Syntax and Semantics of Programming Languages: Understanding CS3723, Study notes of Programming Languages

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Fundamantals

Syntax and Semantics of

Programming Languages

Syntax and Semantics

 Syntax

 The symbols and rules to write legal programs

 Semantics

 The meaning of legal programs

 Programming language implementation

 Syntax −> semantics

 Translate program syntax into machine actions

 Example: date specification

 Syntax

 date ::= dd/dd/dddd d = 0|1|2|3|4|5|6|7|8|

 Semantics

 01/02/2005 => Jan 02, 2005 (or Feb 01,2005)?

Why Describing Syntax?

 A translator/compiler needs to understand

programs via syntax analysis

 Needs to implement syntax analysis in C/C++/Java etc.

 Why does the syntax need to be formally

defined?

 Regular expressions and BNFs are themselves

languages for describing language syntax

 Supports communications between programmers and

translators/compilers

 Supports automated generation and validation of syntax

analyzers

Every configurable automation requires an interface

language

Describing Semantics

 Informal definitions

 Tutorials: learn by working examples

 Reference Manuals

 Natural language explanation for each syntax rule

 Formal definitions (skip)

 Attribute grammars

 Associate attributes (values) with each grammar symbol

 Associate semantics rules with each grammar rule

 Operational semantics

 Interpret the language on an abstract machine or using

another language

 Denotational semantics

 Define language constructs as mathematical functions

 Axiomatic semantics (proof rules)

 Define properties (invariance) of language constructs

 Goal: communication, automation and validation

What language aspects can be

defined by CFG?

 Can we use CFG to define more than just syntax?

 e ::= num | string | id | e+e

 Support both alternative (|) and recursion

 Cannot incorporate context information

 Cannot determine the type of variable names

 Declaration of variables is in the context (symbol table)

 Cannot ensure variables are always defined before used

int w;

0 = w;

for (w = 1; w < 100; w = 2w)

a = “c” + 3;

a = “c” + w

Derivations and Parse Trees

(Semantics of CFG)

 Derivation: top-down replacement of non-terminals

 Each replacement follows a production rule

 One or more derivations for each program

 Derivations for 5 + 15 * 20

 e=> ee* => e+ee* =>n+ee=>d+ee=> 5+ee* =>5+ne=>5+nd

e=>5+dde=>5+1de=> 5+15e* =>…=> 5+15*

 E=> e+e =>…=> 5+e => 5+ee* =>…=> 5+15e* =>…=> 5+15*

e

e

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e e

n

d

n

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e

Parse trees:

Abstract vs. Concrete Syntax

 Concrete syntax: the syntax that programmers write

 Example: different notations of expressions

 Prefix + 5 * 15 20

 Infix 5 + 15 * 20

 Postfix 5 15 20 * +

 Abstract syntax: the program structure recognized by

compilers/interpreters

 Identifies only the meaningful components

 What is the operation and which are the operands?

e

e

e

e

e

Parse Tree for

Abstract Syntax Tree for 5 + 15 * 20

cs3723 11

Abstract syntax trees

 Condensed form of parse tree for representing

language constructs

 Operators and keywords do not appear as leaves

 They define the meaning of the interior (parent) node

 Chains of single productions may be collapsed

If-then-else

B S1 S

S

IF B THEN^ S1 ELSE S

E

E

+ T

T

Ambiguous Grammars

 A grammar is syntactically ambiguous if

 some program has multiple parse trees

 Multiple choices of production rules during derivation

 Consequence of multiple parse trees

 Parse trees are used to interpret programs

 Multiple ways to interpret a program

e

e

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n

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Rewrite ambiguous Grammars

 Solution1: introduce precedence and associativity rules to

dictate the choices of applying production rules

 Original grammar: e ::= n | e+e | e−e | e * e | e / e

 Precedence and associativity

 * / >> + - all operators are left associative

 Derivation for n+n*n

 e=>e+e=>n+e=>n+ee=>n+ne=>n+n*n

 Solution2: rewrite production rules by introducing additional

non-terminals

 Alternative grammar E ::= E + T | E – T | T

T ::= T * F | T / F | F

F ::= n

 Derivation for n + n * n

 E=>E+T=>T+T=>F+T=>n+T=>n+TF=>n+FF=>n+nF=>n+nn

 How to modify the grammar if

 + and - has high precedence than * and /

 All operators are right associative

Additional exercises

 Give a context-free grammar for a small graph

description language

 Terminals: digits(0',1',...,9'),(', )',;' and `->'

 Each node of the graph is represented by an integer

number,

 Each edge is represented by a pair of nodes connected

with `->'

 eg., 3->4 is an edge from node 3' to node4'

 Each graph description is a sequence of edges

 Eg. ( 1->2; 2->5; 5->1)

 Write a parse tree and an abstract syntax tree

for ( 1->2; 2->5; 5->1)

Additional Exercises

(practice on your own)

 Give a CFG to describe the set of symmetric strings over

{a,b}

 Give a CFG to describe the set of strings over {a,b} that

have the same numbers of a’s and b’s?

 Give a CFG for the syntax of regular expressions over {0,1}

. For example

 “0|1”, “0”, (01|10) are in the languages

 “0|” and “*0” are not in the language

 Can you give a CFG to describe the set of strings that have

the format xx, where x is an arbitrary string over {a,b}