BNF Grammar Example design of a data structure

Form of BNF rules n n n n n <BNF rule> : : = <nonterminal> ": : =" <definitions> <nonterminal> : : = "<" <words> ">" <terminal> : : = <word> | <punctuation mark> | ' " ' <any chars> ' " ' <words> : : = <word> | <words> <word> : : = <letter> | <word> <digit> <definitions> : : = <definition> | <definitions> "|" <definition> : : = <empty> | <term> | <definition> <term> <empty> : : = <terminal> | <nonterminal> Not defined here (but you know what they are) : <letter>, <digit>, <punctuation mark>, <any chars> (any printable nonalphabetic character except double quote)

Notes on terminology n n A grammar typically has a “top level” element A string is a “sentential form” if it satisfies the syntax of the top level element A string is a “sentence” if it is a sentential form and is composed entirely of terminals A string “belongs to” a grammar if it satisfies the rules of that grammar

Uses of a grammar n A BNF grammar can be used in two ways: n To generate strings belonging to the grammar n n To do this, start with a string containing a nonterminal; while there are still nonterminals in the string { replace a nonterminal with one of its definitions } To recognize strings belonging to the grammar n n This is the way programs are compiled--a program is a string belonging to the grammar that defines the language Recognition is much harder than generation

Generating sentences n n I want to write a program that reads in a grammar, stores it in some appropriate data structure, then generates random sentences belonging to that grammar I need to decide: n n n How to store the grammar What operations to provide on the grammar These decisions are intertwined! n How I store the grammar determines what operations are easy and efficient (and even possible!)

Development approaches n Bad approach: Design a general representation for grammars and a complete set of operations on them n n n Actually, this is a good approach if you are writing a general-purpose package for general use--for example, for inclusion in the Java API Otherwise, it just makes your program much more complex Good approach: Decide the operations you need for this program, and design a representation for grammars that supports these operations n n It’s a nice bonus if the design can later be extended for other purposes Remember the Extreme Programming slogan YAGNI: “You ain’t gonna need it. ”

Requirements and constraints n We need to read the grammar in n We need to look up the definitions of nonterminals n n But we don’t need to modify it later Any tools for building the grammar structure can be private We need this because we will need to replace each nonterminal with one of its definitions We need to know the top level element of the grammar n n But we can just assume that we know what it is For example, we can insist that the top-level element be <sentence>

First cut n n public class Grammar implements Iterable List<String> rule; // a single alternative for a nonterminal List<String>> definition; // all the rules for one nonterminal Map<String, List<String>>> grammar; // rules for all the nonterminals n n n n public Grammar() { grammar = new Tree. Map<String, List<String>>(); } public void add. Rule(String rule) throws Illegal. Argument. Exception public List<String>> get. Definition(String nonterminal) public List<String> get. One. Rule(String nonterminal) // random choice public Iterator iterator() public void print()

First cut: Evaluation n Advantages n n Small, easily learned interface Just one class Can be made to work Disadvantages n n n As designed, <foo> : : = bar | baz is two rules, requiring two calls to add. Rule; hence requires caller to do some of the parsing, to separate out the left-hand side Requires some fairly complicated use of generics Array. List implements List (hence is a List), but consider: List<String>> definition = make. List(); n This statement is legal if make. List() returns an Array. List<String>> n It is not legal if make. List() returns an Array. List<String>>

Second cut: Overview n n We can eliminate the compound generics by using more than one class public class Grammar implements Iterable Map<String, Definition> grammar; // all the rules public class Definition List<Rule> definition; public class Rule String lhs; // the definiendum List<String> rhs; // the definiens

Second cut: More detail n n n public class Grammar implements Iterable Map<String, Definition> grammar; // rules for all the nonterminals public Grammar() { grammar = new Tree. Map<String, Definition>(); } // constructor public void add. Rule(String rule) throws Illegal. Argument. Exception public Definition get. Definition(String nonterminal) public Iterator iterator() public void print() public class Definition List<Rule> definition; // all definitions for some unspecified nonterminal Definition() // constructor void add. Rule(Rule rule) Rule get. One. Rule() public String to. String() public class Rule String lhs; // the definiendum List<String> rhs; // the definiens Rule(String text) // constructor public String get. Left. Hand. Side() public List<String> get. Right. Hand. Side() public String to. String()

