Name Rascal/Declarations/SyntaxDefinition/Disambiguation/Priority

Syntax

1. syntax Exp = alt1 > alt2 > alt3 is the basic syntax for priorities.
2. syntax Exp = alt1 | alt2 > alt3 | alt4, where the | signifies groups of equal priority
3. syntax Exp = associativity ( $alt_1 | ... ) > $alt_2, where an associativity group denotes a group of equal priority

Description Priority declarations define a partial ordering between the productions within a single non-terminal. The feature is specifically designed to fit with the semantics of expression sub-languages embedded in programming languages. There exist other mechanisms for Disambiguation, if Priority does not work for you.

The semantics of a priority relation A > B is that B will not be nested under A in the left-most or right-most position. Any other position of A will allow B fine. Note that the priority relation you define is transitively closed, so if A > B and B > C then A > C.

A finer point is that Rascal restricts the filtering of priority such that it is guaranteed that no parse errors occur at the cause of a priority. The following table defines when and where Rascal forbids a direct nesting between two productions parent > child, depending on at which left-most or right-most positions the parent and the child are recursive.

If Parent > Child	Parent None: E = "[" E "]"	Parent Left-most: E = E "*"	Parent Right-most: E = "*" E	Parent Both: E = E "*" E
Child None: E = "{" E "}"	No filter	No filter	No filter	No filter
Child Left-most: E = E "+"	No filter	No filter	Filter under right	Filter under right
Child Right-most: E = "+" E	No filter	Filter under left	No filter	Filter under left
Child Both: E = E "+" E	No filter	Filter under left	Filter under right	Filter under left and right

Examples The following snippet uses all Priority features:

syntax Exp 
  = A: Id
  | B: Number 
  > C: Exp "[" Exp "]" 
  | D: Exp "!"
  > E: Exp "*" Exp 
  > F: Exp "+" Exp;
  | bracket G: "(" Exp ")"
  ;

A short explanation:

• C and D share a group of equal priority. They are incomparable in the partial ordering. That's fine because 1![2] is not ambiguous.
• Similarly A and B share a group; yet they are not recursive and so do not play any role in the priority ordering.
• C and D both have higher priority then E and F, which means that E and F may not be directly nested under C or D.
• However: E and F will be allowed under the second argument of C because it is not an outermost position. That's fine because 1 [2 + 3] is not ambiguous.

Here a number of strings for this language, with brackets to show how they will be parsed:

• "1 + 2 * 3" will be parsed as "1 + (2 * 3)" because E > F.
• "1 + 2 [ 3 ]" will be parsed as "1 + (2[3])" because C > F.
• "1 * 3!" will be parsed as "1 + (3!)" because D > E.
• "1 + [2 * 3]" will be parsed as "1 + ([2 * 3])" because priority is only defined for outermost positions.

Benefits

• Short notation for common expression grammars
• Removes ambiguity but can not introduce parse errors
• Allows the use of less non-terminals for the same expression grammar (typically only one), which makes parse trees simpler as well as the mapping to an abstract syntax tree more direct.

Pitfalls

• Please do not assume that Rascal's priorities have the same semantics as SDF's priorities.
• When a priority does not have a filtering effect, such as in E = E "+" > E "*" it is usually better to use normal alternative composition: E = E "+" | E "*". There is no difference in the semantics of parsing, but the latter expression is more intentional.
• You should not hide right or left recursion behind a nullable non-terminal, since the system will not filter the ambiguity then. Example: E = left "a"? E "*" E > E "+" E will remain ambiguous. This should be written as: E = left ("a" E "*" E | E "*" E ) > E "+" E; (unfolding the optional such that E becomes explicitly left-most).

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