Hri 318 GENERATOR OF RECURSIVE DESCENT PARSERS FOR … · 1978] [Koster, 19711 [Leverett, 1980] has two major drawbacks, which are: a. Each one will create a compiler for those languages

Hri 318 061 A GENERATOR OF RECURSIVE DESCENT PARSERS FOR LL(K) 1/LANGUGES(U) AIR FORCE INST OF TECH WRIGHT-PATTERSONAR OH SCHOOL OF ENGINEERING G B PAPROTNY DEC 83

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A GENERATOR OF RECURSIVE DESCENT

PARSERS FOR LL(K) LANGUAGES

THESIS

George B. PaprotnyCapt USAF

AFIT/GCS/MA/8 3D-6

DTIC

DEPARTMENT OF THE AIR FORCEDa,' AIR UNIVERSITY

J AIR FORCE INSTITUTE OF TECHNOLOGYWright-Patterson Air F -rce Base, Ohio

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THESIS

George B. PaprotnyCapt USAF

AFIT/GCS/MA/8 3D-6

DTICS ELECTE

Approved for public release; distribution unlimited

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THESIS

Presented to the Faculty of the School of Engineering

of the Air Force Institute of Technology

Air University

in Partial Fulfillment of the

Requirements for the Degree of

Master of Science

by

George B. Paprotny, B.S.

Capt USAF

Graduate Computer Science

December 1983

Approved for public release; distribution unlimited

64

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[:* *. V U ' ;**

Preface

This thesis has been the most monumental task that I

have ever undertaken. However, because of that, and because

I completed it and met my objectives, I have learned much

about patience and perseverance. I have to thank my wife,

Jan, for putting up with me through the months of torture

that this thesis has brought. Without her smiling support,°o "

I never would have finished.

-." George B. Paprotny

-.4

4- .4%

4.4 ii

* *' .*.* -*.**.".* -". *-".'-'-" ,

Table of Contents

Page

iPreface .. .. .. .. . .. .ii ....

List of Figures . . . . . . . . . . . . . . . . . . . vSNotation . .. .. .. .. ............ vi

.Glossary . .. .. .. .. ............ vii

iAbstract . .. .. .. .. ............ ix

I. Introduction ............ . .. . I-iThesis Justification .I............1-2Problem Statement . . .I........... 1-3Sequence of Presentation . . . . . 1-4

II. Compiler Theory Basics , . . . . . . . . . II-1Compiling and Parsing . . ......... . . II-1Language Theory ......... . . . .. .11-2Parsers . . . . . . . . . . . . . . . .. . 11-8LL(k) and LR(k) Grammars . . . . . . . . 11-8Finite StateAutomata....... . . . . . O-10

III. Standard Data Structures and Techniques . . . . III-1Introduction . . .............. III-iRegular Expressions and Extended BNF . . . . III-1ProductionTrees . . . . . . . . . . . . . .111-3First and Follow Sets . . . . . . . . . . . . 111-4Parser Creation Algorithms . . . . . . . . . 111-7

IV. Requirements and Design . . . ........ . IV-IIntroduction . . . . . . . . . . . . . . . IV-lDesign Methodologies . . . . . . . . . . . . IV-ICommenting. . . . . . . . . . . . IV-2Requirements and Design Decisions IV-3

V. Input Format ..................... V-1Introduction . . . . . . . . . . . . . .. V-1Relationship to YACC and LEX . . . . . . . V-1General InputtFormat ........ V-2Lexical Analyzer Definition . . . . . . . . v-3Production Rules Format ........... .. V-5

VI. Data Structures ..................... VI-IIntroduction . ............... VI-1Finite State Automata (FSA) . ..... . VI-2Production Trees ..... . . . . . . . VI-2

iii

V

Page

Token Definition Structure .......... ... VI-4

VII. Algorithms ..... . . VII-1Introduction ...... . . . . . . . . . . VII-lThe Input Method ....... . . . . . . . VII-lNDFSA to DFSA Conversion ...... . . . . VII-4Decorating the Production Trees . . . . . . VII-7

VIII. Parser and Lexical Analyzer . . . ... . VIII-lIntroduction ................ VIII-1General Structure ..... . . . . . . .VIII-lThe Lexical Analyzer....... . . . . VIII-2The Parser o..P..... . . . . . . . . ..... VIII-4The Values of Productions........ . VIII-6

IX. Test Plan .................. IX-lIntroduction . ......... ....... IX-lGeneral TestPlan............ . IX-2Special Cae......................I-SeilCases ............... IX-3The ADA Test ................ IX-4

X. Conclusions and Recommendations ....... X-1Conclusion . . . . .......... . . . X-1Recommendations ............... x-2

Bibliography ...... ......... . . . .. Bib-i

Appendix A: FIRST 1 and FOLLOW1 Set Calculation . . A-1

Appendix B: LL(l) Parser from Production Trees . . B-I

Appendix C: Data Flow Diagrams .. .......... . C-I

Appendix D: Structure Charts . . . . . . . . ... D-1

Appendix E: Regular Expression Forms Used in LL E-1

Appendix F: Production Rule Format . . . . . . F-i

Appendix G: FSA for Each Regular Expression Form G-1

Appendix H: Maximum Possible K Algorithm . . ... H-1

Appendix I: LL Output for a Partial ADA Grammar I-1

Appendix J: LL User's Manual .. ........... . J-1

Appendix K: Code for LL . . . .............. K-1

!i!Vita . . . . . . . . . . . . . . . . . . . . . . . .Vita-i

iv

-%76

-List of Figures

Figure Page

1. Example Production Trees . . . . . . . . . . 111-4

2. Finite State Automata Data Structures . . . VI-2

. 3. Production Tree Data Structures . . . . . . VI-3

4. Example FSA Creation ....... ....... VII-3p m

5. Non-Deterministic FSA Example . . . . . VII-5

6. Empty Transition Removal ... .......... .. VII-6

7. Conversion of Multiple Transitions . . . VII-6

8. Last Multiple Transition Conversion . ... VII-7

9. After Deleting Inaccessible Transitions VII-7

10. Decorate Production Tree Algorithm . . . VII-8

11. Structure of the Lexical Analyzer . . . VIII-3

12. Example of First Set Calculation . . . o IX-3

13. Possible Core Use Reductions .. .. .... X-4

-a

"4

.4

'5. - -* °...vs. . . • • . . . " . ,

Notation

0 - the empty set

Z - the alphabet for a language

*c - the empty string, or 'is a member of'

U - union

n - intersection

-> - x expands to y, in production rules, as in x -> y

=> - x expands to y, in the description of a parse

=>+- x expands to y in 1 or more production rule applica-tions

=>*- x expands to y in 0 or more production rule applica-tions

-xI - the number of tokens in the string x

x+ - the set of all strings drawn from x of length >= 1

x* - the set of all strings drawn from x of length >= 0

* - closure

+ - closure plus

- option

* - concatenation

- alternation

vi":'.

°. ".. .... ....

. . . . . . .. . | . . . . . .. .. . . .. . . , . . . .,.

Glossary

BNF - (Backus Naur Form) a standard method of describingthe productions in a grammar

Code Generation - the process of creating executable codebased on what tokens the parser has seen

Compiler - a program that accepts a string of charactersand processes them to determine whether the stringexists in the language, and to perform some action(normally produce object code) based upon the string

Deterministic - a process that always knows what to dobased on the input

EBNF - (Extended BNF) BNF with additional rules for de-scribing a grammar more succinctly

Grammar - a set of rules that defines the valid forms ofa language

LL(k) - used to describe a grammar which can be determinis-tically parsed top-down with a lookahead of k symbols

4 Left Recursion - denotes a production which, when it isexpanded, can end up with the production's non-terminalon the left hand side of the sentence created

Lexical Analysis - the process of breaking input down intotokens for use by the parser

4 Non-deterministic - a process that must backtrack when itdiscovers that its actions were incorrect based on theinput

Non-terminal - symbols in a grammar which define acceptablesentential forms, and are expanded to find acceptablestrings of tokens

Parsing - the process of accepting tokens and determiningwhether a string of tokens is acceptable in thelanguage

• Production - one rule in a grammar

Sentence - an acceptable string in a language

. . Sentential Form - a string of terminals and non-terminalsthat occurs during a parse

vii

" " ~° ',o' ' % .'- . ." ,. ". " . . . . , . •.'• .- . . .*- . . . *. . • . " ", - .- ' .... . . ..* * .* % *. . , " "- -

Start Symbol - the non-terminal a compiler must begin with

to perform a correct parse

String - a sequence of tokens

Strong LL(k) - describes a grammar for which a parser does"* not require knowledge of the complete sentential form

to parse deterministically

Terminal - same as a token, except used in reference to agrammar

Token - one item in a language's alphabet

v.

IG

b.

AFIT/GCS/MA/83D-6

Abstract

A computer program was designed to generate a recursive-

descent compiler for LL(k) languages. crammar specification

language was designed using Extended E along with a lexical

analyzer specification language using - "lar expressions.

The program uses a well-tested but not formally proven

method for determining the maximum possible k for a grammar.

-It then uses an iterative first and follow set calculation

algorithm to determine the actual k for the grammar.

V

ix

LL -



I. Introduction

In some form or another, compilers have been in existence

almost since the very first computer was created. They have

been called assemblers, translators, and interpreters, but

they all have had one purpose, which is to take a high level

representation of a computer's instruction set and convert it

through one or more steps into an executable program. The

purpose of these compilers, along with the languages they

represent, was, and still is, to decrease the programmers'

workload by allowing a program to be created in a language

more like English.

These representations of machine language have slowly

evolved into a complex s-t of languages such as FORTRAN,

COBOL, PASCAL, etc. Each one is different, and each needs

its own compiler. Traditionally, each language has also

needed a separate compiler for each machine, because each

machine's instruction set is different. Thus, a whole new

specialty within computer science has arisen, namely, compiler

writing.

As will be seen in this thesis, most compilers can be

set up in similar ways, and can have almost interchangeable

SI-I

-.9

¢*; ~~. . .... . . . . .... .. .- .. . . . ... . .. ,.. . ... .... . ... . . .-..-..

NW .7

parts. Thus, as computers and language theory has progressed,

we have been able to define standard techniques for repre-

senting language structures and for creating the compilers

from those structures. In fact, the state of the art has

progressed to the point that some portions of compilers can

be automatically created for many languages.

Unfortunately, we have been unable to automatically

create compilers for languages such as ADA. [DARPA, 1981]

ADA is a highly complex language that has been in development

since 1974, and even though it has been completely specified

since 1981, only three compilers have been written for it so

far. If a compiler generator could be created that would

accept ADA, the compiler writing task would be simplified,

and the cost of creating the compiler considerably reduced.

Thesis Justification

There is a relatively small number of compiler generators

available on the market today; and, every one the author found

in his extensive literature search [Gert, 1981] [Johnson,

1978] [Koster, 19711 [Leverett, 1980] has two major drawbacks,

which are:

a. Each one will create a compiler for those languages

which only require the compiler to examine the next input in

the source program. (ADA requires the compiler to look ahead

two inputs.)

b. The generators universally create compilers which

consist of a small program with a very large array. This

1-2

.* * *. *-.

.. . . . -. - *..\.'.. - .

array defines e specifics of the language. So, these com-

pilers are almost unintelligible. As will be seen in the

*Q Compiler Theory Basics chapter, it turns out that the class

of languages that the currently available compiler generators

can use is called LR, and that a readable compiler can be

created from the class of languages called LL. (An LL Ian-

*- guage which requires the compiler to look ahead k inputs is

"- normally called an LL(k) language.)

There seems to be a gap in the software available to

compiler writers. If a compiler generator could be created

to examine the specification for a language and make portions

. of a compiler for it, regardless of the required lookahead,

-" and if that compiler could be created in a manner that could

' be easily understood, (and modified if necessary), compiler

writers would be far ahead of where they are now, and could

concentrate on the problems that languages such as ADA create.

Problem StatementC,.

This thesis is concerned with developing software that

will generate recursive-descent parsers for LL(k) grammars.

This generator (called LL throughout this thesis) will accept

a specification for a grammar, determine whether it is LL(k)

for some k, and create the parser. It will also accept a

specification for the lexical analyzer for that grammar, and

create an analyzer that will operate as an integral part of

the parser. Finally, the parser generator will accept user-

.... supplied code fragments as part of the grammar, to allow the

1-3

, 4

- ,V . . . -, , , . . . , ,. . . ., . . ..- . . . . .. . . . . . , - . . .

.%1

user to process application-unique code during the parse.

(Especially semantic analysis code.)

Sequence of Presentation

The presentation of the material in this thesis (chapter

by chapter) is as follows:

a. Compiler theory basics.

b. Standard data structures and techniques, with algo-

rithms used in parts of the project.

c. Design and requirements decisions, with justification

.-' for choice of design tools, and major project decisions.

d. Input format, with justification for placement and

format of each part of the input.

e. Algorithms, with descriptions of the major algorithms

used in LL.

f. Data structures, with complete descriptions of all

global structures used.

g. Parser and lexical analyzer output, with descriptions

of the data structures, support subroutines, and code used for

each part of the output of LL.

h. Test plan, with philosophy of testing, and general

structure of testing procedures, along with descriptions of

all special cases.

i. The conclusion and recommendations, with a discussion

of the project, and opinions of the author.

1-4I,

[ _ - - .- . . . " . . .. . . .. . - . .. . , . . ...

" -°

II. Compiler Theory Basics

This chapter will define the terminology and theory

needed in the chapters that follow. It will discuss compiling

and parsing, language theory, parsers, grammars and finite

state automata.

Compiling and Parsing

Traditionally, a compiler is a program that translates

a source program (written in some high-level language) into

object code (some representation of the computer's machine

language). The compilation process is usually considered to

have three phases. These are: [Davie, 1981: 11-14]

1) Lexical Analysis. This first phase accepts the

actual source program, and divides the character stream into

units called tokens. A token may be a single character, but

it is usually some sequence of characters. For example,

"BEGIN", "(" and "PROCEDURE" are all tokens in PASCAL. Lexi-

cal analyzers also remove comments, spaces, and special con-

trol commands from the source input.

2) Parsing. The tokens generated during lexical analy-

sis are passed directly to the parser, which must determine

whether the program is syntactically and semantically correct.

The parser usually follows some well-structured set of rules

to determine correctness, and to structure the program for

the code generator.

