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bugs - How symbol lookup actually works


Bug introduced in V6 and fixed in V11.3



The behavior indeed changed but now the documentation is clear about it.




This code is inconsistent with the description from Power Programming with Mathematica:



x = 5;
temp`x = 6;
Begin["temp`"]
{x, Global`x, temp`x}

The result in my Mathematica session is {5, 5, 6}, but it's {6, 5, 6} in Section 8.1.1 of Power Programming with Mathematica (page 231 of the hardcopy or page 249 of the PDF).



Answer



This behaviour has changed since that book was published. I am writing this additional answer to make it clear how Mathematica 9 searches contexts for symbols and that even the current version 9 documentation is incorrect in describing this.


How symbol lookup actually works


When you enter a symbol name such as x, Mathematica will check if a symbol with this name already exists. It will first search the contexts from $ContextPath for x, one by one. If it doesn't find it there, it'll search the context from $Context for it. If it still doesn't find it, then it will create a new symbol named x in $Context.



Thus $ContextPath controls where to look for symbols, while $Context controls where to create new symbols.


Your observations are explained by these rules, noting that Begin will change $Context only but not $ContextPath. Note that BeginPackage will change both $Context and $ContextPath.


Warning: the documentation contains an error in Mathematica versions older than 11.3.


The $ContextPath documentation states that



$ContextPath is a global variable that gives a list of contexts, after $Context, to search in trying to find a symbol that has been entered.



In fact $ContextPath is searched before $Context in the current version.


In old versions this was not the case, as the Wagner book describes. I don't know when the change happened.


The Contexts tutorial does correctly state the order of search in the current version:




Since $Context is searched after $ContextPath, you can think of it as having "." appended to the file search path.



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