Difference between Import and Get of mx file

Question

The documentation says

Import["file.mx"] is equivalent to Get["file.mx"] .

However, I have at least one instance where Get["file.mx"] gives Null, while Import["file.mx"] gives some result (the intended result). I can literally start in a clean Kernel and do one or the other and it is perfectly clear that they are not equivalent. (I even renamed the file to be "file.mx" sort of as a joke, just to proof the documentation completely wrong.)

Now I know this is not the place to put a bug report, but does anyone understand what is going on? (As a side note, there isn't any way to attach a file to a question right?).

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This seems to be pretty universal behavior actually. To test it use:

Export["file.mx", {a, b, c}]

and try for yourself. Also adding the format "Package" or "MX" to Get does not affect the result (neither does adding "MX" as the format when exporting).

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In more practical terms. I need a function that reliably reads and evaluates data of this type (i.e. matrices or matrices with some function wrapper around them) whether they are stored in an .mx file or in a .txt file (it needs to be able to handle both). Import does not work as this universal function as it will read in the .txt file as a string. I think that ToExpression[Import[#]]& might work universally but I still have to verify this.

Answer 1

You are correct that Import and Get are not quite the same for MX files.

Import is for importing data. Import generally works with various data formats. It returns a representation of the data as a Mathematica expression.

However, MX files don't exactly hold data. They hold definitions associated with symbols. Loading an MX file with Get simply recreates these definitions.

To explain through an example, it is not possible to store a list like {1,2,3} in an MX file. It is necessary to assign this list to a variable, x = {1,2,3}. Then loading the MX file will create the symbol x (if it does not yet exist) and will associate the x = {1,2,3} definition with it. We can also have other types of definitions, e.g. f[x_] := x^2.

At this point you might be saying: "But that's not how Import works with MX files! Export can store plain expressions in an MX file, without associating them with a symbol, and Import can read this data."

Well, that's really just an illusion that Import/Export create through a small trick. The standard way to write MX files is not Export, but DumpSave. When you Export data such as {1,2,3} to MX, first it is associated with a special symbol that Export and Import use internally. Then the definitions of this symbol are saved with DumpSave.

When you use Import to read an MX file, it will check if this symbol's definition has changed after Getting the MX file. If so, it just returns the value of that symbol. If not, it will leave thing as they are.

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The special symbol that Export/Import use for MX files is called

System`Private`ConvertersPrivateDumpSymbol

When we do Export["file.mx", {1,2,3}], then the MX file will be equivalent to the following .m file:

System`Private`ConvertersPrivateDumpSymbol := HoldComplete[{1,2,3}]

Now Get["file.mx"] does not return anything, but you can evaluate System`Private`ConvertersPrivateDumpSymbol to check that it has gained a value. Import["file.mx"] will check for this and will return this value. This explains your observations.