Operator parsing issues

Precedence

• which operator binds tighter? Is

    1 + 2 * 3
  

  parsed as 1 + (2 * 3) or (1 + 2) * 3? If precedences are different, associativity does not come into play.

• prefix vs. infix -- assuming = is right-associative, and ! is as well, since prefix operators seem to have to associate to the right, consider:

    ! x = 3
  

  Is that !(x = 3) or (!x) = 3?

Associativity

Only matters when precedences are equal.

• left vs. right: 1 + 2 + 3 parsed as 1 + (2 + 3) or (1 + 2) + 3?

• non-associativity: 1 @@ 2 @@ 3 where @@ is a non-associative operator: parse error

• mixed associativity, same precedence: x = 3 + 1 or 2 + 3 = x, assuming that + and = have the same precedence but opposite associativities. Probably should result in parse error.

• prefix vs. postfix

   ! x ++
  

  Is it (!x) ++ or !(x++)? (Probably the latter -- but I guess it should be resolved by precedences)

Prefix and Postfix

• prefix vs. infix: what does each use of - mean?

   3 - - - -- q
  

• prefix vs. postfix: what does each use of ++ mean?

   ++ x + ++ y * z ++
  

• associativity of prefix operators: right-only (???)

   ! ! ! ! x
  

• precedence of prefix vs. postfix: irrelevant, since can't do both on same operand (???) i.e. can't do:

   ++ x ++
  

• associativity of postfix operators: none, b/c only one allowed? i.e. can't do

   x ++ ++
  

  Counterpoint: C and C++ might support multiple postfix operators.

• low-precedence postfix: parse this:

   3 + x ++ * 5
  

  as ((3 + x) ++) * 5, assuming ++ is lower precedence than +?

  • (3 + x) ++ doesn't make sense
  • I haven't found any low-precedence postfix operators in practice
  • would the ++ really interfere with *?

Ternary

• unsolved: how to parse the ternary ? : operator

Error conditions

• mixed associativity, same precedence

   infixr  @@ 5
   infixl  $$ 5
   prefix  ! 5
   postfix # 5
   
   x @@ y $$ z  -- error
   x $$ y @@ z  -- error
   ! x @@ y     -- error
   x $$ y #     -- error
  

• postfix operator in non-postfix context

   ++
  

• non-postfix operator in postfix context

• non-prefix operator in prefix context (can this be reliably recognized?)

• missing operand

   x + 
   a * b ^