Computational models help answer whether tasks can be carried out by computers and how. Grammars are used to generate and recognize languages and provide models for natural and programming languages. BNF (Backus-Naur Form) is a metalanguage that describes syntax through rewrite rules and was developed by John Backus and Peter Naur to describe programming languages. It is used widely in compiler construction.

2. Computers can perform many tasks. Given a task, two questions
arise.
The first is:
 Can it be carried out using a computer?
Once we know that this first question has an affirmative Answer,
we can ask the second question:
 How can the task be carried out?
Models of computation are used to help answer these questions.

3.  There are three types of structures used in models of computation,
namely, grammars, finite-state machines, and Turing machines.
 We will only focus on grammar structural because it will lead to us BNF
 Grammars are used to generate the words of a language and to
determine whether a word is in a language.
 Formal languages, which are generated by grammars, provide models
both for natural languages, such as English, and for programming
languages, such as Pascal, Fortran, Prolog, C, and Java. In particular,
grammars are extremely important in the construction and theory of
compilers.

4. Derivation of BNF:
 LANGUAGE AND GRAMMER
 Phrase-structure grammar
 Types of phrase-structure grammar
 Derivation Tree

5.  G:{V,T,N,S,P}
 Phrase structure grammar consists of a finite
set V: consisting of the vocabulary
 A finite set of T: Terminal symbols(cannot be
replaced)
 V-T = N: A set of non-Terminal symbols.
 A start position set S: starting
 And a finite set of P: Production rules.
 V*: The superset of V, consisting of the
language generated by V.

7.  Consists of finite set of grammar rules.
 Ambiguity occurs in CFG ( Context free grammar ).
 BNF is a CFG( Context Free Grammar ).
 A context-free grammar (CFG) G is a quadruple (V, Σ,
R, S) where
 V: a set of non-terminal symbols
 Σ: a set of terminals (V ∩ Σ = Ǿ)
 R: a set of rules (R: V → (V U Σ)*); left side always non-
terminal
 S: a start symbol.

8.  G=(V,T,N,S,P)
 V=(a, boy, sleeps, soundly, sentence, noun
phrase, verb phrase, article, noun, verb, adverb)
 T=(a, boy, sleeps, soundly)
 N=(sentence, noun phrase, verb
phrase, noun, verb, article, adverb)
 P=(<sentence> <noun phrase> <verb phrase>,
<noun phrase> <noun> <article>, <verb phrase>
<verb> <adverb>, <article> a, <noun> boy,
<verb> sleeps, <adverb> soundly).

9.  <sentence> = <noun phrase> <verb phrase>
= <article> <noun> < verb > <adverb>
= a <noun> <verb> <adverb>
= a boy <verb> <adverb>
= a boy sleeps < adverb>
= a boy sleeps soundly.

10. Sentence
noun phrase verb phrase
article noun verb adverb
a boy sleeps soundly

11.  It describes the syntactical hierarchy of a
grammars productions
 If ambiguity exists their can be more then one
parse trees
 Basically is a graphical representation.

12.  Backus-Naur notation (more commonly known as BNF or Backus-Naur Form) is a
Meta Language used to describe a language, which was developed by John
Backus (and possibly Peter Naur as well) to describe the syntax of the Algol60
programming language.
 It was primarily developed by John Backus ,but adopted and slightly improved by
Peter Naur for Algol60, which made it well-known. Because of this Naur calls BNF
Backus Normal Form, while everyone else calls it Backus-Naur Form.)
 It is used to formally define the grammar of a language, so that there is no
disagreement or ambiguity as to what is allowed and what is not. In fact, BNF is so
unambiguous that there is a lot of mathematical theory around these kinds of
grammars, and one can actually mechanically construct a parser for a language
given a BNF grammar for it. (There are some kinds of grammars for which this isn't
possible, but they can usually be transformed manually into ones that can be
used.)
 Programs that do this are commonly called "compiler compilers". The most famous
of these is YACC, but there are many more.

13. The Principles
BNF is sort of like a mathematical game: you start with a
Symbol and are then given rules for what you
can replace this symbol with. The language defined by the
BNF grammar is just the set of all strings you can produce
by following these rules.
 The rules are called production rules, and look like this:
 symbol := alternative1 | alternative2 ...

