Dangling else


The dangling else is a problem in computer programming in which an optional else clause in an if–then statement results in nested conditionals being ambiguous. Formally, the reference context-free grammar of the language is ambiguous, meaning there is more than one correct parse tree.
In many programming languages one may write conditionally executed code in two forms: the if-then form, and the if-then-else form – the else clause is optional:
if a then s
if b then s1 else s2
This gives rise to an ambiguity in interpretation when there are nested statements, specifically whenever an if-then form appears as s1 in an if-then-else form:
if a then if b then s else s2
In this example, s is unambiguously executed when a is true and b is true, but one may interpret s2 as being executed when a is false or when a is true and b is false. In other words, one may see the previous statement as either of the following expressions:
if a then else s2
if a then
The dangling else problem dates to ALGOL 60, and has been resolved in various ways in subsequent languages. In LR parsers, the dangling else is the archetypal example of a shift-reduce conflict.

Avoiding ambiguity while keeping the syntax

This is a problem that often comes up in compiler construction, especially scannerless parsing. The convention when dealing with the dangling else is to attach the else to the nearby if statement, allowing for unambiguous context-free grammars, in particular. Programming languages like Pascal, C and Java follow this convention, so there is no ambiguity in the semantics of the language, though the use of a parser generator may lead to ambiguous grammars. In these cases alternative grouping is accomplished by explicit blocks, such as begin...end in Pascal and in C.
Depending on the compiler construction approach, one may take different corrective actions to avoid ambiguity:
The problem can also be solved by making explicit the link between an else and its if, within the syntax. This usually helps avoid human errors.
Possible solutions are:
Concrete examples follow.

C

In C, the grammar reads, in part:

 statement =...
 | selection-statement
 selection-statement =...
 | IF statement
 | IF statement ELSE statement

Thus, without further rules, the statement

if if s; else s2;

could ambiguously be parsed as if it were either:

if

or:

if
else
s2;

In practice in C the first tree is chosen, by associating the else with the nearest if.

Avoiding the conflict in LR parsers

The above example could be rewritten in the following way to remove the ambiguity :

statement: open_statement
 | closed_statement
 ;
open_statement: IF  statement
 | IF  closed_statement ELSE open_statement
 ;
closed_statement: non_if_statement
 | IF  closed_statement ELSE closed_statement
 ;
non_if_statement:...
 ;

Any other statement-related grammar rules may also have to be duplicated in this way if they may directly or indirectly end with a statement or selection-statement non-terminal.
However, we give grammar that includes both of if and while statements.

statement: open_statement
 | closed_statement
 ;
open_statement: IF  statement
 | IF  closed_statement ELSE open_statement
 | WHILE  open_statement
 ;
closed_statement: simple_statement
 | IF  closed_statement ELSE closed_statement
 | WHILE  closed_statement
 ;
simple_statement:...
 ;

Finally, we give the grammar that forbids ambiguous IF statements.

statement: open_statement
 | closed_statement
 ;
open_statement: IF  simple_statement
 | IF  open_statement
 | IF  closed_statement ELSE open_statement
 | WHILE  open_statement
 ;
closed_statement: simple_statement
 | IF  closed_statement ELSE closed_statement
 | WHILE  closed_statement
 ;
simple_statement:...
 ;

With this grammar parsing of "if if c else d" fails:

statement
open_statement
IF  closed_statement ELSE open_statement
'if'  closed_statement 'else' 'd'

and then the parsing fails trying to match closed_statement to "if c". An attempt with closed_statement fails in the same way.