II-1

3) Code Generation. This phase accepts the structural

'. output of the parser, and creates the object program. Gener-

ally, optimization on the object code is performed at various

points in this phase. Some compilers mix the parsing and

code generation to avoid the intermediate representation of

the original program.

Lexical analysis is usually not discussed in compiler

theory textbooks, because it is the easiest of the three

phases to understand. Many compiler generators have some

easy way to specify the rules for token creation.

Parsing, on the other hand, has a large body of theory

devoted to it. Almost all of language theory applies exclu-

sively to the syntactic analysis of programs. The other part

c. of parsing, semantic analysis, has almost no developed theory.

Therefore, existing compiler generators usually take care of

syntax examination automatically, and leave any semantic work

for explicit inclusion by the user.

The last phase of compilation, code generation, is the

only one of the three that is still almost entirely an ad hoc

process. Some work has been done in the specification of

program semantics, but there are still many difficulties.

[Leverett, 1980: 38-40]

Language Theory

*.Z Before beginning any discussion of automatic compiler

* generators, a basic understanding of language theory is neces-

sary.

... I -11-2

°.

Language Elements. The basic element of a language is

the token. Tokens are analogous to letters in a natural

language (i.e. English) since they are the basic building

blocks of the language. Each language has a finite set of

tokens, called its alphabet. The alphabet is usually desig-

nated E. Every source program is a sequence of tokens drawn

from its language's alphabet. In this thesis, tokens will be

represented by letters drawn from the beginning of the English

alphabet (a,b,c etc.). [Gries, 1971: 151

A string is a sequence of tokens drawn from E. The set

of all possible strings of length 1 or more is E+. The string

of length zero (the empty string) is written e. The closure

of E, or the set of all strings of length 0 or more, is E*,

which is equivalent to (Z+ U e). Strings are usually repre-

* sented by lower case letters drawn from the end of the alpha-

bet (w,x,y, etc.). [Gries, 1971: 15]

Grammars and Languages. A language is some subset of

E*. This subset may be finite or infinite. Most programming

languages have no bound on the length of strings, therefore

they are infinite. A language must also have a structure.

There must be a set of rules that determine the various ways

that tokens from E may be organized to form strings in the

language. This set of rules is called the language's grammar.

A grammar consists of terminals and non-terminals. A

terminal is a member of E, and is the same as a token. A

non-terminal serves as a placeholder in the grammar, and is

11-3

S.............................

not in E. Each non-terminal stands for some set of strings

in E*. For example, consider the structure of telephone

numbers in the United States. [Barrett, 1979: 18] A tele-

phone number might be:

(212) 438-7021 (1)

This can be represented by the following structure

<area code> <exchange> <party> (2)

* .Each of these three also has its own structure. For example,

the area code might be:

(<digit><digit><digit>) (3)

where a digit is one value from (0,1,2,...,91. In this exam-

ple, <area code>, <office>, <party>, and <digit> are non-

terminals, and 0..9, dash, and parentheses are terminals.

Throughout this thesis, non-terminals will be represented by

a capital letter.

Grammars are represented by production rules, or produc-

tions, of the form x -> y where x and y are strings in a

.5 language's terminal and non-terminal set. (Aho, 1972: 85]

For general productions, y may be any string of terminals and

non-terminals, including e, and x may be any string of non-

terminals and terminals, where there is at least one non-

terminal in x.

These production rules are used to derive strings from

other strings, that is, from

w x z (4)

and applying x -> y, we derive

w y z (5)

.o11-

-""

In order to specify the language completely, some start-

ing string must be specified. If we could begin with any

string at all, we would end up with Z* as the language. Thus,

*some string w is usually specified as the starting string.

In fact, a single non-terminal is normally designated the

start symbol, with no loss of generality. This is so because

we can always have a production S -> w to begin a grammar.

When strings are derived in the language, the derivation

process ends when no more non-terminals exist in the string.

S. Thus, the terminal and non-terminal sets must be disjoint.S"..

Also, the reason for forcing all productions x -> y to have

at least one non-terminal in x now becomes clear. We are not

supposed to derive a new string from any string that consists

of only terminals.

Now we have all the necessary ingredients for a formal

.'," definition of a grammar. A grammar G is a tuple (N,E,P,S),

where N is the set of non-terminals, E is the set of termi-

- nals, P is the set of productions, and S is the start symbol.

[Barrett, 1979: 20]

Classes of Grammars. There are basically two grammar

classes that take on the form described earlier. These are:

context-sensitive, and context-free. [Barrett, 1979: 21-25]

The most general grammars are the context-sensitive

grammars. These are characterized by productions of the form

X-> y (6)

where x and y are elements of (E U N)*, where x contains at

least one member from N, and the length of x is less than or

11-5

* 5i *4* ... **.- *.. I .I- * 5

- %

equal to the length of y (lxi <= jyl). Note that this ex-

* '--':" cludes any production of the form x -> e. An example of a

context-sensitive grammar is: [Barrett, 1979: 20-21]

S -> aSBC (7)

S-> abC (8)

CB -> BC (9)

bB -> bb (10)

Cc-> cc (11)

and a possible derivation, with the rule used at each step,

IS

S (12)

aSBC S -> aSBC (13)

aabCBC S-> abC (14)

aabBCC CB -> BC (15)

aabbCC bB -> bb (16)

aabbcC bC - bc (17)

aabbcc cC-> cc (18)

. The other class is the set of context-free grammars.

These are the most common grammars, and the syntax for most

programming languages is specified in some form of a context-

free grammar. These grammars have productions of the form

A-> x (19)

where A is a member of N, and x is an element of (E U N)*.

,. Note that in this case x may be e. A standard example of a

context-free grammar is the following arithmetic expression

grammar:

11-6• .i

** •% *q• * * * % . *. .

*! ,..- G = ( {E,T,F}, {+,*,(,),a}, P, E ) (20)

where P is the set of productions

E ->E + T (21)

E -> T (22)

T >T *F (23)

T-> F (24)

F-> ( E) (25)

F-> a (26)

An example string, with a derivation starting at E, might be

E (T+T)*F E -> T (27)

T-> T (F+T)*F T F (28)

T*F T> T *F (a+T)*F F ->a (29)

F*F T -> F (a+F)*F T-> F (30)

(E)*F F-> ( E ) (a+a)*F F-> a (31)

(E+T)*F E -> E + T (a+a)*a F -> a (32)

Sentential Forms. Derivations in a language are de-

scribed in a manner similar to the material we have already

discussed. One derivation step in a transformation is denoted

wxz => wyz (33)

(Remember our original example, where x -> y was the produc-

tion used.) In this example, wxz and wyz are sentential

forms, if the derivation began with the start symbol.

[Gries, 1971: 20] One or more derivation steps is =>+, and

zero or more is =>*. A sentential form that consists of only

terminals is called a sentence.

-* .From these definitions, we can define a language L which

11-7

- . *

* .

d

is described by a grammar G, as [Barrett, 1979: 27]

L(G) = { x x e E* and S =>+ x } (34)

Parsers

As previously mentioned, parsers determine the syntactic

correctness of programs. There are two basic types of

parsers: top-down and bottom-up. [Pyster, 1980: 34-71]

Top-Down Parsing. Top-down parsers attempt to recognize

a sentence by beginning with the start symbol, and using the

production rules to replace the non-terminals in the various

* derivation steps with the right-hand sides of the productions.

A top-down parser uses a leftmost derivation. This means the

non-terminals in the sentential form are replaced by their

productions in a left to right order. Note that the example

0arithmetic expression derivation was leftmost.Bottom-Up Parsing. On the other hand, bottom-up parsers

accept symbols from the source program, and attempt to work

from the sentence up to the start symbcl. Thus, as symbols

are collected, the right hand side of the sentential form is

examined and replaced with a new non-terminal. This corres-

ponds to a rightmost derivation (always replacing the right-

most non-terminal), in reverse order (bottom-up). Note that

the parse is still being performed left to right.

LL(k) and LR(k) Grammars

LL(k) and LR(k) grammars correspond to top-down and

bottom-up parsing, respectively. [Berry, 1982: 17-191 Both

" . °1-

"" II-8

- t -.- '* , S.*. S. *.* . . . . . . . . .

type of grammars are the largest subset of the context-free

grammars for which a deterministic parser can be constructed

for their parser type (with lookahead of k symbols).

[Aho, 1972: 333,371] A deterministic parser with lookahead

is one that always knows which production to use at any stage

in the parse, based upon the sentential form already created,

and the next k symbols in the input.

It is interesting to note that, traditionally, LR

(bottom-up) parsers have been written as table-driven pro-

grams. That is, the parser program is quite small, and serves

only to manipulate the input and examine tables, which are

generally represented as large arrays of integers. (See Aho

'a [Aho, 1972: 368-3961 for details on table-driven parsers.)

p' LL parsers, on the other hand, are traditionally written as

large groups of recursive procedures, where each procedure

-corresponds to one production in the grammar. Note that these

recursive, top-down parsers are uniformly designated recur-

sive-descent parsers. [Davie, 1981]

Formal LL(k) Definitions and Properties. This thesis is

concerned with parser construction for LL(k) grammars. There-

fore, some definitions of what constitutes an LL(k) grammar

are now in order.

Formally, a grammar G is LL(k) if, for every production

A -> x in G, [Barrett, 1979: 148]

S =>* wAy => wxy =>* wz... (35)

* and

.1I-9

4 q* % "-"% '% , "% "% ,,. "." , . "% . - % " " , " . . " . " . "

S =>* wAy => wx'y =>* wz... (36)

where Izi = k and z e Z*, then

x = x' (37)

There is an important theorm that involves LL(k) gram-

mars, which is: An LL(k) grammar has no left-recursive non-

terminals. [Barrett, 1979: 149-150] An example of a left-

recursive grammar which fails to be LL(k) follows:

Let G have the productions

A-> Ax (38)

A ->y (39)

Then we have two derivations

k-1 k kS =>* wAz =>+ wAx z => wAx z => wyx z =>* wr... (40)

and

S =>* wAz =>+ wAxk - 1 Z => wyxk- I z =>* ws... (41)

i I iwhere x means xxx...x, with lxxx.. .x = i. It is easy to

k-i k-isee that if Irl = Isl =k, then r yx and s =yx ,so

r = s, but the two derivations are different. This results

in an ambiguity.

Finite State Automata

Definition. A finite state automaton (FSA) is a system

which has states, and transitions between those states.

Based on an input, a FSA will move between its states along

the transitions. A FSA is always considered discrete, that

is, it is always in exactly one state, or is moving through

exactly one transition to another state. [Barrett, 1979: 63]

II-10

* -. - * ,

A finite state automaton has four parts. These are:

a. A start state

b. A set of intermediate states

c. A set of ending states

d. Transitions between states

This simple apparatus can recognize input defined by regular

expressions, [Barrett, 1979: 104-110] which are defined ex-

tensively in Chapter III. Since regular expressions can

easily define the tokens for a language, this will be impor-

tant to LL.

Non-Deterministic vs Deterministic FSA. A FSA is deter-

ministic when no choices are provided in any of its moves.

Each move is completely specified by the current state andthe next input. A non-deterministic finite state automata

(NDFSA) is one in which arbitrary choices are permitted in

some of its moves. Therefore, a NDFSA is forced to backtrack

if it can not continue its moves, because it may have made an

arbitrary choice, and must go back to take a different choice.

A NDFSA is defined exactly the same as a deterministic

FSA (DFSA) with two additions. A NDFSA may have multiple

transitions on the same input from the same state, and it may

have empty transitions, that is, a transition where no input

qis processed.

FSA Representation. In this thesis, FSA are diagrammed

as follows:

a. States are circles containing state numbers.

i.[- II-11

b. Directed arcs from one state to another are transi-

tions. Each arc will have a character or £ (empty) marking

.- [ it.

c. The start state will be state 1. Also, no start

state will be an ending state.

d. The ending states will have a double circle. If

some end state has an action that must be performed, there

will also be an action number in parentheses.

.11

im11-12

* - - . .o. . . . . . . . . . .

.,,V o;W

III. Standard Data Structures and Techniques

Introduction

There have been many tools and techniques relating to

compiler construction described in the literature. This

chapter will describe some of these techniques.

First, regular expressions and extended BNF will be dis-

cussed. Then, production trees and their construction will

be defined, followed closely by First and Follow Set construc-

tion using these trees. And last, an algorithm for automatic

LL(l) parser construction will be described.

Regular Expressions and Extended BNF

Backus-Naur Form. Backus-Naur Form (BNF) is a practical

* method of specifying a grammar. [Davie, 1981: 39] In it,

the symbol -> is replaced by ::=, non-terminals are sur-

rounded by "<" and ">", and two productions such as A -> x

and A -> y can be represented as A ::= x I y. (The symbol I

is used as "or".) For example, the arithmetic expression

grammar specified in the Language Theory Section of Chapter

II might be represented in BNF as

<E> :: <E> + <T> I <T> (42)

<T> :: <T> * <F> j <F> (43)

<F> :: ( <E> ) a (44)

Regular Expressions. A regular expression is a compact

way of representing the grammar of a regular language.

,111-1

c- , ... .... .. ......* *.* ....*....... .. . * - .. ,* ..- .... . .. .. -. .A. -, o

[Barrett, 1979: 100] Regular languages are a subset of the

context-free languages, and are represented by productions

of the form

A -> aB where B e N, and a E Z (45)

and

A->b where beE (46)

Regular expressions are quite formal, and have three basic

operations. These are concatenation, alternation, and

closure. Parentheses may also be used. In the following

definitions, E and F are regular expressions, x and y are

strings, and X and Y are sets of strings.

4... a. Concatenation is represented by placing two regular

expressions next to each other. EF is the concatenation of

, o 'E and F, and is formally

EF= x x E and y e F} (47)

b. Alternation is represented by I or +. (This thesis

.-. will always use I-) EJ F is the alternation of E and F, and

is formally

El F {x x E or x F (48)

c. Closure is represented by {E}, and is formally

{ E } = { xY x e E and Y e {E} U {e} (49)

d. Parentheses may surround any part of a regular ex-

pression to change the way the expressions are handled. For

example, ablbcd is equivalent to (ab)l(bcd), not a(bjbc)d.

The symbols {, }, (,), and j are all in the regular

111-2

.

.i.

expressions, and therefore can not be used as part of anylanguage a regular expression represents. A solution to this

might be to surround any occurrences of these characters in

the language by quotes.

