For each of the following, give a fixity (precedence and associativity) for the infix operators in the string so that the string would parse as intended or give a reason why it's impossible.

For example, if we wanted the string "A * B * C + D + E" to parse as "((A * (B * C)) + D) + E", we could give the operators the following fixities: + is left-associative with precedence 1 * is right-associative with precedence 2

However, the string "A + B + C + D" can't possibly parse as "(A + B) + (C + D)", because the + operator must be left-associative, right-associative, or non-associative, and none of those associativity choices choice will produce that parenthesization.

In most cases there will be multiple valid answers, but you only have to give one.

a) "A + B * C + D" parses as "A + ((B * C) + D)" b) "A & B | C ^ D ^ E" parses as "(A & B) | ((C ^ D) ^ E)" c) "A % B @ C = D @ E % F" parses as "((A % B) @ C) = ((D @ E) % F)" d) "A + B * C = A * B + A * C" parses as "(A + (B * C)) = ((A * B) + (A * C))"

Slides on the topic

Precedence and associativity For two arbitrary infix operators,and Ifa has higher precedence than , then "ab c" parses as "(ab) c" Ifa is left-associative, then "abc" parses as "(ab)c" -If s is right-associative, then "abc" parses as "a(bc)" -Ifa is non-associative, then "abc" is a syntax error Fixity = precedence + associativity