Second cut: Evaluation n Advantages: n n Simplifies use of generics Disadvantages: n n Many more methods Definitions are “unattached” from nonterminal being defined n n This makes it easier to parse definitions Seems a bit unnatural Need to pass the tokenizer around as an additional argument Doesn’t help with the problem that the caller still has to separate out the definiendum from the definiens

Third (very brief) cut n Definition and Rule are basically both just lists of strings n n Why not just have them implement List? Methods to implement: n public public public public public public boolean add(Object o) void add(int index, Object element) boolean add. All(Collection c) boolean add. All(int index, Collection c) void clear() boolean contains(Object o) boolean contains. All(Collection c) Object get(int index) int index. Of(Object o) boolean is. Empty() Iterator iterator() int last. Index. Of(Object o) List. Iterator list. Iterator(int index) boolean remove(Object o) Object remove(int index) boolean remove. All(Collection c) boolean retain. All(Collection c) Object set(int index, Object element) int size() List sub. List(int from. Index, int to. Index) Object[] to. Array(Object[] a)

Fourth cut, not quite as brief n n The class Abstract. List “provides a skeletal implementation of the List interface. . . the programmer needs only to extend this class and provide implementations for the get(int index) and size() methods. ” I tried this, but. . . n n n If I don’t know how Abstract. List is implemented, how can I write these methods? No book or API class that I looked at provided any clues I may be missing something, but it looks like the only thing to do is to look at the source code for some of Java’s classes (like Array. List) to see how they do it n Doable, but too much work!

Letting go of a constraint n n n It is good practice to use a more general class or interface if you don’t need the services of a more specific class In this problem, I want to use lists, but I don’t care whether they are Array. Lists, or Linked. Lists, or something else Hence, I generally prefer declarations like List<String> list = new Array. List<String>(); In this case, however, trying to do this just seems to be the cause of many of the problems What happens if I just make all lists Array. Lists?

Fifth (and final) cut n n n public class Grammar n Map<String, Definitions> grammar; // rules for all the nonterminals n public Grammar() { grammar = new Tree. Map<String, Definitions>(); } n public void add. Rule(String rule) throws Illegal. Argument. Exception n public Definitions get. Definitions(String nonterminal) n public void print() n private void add. To. Grammar(String lhs, Single. Definition single. Definition) n private static boolean is. Nonterminal(String s) { return s. starts. With("<"); } public class Definitions extends Array. List<Single. Definition> n @Override public String to. String() public class Single. Definition extends Array. List<String> n @Override public String to. String()

Final version: Evaluation n Advantages: n n n Grammar has one constructor and three public methods Definitions and Single. Definition are just Array. Lists, so there are no new methods to learn All rule parsing is consolidated into a single public method, add. Rule(String rule) I was able to come up with more meaningful names for classes Disadvantages: n User has to do a bit more list manipulation; in particular, choosing a random element from a list n This doesn’t seem like an appropriate thing to have in a grammar, anyway

Morals n n “Weeks of programming can save you hours of planning. ” The mistake most programmers make is to use the first design that comes to mind n n n Much as we would like to pretend otherwise, programming is an iterative process--we design, then try to implement, then change the design, then try to implement. . TDD (Test-Driven Development) is a “lightweight” (low cost) way to try out a design n This usually can be made to work, but it’s seldom optimal For example, in my first design, I discovered how difficult it was to write tests that used the complex generics Consequently, I never even tried to implement this first design Morals to take home: n n Be flexible; try out more than one design Do TDD

Aside: Tokenizing the input grammar n I wrote a Bnf. Tokenizer class that returns every token as a String n n Nonterminals keep their angle brackets, and may be multiword Double-quoted strings are returned as a single token (minus the double quotes) : : = and | are returned as single tokens Bnf. Tokenizer uses Stream. Tokenizer n n It provides two constructors, Bnf. Tokenizer() and Bnf. Tokenizer(String text) And two methods, void tokenize(text) and String next. Token()

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