Extended BNF. Regular expressions and BNF have been

combined in a relatively straightforward way to come up with

a more concise grammar specification language called Extended

BNF (EBNF). [Gert, 1981: 2-6] Unfortunately, there is no

standard for EBNF, but the methods in use are similar enough

to avoid confusion. A common one is described here.

The symbols [ and I are used in EBNF to show that a

* particular string is optional; i.e. it can occur 0 or 1 times.

Then, the EBNF production

<A> :=a~bc~d (50)

is equivalent to the BNF production

<A> ::= abcdI ad (51)

The symbols { and } are used to show that a string can

occur 0 or more times. Then, the EBNF production

<A> ::= a{bc}d (52)

is equivalent to

<A> :: ad (53)

 :: bc re (54)

Production Trees

Barrett [Barrett, 1979: 178-179] has a method of repre-

senting productions that can be useful in parser construction.

111-3,l.

,.. . - . - ... . . . . . . . . . . . . . . . .. . . . . . . . .

He represents EBNF as production trees.

Each production tree in a set represents one non-terminal

A. The interior nodes are from the set {., , *, ? } ,

where - is concatenation, I is alternation, * is closure, and

? is option. Since - and I are binary operations, each has

two children in a tree. But * and ? are unary operations, and

therefore each has one child. The leaves of the tree are from

the set N U E U {e)

As an example, the grammar G with productions

S -> a{B}d (55)

B ->[bic Ibb (56)

can be represented by the production trees in Figure 1.

First and Follow Sets

S. i When the definition of LL(k) grammars was given earlier

in this thesis, we saw it was: A grammar G is LL(k) if and

only if for every production A -> x in G,

S => wAy => wxy =>* wz... (57)

S -

a

B

and

Figure 1. Example Production Trees

'1 1

" S...III-

7.7.. . . . . . . .7. .... . . . .. . . . . . ..

and

S =>* wAy => wx'y =>* wz... (58)

where izi = k and z £ then

x = x' (59)

This definition does not appear to be easy to implement

in an algorithm, so it might not be useful for reading a

grammar and determining if the grammar is LL(k). But, first

and follow sets appear to solve this problem.

The FIRSTk set of a string w is defined as [Aho,1972:300]

{ x I w =>* xy and lxi = k or w =>* x and lxi < k 1 (60)

and the FOLLOW set of a string is defined as [Aho, 1972:k

3431

x I S =>* vwy and x e FIRSTk (y) } (61)

With these definitions, we can define an LL(k) grammar as

follows: [Barrett, 1979: 153]

A grammar G is LL(k) if and only if, for every pair of produc-

tions

A-> u and A-> v (62)

and every leftmost sentential form wAx derivable in G,

FIRSTk (ux) n FIRSTk (vx) = 0 (63)

Note that for this sentential form, x is FOLLOW (A). Thisk

means that the definition can be restated as follows:

G is LL(k) if and only if for every pair of productions.'%

A-> u and A-> v (64)

and every leftmost sentential form wAx derivable in G,

FIRST (u FOLLOWk (A)) l FIRST (v FOLLOWk (A)) = (65)

k k k

111-5

This definition of LL(k) is only valid for each senten-

tial form wAx. It is not true for all forms of that type.

An example of this is the following grammar G with produc-

tions

S-> aBbc I Bc (66)

B-> b I c IC (67)

In this grammar, S derives aBbc and Bc. For aebc, the possi-

ble sentences in G are abbc, abcc, and abc. So, for aBbc,

FIRST2 (b FOLLOW2 (B)) = bb (68)

FIRST2 (c FOLLOW2 (B)) = cb (69)

FIRST 2 (e FOLLOW2 (B)) = bc (70)

which are all pairwise disjoint. For Bc, the possible sen-

* -tences in G are bc, cc, and c. So, for Bc,

FIRST 2 (b FOLLOW2 (B))= bc (71)

FIRST2 (c FOLLOW2 (B)) = cc (72)

FIRST (e FOLLOW (B)) = c (73)2 2

which are also pairwise disjoint. However, if the calcula-

tions were performed without regard to the leftmost sentential

form, the six FIRSTk sets would not be disjoint, because the

db string bc occurs in two different calculations. [Barrett,

- 1979: 155]

A grammar which has disjoint FIRST sets without consid-

ering the leftmost sentential form is defined to be strong

LL(k). The difference between a strong LL(k) grammar and an

LL(k) grammar will become important when generating a parser

for the grammar. Succinctly stated, it is easier to look

111-6

V.-."- I-6.-*. . . . . . . . . . . . ..... * *

ahead k symbols than it is to look ahead and look behind to

see what the leftmost sentential form is.

Parser Creation Algorithms

. There are two published algorithms that are useful for

creating recursive-descent parsers from EBNF. The first is

FIRST1 and FOLLOW 1 set calculation on production trees, and

the second is construction of recursive-descent LL(l) parsers

from the production trees decorated with first and follow

sets. (In the rest of this chapter, FIRST and FOLLOW is used

instead of FIRST1 and FOLLOW if no ambiguity will result.)

[Barrett, 1979: 180-187]

FIRST and FOLLOW Set Construction. The algorithm for

FIRST and FOLLOW set calculation is a multi-pass process. In

it, the FIRST sets are completely calculated, and then the

FOLLOW sets are calculated. Each set of calculations will

be performed until no changes are observed in the FIRST or

FOLLOW sets for any node on the production trees. Since the

entire algorithm is in Appendix A, only one example is given

here.

To calculate the FIRST set of the node I (alternation),

calculate the FIRST sets for the right and left children of

the node, and then add the FIRST sets of both children to the

FIRST sets of the alternation node. To calculate the FOLLOW

set for the same node, add the FOLLOW set of the node to the

FOLLOW set of both children, and then calculate the FOLLOW

sets of the children.

S111-7

ill..

Parser Construction for LL(l) Grammars. Parser creation

is the final phase of the compiler construction process. The

complete algorithm is described in Appendix B. This process

assumes an unambiguous LL(l) grammar. The parser is created

using the production trees that have been decorated with

FIRST and FOLLOW sets. There is no error recovery in this

created parser, and, when executed, it will stop as soon as

an input error is discovered. As given, the procedure is

rudimentary, but it is an excellent first step towards creat-

ing a more complex parser.

.1 1

'" III-8

IV. Requirements and Design

Introduction

In any software development project, the development

process is very important to the success of the project.

This chapter will first describe the software engineering

tools chosen by the author. Then, some philosophies on com-

menting will be discussed, and last, the requirements and

design decisions will be detailed.

Design Methodologies

There are innumerable techniques in use today for de-

signing and developing computer software. Choosing one or

more techniques for a project such as LL, which is designed,

developed and implemented by one person, is a very introspec-

tive decision. The author believes that the technique chosen

must be flexible enough to accept any type of project, be

formal enough to force a good design process, while at the

same time be easy enough to use so that time is not spent on

excessive detail. Also, the technique chosen should create

paperwork that will be very useful as maintenance documents,

and be understandable enough so that another relatively ex-

perienced programmer can learn how the system works.

To satisfy these requirements, the author has chosen

Data Flow Diagrams (DFDs), [Peters, 1981: 139-140,145] and

Structure Charts (SCs). Peters, 1981: 60-62] The DFDs were

IV-li"

p {~ .. . . .. . . . . . . . . . . . . ... . . . . . . .

--used at the higher levels of the design phase. They assisted

- in breaking down the complex structure of the project into

manageable, understandable pieces. At each stage of the DFDs,

* the author stopped breaking down the pieces when he had a

*sub-system that he could understand completely. At that

point, SCs came into play.

The SCs were used to cut the pieces into multiple, stand-

alone modules. The criteria for breaking a task into modules

were:

a. Does each sub-task stand by itself?

b. Is the interface with the calling routine fairly

small?

c. Is the task large enough to warrant its own module?

The DFDs and SCs in Appendices C and D were developed

with all of the above in mind. It should be noted that the

format is not formal, because each diagram was written to

make the meaning of the diagram as clear as possible, while

at the same time maintaining a high level of accuracy.

Commenting

*DFDs and SCs are extremely valuable in all phases of a

large project. However, nothing can replace in-code comments

and program headers to completely round out the information

available to the reader.

* .. Program headers in LL consist of all pertinent informa-

tion about each module. This includes the module's purpose,

interface, variable list, and basic algorithm, along with

IV-2

--.7*. - -

other valuable information. Comments are placed in the code

to enhance all the other information that already exists.

The author used the philosophy that having too many comments

is a very poor programming practice, since readers may be-

come just as frustrated with meaningless comments as with no

comments.

Requirements and Design Decisions

The purpose of this thesis is to create an LL(k) parser

generator along with a lexical analyzer. Before progressing

into the design stage, some decisions needed to be made, and

specific requirements determined. This section lists and

justifies these decisions and requirements.

Use of AFIT VAX 11/780 (SSC). The lack of a sponsor to

this thesis severely limited the choice of computers. Ex-

cluding microcomputers, which are not reasonable for a pro-

ject of this type, there are only three; the AFIT VAX 11/780

(Scientific Support Computer), the AFIT VAX 11/780 (database

research), and the ASD CDC 6600. The ASD CDC 6600 is no

longer used by most AFIT students, (because of its poor re-

' sponse and "unfriendly" operating system), and is therefore

unreasonable for this project. Also, the database research

computer has very limited disk space, and is frequently un-

" -available for use. The SSC is the "standard" student com-

..°-. puter, and has enough disk and memory to satisfy any LL's

requirements, therefore it became the computer of choice.

Use of C Programming Language. During the design and

IV-3

*. ,, . . ... . . . .. ... .. . .. . .. . .-- - . -o, -- - - '- " -¢''''',--,-' - .- '--7 -- &i: < : -,2 " , 7 %Z 1, 7,,,...-. -, ..

.7 .

implementation stage, many data structures were built and

manipulated, and therefore LL will require a pointer-oriented

language to give maximum flexibility to the code. C and

PASCAL were the only two languages available that have

pointers. Each one is a high-level language, but C can also

be used at the bit level to manipulate data, and is the lan-

guage that most of the systems that exist on the SSC are

written in. Even though C is more cryptic than PASCAL, its

advantages far outweigh this single disadvantage.

Use of YACC and LEX. YACC (Yet Another Compiler Com-

piler) [Johnson, 1978] and LEX (LEXical analyzer creator)

[Lesk, 1978] are both resident on the SSC. The use of a

YACC/LEX input processor alleviates the need for a massive

amount of coding for reading in the grammars, processing them,

and recognizing what all the strings mean. It is a standard

tool used by many other systems, and so is proven effective.

Also, as we will see later, the YACC input can be massaged to

create an input to LL as a test case. Therefore, YACC and

LEX were chosen to process the input.

Use of C for Output Parser. C is used in the output for

all the same reasons that was used for LL itself.

Interface Between LL Parser and Lexical Analyzer. The

interface between the parser and lexical analyzer is important

at this point because one of the first tasks in design is to

create the input formats and data structures, and this inter-

face will have an effect on them. Also, since LEX already

IV-4

I.

exists, it would be wise to allow the use of LEX rather than

the LL lexical analyzer if the user chooses. Therefore, it

is desirable that thL interface between the parser and lexical

analyzer be as close to the YACC/LEX interface as possible.

Other Requirements. The rest of the iequirements are

not directly justified, but are either obvious, or are per-

sonal preferences that have little effect on the objective.

These are:

a. The output parser and lexical analyzer should be as

simple and easy to understand as possible.

b. Both the lexical analyzer and parser should be non-

backtracking. That is, they should be able to make decisions

deterministically.

c. The lexical analyzer should be a deterministic finite

state automata (DFSA). (This is the only method known to the

author for performing this task.) Aho [Aho, 1972: 113-137]

is a valuable reference to understand FSA.

d. The CPU, memory, and disk requirements of LL are not

important, unless they become totally unmanageable. (This

alleviates the need to make very compact and complex data

structures, thereby increasing the project's simplicity.)

e. For practical reasons, there must be a facility to

allow the productions to have a value, and to allow actions

and other elements of a production to have values. The user

should be able to retrieve and store these values, in a manner

similar to that of YACC.

IV-5

* - .. . . . . ... - ". -- " - .. . .V . °

V. Input Format

Introduction

This chapter discusses the decisions made during the

initial design phase, specifically the reasons for the input

format. First, the general outlines of the format will be

discussed. Then, the specific design decisions for the lexi-

cal analyzer will be given, and finally the format of the

production rules will be discussed.

Relationship to YACC and LEX

As indicated in the previous chapter, the decision to

use YACC and LEX to accept the input to LL was made during

the first days of design. However, this decision was not

made strictly to decrease the programming workload.

Both YACC and LEX are very similar to the products that

are contained within LL. YACC is a parser generator, and LEX

is a lexical analyzer creator. It became easy to see that it

should be possible to take the input definitions written for

YACC, and modify them so they would input easily to LL as a

test case. Thus, the format of the input to LL became impor-

tant, because any similarity to the input format of YACC

would be advantageous in that conversion. (This similarity

would also provide YACC users an easy transition to LL use.)

The input format for the LL lexical analysis portion

became similar to LEX for reasons that were much the same.

V-1

, - : - " , .< J -- ' . " ' > ,- ' . - .. . .. . .4.-. . - .* . . v * .

Because the purposes of the two lexical analyzers are the

same, namely, to return tokens from the input stream, the

decision was made to keep the two as generally similar as

possible.

General Input Format

At this point, it was necessary to formalize the input

formats, determine where to place variable and subroutine

declarations, and decide whether to force the user to declare

the names of tokens.

Placing the Variables and Subroutines. There were two

considerations as to placing the variables and subroutine

declarations. One, what effect would the placement have on

the user, and two, what effect would it have on the ease of

development. For the user, placing them at the beginning or

N" the end seemed to be best. For the ease of writing the YACC

and LEX input routines, any location was acceptable, but the

end seemed to be the best, because no other types of input

would be expected, and the processing of the declarations

would be merely a copying operation. The deciding factor

was, once again, the format of YACC. It places these types

of inputs at the end, and so LL also places them at the end.

To Declare or Not to Declare Tokens. Whether or not to

force the user to explicitly declare token names was a more

difficult and complex decision. To a sophisticated user,

placing all of the token names in a separate list is an un-

necessary task, since every name in a grammar that is not

V-2

• - - ,~~~ ~~ ~ .. . ._ ' ..- .- ". .. ' .. - .-- , , . .;- - . - ." -. - . - - . - -.- - " " ' .' . -" .'.' ..

