symbol to stack 
 
 pop N symbols from stack 
 
 reduce top stack symbol to symbol S 
 
 pop N symbols from stack, then reduce 
 top stack symbol to symbol S 
 
 bar stack manipulation 
 BP3H (B) 
 BP0P 
 
 push bar symbol B into bar stack 
 pop a bar symbol from bar stack 
 
 program control 
 
 SETS (A) 
 
 Gj&Tp (A) 
 
 XBGp (E, A) 
 
 SKIP (N) 
 
 store A as address of next production 
 
 transfer to address A 
 
 test bar symbol entry- field for value E 
 true => branch to address contained in 
 bar symbol 
 false => branch to A 
 
 skip next N characters of instruction 
 
 antic calls 
 
 EXSM (E) 
 XTSM (E) 
 
 execute EXEC (E) 
 
 execute EXEC (E), test SEMANTICTEST 
 false => branch to next production 
 
69 
 
 error 
 
 XSLR (E) 
 
 ERRT (E, A) 
 
 ERRN (S, A) 
 
 ERRR 
 
 test for lookahead symbol valid after 
 nonterminal E, false => execute ERRR 
 
 insert terminal symbol E a.nd go to A 
 
 change stack to S (reduce or push bar) 
 by going back to address A 
 
 skip to first symbol that can follow bar 
 symbol and put appropriate nonterminal 
 in stack and branch to address in bar 
 symbol 
 
70 
 
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 CD CO 
 
 
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 LIST OF REFERENCES 
 
 [1] McKeeman, W. M., "An Approach to Computer Language Design", 
 Technical Report CS-48 , Computer Science Department, 
 Stanford University, Stanford, California, August, 1966. 
 
 [2] Wirth, N-, and Weber, H., "EULER - A Generalization of ALGOL and 
 its Formal Definition", Part I, Part II , Comm. ACM , 
 2 (Jan., Feb., 1966), pp. 13-25, 89-99. 
 
 [3] Ingerman, P. Z., " A Syntax Oriented Translator ", Academic Press, 
 Inc., New York, I966. 
 
 [4] Brooker, R. A., and Morris D., "A General Translation Program for 
 Phrase Structure Languages", J. ACM , ^ (Jan., 1962), pp. 1-10. 
 
 [5] Trout, R. G., "A Compiler-Compiler System", Proc ACM 22nd 
 National Conference , 1967, pp. 317-322. 
 
 [6] Floyd, R. W., "A Descriptive Language for Symbol Manipulation", 
 J. ACM , 8 (Oct., 1961), pp. 579-584. 
 
 [7] Evans, A., "An ALGOL 60 Compiler", Annual Review in Automatic 
 Programming , k (1964), PP- 87-124. 
 
 [8] Feldman, J. A., "A Formal Semantics for Computer Oriented 
 Languages", Carnegie-Mellon University , Pittsburgh, 
 Pennsylvania, 1964. 
 
 [9] Chomsky, N., "Formal Properties of Grammars", Handbook of 
 
 Mathematical Psychology , Vol. 2, Luce, Bush and Galanter 
 (Eds.), John Wiley and Sons, Inc., I963, pp. 323-4l8. 
 
 [10] Earley, J. C, "Generating a Recognizer for a BNF Grammar", 
 Computation Center Report , Carnegie-Mellon University, 
 Pittsburgh, Pennsylvania, 19&5' 
 
 [11] DeRemer, F. L., "On the Generation of Parsers for BNF Grammars: 
 An Algorithm", ILLIAC IV Document No. 199 , Department of 
 Computer Science, University of Illinois, Urbana, Illinois, 
 1968. 
 
 [12] Floyd, R. W. , "Bounded Context Syntactic Analysis", Comm. ACM , 
 7 (Feb., 1964), pp. 62-67. 
 
UNCLASSIFIED 
 
 Security Claaalflcatton 
 
 DOCUMENT CONTROL DATA R&D 
 
 (Security claaalllcatlon ol tltlu, body ol aba tract and Indamrng annotation mumt he entered when the overall report I* clemtllled 
 
 I. ORIGINATING ACTIVITY (Corpormt* muthar) 
 
 Department of Computer Science 
 University of Illinois 
 Urbana, Illinois 6l801 
 
 4*. NtPO" T 1ECUBI T Y CI AtllFIC A TlOf 
 
 2b. qkoup 
 
 UNCJ.Afi.STFTfln 
 
 J. WPOUT TITLE 
 
 THE GENERATION OF A DETERMINISTIC PARSING ALGORITHM 
 
 4. DESCRIPTIVE NOTII (Type ol report and htclueire daft) 
 
 Research Report 
 
 V authorisi (Firm! mm, middle Initial, Jm niiuj 
 
 Alan James Beals 
 
 I RIPOUT OATC 
 
 January 6, 1969 
 
 7a. TOTAL NO. OF PACE* 
 
 113 
 
 76. NO. OF REFS 
 
 12 
 
 M CONTRACT OR GRANT NO. 
 
 .46-26-15-305 
 b. PROJECT NO. 
 
 USAF 30(602)Ul)+4 
 
 ••. ORIGINATOR'S REPORT NUMBERIS) 
 
 DCS Report No. 304 
 
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 thla report) 
 
 10. DISTRIBUTION STATEMENT 
 
 Qualified requesters may obtain copies of this report from DCS, 
 
 II. SUPPLEMENTARY NOTES 
 
 NONE 
 
 12. SPONSORING MILITARY ACTIVITY 
 
 Rome Air Development Center 
 Griffiss Air Force Base 
 Rome, New York 13*A0 
 
 IS. ABSTRACT 
 
 This paper describes an algorithm for the conversion of a grammar in the 
 form of a set of BNF productions into a deterministic parsing algorithm as 
 described by a set of modified Floyd productions. The algorithm is extended 
 in such a way that it may easily become a part of a complete translator 
 writing system and make use of the information available in the semantic part 
 of such a system. The paper also includes a discussion of the implementation 
 of the extended algorithm and describes potential related research. 
 
 DD ,?~..1473 
 
 UNCLASSIFIED 
 
 Security Classification 
 
UNCLASSIFIED 
 
 Security Classif u-gtion 
 
 k e v «o ma 
 
 algorithm 
 
 parsing 
 
 BNF 
 
 Floyd productions 
 
 grammar 
 
 translator writing system 
 
 semantics 
 
 syntax 
 
 compiler 
 
 UNCLASSIFIED 
 
 Security Classification