Create a valid expression using the grammar below For the…
Create a valid expression using the grammar below For the same expression above list the nodes you will visit as you trace through the grammar provided by the digraph. For example, the expression s+b*c-d would produce the following VISIT-LIST: S, C, D, C, D, C, D, C
Answer
To create a valid expression using the given grammar, we will use the following production rules:
1. S -> E
2. E -> E + T
3. E -> T
4. T -> T * F
5. T -> F
6. F -> (E)
7. F -> id
Let’s create an expression using this grammar: a+b*c-d
To analyze the nodes that will be visited as we trace through the grammar, we need to consider the productions that will be used for each non-terminal symbol in the expression. Let’s analyze the given expression based on the grammar:
Step 1: Start with the start symbol S: S -> E
Step 2: Apply production rule 2 to E: E -> E + T
Tracing the first part of the expression, we visit node E.
Step 3: Apply production rule 3 to E: E -> T
Tracing the second part of the expression, we visit node T.
Step 4: Apply production rule 5 to T: T -> T * F
Tracing the third part of the expression, we visit node T.
Step 5: Apply production rule 5 to T: T -> F
Tracing the fourth part of the expression, we visit node F.
Step 6: Apply production rule 7 to F: F -> id
Tracing the fifth part of the expression, we visit node id.
Step 7: Apply production rule 4 to T: T -> T * F
Tracing the sixth part of the expression, we visit node T.
Step 8: Apply production rule 5 to T: T -> F
Tracing the seventh part of the expression, we visit node F.
Step 9: Apply production rule 7 to F: F -> id
Tracing the eighth part of the expression, we visit node id.
Step 10: Apply production rule 2 to E: E -> E + T
Tracing the ninth part of the expression, we visit node E.
Step 11: Apply production rule 3 to E: E -> T
Tracing the tenth part of the expression, we visit node T.
Step 12: Apply production rule 5 to T: T -> F
Tracing the eleventh part of the expression, we visit node F.
Step 13: Apply production rule 7 to F: F -> id
Tracing the twelfth part of the expression, we visit node id.
In summary, the visit-list for the expression a+b*c-d using the provided grammar is: E, T, T, F, id, T, F, id, E, T, F, id.
In this visit-list, we can see the order in which the nodes are visited as we traverse through the grammar, applying the appropriate production rules at each step. This visit-list demonstrates the derivation process for the given expression in the context of the given grammar.