-•defined as a production is automatically a token. However,

it is easier to detect such things as spelling errors and

forgotten production rules when the token names are specified

beforehand, and the less sophisticated user will appreciate

that. After considering these arguments, the decision was

made to force the user to declare tokens specifically. The

time required to key in the token names is not so great as

to outweigh the advantages (to the user) of having extra error

checking capability.

Final Input Format. All the input parts have been dis-

cussed, and now all that is left is to show the order of the

parts. Again, YACC has been used as a model. In it, the

tokens are defined at the beginning. Since the token names

are used throughout the rest of the grammar, this is a good

* *."practice, and was adopted for LL. The lexical analysis output

has been placed second, and the production rules placed third.

All these are followed by the variable and subroutine declara-

tions. The delimiters between the parts are the same as

YACC's, specifically "%%".

Lexical Analyzer Definition

As stated earlier, this part of the input will look very

much like the input to LEX. The Requirements and Design

Chapter defined the necessary parts of this input to be: (1)

the definition of the character sequences that make up tokens,

and (2) the definitions of the actions to be performed when a

specific character sequence is recognized. (Because of the

V-3

• •.

interface requirements between the LL parser and lexical

analyzer, each character sequence that defines a token must

have, at a minimum, a "return (token-name)", since the lexical

analyzer is a subroutine.)

The following defines the basic structure of the lexical

input:

a. Token definitions begin in column 1.

b. Token definitions are terminated by a space, tab or

newline.

c. Actions consist of a sequence of C statements.

d. Actions begin after the token definition, and can be

continued on subsequent lines.

e. A line beginning with a space, tab, or newline is

part of the action for the immediately preceding token defi-

nition.

f. A token definition need not have an action.

Structure of the Token Definitions. In LEX, tokens are

defined using a modified form of regular expressions. (Regu-

lar expressions are defined in Chapter III.) These regular

expressions are an easy way to represent token definitions,

and actual regular expressions can be converted into a deter-

ministic finite state machine.

The LL lexical analyzer will use the standard regular

expression forms, as described in Appendix E. These do not

include the following LEX forms:

a. 'a' In LEX, this character is used to denote the

V-4

.. ... . . ... *.*% .. .. . ~. .. . . ....... ... ... .

- .7 .,,-.

* beginning of a line; i.e. the regular expression only suc-

ceeds if a beginning of line is found at the point of the

carat.

b. '$'. This character denotes the end of a line, in

a manner similar to (a).

c. '<...>'. Denotes a start state. [Lesk, 1976: 48]

d. 'x{m,nl' Denotes m through n occurrences of 'x'.

None of these are standard regular expression forms, so they

are not included in the LL lexical analyzer input.

Production Rules Format

The format for the production rules is similar to EBNF,

with one addition, which is "closure plus". Closure plus is

the same as closure, except that the expression inside the

braces will be repeated one or more times, rather than zero

or more times.

The complete definition of the format can be found in

Appendix F, but the following list gives the highlights of

the changes and additions from EBNF, along with the reasons

for each one:

a. The first production rule defines the starting sym-

bol. If the starting non-terminal was generalized by having

it be any of the non-terminals, a new input to LL would be

needed to define that symbol. As it is, no generalization is

lost, since any grammar can be modified to move the starting

production S to the beginning, or to make a new production

NewS -> S.

V-5

-, -. .. . ' : xK..> '. . .,- ... ,-..-,.. . ..... ~~~~~........ ......... ' ..... -,... .... .. . .... .....,.. . • ;.-

b. Multiple production rules may define the same non-

terminal. This rule allows an extra measure of generality

LL would not otherwise have had.

. c. Non-terminal names may be surrounded by < and >, as

long as all instances of the name are surrounded. This allows

a user to separate terminals and non-terminals with a quick

glance, and also allows grammars that come from technical

*manuals to be copied directly. (Often the non-terminals have

these surrounding characters.)

d. Every production rule ends with a semicolon. This

rule allows LL to perform more accurate error detection, and

provide the user with more accurate feedback if an error is

found.

AM e. Actions begin with '={' and end with '1' These

actions need to be set off by some delimiter, and { } was

already taken, because of closure. They would have been best,

since they also delimit C statement blocks. The character

"*'* '-' was chosen as the prefix to '' because of the proximity

of the two characters on the keyboard of the computer system

that LL was created on.

f. "Closure Plus" is defined by { expression 1+. Note

the + to signify the difference from closure. This is an

extension from regular expressions, where "one or more" is

also represented with a +.

V-6

. . . ."

VI. Data Structures

S.Introduction

After the initial design decisions have been made, and

what is to be done has been determined, the next step is to

determine how it is to be done. For a project such as LL,

which must maintain a large amount of data, manipulate that

data, and finally create output from the data, the data struc-

tures involved are vital.

For this project, two considerations were used in build-

ing the required data structures. First, they should be easy

to build, to use, and to modify if necessary. These are

* desirable attributes in any project, but especially in one

which is a prototype. And second, these data structures

should correspond as closely as possible to the generalized

data structures as described in Chapter III. This makes them

easy to understand by someone studying LL, and a direct rela-

tionship can be drawn between the theory and the implementa-

tion.

This chapter describes three sets of data structures.

First, those dealing with the lexical analyzer/finite state

automata will be discussed. Second, the structures for the

* •• parser/production trees will be described, and third, the

token definition structure will be detailed.

VI-I

". - ' :. i - 6 .-

, r v -. -L .. .- ,. .- .; , - . -- . . -.J -. . o ...- ,. .. .

Finite State Automata (FSA)

The data structure for FSA will exactly model the

theoretical FSA as described in the Finite State Automata

K[- Section of Chapter II. Figure 2 shows the format of this

data structure. The reader must remember that for those FSA

which are non-deterministic, a particular character may have

multiple transitions from one state to other states, so the

data structure is not quite as easy to comprehend as it might

otherwise be.

Production Trees

The data structure for the production trees is more com-

plex, but that is because there is more data involved. There

are basically two sets of data. First, the production trees

themselves must be represented. (Chapter III describes pro-

State Data Structure

1. Action-id ( >0 if end state. Points to a particularaction. =0 if not end state)

2. State number3. Pointer to next state (connects states together)4. Pointer to first empty transition5. Array of 128 pointers to first transitions, one for

each of 127 possible characters, and also onefor the character NUL, which = 0. (Since eachletter has its own ASCII code, the code isused to enter the array.)

Transition Data Structure

1. Points to state which the transition is to2. Pointer to the next transition, if there is more

than one transition on this character fromthis transition's state

. . Figure 2. Finite State Automata Data Structures

VI-2

,-" .' ... ,.......-.- ....... '.. " ...-. - , -'. - . " .. -.S %- S,, ,, ,' .. ", •

duction trees in detail.) It is important to note that the

structure must be flexible enough to allow for nodes with

zero, one, or two children. Second, the first and follow

sets for nodes must be represented. Since these may be of

any length, the data structure must be flexible enough to

handle it. Figure 3 shows the data structures that have been

designed.

Production Tree Head

1. Pointer to next production tree head2. Name of non-terminal3. Pointer to top of tree

Tree Node

1. Node type (closure, alternation, etc.)2. Pointer to first set3. Pointer to follow set4. Pointer to left child if binary node, only child,

if unary node5. Pointer to right child if binary node, or a unique

reference number if the node is a non-terminal6. Action number, if the node is an empty node because

an action is required

First/Follow Node

1. Pointer to next first/follow node2. Pointer to first token node for this first/follow

item

Token Node

1. Pointer to next token node in this first/follow item2. Pointer to a terminal definition node

Figure 3. Production Tree Data Structures

VI-3

There are two non-trivial parts of the production tree

data structure that should be discussed at this point. First,

a non-terminal node needs a reference number because of the

requirement to remember the leftmost sentential form, which

is shown in the First and Follow Sets Section of Chapter III.

With the reference number, which would be unique for each

reference of a non-terminal, references to the follow set of

a non-terminal can be made distinct based on which production

rule referenced that non-terminal. And second, a method of

placing actions into the production tree is necessary, so

empty nodes are created whenever actions are found, and an

action identification number is placed in the node. Of

course, those empty nodes which are part of a grammar will

not receive an action number.

Token Definition Structure

This final data structure is the simplest one in LL. It

consists of a token name, a token number, and a pointer to

the next terminal in the list. The token number will be used

to identify each token, without resorting to the character

string.

VI-4, . -

m.

VII. Algorithms

Introduction

The two previous chapters in this thesis define the

input format and the data structures for the LL project.

Once both of these were defined, creating the algorithms for

the project was a relatively straightforward task. Almost

all of these algorithms were either in a book, or were very

similar to other common algorithms. The only major difficulty

occurred in decorating the production trees for a grammar.

The algorithms will be described in the following order:

a. the input method, to include the creation of the

NDFSA and the production trees

b. converting the NDFSA to a DFSA, and outputting the

appropriate C code for the lexical analyzer

c. decorating the production trees

The Input Method

As we saw in the introduction to Chapter V, the input

consist of four parts. These are the token definitions, the

regular expressions, the production rules, and the variable

and subroutine declarations. This section shows how YACC

was used to process these inputs and perform the required

actions. At this time it should be noted that some under-

standing of YACC is necessary to fully understand this

section. [Lesk, 1976] Also, note that each time output is

VII-I

mentioned, the format and reasons for the output is not clear.

These problems will be cleared up in the next chapter.

The Token Definitions. Two actions were required to

input the token definitions. The first was to create a list

of token names and their corresponding integer values for use

during the production input, and the second was to output a C

"define" statement for each token to be used in the created

parser. This task required only one production rule, and was

straightforward.

The Regular Expressions. Processing the regular expres-

sions and creating the NDFSA required productions very much

like those found in Appendix E. There were essentially two

tasks involved here. The first one involved creating and

linking states at the appropriate places in the production

rules, and the second involved accepting the actions and out-

putting them, along with appropriate surrounding code.

An example of the method used to link the states is

included at this point. This example will show how multiple

alternatives would be linked together to form a sub-automata.

Assume that the following YACC production rule exists:

sub FSA : alternative I sub FSA (74)

and that the input is

ablcdle (75)

Each of 'ab', 'cd', and 'e' are alternatives. Assume that as

each alternative is parsed, the appropriate sub-FSA is re-

turned. The alternative 'ab' returns as in Figure 4(a).

VII-2

(a) © a b

~a XD b

(b) _

Figure 4. Example FSA Creation

So, the task is to accept the three alternatives and

meld them into one sub-FSA. When the FSA for 'cd' is re-

turned, two empty transitions are added, and the FSA is as

shown in Figure 4(b). When 'e' has been parsed, two empty

transitions are again added, and we have the FSA in Figure

4(c).

These empty transitions are added in the actions for the

regular expression productions. The FSA in Figure 4Cc) will

accept 'ab', 'cd', or 'e' as input. That FSA is non-

deterministic. (See Appendix G for a complete list of all

the structures that are created for each type of regular

expression.)

Ending states have an action number attached to them.

VII-3

-- "-

When the action is parsed by LL, it is immediately output with

the surrounding code, and the ending state is marked.

The Production Rules. The production rules are parsed

in much the same way as the regular expression, so no example

will be given here. The general scheme, however, is to create

the trees from the bottom up, and for each production rule to

accept one or two subtrees, create a parent node, and then to

pass the new tree up to the next production rule.

When actions are parsed, an empty node is created, and

it is marked with an action number. The actual code is out-

put, along with appropriate surrounding code, which uses the

action number as part of the identification for the action.

The Variable and Subroutine Declarations. These declara-

tions were the easiest to parse. All that was required was

to accept the code and output it with no changes.

NDFSA to DFSA Conversion

One of the requirements of the project is to avoid all

types of backtracking. Therefore, the FSA must be determin-

istic. The following algorithm to convert a NDFSA to a DFSA

has been proven effective. [Barrett, 1979: 75-87] It con-

sists of three steps, which are

a. Remove all empty transitions.

b. Remove all transitions to multiple states on one

character and replace them with a single transition to a new

state. Place the transitions of all the old states into the

new state.

VII-4

..

c. Remove all inaccessible states.

A series of figures best demonstrates this algorithm.

Figure 5 shows a set of regular expressions and the FSA

created from them. Figure 6 shows the FSA after removing

the empty transitions. Since there are multiple transitions

on 'a' from state 1, a new state must be created. Figure 7

shows this conversion. Then, since there are still two

transitions from state '2,7,9' on 'b', one more conversion

must be performed. Figure 8 is the result. The entire FSA

is now deterministic. However, the last step must still be

performed. States 2, 3, 4, 6, and 8 may be removed. Figure

9 shows the final DFSA. Examination shows that both the

original and the final FSA describe equivalent finite state

machines.

