This is not the case with fib2 that outputs the local function. However, local variables in Module have attribute Temporary and the DownValues of f are lost after the evaluation was completed. Thus it seems like fib uses less memory than fib3 but one might argue that the memory is stored in the local variable f.

To see what Mathematica is doing let's consider a 'functional' fib2 where fib2 outputs a function generating the fib sequence rather than a number: fib2 := Module = f = 1 Īnd checking DownValues//LengthĪfter evaluating fib3 on 10^3 one can check that DownValues // Length That method has the drawback however of recomputing everything each time fib is called as the temporary storage of values in the definition of f is lost at the end of the computation.ġ) Experiment to see what Mathematica is doing. This can be useful for problems that require using a lot of memory. The local function and Module in the example given is useful as it has the attribute Temporary which means that, in the example given, the information that it has will be erased once the computation is over. That is used to ensure that the f inside the module is different than an f that is outside the module. Mathematica sees something similar to the output of Unique which will be something like f$6729 but possibly with different numbers. The f that is written inside the module is not the f that Mathematica sees. The second is a tech note for Module in the documentation that has a discussion on local variables and in particular Module. The first to an answer that distinguishes Module, With and Block to have a better idea of the design choice for Module. 5) Why localize a function when storing values ?Ĭontent How could the local function in the Module of the example from the question be useful ?Ĭontent 2 references.

Can we use $ModuleNumber and maybe Block to trick Module into reproducing the same local variable twice ?

2) Why changing the variable inside Module is important.Ĭontent: A common example, see references for more scenarios.Ĭontent : Using Module to prevent index clashes when multiplying sums.Ĭontent : Module supposedly works by incrementing $ModuleNumber.

1) Experiment to see what Mathematica is doing.Ĭontent: Showing that the f in Module is actually something like f$6729.

(See summary section below for a shorter answer)įeel free to skip around as the sections are somewhat independent

Mathematica dynamic programming