system programming introduction, Slides of Introduction to Computing

Download system programming introduction and more Slides Introduction to Computing in PDF only on Docsity!

System Programming

Lecture #2,

Language Representation

2

• Human Languages
• Programming Languages
• Formal Languages

Languages

4

C, Java, Python, Prolog, Pascal,...

When is a program:

1. syntactically correct?

2. compilable?

3. free from fatal exceptions at runtime?

4. free from deadlock or infinite loops?

5. a correct implementation of its

specification?

Programming Languages

Formal Languages Definition ---

Study of “strings of symbols,” including their

 descriptions, properties,

 generations, recognitions,

 compiling, applications, … Strings of symbols include those of

 natural languages,  computer languages,  discrete signals, …

Language Definition

Dr. Gouda

Language Definition

Dr. Gouda

Strings

 The empty string will be denoted by e

 Examples

A string over alphabet S is a finite sequence

of symbols in S.

abfbz is a string over S 1 = {a, b, c, d, …, z} 9021 is a string over S 2 = {0, 1, …, 9} ab#bc is a string over S 3 = {a, b, …, z, #} ))()(() is a string over S 4 = {(, )}

Languages

 Languages can be used to describe problems

with “yes/no” answers, for example:

A language is a set of strings over an alphabet.

L 1 = The set of all strings over S 1 that contain the substring “fool” L 2 = The set of all strings over S 2 that are divisible by 7 = {7, 14, 21, …} L 3 = The set of all strings of the form s#s where s is any string over {a, b, …, z} L 4 = The set of all strings over S 4 where every ( can be matched with a subsequent )

 EXAMPLE 1 The language defined by the expression aba language (aba) = {aa aba abba abbba abbbba ...}**

 EXAMPLE 2 The language of the expression ab language(ab) = {λ a b aa ab bb aaa aab abb bbb aaaa ...} we should be very careful to observe that ab ≠ (ab)***

 EXAMPLE 3 Consider the language T defined over the alphabet Σ = {a, b, c} T = {a c ab cb abb cbb abbb cbbb abbbb cbbbb ...} T = language ((a + c)b) = language (either a or c then some b's)*

 EXAMPLES 1- Consider a finite language L that contains all the strings of a's and b's of length exactly three. L = {aaa aab aba abb baa bab bba bbb} we may write L = language ((a + b)(a + b)(a + b)) or for short, L = language ((a + b)^3 ) 2- The set of all possible strings of a's and b's of any length whatsoever we could write, (a + b)*

3- We can describe all words that begin with the letter a simply as: a(a + b) 4- All words that begin with an a and end with a b can be defined by the expression a(a + b)b = a (arbitrary string) b**

Definition

 For primitive regular expressions:

 L( ∅ ) = ∅

 L(λ ) = {λ}

 L(a) = {a}