For the regular expressions

abc action 1;a+ action 2;ab*d action 3;

the FSA created would be

a b c

,a d(3I

Figure 5. Non-Deterministic FSA Example

VII-5

................

le![ a b

i°-a

6... 7 (1 )

(2) a

.~ d8. 9 1 0 ( 3)(3

~~~Figure .CnErsonopMuil Transitions

a IIIII.II., ,1,1,

1

a -d

[,.--.d 9 1 0 ( 3- .) ...- , . , o, .- . , ., .... ..., .. .., . , .-. .- , , .-..-> : ... .

3,7, 4, 7 (2)~~(2)

Figure 8. Last Multiple Transition Conversion

7<"i (2) 5(1)a c bb~b

Iid dd

10 (3)

Figure 9. After Deleting Inaccessible Transitions

Once the FSA has been defined, all that remains is to

output the appropriate code for each state.

Decorating the Production Trees

As stated earlier, this particular algorithm was the

most difficult to create. The objective is to have the

first sets on the child(ren) of each node for which k isk

greater than 0. The first sets of the children are important

because it is through their first sets that one can determine

VII-7

. . . . . . . . . . . . . . . 4..

." -.. .. °. m

whether or not to take a particular path through the tree.

The algorithm to accomplish this has four basic parts,

which are organized to accomplish their task as shown in

* -Figure 10. (The Conclusions chapter gives the practical

reason why the algorithm does not merely find the first and

*follow sets for the maximum possible k, and avoid the looping

construct.)

The algorithm to find the first and follow sets follows

the algorithms in Appendix A very closely. Of course, since

k can be greater than i, some parts of the algorithm were

more difficult, but it was a straightforward extension. It

was interesting that these two algorithms were the most

troublesome. (See the Test Plan chapter.) This probably

happened because the first and follow set data structures

are manipulated quite a bit, and therefore the number of

places for possible error increased greatly.

Find maximum possible k (part 1)FOR i = 1 to maximum k do

Find first sets at k =i (part 2)Find follow sets at k = i (part 3)Find k for each node and determine whether

all nodes have k <= i (part 4)If (all nodes have k <= i)THEN stopEND IF

END FOR

Figure 10. Decorate Production Tree Algorithm

VII-8

0 o -. % 7 .7

.. Determining k for each node was a relatively simple

task. For each node which could have k > 0, there is a

simple test which determines k. These tests are:

a. For closure, closure-plus, and option, compare the

first set of the child to the follow set of the node.

b. For alternation, compare the first sets of the two

children.

It should be noted that before determining k, each node

needs to have its first sets adjusted by concatenating the

follow sets on to them. This takes care of the situation

where the follow set of a particular non-terminal is signifi-

cant when the non-terminal is LL(k) but not strong LL(k).

Determining Maximum Possible k. The method for deter-

mining the maximum possible k is relatively straightforward.

The idea is to count the absolute largest lookahead that

might be possible at the beginning of a parse. Each node

has a particular counting method, and these are described

in the following list:

a. empty node : 0

b. terminal : 1

c. non-terminal : If this non-terminal is recursive,

and it has already been examined, return 1 and a recursion

indicator. If not, count the non-terminal.

d. closure, closure-plus and option: count the child.

e. concatenation : count each child. If the left child

*. .- .has the recursion indicator set, return its value, otherwise

VII-9

I- .0

*. -" ~ ~ ~ . ..

add the two counts and return.

f. alternation : count each child and return the

larger. (A more detailed description and a non-mathematical

proof of this algorithm is in Appendix H.)

Final Parser Output. Once all of the decorating has

been completed, all that is left is to walk the trees and

output the parser. The format of the parser is described in

the Parser Section of the next chapter, so the code for each

node will not be described here.

VII-lO

7Z_

-" VIII. Parser and Lexical Analyzer

Introduction

The character of the LL project depended on the output

code at least as much, if not.more, than it depended on the

input. This chapter is devoted to the structure of the out-

put parser and lexical analyzer. It will discuss the general

structure, the data structure and code for the lexical ana-

lyzer, the data structure and code for the parser, and the

method used to remember the values of items in productions.

General Structure

The general structure of LL output is fairly straight-

forward. There are seven divisions, which occur in order

from the beginning to the end of the output as follows:

a. the variables and subroutine declarations specified

by the user

b. statements that define each token as an integer for

. use in all parts of the program

c. the global variables, to include a definition of the

maximum token size, the declarations for the character string

of the "current" token during a parser, and the declarations

Wfor that token's length

- d. the variables, code, and support subroutines for the

"*'. lexical analyzer

e. the variables, code, and support subroutines for the

VIII-'

parser

f. the variables and subroutines that support remember-

ing the values of items in a production

g. genz.ral support routines.

The Lexical Analyzer

As seen in the Requirements and Design Decisions Section

of Chapter IV, the lexical analyzer must return the integer

value of a token recognized, as well as the string that is

the token. Also, the lexical analyzer must be a deterministic

finite state automaton. To accomplish this, the following

data structures, support subroutines, and code were created.

Data Structures.

a. A stack of characters that have been recognized,

along with the action number that applied to the state that

recognized the character.

b. A character array that an entire input line will be

read into, and characters retrieved from and returned to by

the DFSA.

Support Subroutines. The support subroutines all support

the reading of data from the input, and the maintaining of

that data. All of these manipulations are performed by the

subroutines, and the only interface to the lexical analyzer

is through two routines that get characters from the input,

and put characters back onto the input.

Code. The lexical analyzer itself consists of one rou-

tine. The structure of that routine is in Figure 11.

VIII-2

P , i,; " .-_', -.--'i'i' '. -./ -' .-..- '-' " - v .. - ..'.. -'. .. .-..-. '-. .. .. -. ".- . .. ..5• - -

while (forever)"Begin a new token"set current state to 1initialize the stackwhile (there was a transition from the previous state)

get a character and place it on the stackcase (current state)

state 1 : "state code"state 2 : "state code"

state n : "state code"end case

end whilewhile (the last state on the stack does not have an

action) pop the stack and put character back on theinput

end whilecase (action number on top of stack)

acticn 1 : "action code supplied by user"action 2 : "action code supplied by user"

action m : "action code supplied by user"end case

end while

Figure 11. Structure of the Lexical Analyzer

The "state code" is what is derived from the DFSA data

structure. For each character that has a transition from

that state, there will be an IF statement. For example, if

a state has transitions on 'a', 'b', and 'c' to states 1, 2,

and 3 respectively, the state code would be

Place state's action number on stackIF (current char = 'a')THEN current state = 1ELSE IF (current char = 'b')THEN current state = 2ELSE IF (current char = 'c')THEN current state = 3

. ELSE there is no transition from this stateEND

VIII-3

The action code is taken directly from the input. The

while loop that surrounds the entire subroutine exists in

case a "return" does not appear in an action, so that some

sequence of characters is not passed back to the parser as a

token, and the lexical analyzer must find the next token.

The Parser

The parser consists of many subroutines. The technique

is to create a single entry point for the user to call which

begins the parse, and then make each non-terminal and each

action be a separate subroutine. The entry point's only

function is to call the subroutine for the start symbol, and

to test whether the parse read all the input.

Inside each non-terminal subroutine, the code consists

of groups of standard pieces. These pieces are generated by

walking the production trees, and the code generated for eachN-

type of node (without the value manipulation code) is shown

in the following list:

Terminal get a tokenif (token not = terminal-id)

then syntax errorend if

non-terminal call the non-terminal subroutine

concatenation : "code for left child""code for right child"

alternation : if (next k tokens equals a first setof the left child)

then "code for left child"else "code for right child"

end if

VIII-4

. . .• . -4-. . - -. - - -

closure while (forever)if (next k tokens equals a first set

of the child)then "code for child"else break out of while loop

end ifend while

closure plus : while (forever)"code for child"if (next k tokens equals a first set

of the child)then do nothingelse break out of while loop

end ifend while

option if (next k tokens equals a first setof the child)

then "code for child"end if

empty call the action subroutine{ if there is an action }

There are two major subroutines needed for these rou-

tines. The first is the "get a token" subroutine. Its

purpose is to accept a token, and remove it from the input.

The second is the "lookahead" subroutine. This is used

during the various IF statements to compare the first sets

against what is in the input. To perform these functions, a

table of size k is available, which will contain tokens that

have been accepted from the lexical analyzer. Whenever look-

* ahead is requested, enough tokens will be requested from the

lexical analyzer to do the compare, and whenever a token is

retrieved by the "get a token" routine, one entry will be

removed from the table.

VIII-5

The Values of Productions

The most important part of the generated parser is its

ability to place a value on each item in a production. This

allows the user to "remember" how many, or what kind, or any

other information desired. These values are all integers,

therefore any type of information that fits into an integer

can be used. In particular, pointers may be used. The fol-

lowing example shows how to use these values. (The $n values

are used as variables in actions.)

S A $1 has the value of production Ab $2 has the value of terminal b

$3 has the value 0, unless the actionused $$ = ... ; in which case $3has that value. This action mayreference $1 and $2.

(a b ) $4 (see note)a b } $5 (see note)

[a b] $6 (see note)I a b }+ $7 (see note)

$8 same as $3, except that $1 through$7 may be referenced.

The value of S is whatever the last item's value was, inthis case, whatever $8 is.

Note: Any group of items surrounded by 0, [], (1, or0{+ is a set on its own. So, each of $4 - $7 has asubset, and in each one, a = $1 and b = $2. $4's valueis whatever b's value is. However, each of $5 - $7 mayhave an unknown number of occurrences. Therefore, eachone is represented as an array. The 0th element hasthe number of occurrences, and the 1st through the nthare the values. So, for { a b 1, with input ababab,$5[0] = 3, and $5[1] = $5[21 = $5[3] = b. This isvaluable if the last item is an action, so that thevarious values may differ. If the last item in a setis one of these multiple occurrences, then the set hasthe value of the last occurrence.

The values are placed on two large stacks. One stack is

* the "normal" stack, and contains the values of all items in a

VI I-6

rp - , - - - . - . - - . -

set. If any item in a set is a closure of some type, then

the value will point into the second stack, where each

element of a closure will be held, be there 1 or 1000.

To go along with these stacks, there are manipulation

routines. These include:

a. Begin a new set

b. End a set

c. Create a new entry within a set

d. Check the stacks for overflow

The "begin a new set" routine returns a pointer to the new

set, which is placed in local variables in the parsing sub-

routines. This data is used in actions to retrieve the

various $ values. (A limitation on the actions is that only

integers and identifiers may exist between the brackets of a

$n array reference.)

Additional insight into the uses of this value capability

can be found in the YACC reference manual, [Lesk, 1976] from

which LL's was patterned.

VIII-7

IX. Test Plan

Introduction

An important facet of any good design is a test plan.

Many times this test plan is extremely formal, with bench-

marks, acceptance criteria, etc. The amount, complexity and

completeness of the test plan is dependent on a number of

variables. First, is it possible to test every aspect of a

program? The author has worked on projects that were online

systems, and there was some code that could only be "assumed"

correct until an error occurred. Next, how important is the

program? Code that performs missile targeting is obviously

critical, while code to calculate a batting average might not

receive as much attention if it fails. Finally, how often

will the program be used? A job scheduling algorithm in an

operating system is used constantly, but most student projects

are used only once.

For a project that is relatively large, such as LL,

these same criteria apply to each section of code. There

are also other criteria that are important to large projects.

The most important is the "tightness" of the design. Well-

. designed programs that have straightforward data structures,

and whose interfaces between modules are very small, can be

tested in different ways from "loose" programs. The testing

program for LL reflects these considerations. LL was de-

IX-I

veloped in a modular manner, and can be tested in the same

* way.

General Test Plan

Testing for LL was done by major submodule. As can be

seen from the Data Flow Diagrams in Appendix C, LL's structure

is very linear. This means that data structures are operated

on in a subsystem, and only the data structure is passed

between subsystems. Also, LL's data structures are extremely

consistent and general. Therefore, there are very few special

cases that need to be tested. (Special cases are the bane of

programmers. Each special case must be tested separately,

and sometimes they can double or triple the testing workload.)

Each subsystem of LL was tested as it was developed. A

set of inputs that exercised every general case was developed

and used for each subsystem as it was developed. Extra rou-

tines were created whose task was to print the data struc-

tures, and these were used extensively during the tests of

each subsystem. Also, a trace facility was set in place from

the very beginning, which can be turned on and off at will.

This trace capability aided testing tremendously, as the loca-

