1 CFGS Consider the following grammar. erpr := erpr + expr | erpr + erpr|(crpr) | number number := number digit | digit digit := 0 I 1 | 21 3I 4I5I 6I7 | 8 I 9 1. Redefine the grammar in a way that numbers are defined by regular expressions. That is, remove two grammar rules for number and digit nonterminals, and replace them with a single regular expres- sions for numbers. 2. Modify the grammar to define assignment statements with a syntax similar to C/C+, where ex- pressions are assigned to identifiers. Here are the steps: (a) Add identifier token ID to the CFG. You may define it with regular expressions (since identi- fiers are tokens). We have already seen how to define identifiers with regular expressions, in previous sessions. (b) Consider a nonterminal for assignment. Let's call this nonterminal assignment. You need to define a CFG rule that defines assignment. An assignment in C/C+ grammatically consists of an identifier (defined in previous step), folowed by equality symbol (a terminal), followed by an expression (an already defined nonterminal). This sequence of terminals and nonterminals should be given in the RHS of your CFG rule.

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1 CFGS
Consider the following grammar.
erpr := erpr + expr | erpr + erpr|(crpr) | number
number := number digit | digit
digit := 0 I 1 | 21 3I 4I5I 6I7 | 8 I 9
1. Redefine the grammar in a way that numbers are defined by regular expressions. That is, remove two
grammar rules for number and digit nonterminals, and replace them with a single regular expres-
sions for numbers.
2. Modify the grammar to define assignment statements with a syntax similar to C/C+, where ex-
pressions are assigned to identifiers. Here are the steps:
(a) Add identifier token ID to the CFG. You may define it with regular expressions (since identi-
fiers are tokens). We have already seen how to define identifiers with regular expressions, in
previous sessions.
(b) Consider a nonterminal for assignment. Let's call this nonterminal assignment. You need to
define a CFG rule that defines assignment. An assignment in C/C+ grammatically consists of
an identifier (defined in previous step), folowed by equality symbol (a terminal), followed by
an expression (an already defined nonterminal). This sequence of terminals and nonterminals
should be given in the RHS of your CFG rule.
Transcribed Image Text:1 CFGS Consider the following grammar. erpr := erpr + expr | erpr + erpr|(crpr) | number number := number digit | digit digit := 0 I 1 | 21 3I 4I5I 6I7 | 8 I 9 1. Redefine the grammar in a way that numbers are defined by regular expressions. That is, remove two grammar rules for number and digit nonterminals, and replace them with a single regular expres- sions for numbers. 2. Modify the grammar to define assignment statements with a syntax similar to C/C+, where ex- pressions are assigned to identifiers. Here are the steps: (a) Add identifier token ID to the CFG. You may define it with regular expressions (since identi- fiers are tokens). We have already seen how to define identifiers with regular expressions, in previous sessions. (b) Consider a nonterminal for assignment. Let's call this nonterminal assignment. You need to define a CFG rule that defines assignment. An assignment in C/C+ grammatically consists of an identifier (defined in previous step), folowed by equality symbol (a terminal), followed by an expression (an already defined nonterminal). This sequence of terminals and nonterminals should be given in the RHS of your CFG rule.
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