Connect with experts and get insightful answers on IDNLearn.com. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.
Sagot :
The BNF description, or BNF Grammar, of the precedence and associativity rules are
[tex]<identifier>\text{ }::=a|b|c|d|e[/tex]
[tex]<operand>\text{ }::=\text{ }NUMBER\text{ }|\text{ }<Identifier>[/tex]
[tex]<factor>\text{ }::=\text{ }<operand>|\text{ }-<operand>|\text{ }(<expression>)[/tex]
[tex]<power>\text{ }:=\text{ }<factor>\text{ }|\text{ }<factor>\text{**} <power>[/tex]
[tex]<term>\text{ }::=\text{ }<power>\text{ }\\|\text{ }<term>*<power>\text{ }\\|\text{ }<term>/<power>\\\\<expression>\text{ }::=\text{ }<term>\text{ }\\|\text{ }<expression>+<term>\text{ }\\|\text{ }<expression>-<term>[/tex]
BNF, or Backus-Naur Form, is a notation for expressing the syntax of languages. It is made up of a set of derivation rules. For each rule, the Left-Hand-Side specifies a nonterminal symbol, while the Right-Hand-side consists of a sequence of either terminal, or nonterminal symbols.
To define precedence in BNF, note that the rules have to be defined so that:
- A negation or bracket matches first, as seen in the nonterminal rule for factor
- A power matches next, as seen in the rule defining a factor
- A multiplication, or division expression matches next, as seen in the rule defining a term
- Finally, addition, or subtraction match, as seen in the rule defining an expression.
To make sure that the expression is properly grouped, or associativity is taken into account,
- Since powers associate to the right (that is, [tex]x \text{**} y\text{**}z=x \text{**} (y\text{**}z)\text{ and not }(x \text{**} y)\text{**}z[/tex]), the rule defining power does this
[tex]<power>\text{ }:=\text{ }<factor>\text{ }|\text{ }<factor>\text{**} <power>[/tex]
and not
[tex]<power>\text{ }:=\text{ }<factor>\text{ }|\text{ }<power>\text{**}<factor>[/tex]
- Since multiplication/division are left associative (that is, [tex]x \text{*} y\text{*}z=(x \text{*} y)\text{*}z[/tex]), the rule defining a term takes this into account by specifying its recursion on the right of the operators like so;
[tex]<term>\text{ }::=\text{ }<power>\text{ }\\|\text{ }<term>*<power>\text{ }\\|\text{ }<term>/<power>[/tex]
- Also, addition and subtraction are left associative (that is, [tex]x \text{+} y\text{+}z=(x \text{+} y)\text{+}z[/tex]), the rule defining an expression takes this into account as seen below
[tex]<expression>\text{ }::=\text{ }<term>\text{ }\\|\text{ }<expression>+<term>\text{ }\\|\text{ }<expression>-<term>[/tex]
Learn more about BNF grammars here: https://brainly.com/question/13668912
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.
