Question

In: Computer Science

Here are two sets of BNF grammars specifying the syntax of a language: <exp> ::= <term>...

Here are two sets of BNF grammars specifying the syntax of a language:

<op> ::= <int> | <id> | (<exp>)

*********************************************

<exp> ::= <term> | <term> + <exp> | <term> - <exp> | (<exp>)

<int> will lead to non-terminals of a digit or digit sequence '123' etc.

<id> will lead to non-terminals of letters 'ABC' etc.

Do these grammars have the same set of possible outputs?

Are these grammars syntactically different? Are they semantically different? Explain

Expert Solution

1. Do these grammars have the same set of possible outputs?

No

2. Are these grammars syntactically different?

Yes

3. Are they semantically different?

Yes

Consider an example 3*(4+5)

Leftmost derivation with first set of BNF grammar:

::= <op>*<term>

::= <int>*<term>

::= 3*<term>

::= 3*<op>

::= 3*(<exp>)

::= 3*(<term>+<exp>)

::= 3*(<op>+<exp>)

::= 3*(<int>+<exp>)

::= 3*(4 +<exp>)

::= 3*(4+<term>)

::= 3*(4+<op>)

::= 3*(4+<int>)

::= 3*(4+5)

But the expression 3*(4+5) can't be generated with second set of BNF grammar.

Hence, we can say that these grammars do not have the same set of possible outputs

Syntax: grammatical structure and spelling
Semantics: meanings

From this example, we know that these grammars have different output set. So, these grammars are syntactically and semantically different.

venereology answered 1 year ago

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