tion of an error could be exactly placed most of the time.

When all the normal tests were made, then the YACC input

was modified, and used as a test case. It succeeded, but

caused some repercussions in the ..L algorithms. (See the

Recommendations Section of Chapter X for an explanation.)4

~IX-2

. . . . . .. , . . . . .. . -. --- .. ... . . . ... . . . . . . . .. . .i 12 •:, ; , .

-- 07

*-"Special Cases

A special case is essentially some input that causes a

global effect on the program, and must be carefully considered

during some phase(s) of the development. There were three

special cases in LL. These were: recursive productions

* (for first and follow set calculation), closure as the last

item in a set (for remembering the value of a subset of a

production), and no regular expression input (for users who

want to use their own lexical analyzer).

Recursive Productions. Because the algorithm for calcu-

lating first and follow sets requires that each non-terminal

be calculated when encountered, each non-terminal had to be

marked when it was calculated, so that endless loops would

not occur. For example, the production

S : a S I b; (76)

would have the first sets calculated as in Figure 12. If the

algorithm calculated the non-..-rminal S when it saw it without

* . considering recursiveness, it would continue forever.

Begin calculate SBegin calculate alternation

Begin calculate concatenationBegin calculate aEnd calculate aBegin calculate SEnd calculate S

* End calculate concatenationBegin calculate bEnd calculate b

End calculate alternationEnd calculate S

" -' Figure 12. Example of First Set Calculation

IX-3

Closure as the Last Item in a Set. As specified in the

Values Section of Chapter VIII, each subset of a production

has a value. Whenever closure, closure plus, or option is

the last item in a set, the value of that set is the last

item in the array of closure items. Therefore, an indicator

as to whether or not the last item as a closure was needed.

No Regular Expression Input. The FSA for a grammar is

"hung" from a global variable. If no regular expressions

are found in a grammar specification, then this variable is

set to null, and when the final output is created, no lexical

analyzer code is output.

The ADA Test

As we saw in the introductory chapter, ADA [DARPA, 1981]

is an on-going project to create a new high-level language.

Since it is very complex, and the justification for work such

as this thesis comes from languages such as ADA, the author

decided to create a test case using the ADA EBNF specifica-

tion. [DARPA, 1981: El-ES] The outputs from LL, along with

an explanation of the test, are in Appendix I.

IX-4

,. . -*. . . - . . . . . . . .

X. Conclusions and Recommendations

Conclusion

Throughout the course of this thesis project, there were

three main questions. There were:

a. Can a generalized LL(k) parser generator be created

that determines what k is?

b. Is the parser generated relatively economically?

c. Is the output product easy to understand?

The answer to question "a" is a qualified yes. It is

qualified because of a flaw that could not be rectified within

the time constraints. This relates to LL(k) grammars that are

not strong LL(k), and is only a problem when the applicable

follow sets must traverse more than one production to reach

the production that is not strong LL(k). For example, if the

productions are

S ->aBbc Bc (77)

B. B-b ci (78)

then all is well. The two references of B will be used to

good effect to separate the follow sets. If, however, the

productions are

S-> aBbc Bc (79)

B -> C (80)

C-> b cI £ (81)

then there is only one reference of C, and the multiple refer-

X-1

i -, .• ° .. . .. . . ...

ences to B (with their follow sets) are lost because of the

indirect reference.

The second question, is the process economical, is an

unqualified no. As built, the data structures are too large

and use too much memory for any "reasonably" sized grammar

with k larger than two or three. It is, however, excellent

for grammars that are relatively small.

The last question is an unqualified yes. The output pro-

duct is very easy to understand and use. It seems to be

S.- organized well, with data structures that fit the necessary

algorithms very nicely.

Recommendations

There are two problems in LL that make it somewhat less

than practical for many applications. These are: 1) core

usage, and 2) maximum k calculation.

Core Usage. The only area of concern in LL is the amount

of core that is used during a large grammar's processing. The

first and follow set calculation seems to be the root cause of

this problem. During the testing phase, the YACC input was

modified so that it could be read into LL, and it was. All

the phases worked well, until the first sets were to be cal-

culated. This calculation for the maximum k came to be 39,

and at that time the first sets were not calculated in a loop

starting at 1. The algorithm attempted to perform this feat

for k = 39. LL began to request more and more memory, and

x- 2'-"

bm° .~*. .

S- .. had barely begun the calculation when it finally reached 6

megabytes (MB) and was killed by the system. At that time,

the loop was put in, and the process was restarted. It

happened that k = 2 for the grammar, and LL went to 6 MB

again, but not until the process was almost completed. At

that time, the grammar was modified to be LL(l), and then

everything went smoothly. The YACC -> LL input modification

test showed this failing of LL very well.

Since LL is a prototype, the author decided that simpli-

city of the data structures and ease of programming, (along

with an immovable time constraint), was more important than

"S algorithm efficiency. So, LL constant use of the memory

allocate and deallocate functions in UNIX to build the first

and follow sets. Each first and follow set item requires

one piece of memory, which contains the actual data, along

with a pointer to the "next" item. Unfortunately, the memory

manager also places a header on each piece of memory that is

given to the user. If the data structure was modified so

that the memory manager would only be needed occasionally,

and so that the "next" pointer could be disposed of, a 75%

reduction in core use would occur. (See figure 13(a).)

Then, if the data could be compressed so that four data items

would fit where only one fits now, another 75% reduction

would occur. (See figure 13(b).) If both could be imple-,'.

mented, there would be a 93.75% total reduction in core use,

" i--- and LL could be used on a much larger class of grammars.

X-3

..

two wordheader

(a) data --- >> data75%

pointer reduction

data 1

'data 2 -"4data 3 75%

reductiondata 4

Figure 13. Possible Core Use Reductions

Maximum k Calculation. The other area of concern in LL

is in the calculation of the maximum possible k for a grammar.

Because this value is LL's limit in its loop to find the

actual k, it is advantageous to have it be as small as pos-

sible. Unfortunately, for any large grammar, the number cal-

culated by the algorithm in Appendix H is relatively large.

This limiting algorithm needs more work to bring the value

down.

In order to solve this problem of practicality, an option

to the program was added to allow the user to insert a value

for the maximum possible k. Thus, if a grammar is known to

,' have k less than or equal to some small value, then this value

can be inserted as an option. However, in that case LL can

not assure the user that the grammar is not LL(k) for any k,

X-4

.f I . . . . . . . .

but only for k up to the input value.

Final Comments. LL is a prototype that shows that cal-

culation of k is possible for k > 1 in a language with an

LL~k) grammar. With the above mentioned modifications in

place, and possibly rewritten to remove other inefficiencies,

there should be no difficulty in using it as a production

quality compiler writing tool.

.-

S"

x-5

.

Bibliography

Aho, Alfred and Jeffrey Ullman. The Theory of Parsing,Translation, and Compiling (Volumes I and 117 Engle-wood Cliffs, New Jersey: Prentice-Hall, Inc., 1972.

Baker, Theodore P. "Extending Lookahead for LR Parsers"Journal of Computer and System Sciences, 22: 243-259,1981.

Barrett, William A. and John D. Couch. Compiler Construc-tion: Theory and Practice. Chicago: Science ResearchAssociates, 1979.

Berry, R. E. Programmin Languag Translation. New York:John Wiley and Sons, 1982.

DARPA (Defense Advanced Research Projects Agency). ADAReference Manual. US Government, 1981.

Davie, A. and R. Morrison. Recursive Descent Compiling.New York: John Wiley and Sons, Inc., 1981.

Gert, Florjin and Rolf Geert. PGEN - A General PurposeParser Generator. Amster ai, Netherlands: MathematicalCentre, January 1981 (N81 - 30844).

*. Gries, David. Compiler Construction for Digital Computers.New York: John Wiley and Sons, Inc., 1971.

Johnson, Stephen S. YACC: Yet Another Compiler Compiler.UNIX Programmer's Manual, 7th Ed, Volume 2A, 1978.

Koster, C. H. A. A Compiler Compiler. Amsterdam, Nether-lands: Mathematisch Centrum Amsterdam, November 1971(AD - 900731)

Lesk, M. E. Lex - A Lexical Analyzer Generator. UNIXProgrammer's Manual,7th Ed, Volume 2A, 1978.

Leverett, Bruce W. et al. "An Overview of the ProductionQuality Compiler-Compiler Project". Computer Magazine:38-49, August 1980.

Meertens, L. G. and Vliet, J. C. van. On Top-Down Parsin ofAlgol 68+. Amsterdam, Netherlands: Mathematisch Ce -trum Amsterdam, November 1981 (AD - B064127).

Bib-l

* .. .- *-"-k A U

-. Peters, Lawrence J. Software Design: Methods and Tech-niques. New York: Yourdan Press, 1981.

Pyster, Arthur. Compiler Design and Construction. New York:Van Nostrand Reinhold Company, 1980.

Wirth, Nicklaus. Algorithms + Data Structures = Programs.

Englewood Cliffs, New Jersey: Prentice-Hall, Inc.,1975.

J.7

.

S

~Bib-2

* Appendix A

FIRST, and FOLLOW1 Set Calculation

This algorithm operates on production trees as described

in the Production Tree Section of Chapter II. The only non-

obvious part of the algorithm is the symbol ~.This symbol

stands for the end of input, end of string, or end of file.

(Note that the FOLLOW set of the start symbol should include

the end of string, or j.) [Barrett, 1979: 180-184]

Set all FIRST sets for all nodes in all trees to the empty set.REPEAT

* FOR all trees DOECALCULATE-FIRST-SET(root of tree)EDFOR

* UNTIL no change in any FIRST setSet all FOLLOW sets for all nodes in all trees to the empty set.Set FOLLOW(root node of start symbol's tree) toJ

* - REPEATFOR all trees DO

CALCULATE-FOLLOW-SET (root of tree)END FOR

UNTIL no change in any FOLLOW set

CALCULATE-FIRST-SET (tree node)CASE node OF

e add {01 to FIRST(node)terminal x : add {xl to FIRST(node)non-terminal N : add FIRST(root node of tree N) to

FIRST (node)* * :CALCULATE-FIRST-SET(left child)

CALCULATE-FIRST-SET (right child)add FIRST(FIRST(left child) FIRST(right child)) to

FIRST (node)CALCULATE-FIRST-SET(child)add {el to FIRST(node)add FIRST(child) to FIRST(node)

CALCULATE-FIRST-SET(left child)CALCULATE-FIRST-SET (right child)add FIRST(left chil"l) to FIRST(node)add FIRST(right ch.A.) to FIRST(node)

END CASERETURN

A-1

i~ . ... m . . . . . . ?. .-.. :. , ., -, - - .-.... ..- ' .. -' .

END CALCULATE-FIRST-SET

CALCULATE-FOLLOW-SET (tree node)CASE node OF

terminal x,c :(*no action*)non-terminal N : add FOLLOW(node) to FOLLOW(root of N)*:add FIRST(FIRST(.right child) FOLLOW(node)) to

FOLLOW (left child)add FOLLOW(node) to FOLLOW(right child)CALCULATE-FOLLOW-SET (left child)CALCULATE-FOLLOW-SET (right child)add FOLLOW(node) to FOLLOW(right child)add FOLLOW(node) to FOLLOW(left child)CALCULATE-FOLLOW-SET (left child)CALCULATE-FOLLOW-SET (right child)

? : add FOLLOW(node) to FOLLOW(child)CALCULATE-FOLLOW-SET (child)

*: ADD FIRST(FIRST(child) FOLLOW(node)) toFOLLOW (child)

CALCULATE-FOLLOW-SET (child)END CASERETURN

END CALCULATE-FOLLOW-SET

A-2

j ' -. - . . .. , . S. . . - . - . - , ., .- . . .. -. .- -.. - .

Appendix B

LL(1) Parser from Production Trees

This Appendix gives an algorithm to generate a parser

for LL(I) grammars by using production trees that have been

decorated with FIRST and FOLLOW sets as in Appendix A. The

algorithm assumes an unambiguous grammar, and performs no

error-correction. It will, however, recognize a syntax error.

[Barrett, 1979: 185-187]

There are two variables. TOKEN is the value of the

current token in the parse, and FLAG is used as a boolean

variable to decide whether some part of the parse was success-

ful or not. There is also a function called NEXT. NEXT gets

" " the next token on the input stream and returns its value. It

should be noted that the symbol , as in Appendix A, is the

end of input symbol. Also, the FIRST and FOLLOW sets will be

taken from the tree and placed in the parser wherever FIRST

and FOLLOW appear in the algorithm. The parser will be

created in pseudo-PASCAL, and is generated by the algorithm

that follows.

Generate: Program header with declaractions of FLAG and TOKEN.FOR each tree DO

Generate:"procedure A; " where A=non-terminal symbol for the tree"begin"

GEN-CODE(tree root)Generate:

"end"*Q END FOR

Generate:

B-I

-. . ' ' : '. ' , - , -. . , - . - - .. - L - ' . ' - '

. . . r r r ' ' - '- " " ,' . - " " " "

"begin""call G;" where G is the start symbol"if (FLAG = FALSE) or (TOKEN <> 'J') then ERROR;"

"end"

GEN-CODE (tree node)CASE node OF

e : Generate:"FLAG := TOKEN in FOLLOW(node)"

terminal x : Generate:"FLAG := (TOKEN in 'x');""if FLAG then NEXT;"

non-terminal N : Generate:"call N;" (*proc for non-terminal n*)

S: Generate:"if TOKEN in FIRST(child)""then begin"

"repeat"GEN-CODE(child of node)

"until not FLAG;""FLAG := TRUE;""end (*begin*); "

"else FLAG := TOKEN in FOLLOW(node);"* : GEN-CODE(left child)

Generate:"if FLAG"

Si "then begin"GEN-CODE (right child)"if not FLAG then ERROR;""end (*begin*);"

: GEN-CODE(left child)Generate:

"if not FLAG""then begin"

GEN-CODE (right child)"end (*begin*) ;"

?: GEN-CODE(child)Generate:

"if not FLAG""then FLAG := TOKEN in FOLLOW(node);"

END CASEEND GEN-CODE

B-2

Appendix C

Data Flow Diagrams

System Diagram

Parser-Definition

LLParser

Generator

B0

Completed-Parser

F.

.:::, C-'1

Diagram 0

Parser-Definition

and-Acions c eoratd

Production

Codei Dtrmn

C-2

Diagram 1

Parser-Definition

Variable-Subroutine-Declarations

ToknsProduction- Regular-Rules Expressions

InputIptIptInput ariable

Inputs Production Regular andToknsRules ression ubroutine

1.3 l.4-

ProductSubroutlyne-Token-Declarationsn

and-Ation

Vaiale

Suruie

. . .. . . .. . . . . . . . . .

Diagram 2

NDFSA

RemoveEmptyansitions

2.1

NDFSA-Without-Empty-Transitions

MultipleTransitions

V 2.

DFSA-With--SaeUnreachable-Sae

UnreachableStates

2.3

t

elt

* DFSA

C-4

. . *

Diagram 3

Production-Trees

Number

References

3.1

Production-Trees-With-References-Numbered

FindErrors

Production-Trees-With-Refe ences-Numbered

.. 3

Decorated-Production-Trees

C-5

