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What's the AST(Abstract Syntax Tree) for the expression a+b*c-4 according to the following grammar, and what’s...

What's the AST(Abstract Syntax Tree) for the expression a+b*c-4 according to the following grammar, and what’s left most derivation of this expression?

expression → expression ‘+’ term | expression ‘-’ term | term

term → term ‘*’ factor | term ‘/’ factor | factor

factor → identifier | constant | ‘(‘ expression ‘)’

Expert Solution

Given Information

expression → expression ‘+’ term | expression ‘-’ term | term

term → term ‘*’ factor | term ‘/’ factor | factor

factor → identifier | constant | ‘(‘ expression ‘)’

Abstract Syntax Tree: Each node represents an operator and children of the operator node represent operands.

All the unimportant details are neglected. We will directly draw a tree neglecting grammar rules.

a+b*c-4 is the given expression. Here * has precedence over + and -

+ and - are left-associative as they are right of expression or start symbol

Order of Evaluation

b*c

a+b*c

a+b*c-4

Here is the abstract tree

Left Most Derivation of a+b*c-4

expression: expression '+' term
term '+' term
factor '+' term
identifier '+' term
a '+' term
a '+' term '*' factor
a '+' factor '*' factor
a '+' identifier '*' factor
a '+' b '*' '(' expression ')'
a '+' b '*' '(' expression '-' term ')'
a '+' b '*' '(' expression '-' term ')'
a '+' b '*' '(' term '-' term ')'
a '+' b '*' '(' factor '-' term ')'
a '+' b '*' '(' identifier '-' term ')'
a '+' b '*' '(' c '-' term ')'
a '+' b '*' '(' c '-' factor ')'
a '+' b '*' '(' c '-' constant ')'
a '+' b '*' '(' c '-' 4 ')'

venereology answered 1 hour ago

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