14.  Terminal symbols are literal symbols which may appear in the inputs to or outputs
from the production rules of a formal grammar and which cannot be changed
using the rules of the grammar (this is the reason for the name "terminal").
 For concreteness, consider a grammar defined by two rules:
 x can become xa
 x can become a
Here a is a terminal symbol because no rule exists which would
change it in to something else. (On the other hand, x has two rules
that can change it, thus it is nonterminal.) A formal language defined
(or generated) by a particular grammar is the set of strings that can be
produced by the grammar and that consist only of terminal symbols.

15. Nonterminal symbols are those symbols which
can be replaced. A formal grammar
includes a start symbol, a designated member of
the set of nonterminals.
e.g:
digit = “0”|"1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
So digit is non-terminal because it‟s value lies at any
range in 0 - 9.

16. What is an integer?
 An integer can be a single digit and so:
<integer> ::= <digit>
 However, what is a digit?
A digit is 0 or 1 or 2 or … or 9.
 <digit> ::= 0|1|2|3|4|5|6|7|8|9
 The vertical line is read as or.

17.  All integers of more than one digit start with a single digit and are
followed by an integer and the final integer is a single digit integer.
 An indefinitely long integer is defined as
› <integer> ::= <digit><integer>
 E.g. 147
› Is a single digit integer ( 1 ) followed by the integer 47.
› 47 is a single digit integer ( 4 ) followed by a single digit integer (
7 ).

18. SAMPLE CODE OF BNF
Int A=1+2/3;
Console.writeLine(“{0}”,A);
BNFC Code:
EAdd ( (Eint 1) (Ediv (Eint 2 ) (Eint 3) ) )
Echo (A)
EXPLANATION:
;EAdd == exp1 + exp2 (exp can be of any type of num)
;Eint == Exp is of type int
;Echo == prints the value

19. C# code :
Int a=5
Int i=1;
Int ans=0;
While(i!=10)
{
Ans=a*i;
Console.writline(“{0}”,ans);
i++;
}
BNF CODE:
Eint A ::= 5
EInt I ::= 1
EInt ans ::= 0
While ::= <i != 11>
<
Eint ans ::= Emul (Eint A )(Eint i)
Echo ans
Eint i ::= Eadd (Eint i + 1)
>

20. Note: In some cases a lexical analyzer with syntax and
semantic analyzer make up a Parser!!

21.  Scans the Code, breaks it
down into „Tokens‟:
 constants (integer, double,
char, string, etc.)
 Identifier(Variables)
 Operators
 Punctuation(separator)
 reserved words(keywords)
 Process is called
„Tokenization‟

22.  Syntax tells of the valid
form of the program
 Described via CFG
 Determines whether a
statement is valid and
can be produced via
the production rules.
 Semantic tell of the
behavior of the
program.
 Two types:
 Static semantic
check(compile time
error checking).
Example: using
undeclared variables,
type checking.
 Dynamic semantic
check(run time error
checking). Example:
Array out of bounds,
division by zero

23.  BNF = Backus-Naur Form (also known as Context-Free Grammars).
 BNF is the standard format for
the specification and documentation of programming languages.
 BNFC makes BNF usable for implementation as well.
 BNFC is a high-level front end to traditional implementation formats
(in the style of Lex and YACC): "BNFC is a compiler compiler"
 BNFC saves 90% of source code writing in a typical compiler front
end.
 BNFC can be used for projects carried out in C, C++, C#, F#, Haskell,
Java, OCaml.

24.  Strongest case: when designing and implementing a new
programming language
 rapid development(can build on a previous language)
 guaranteed consistency of components
 freedom to change implementation of language(change
its grammar)
 ANSI C and Java have been implemented
but some languages have rough corners (e.g. Haskell)

25.  Q) What is computational model?
 Q)Description of Language and Grammar?
 Q)What is Parse-Structure grammar?
 Q)What is Context free Grammar?
 Q)Define BNF; who were main contributors to its
development?
 Q)BNF Model: Compiler. Explain?