...............................

- Appendix D

Structure Charts

MakeDecoateOupu

55

D- 1

Inu

1,,

Definitions ExpressionsPrdcinSuotne

D-2

41t

6i

D-13

*12 1 12 ....

*.13 4. . . . . . . . . . .. . . . .

14 1

14 15

Z 71D4L5

4'4

14,23 ~ 21 2,2322

EFin

D-5

61 5

MakeParser

4

-. 4

;,-;iMake

Definitions Make One-.. and Main Non-Terinal"-""" Procedu el42

4.

19 is1

18i 19118 191.18 19 18 19 o 1, :1 9181 Q1

Make Make Make Make Make Make MakeSubtree Subtree Subtree Subtree Subtree Subtree ubtreeEmpty Terminal Non-term * or *+ ?

4.2.1 4.2. 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7

Note: 4.2.1 to 4.2.7 are 0called from 4.2 19t 418 19 118 1and 4.2.4 to 4.2.7. 191 18 1 18

D-6

.. . . . . . . . . . . . .-

Numbered Data Items List

1. Non-deterministic FSA

2. Production Trees

3. Complete grammar input. Includes (7) through (10)

4. Lexical analyzer code

5. Decorated production trees

6. Parser code

7. Token definitions

8. Lexical analyzer actions

9. Production actions

10. Variable/subroutine declarations

11. NDFSA without empty transitions

12. DFSA with unreachable states

13. DFSA

14. Production trees with numbered references

15. Maximum possible k

" 16. One production tree

17. Code for one production tree

18. Subtree

19. Code for subtree

20. Production trees with first sets

21. Production trees with first and follow sets

22. Production trees with first set of length k

23. Temporary value of k

24. Main procedure for output code

D-7

:: -,<.,-;;-;--?', -? ? : - ' *: -*-,* -* - ... .. ....-. .- ..-..--. ,.. * . ..

Appendix E

Regular Expression Forms Used in LL

regular-expression alternate { "j" alternate } ;

alternate : { element I+ ;

element sub-element [ "*" j "+" I "?" ] ;

sub-element "(" regular-expression ")"

I "[" [ "" ] { bracketed-char I+ "1"

I sub-element-character

bracketed-char

Any cAracter defined for C, to include octal numbers for

unprintable characters, any of \t, \n, etc., excluding

'] . Any character, including \ and ], may be preceded

by a to force it into the character set.

quoted-char

Same as for bracketed-char, except that " is the charac-

ter that may not be included in the set unless it is pre-

- ceded by a V

sub-element-char

Any character defined in C except for space, newline,

tab, [ and " unless preceded by a\

8hE- 1

... "-_.:. .. .. ..... .... .. . ..

.'

Appendix F

Production Rule Format

production-rule non-terminal-IDENTIFIER

alternate-list

If • I

alternate-list alternate { "j" alternate 1 ;

alternate { item I ;

item "C" alternate-list ")"

, "[" alternate-list "1"

I "{" alternate-list "}" [ "+" ]

IDENTIFIER

. "={" action-code "}"

F

-F-i

9-'"

iD-Ai38 061 A GENERATOR OF RECURSIVE DESCENT PARSERS FOR LLMK 2/4.LANGUAGES(U) AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH SCHOOL OF ENGINEERING G B PAPROTNY DEC 83

UNCaRSSIFIED AFIT/GCS/MA 83D-6 F/G 9/2 N

-.-

1266

0 W.o

_L4

MIROOP REOUTO T ~ EST CHART

• 111- .

. 9

• .' -MICROCOPY RESOLUTION TEST CHART

- 5'-., NATIONAL BUREAU OF STANDARDS-1963-A

6 " Y%- *.. -

'*4 " . ,, N == % " - , ..5. 4 ' # * ~ % % . % ", - ,% % % % ' - - -- . .- . ,,. .. , .

,:.. . , ** . . .. .. . , , ., .. ., - .. . .. .. , . .. . . . . .' . , ... . . . -

FSA for Each Regular Expression Form

* * In the following structures, n denotes a state, and n

denotes a stop state. The beginning state is always state 1,

* and the ending state is marked with an S. An expression may

be any of the following, or (E).

*El action 1E2 action 2E3 action 3

El-

4 3

1

.j

(S2

6 7 (S3)

El E1E2

2 (S)

El*

(S)

El+

El?

alo (S)

[ set of chars ]

G-2

-p

-p

Appendix H

Maximum Possible K Algorithm

This appendix describes and justifies the algorithm for

calculating the maximum possible k. The author has developed

Sthis algorithm through his knowledge of what lookahead is

* possible for each of the nodes, and then had tested on a

number of cases that used differing combinations of nodes.

The algorithm begins at the head node for the start sys-

-bol, and essentially traverses all the production trees during

its calculation. The following list describes the algorithm

* for each production tree node in turn, and gives the justifi-

* 0 cation of the algorithm for that node.

- General Comments

a. Counting is the process of determining what the max-

imum possible lookahead is for a node.

b. The recursion indicator is set in order to remember

whether the counting process for a particular non-terminal

node ended when recursion was encountered.

c. The maximum k value is a variable that is set when-

*ever a node is found that has a value b greater than the

* value that is in the variable. This is done because the max-

* imum value for the start symbol may be smaller than some sub-

* ordinate production's value.

1-1

-p

* 5 . . . . . *..o- . . . . . . . . . .

. . . .

*. . . . .... ,*,.-*.

..

:.-..:Empty Node

This node is counted as 0, because nothing will be

parsed for it.

V" Terminal Node

The terminals are all counted as 1, because exactly one

token will be parsed.

-4

Closure Node

A closure node defines a sentence that may occur 0 or

more times. The problem in determining the maximum k for

this node is: How many times will the sentence occur in the

input, and how many occurrences of the sentence must be looked

ahead to determine whether to accept it or not. There are two

separate considerations here, which are:

a. When parsing the actual closure node, the maximum k

is the count of the child, since that is the maximum that can

be viewed at that point.

b. If the closure is inside an alternation node, do we

'.5 parse the closure node or not? This problem is more complex.

The following examples show various occurrences of closure

". nodes in grammars:

S ->{a b c Ia b a b d (82)

S-> {a b c I a b c d (83)

S-> a b }c J ab d (84)

Equation 82 is LL(5). This is because the two alternates

can parse "ababc" and "ababd". The concatenation node alqo-

H-2

rithm will return a count of 5, so the closure node's sentence

may be counted only once, for a total count on the left hand

side of 3. Equation 83 is LL(4), because the alternates may

parse "abcj" and "abcd". Once again, each closure's sentence

only needs to be counted once. The last example, equation 84,

is not LL. This type of closure and alternation problem is

the only closure case where the lookahead is unknown. LL will

not accept grammars with such productions.

Intuitively, we must count a closure node's child once

and only once. If we had to count it twice because of some

case, why wouldn't there be a case where it needed counting

three times? Or four? The algorithm would break down and be

unworkable in this case. Fortunately, such a case does not

6exist.

Closure-Plus

For this node, count the child and return its value, by

the same reasoning as for the closure node.

Option Node

Since an option node is parsed 0 or 1 times, the maximum

possible k is the child's count.

Non-Terminal Node

Normally, the maximum k for a non-terminal node is calcu-

lated by going to the non-terminal's production and counting

it. However, a non-terminal may be recursive, as in

H-3

'* -.- •*..:. .-.' . - - . 7 . ... *.'.*** . I, . -*. - .. . .- .. >. >

S ->a b S c a b (85)

If the above algorithm were used, it would never terminate on

this example. The same type of intuitive reasoning applies

to this node as applied to the closure node. We should end

the counting process when the non-terminal comes up for

counting the second time, and return 1 as its count. Thus,

- the count for the left hand side of the example would be 3.

Also, the recursion indicator needs to be set, because the

concatenation node will use that to determine whether to use

the subsentence to the right of a non-terminal or not. It

should not in the recursive case, because if the grammar re-

." quires the compiler to look ahead further than the non-

terminal, it would not be LL anyway.

Concatenation Node

The coicatenation node's count is normally the sum of

its two children. However, if the left child has the recur-

sion indicator set, then the sum is no longer appropriate,

as we saw for the non-terminal node. In that case, the count

for the left hand side only will be returned.

Alternation Node

'S Since the alternation node defines the "choose A or B"

construction, the maximum possible k is the larger of the

counts of its children.

H-4

.. ,,-, 'S*. 5 - - - . -.'. V . .'-' . .' ' " -. ' ' . . " .'

Appendix I

LL Output for a Partial ADA Grammar

This appendix contains the grammar input file and the

output files for a partial ADA grammar processed by LL. Only

a small part of the actual ADA specification was used because

the actual ADA grammar is quite large.

The files in the appendix are:

a. The input grammar.

b. The C program that LL created.

c. The LL.output file. This file contains a summary of

the FSA for the lexical analyzer, a list of those productions

which were not LL(l), and a graphic representation of the

decorated production trees. (This file would have a list of

all those productions which were not LL(i) for all i from 1

to k. The ADA grammar used here is LL(2).)

4°..

a.°

°-

.. . *. .- .

/-- Ada Grammar Subset

C .

C W9

CL =LL0S CL >;4.U 0 L

4 - I--QC0 0. 0 -

SI- 0 ; 0

41 -0 LW

NU a - 0% 0.0 0S. .0a 0. *0 *- .1

0. 0 c =OC 4uc 0 M LC

%0 S C I L-a-0 00S S4.4 0.- Vi 0 U 0 41CU CL lI-1 01 5 U C0 -05- lo Z 00C oo 0 C 0) LA1. M4E - 0CU LO U C; C1L0 wu0 .- C I o - . U :4.10 x- U- 0 2) 0-) J CL S )0Nfl a 4WI - -U --- Un N4. - 01 c X4.U 0. co ~ IC L 4c' cL 0 O- -

L I-.- L L 0. LU -I me nu 40so w>I OVX U) 2 0. -U M Z- 4j LU Z

0 00 -0 a 0 0L vp 6 U, 0 0.UI 39c 0.1a0I fl0 -' VN U 0 U 4 ' 0 CLC a X - C

UN M CC a. 0"~ - . 0 0- 0V La

ON WUI Z - 020 S - LU) - 8t U .-0. SZ 4 1.41. N0f 00.740. L WW4.I W

4F 44 650 4. 1!L1 .0I e 4 0 owL60 1.C LLL ) NMSE 4 6 0 j 02 - 5 . 44'0

C c- cc 0 LUU -1 3O E - L L 0e 0 <--04

aL W W C IV flU CE1 -(C L 0* Mu<taI--1%--4.-I0 .at 0j 10 UIU 0.. c 0. -6- 4J L m-WOOOW

W-i - .0 30.0 v3 C 1.- 1 0 J JCC 1as ww 41 I -0 S ao 41 OW L z V~~ 003 41 -U) f41 4I 0

C Z Ui. I C U In0 CL CC 0) CU OV suwcnw le -OL L CoI- a 0 0 0 0. >S ) LW - LV

60 .. IOW - 3 -- .. - U - 0- -VM - U- cc 0- .a -. 4 -0

. 0Cf '' W9 S 0 1 01 -1

64-U Ca 1 N xIUUS U U I

N'2 1MW <-U, -) - M 14 U e12 CO (1 )C ft m U. .4& - - 2 C 0) 0 0)

.'Ua - 031 14 < V M EC U U 1- S1sls 5 w Z -U10 CL e 0 0 0 0 0) 0 0 Vg 6V-V Ca0b'" U 4L U U V V0 4- - C C

-2

.1.

A'

z 0Ldi

* C)

0 0

U- C

6 4C-M 6 jL4 4

vi 0.

aa0C4 'v 4. V

44 Z .( JC

a2 >1"Ca0X . 4

L 0 -1+)004

L* Ce .430aC -f0 ft-)0 - C L

4 -y Vaw 4 4 00 IU4J 4JW m0m0 - 0

06Cl*0m4 - *0 Z - L - LL X U .L, - W C ) 0

a. 4- U 41 4-U-i 0 4-m-a U.0.-a>00-U 4-' U 0ISO OW' >

C404 C- (.U-0 aO .x4-'4) '21> 20- 0. 0C - 0- 0 mc C bI Z m

0 6. 01O C 1JL. 1c0 - z C E90W FA .. CLf - 4-1 0

I 0u -VC 1-U 07Wv.: U) 1Lf- - .4 C*Z oed 4-c> -m- 00 0 mt)~ VIC U;muw 4* jW -4(-- u 41 Oau 0LZU-4 0.0Z U 0.*4 uw' 04 uag 1C Q 4 Mc .a-x M0. 40a CCm>-

-C *uow ac I,9UC .0owwo 1.0 IaL ..0 c a4 0.4 -c A oLa~ z *Z E

A L- W V CC L-- cc- , .'. a .- w mm-D - x -I I I L L LL

*0 W S .4 a) a)-w Lo a) 01 0 0 K. E .*4c A 2 L . L >

U .J L .. 0 .1 a0

06 06 0. 0. a(A vi FA v 4J

-. w'mrw '--%-~ -. - -. --- I-.

I'

4

a

SU

C -'

Ia S(a U

UC

U~( I-a. -zzz *(o zU K

0'-. U

*U* 0C 2I U

Ia C(a~( I-.~' -

* U Za' a. -

* S -

Ia S~-* U ~ bl-

OC *1~ ~* . U* -..-. U U -

* - ... C - (4* * I 'J I

* I-. I- Sz .~ -

* =

1-4

Parser for Partial Ada Grammar

0 4.'

0 0

-j 41

u 1c 000

c 4 j1 0

4AU N 01M

61~~ A4"a1*1

c 4' M' -j 4

0~~~ ~~~ c 00jI-< - dcc~~~~~~ 0 L.c0 = LO z w-

es04 01 0 0 a . x=2. L. X J

* aUL1L-00:;c I.1 0L . x - 1M - - X -

&TO- 0Lu f-- vz- o O U- =j 4j IM 4 < .K i I

9 0 410 V-U -I- - 0 44j -. (al IV. M -J --

4- 0- 1U 1. Z01 W 4j

- - U- - - - - - - - -40 - - U.-- - ' - -~ - -U - -. -- 0 -1 - -- j4-4L- O * 4.a. 4I 40 W. W. W.o- W. W. W. 4- 4*0 -1 4- -- 4

z* - 4 j .C C1 -

**g44111144441111444441111444411114444 M44 o u u - 4

-IW -- 'Z-..- -4 -

- .---. I, - - . '... .4

I=pu

o; o 4.' 0

4J4 4J 0

04Z 041 0J

O- 4.' UN

4 4j - - fifi .

Uo g 0 01 LJ +

0. I. am x c0 4LU -j 4j 3 .

O C . 40 4. -!-1 .

hil -aC<U0 0 UL 00 OJ0 4 a i 40 - 6 - -%1- , U

a0 4 U a c 9 uu )4 4 j4

-0 4 CX4J4 +j 0) IV 11 -a4000 41 X1 4d -a -a. *. -<. -a- ..1 !a-a

40 4141 to U0 -a' 1 UU- . -a10 a-a10 .

- L U 0 C .. fa C IIIJ41UO 0 -x v i 0 OlI = 0to1 4 ~

it1 @4 C n1 . +0 tV ".' U. 0 - VV 0. 0~'. LIcXc +C +) +£ 00 41 - 1 44 ? - 4 41

4J 4. V U 0j to - kv (a +) M1/ 400 410 0

-9C A10 41 X 41 u. 4J ~ -k. 4JN l b: If 1 4* 4

4 10 4J . ~0 0 '~J O 8 0 * ~ 0 '

U 4CW1O-O - 0 0il I-11 1 I c 0 0 m ci m 0 I cCO >.- 4 U 0 4.' .CO U- C UII4J 4 1 + U CJM 4 U" C 4M I). 4

-u )Iv 0 U.C 41 o 04 t" 0N X0 0 0- X4 0 4-00 X -XL0A4 II XLX -

o ie 0 - 41II C 0- 041 . 0. 041 0 041. -. 0

041 UL Ju - C 0 C0 0 I- u- I- C 00 a 0 IC 0 ICQ 4 VIA 41 U' 0414 44 1 LU4 410 N 4104- 10 4104 10 + 4-U4

L .. 0 *x C a 000 4J 114X4 CII 04 vI X 0 XL 0 X

.A-1 0 4 ) cc 0c -.I 041 -'0-.0- -0 1 1-* -) 10 -' 0 10

C =.. 0U 0 do 0 S.UC -L- u0 - 00j4j 4- -41.~ 4A04 0MU 4J 00 4A 00 00 0

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Appendix J

LL User's Manual

George B. Paprotny, Capt, USAFDecember, 1983

Introduction

LL provides a tool for creating a parser and lexical

analyzer for any LL~k) grammar. The user provides a parser

specification which includes the tokens used, the rules

describing the lexical analyzer, the grammar rules for the

parser, and a set of code which is user-unique. The lexical

and grammar rules may have actions, which are also user-

specified. LL then determines the value of k, and creates

the output parser.

LL is written in C, and creates a parser/lexical analyzer

also written in C. In addition, many of LL's rules follow the

syntax rules of C.

The terminology used in this manual is standard. Any

textbook on compilers may be referenced if confusion arises,

however, a complete reference to the terminology and theory

behind LL may be found in the author's thesis.

General Format

The general format of an LL input specification is:

token declarations

lexical rules-%%

'" J-1

production rules

variable and subroutine declarations

The lexical rules section may be empty. Also, the variable

and subroutine declarations section may be omitted, and if it

is, the %% immediately preceding it is optional. If both are

omitted, the format would be

token declarations

production rules

LL has the capability to trace its progress through an

input grammar, and report that progress on the standard out-

put. To turn this on, the token declarations must be preceded

by a line which has "%TRACE" beginning in column 1. No token

63 declarations may be on this line.

*" . Throughout the rules, tokens and non-terminals may be of

arbitrary length. They consist of an alphabetic character,

followed by a sequence of digits, underscores, and alphabetic

characters. In addition, non-terminals may be surrounded by

"<" and ">'"

The Token Declarations

