[PDF] Fun with Syntax - ezekiel

Assignment #1, Fun with SyntaxCS 355Due Tuesday Jan 25, 2011You may need more room than the space provided; use the back of each page or attach separate sheets.1. Say we wish use a caret ^ as an exponentiation operator which has a higher precedence than additionand multiplication and is right associative. Here is the initial ambiguous grammar:E → E + EE → E ∗ EE → E ^ EE → ( E )E → NUM(a) Draw two different parse trees for 4 ∗ 5^2^3.(b) Fix the grammar for expressions so that it is both unambiguous and reflects the proper order ofoperations. The expression 3+4∗5^2^3 should be evaluated as 3+(4∗(5^(2^3))). (Left recursionis okay).(c) Draw a parse tree for 4 ∗ 5^2^3 using your new grammar.1

2. Below is a grammar involving C’s ternary operator ?: which has lower precedence than addition.E → E ? E : EE → E + T→ TT → ( E )→ NUM(a) Draw two parse trees for NUM ? NUM ? NUM : NUM : NUM + NUM(b) Modify the grammar so that it is unambiguous; ?: is right associative and has lower precedencethan addition.(c) Draw a parse tree for NUM ? NUM ? NUM : NUM : NUM + NUM using your new grammar.2

3. C also has a comma operator that is left associative and has the lowest precedence of all operators.The grammar below uses commas for two different purposes: one as an operator (top production), andanother to separate arguments to a function call (second to last production).E → E , F→FF → F + T→TT → ( E )→NUM→ ID ( A )A → B→ɛB → B , F(a) Draw a parse tree for ID(NUM,NUM+NUM) (two parameter function call).→F(b) Draw a parse tree for ID((NUM,NUM+NUM)) (one parameter function call).(c) How does this grammar syntactically differentiate between the two uses of commas?3