MELJUN CORTES Programming languages syntax and semantics

Syntax and Semantics

Programming Languages

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The syntax of a programming language is

the form of its expressions, statements,

and program units.

Its semantics is the meaning of those

expressions, statements, and program

units.



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What are Languages?

sets of strings of characters from some

alphabet

defined by a set of rules specifying which

strings of characters from the language’s

alphabet are in the language



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Language Components

Lexeme

the lowest level syntactic unit that includes

the language’s identifiers, literals,

operators, and special words

Token

category of its lexemes

Example:

index = 2 * count + 17;

The lexemes and tokens of this statement are:

Lexemes Tokens

index identifier

= equal_sign

2 int_literal

* mult_op

count identifier

+ plus_op

17 int_literal

; semicolon



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Backus-Naur Form (BNF)

In 1956, Noam Chomsky introduced

context free grammars. He described four

classes of generative devices or grammars

that define four classes of languages.

BNF began as an abbreviation of Backus

Normal Form. It was later changed to

Backus-Norm Form to recognize Peter

Naur’s contribution as editor of the ALGOL

60 report.



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Example:

list list + digit

The LHS of the example which is list is

called an abstraction.

Abstractions in a grammar are often called

nonterminal symbols or simply nonterminals.

The RHS which is list + digit is called the

definition of the LHS. It consists of a

combination of tokens, lexemes, and

references to other abstractions which are

all called terminal symbols or simply

terminals.

Altogether, the example is called a

production or rule.



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Nonterminal Symbols

These symbols can have two or more

distinct definitions, representing two or

more possible syntactic forms in the

language.

Example:

list list + digit

list list – digit

which can be rewritten as:

list list + digit | list - digit



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Recursive Rule

A rule is said to be recursive if its LHS

appears in its RHS, as in the following

example:

list list * digit | list | digit

This defines list as either a product or as a

quotient of a list and a digit.



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Grammars and

Derivations

How are sentences in the language formed?

A sequence of rules are being applied to

generate the desired sentence. This

sentence generation is called derivation.

Consider the following grammar:

list list + digit

list list - digit

list digit

digit 0|1|2|3|4|5|6|7|8|9

list is known as the start symbol



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Sentence Derivation

Using the grammar given in the previous

slide, a derivation of the program is as

follows:

list list + digit

list list – digit + digit

list digit – digit + digit

list 9 – 5 + 2



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Parse Trees

Hierarchical structures of the sentences

defined by a language

Graphically show how the start symbol of a

grammar derives a string in the language

Given a context-free grammar, a parse tree

has the following properties:

The root is labeled by the start symbol.

Each leaf is labeled with a terminal symbol.

Each internal node is labeled by a non-

terminal.

Every subtree of a parse tree describes one

instance of an abstraction in the statement.



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Ambiguous Grammars

A grammar that generates a sentence for

which there are two or more distinct parse

trees is said to be ambiguous.

Example: Generate ‘9-5+2’

We can represent the expression using two

parse trees from an ambiguous grammar.

string

string string+

string string-

9 5

2

string

string string-

9 string string+

5 2



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Associativity of

Operators

Operators for addition, subtraction,

multiplication, and division are all left

associative while the assignment operator

is right associative.

string

string string+

string string+

9 5

2

right

letter right=

x letter letter=

y z



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Extended BNF or EBNF

Brackets – to delimit an optional part of a

RHS.

<selection> if (<expression>)

<statement> [else <statement>];

Braces – to indicate that the enclosed part

of the statement can be repeated

indefinitely, or left out altogether.

<ident_list> <identifier> {, <identifier>}

Parenthesis – to indicate options separated

by the OR operator.

<for_stmt> for <var> := <expr> (to |

downto) <expr> do <stmt>



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Syntax Graphs

A graph is a collection of nodes, some of

which are connected by lines, called edges.

A directed graph is one which the edges are

directional; that is, they have arrowheads

on one end to indicate a direction.

Syntax graphs use rectangular nodes for

non-terminals while ellipses or circle nodes

for terminal symbols.



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Attribute Grammars

device used to describe more of the

structure of a programming language than

is possible with a context-free grammar

extension to a context-free grammar

the extension allows certain language rules

to be described, such as type compatibility



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Language Semantics

Static Semantics

Only indirectly related to the meaning of

programs during execution; rather, these

have to do with the legal forms of program

Dynamic Semantics

The meaning of the expressions,

statements, and units of programs

Provide valuable information to

programmers and compiler writers



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Operational Semantics

With operational semantics, describing the

meaning of a program is done by executing

its statements on a machine (real or

simulated).

The changes that occur in the machine’s

state when it executes a given statement

define the meaning of that statement.

A translator is needed to convert the

statements in a programming language,

say L to a particular low-level language.

A virtual machine is needed for the low-

level language derived.



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Axiomatic Semantics

Defined in conjunction with the

development of a method to prove the

correctness of programs.

The proof is composed of statements of a

program each of which are preceded and

followed by a logical expression.

The logical expression specifies constraints

on the meaning of the statement. The

notation used to describe constraints is

predicate calculus.



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Assertions

Assertions or predicates are logical

expressions based on mathematical logic.

Two types:

Precondition describes the constraints on

the program variables at that point in the

program. It immediately precedes the

program statement which contains the

variables.

Postcondition immediately follows the

program statement. It describes the new

constraints on the variables in that

statement after execution.



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Weakest Preconditions

The weakest precondition is the least

restrictive precondition that will guarantee

the validity of the associated postcondition.

It can be computed either by axioms or

inference rule.

An axiom is a logical statement that is

assumed to be true.

An inference rule is a method of inferring

the truth of one assertion on the basis of

the values of other assertion.



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Weakest Preconditions

Example 1: In the statement and

postcondition, {x > 10}, {x > 50}, and {x >

1000} are all valid preconditions. The

weakest of all preconditions in this case is

{x > 10}.

Example 2: The weakest precondition is

computed by substituting y/2-1 in the

assertion {x > 5}, as follows:

Y * 2 – 1 < 5

Y < 3

Thus, the weakest precondition for the

assignment statement is {y < 3}.



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Denotational Semantics

Denotational semantics is the most

rigorous widely known method for

describing the meaning of programs.

It is solidly based on recursive function

theory.

Its fundamental concept is to define for

each language entity both a mathematical

object and a function that maps instances

of that entity onto instances of the

mathematical object.

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