The token declarations section consists of a series of

*g token names. Each token used in any part of the lexical

analyzer and parser must be declared here. Blanks, tabs, and

newlines are ignored in this section.

J-2

.2.- ...

* - . The Lexical Rules Section

Each rule in the lexical rules section consists of a

regular expression followed by an optional action. The rules

must begin in column 1, and may continue for many lines. The

regular expression is terminated by a blank, tab, or newline,

and the action is a series of C statements. If the action

continues on multiple lines, each successive line must begin

with a blank, tab, or newline. When an action is not present,

the characters recognized by the regular expression are

ignored, and a new rule is begun.

Regular expressions in LL use the following operators:

x - the character "x""- "x, even if x is an operator or space\x - x, even if x is an operator or a space,

unless it is one of the standard Ccodes, such as n, t, etc.

[xy] - x or y[x-z] - any character between x and z, including

x and z•xy] - any character except x or y

- any character except newlinex? - optional xx* - >= 0 instances of xX+ - >= 1 instances of xxly - x or y

i, .(x) - x

Note that parentheses may surround a sub-expression. For

example, (ab) l (cd) is the same as ablcd, but not the same as

a(blc)d.

For a token to be passed to the parser, a "return(token-

name)" must be issued in the action for the regular expression

that recognized the character string. If no return is issued,

the action will be executed, and then the lexical analyzer

J-3

.

will begin reading the next token.

The lexical rules in a grammar may allow the same token

to be recognized by two different lexical rules. If this is

*- so, then the first rule will be the one whose action will be

performed.

The Production Rules

A production rule in LL has the form:

A : production-set ;

where A is a non-terminal, and production-set is a series of

zero or more terminals, non-terminals, options, closures,

closure-pluses, and actions.

An option is one entry in a production set, and is

designated by [ production-set ]. This defines that the pro-

duction set is optional. A closure is { production-set 1,

and defines zero or more occurrences of the production set.

Finally, closure-plus is { production-set )+, and defines one

or more occurrences of the production set.

.. Actions in a production set are delimited by ={ and 1.

They consist of a sequence of C statements that will be exe-

cuted during the parse.

One last method of defining a production set is by sur-

rounding it with parentheses, as in A : B ( C I D ) E ;

When LL production rules are defined, one of the non-

terminals is the start or goal symbol. By default, the start

symbol is the non-terminal on the left-hand side of the first

production rule.

J-4

'f % ftf. . . . ft . * . . . . . . . . . . . - f

- -.." . . . . ..,

Errors in Production Rules

There are a host of errors which may occur in production

rules, other than "standard" syntax and spelling errors.

These include the following:

a. Left Recursion. By definition, no LL(kI grammar may

* .ihave a left resursive non-terminal. Thus, grammars of the

form

A: Ba cB:Ab d;

are illegal.

b. Undefined names. Any names that are not declared as

a token or non-terminal are considered undefined.

c. Unused productions. Only the first production rule

may have its non-terminal unused by another production rule.

Also, all non-terminals must be used by some sequence of

references that started at the start symbol.

d. Closure contains empty. Option, closure and

closure-plus production sets may not have the empty string as

a member of their first sets.

Also, a grammar may not be LL(k) for any k. Most gram-

*. mars which do not have one of the above problems are LL(k),

but there are some which are not, and the list of possible

problems is endless. For example:

A: { a I b I a I c

is not LL(k), because determining which alternate to pursue

°- requires an infinite amount of lookahead.

J-5

Values

LL provides the user with the capability of giving each

item in a production set a "value". For tokens, this value

is a unique integer for each different token, and for non-

terminals, the value is the value of the non-terminal's pro-

duction rule. Actions may also have values.

The values are referenced in the actions by using $1,

$2, etc. For example, in:

A : B C D ={ action I ;

the value of B is $1, C is $2, and D is $3. (The $n values

are used as variables.) The action is $4. The value of A

upon completion of the rule is the value of the last item in

the production set, which in this case is the action. Actions

have an intrinsic value of 0, but the value may be changed by

setting $$. In the previous example, if the user wanted to

preserve the value of C, the statement $$ = $2; would be

inserted in the action.

Each production set within a rule is numbered separately

for the purpose of using values. For example, in

A : B { C D } [ E F ] ( G ( H I )+

{ C D } is $2, [ E F ] is $3, and ( G { H I J+ ) is $4. C

and D are $1 and $2 respectively for the production set within

the braces. Because {} defines a set of zero or more, there

may be many values for $2. Each of these values may be

referenced using the C array construct, i.e. $2[i]. Here,

$2[0] is the number of occurrences, and $2[1] through $2[n]

J-6

.-.-... "£ - ".-.. - .%".-. . "... . . -. . - . -.---. --... . -. -.- . -- - - ---,. • . . - . .-." ,

: .are the values of the occurrences. (This applied to f] and

0+ as well, except that 1] will only have zero or one

element.)

For the example in the above paragraph, with the input

B E F GH I H I

the values for each nested production set would be

$1 B$2[0] = 0$3[0] = 1$1 = E$2 = F$$ = F

$311] = F$1 =G

$2[0] = 2$1 = H (first)$2 = I (first)$$ = I (first)

$2[I] = I (first)$1 = H (second)$2 = I (second)$$ I (second)

$2[2] = I (second)$$ = I (second)

$4 = I (second)$$ = I (second)

Note that the value of $4 in the outer production set is the

value of the last item in the array for the closure.

The LL Environment

LL has a host of output files, some temporary and some

permanent. All the files have names that begin with "LL.",

so the user is warned not to keep any files that begin with

those characters in the working directory while LL is running.

The output file LL.c is the parser, which must be compiled by

*the user. The file LL.output contains straightforward graph-

.. J-7

.

. ..

ical descriptions of the finite state machine and production

trees created from the lexical and production rules. The

standard output is not used, unless %TRACE is specified. In

that case, LL's progress is printed there. Also, the standard

error is used only when an error occurs. Any detailed de-

scriptions of the error can be found on the standard output.

The standard input is where the input grammar is taken

from. There is one option for LL. If a grammar is known to

be LL(n), the value of n may be input on the command line.

The output parser in LL.c has the entry point "compile",

which is a subroutine with no arguments. If a syntax error

occurs, the parser will stop, and an error message will print.

Under normal circumstances, the parser will print (on the

standard output) each input line as it receives it from the

standard input.

The use of values in actions has already been discussed,

but LL also provides the string that made up the last parsed

token in the character array "LL text", and that token's

length in "LLlength".

User-Supplied Lexical Analyzer

If no lexical rules are given, no lexical analyzer will

be created. In this case, the interfaces to the parser must

be taken into consideration. LL expects the lexical analyzer

routine to be called "LL lex", for it to have no arguments,

and for it to return an integer defining which tokens are

J-8

found. It also expects the string of characters that make

up the returned token to be placed in a character array

called "LL-area". This variable must be explicitly declared

in thi variable and subroutined declarations, and the LL lex

function must also be supplied.

LEX is another UNIX-supplied lexical analyzer creator.

LL will interface to LEX if the following statements are

included in the declarations:

# define LL lex yylex# define LL area yytextextern char LL area[ I;

If no lexical analyzer is declared, LL will anticipate

that the user needs a list of defines for the tokens. This

list will be placed in the output file "LL.h", and is suit-

able for inclusion in LEX, or any user-supplied lexical

analyzer. This file will also contain the defined name

ENDOFFILE, which has the value 0 (zero). Zero must be

returned from the lexical analyzer when it finds the end of

file.

Re-Definition of Internal Maximums

There are two limitations within LL that may be changed

by the user. First, a token received may be of any size up

to 200 characters. This maximum size is defined by the de-

fined name LLMAXCIIAR. It may be redefined to any size by

the user. Also, there is a maximum number of $n items that

can be saved during a parse. This value is 10,000. There

J-9

.. . .

-" There are also 10,000 possible entries for the various values

in closures. If either one of these overflows, LL will abort

with a value stack overflow message. They may be redefined

by defining the name LL VAL STACK.

Bugs

LL has three problems. These are:

a. It uses too much memory for large grammars that have

k > 2 or 3, and may go beyond the 6 MB limit set by UNIX.

Smaller grammars can be almost any k and still be completed.

b. Some grammars which are LL(k) but not strong LLCk)

may not be recognized as LL(k) by LL. For example, the fol-

lowing are two grammars for an LL(2) language:

A : aBbc J. Bc ; A : aCbc ICcB :b I cI; C: B ;

B:b I c;The right grammar is equivalent to the left one, but the right

one will not process correctly. This problem occurs because

- the parser must have the follow set of B to determine which

alternative in B to take. On the left, the two possible fol-

low sets are well defined, and can be used to decide which

path to take. LL can not look back more than one production

to find the appropriate follow sets, so the one on the right

will be an error. (This error occurs very infrequently, but

is difficult to find when it does.)

c. The value processor will accept only variable names

q "or integers between the brackets for a $n[] construction.

J-10

............

4 ."*

a r <, <~. 2 .- .

077 7W 7"-7-.

Thus, expressions of any sort are not allowed.

Acknowledgement

The material reported herein is based on the author's

thesis: LL - A Generator of Recursive Descent Parsers for

LL(k) Languages, submitted in partial fulfillment of the

requirements for the Master of Science Degree at the Air Force

Institute of Technology, Wright-Patterson Air Force Base,

Ohio, in December 1983.

J-11

Appendix K

Code for LL

The code for LL was created in many separate files, and

each was compiled separately. Each file begins on a new page

in this listing. The first file is a C "include" file, and

contains the definitions of all data structures, and some

global variables. The second file is the entry point to LL.

The last five files are marked "Standard Code File",

and are used by the "finish write" routine during the final

output.

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VITA

George Bernard Paprotny was born on 25 June 1957 in

St. Paul, Minnesota. lie graduated from high school in Bowie,

Maryland in 1974 and attended the University of Maryland in

College Park, Maryland, from which he received the degree of

Bachelor of Science in Computer Science in June 1978. Upon

graduation he was commissioned in the United States Air Force.

In October, 1978, he was assigned as a Computer Systems

Analyst to the Directorate of Data Automation, Deputy Chief

of Staff/Comptroller, Headquarters Air Training Command,

" Randolph Air Force Base, Texas. He entered the School of

Engineering, Air Force Institute of Technology, in June 1982.

He is married to the former Janice Gail Hobbs of Minot,

North Dakota.

Permanent Address: 2706 Keyport Lane

Bowie, Maryland 20715

Vita-l

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SECURITY CLASSIFICATION OF THIS PAGE

REPORT DOCUMENTATION PAGE.a REPORT SECURITY CLASSIFICATION lb. RESTRICTIVE MARKINGS

UNCIASi3IFIED2& SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABILITY OF REPORT

2b. OECLASSIFICATION/OWNGRAOING SCHEDULE Approved for public, release;distribution unlimited.

4, PERFORMING ORGANIZATION REPORT NUMBERIS) 5. MONITORING ORGANIZATION REPORT NUMBER(S)

AFIT/GCS/MA/83D-6

NAME OF PERFORMING ORGANIZATION b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION

School of Engineering lfapp;cebl

Air Force Institute of Tech.[ AFIT/ENke. ADDRESS lCily. State and ZIP Code) 7b. ADDRESS (City. State and ZIP Code)

Wright-Patterson AFB, Ohio 45433

Ur. NAME OF FUNDING/SPONSORING Sb. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBERORGANIZATION (If applicable)

Sc. ADDRESS ICIty. State and ZIP Code) 10. SOURCE OF FUNDING NOS.

PROGRAM PROJECT TASK WORK UNITELEMENT NO. NO. NO.

1 1 TITLE (include Security Classification)

See Box 19.12. PERSONAL AUTHORISI

George B. Paprotnv Captain USAF3& TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Yr., Mo., Day) 15. PAGE COUNT

MS Thesis FROM TO December 1983 31016. SUPPLEMENTARY NOTATION Ar L%71 AFlR 190-17.

LYjr.I

17. COSATI CODES 18. SUBJECT TERMS fContinue on reverse if b

FIELD GROUP SUB. GR.

* 09 02 ccpilersranr~ing languages

1. ABSTRACT Continue on reverse if necessary and identify by block number)

Titi. LL - A GENERATOR OF RECURSIVE DESCENT PARSERS FUR IL(K) LANGUAGES

Thesis Advisor: Captain Patricia K. Lawlis

2(k OISTRISUTION4AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION

'NCLASSIFIEDIUNLMITED SAME AS RPT. 0 OTIC USERS C UNCLASSIFIED22 AEO RSOSBE1NIIUL22b. TELEPHONE NUMBEF " 22c

". OFFICE SYMBOL

I (include A-rea Code)Patricia K. Lawlis, Instructor in Mathemati s (513)255-4185 I AFI T /ENC

00 FORM 1473, 83 APR EDITION OF I JAN 73 IS OBSOLETE. UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGO

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UNL-AS IFIEfl

SECURITY CLASSIFICATION OF THIS PAGE

A computer program was designed to generate a recursive-descent compiler

for LL(k) languages. A grammar specification language was designed using

Extended BNF, along with a lexical specification language using regular expressions.

The program uses a well-tested but not formally proven method for determining

the maximum possible k for a grammar. It then uses an iterative first and follow set

calculation algorithm to determine the actual k for the grammar.

S4 -.

i UNCILASSTF[i<'.[SECURiTY CLASSIFICATION OF ,,'

-1

Documents

Hri 318 GENERATOR OF RECURSIVE DESCENT PARSERS FOR … · 1978] [Koster, 19711 [Leverett, 1980] has two major drawbacks, which are: a. Each one will create a compiler for those languages