Why does variable expansion without $ work in expressions?

Question

#!/bin/bash

VALUE=10

if [[ VALUE -eq 10 ]]
then
    echo "Yes"
fi

To my surprise, this outputs "Yes". I would have expected it to require [[ $VALUE -eq 10 ]]. I've scanned the CONDITIONAL EXPRESSIONS section of man bash, but I did not find anything to explain this behaviour.

Answer 1

[[ is bash reserved word, therefore special expansion rules such as arithmetic expansion are applied, not like in case with [. Also arithmetic binary operator -eq is used. Therefore shell looks for integer expression and if text is found at the first item it tries to expand it as parameter. It is called arithmetic expansion and is present in man bash.

RESERVED WORDS
       Reserved words are words that have a special meaning to the shell.  
       The following words are recognized as reserved 
       …
       [[ ]]

[[ expression ]]
       Return  a  status  of 0 or 1 depending on the evaluation of 
       the conditional expression expression.  Expressions are 
       composed of the primaries described below under CONDITIONAL 
       EXPRESSIONS.  Word splitting and pathname expansion are not 
       performed on the words between the  [[  and  ]];  tilde 
       expansion, parameter and variable expansion, >>>_arithmetic 
       expansion_<<<, command substitution, process substitution, and 
       quote removal are performed.  

Arithmetic Expansion
       …
       The evaluation is performed according to the rules listed below 
       under ARITHMETIC EVALUATION.

ARITHMETIC EVALUATION
       …
       Within an expression, shell variables may also be referenced 
       by name without using the parameter expansion syntax.

So for example:

[[ hdjakshdka -eq fkshdfwuefy ]]

will return always true

But this one will return error

$ [[ 1235hsdkjfh -eq 81749hfjsdkhf ]]
-bash: [[: 1235hsdkjfh: value too great for base (error token is "1235hsdkjfh")

Also recursion is available:

$ VALUE=VALUE ; [[ VALUE -eq 12 ]]
-bash: [[: VALUE: expression recursion level exceeded (error token is "VALUE")