Language Design $(20$ points$)$

Pat is writing a compiler for equality tests on numbers, and wants to handle both integers and floating point values. Pat's initial version looks like this:

This version works fine with Pat's shift$-$reduce parser generator, but Pat wants the lan$-$

guage to also allow comparisons between integers and floating point values $($converting the integer to floating point before comparison$),$ and adds one more production to the

grammar, changing the fltval rule to:

fltval rarr FLOAT $|$ INT

a$)(5$ points$)$ This augmented grammar is no longer SLR$(1).$ What conflict$($s$)$ will there

be in the generation of the parsing table? Can they be resolved with precedence

declarations on operators? Why or why not?

b$)(5$ points$)$ Pat's friend Chris suggests using a recursive descent parser instead. Will a

recursive descent parser $($using the augmented grammar as written$)$ generate the parse

tree that Pat wants in all cases? Justify your answer.

c$)(5$ points$)$ Pat's other friend Francis thinks that the problem can be solved in the

lexical analysis. Is this possible? Justify your answer.

d$)(5$ points$)$ Drew thinks the right answer is to change the language to use a different operator $($e$.$g$.^(=))$ for floating$-$point comparisons. Explain how this resolves the

conflict$($s$)$ in the SLR$(1)$ parsing table, or show what conflict$($s$)$ remain.