Module

Module[{x,y,},expr]

specifies that occurrences of the symbols x, y, in expr should be treated as local.

Module[{x=x0,},expr]

defines initial values for x, .

Details

  • Module allows you to set up local variables with names that are local to the module.
  • Module creates new symbols to represent each of its local variables every time it is called.
  • Module creates a symbol with name xxx$nnn to represent a local variable with name xxx. The number nnn is the current value of $ModuleNumber.
  • The value of $ModuleNumber is incremented every time any module is used.
  • Before evaluating expr, Module substitutes new symbols for each of the local variables that appear anywhere in expr except as local variables in scoping constructs.
  • Symbols created by Module carry the attribute Temporary.
  • Symbols created by Module can be returned from modules.
  • You can use Module[{vars},body/;cond] as the righthand side of a transformation rule with a condition attached.
  • Module has attribute HoldAll.
  • Module constructs can be nested in any way, with inner variables being renamed if necessary.
  • Module is a scoping construct that implements lexical scoping.

Examples

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Basic Examples  (1)

Applications  (2)

Dynamic programming with a local function:

Euclid's algorithm for the GCD using initialized local variables:

Properties & Relations  (8)

Every time a module is evaluated, a new temporary symbol is created:

Module symbols are temporary and are removed if they are no longer referenced:

Each use of Module increments $ModuleNumber:

If there is no need to assign to a local variable, a constant should be used instead:

With is faster than Module:

Block localizes values only; it does not create new symbols:

Unique creates new variables in a way similar to Module:

Local variables are not affected by global ones, and vice versa:

A symbol brought into the scope of Module is not affected by naming conflicts:

Possible Issues  (3)

Module is a scoping construct; inner local variables shield outer ones:

Variables are renamed in nested scopes:

Build the function from its parts to avoid the renaming:

Parallel assignment is not available for Module variables:

Introduced in 1991
 (2.0)