38 | Assigning Names to Things |

Particularly when you’re doing quick experiments in the Wolfram Language, it’s often convenient to use % to refer to the result of your most recent computation.

Do a simple computation:

In[1]:= |

Out[1]= |

% gives the result of the previous computation:

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This squares the most recent result:

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If you expect to refer to a result later, you can assign it a name. For example, you can say thing=Range[10] to assign thing as a name for the result of Range[10].

Assign thing to be the result of Range[10]:

In[4]:= |

Out[4]= |

In[5]:= |

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Square the value of thing:

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Out[6]= |

Assign a name to a list of a million elements, but don’t display the list:

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In[8]:= |

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When you assign a name to something, the name will stay until you explicitly clear it.

Assign x the value 42:

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You might have thought this would be {x, y, z}—but x has value 42:

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Clear any assignment for x:

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Now x, like y and z, isn’t replaced:

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In[13]:= |

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Outside the module, x still has no value assigned:

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Define local variables x and n, then compute x^n using the values you’ve assigned:

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In the

*functional*style of programming that we’ve used in most of this book, you carry out sequences of operations by applying sequences of functions. This is a very powerful and direct style of programming that’s uniquely suited to the Wolfram Language.But once one’s defining variables, one can use a different style, in which one doesn’t feed results directly from one function to another, but instead assigns them as values of variables to be used later. This kind of

*procedural programming*is what’s been used in lower-level languages since the very earliest days of computing.It’s still useful in the Wolfram Language, though in many ways it’s eclipsed by functional programming, as well as by the

*pattern-based*style of programming that we’ll discuss later.To specify sequences of actions in the Wolfram Language one just separates them by semicolons (;). (Putting a semicolon at the end is like specifying an empty final action, which is why this has the effect of not displaying a result.)

Do a sequence of operations; the result is what the last operation produces:

In[16]:= |

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This defined global values for x and y; don’t forget to clear them:

In[17]:= |

You can use semicolons to do sequences of operations inside Module.

This does a sequence of operations, with x and y maintained as local variables:

In[18]:= |

Out[18]= |

You can mix local variables that do and don’t have initial values:

In[19]:= |

Out[19]= |

38.2Use Module to generate a list of 10 random integers up to 100, then make a column giving the original list, and the results of applying Sort, Max and Total to it. »

38.3Use Module to generate an image collage from a picture of a giraffe, and the results of applying Blur, EdgeDetect and ColorNegate to it. »

38.4Inside a Module, let r=Range[10], then make a line plot of r joined with the reverse of r joined with r joined with the reverse of r. »

38.7Generate 10 random strings made of 5 letters, in which consonants (non-vowels) alternate with vowels (aeiou). »

Q&A

How come we’re at Section 38, and only now introducing variable assignments?

Because, as we’ve seen, in the Wolfram Language one can go a very long way without introducing them. And it tends to be a lot cleaner to program without them.

Can I assign a name to anything?

Yes. Graphics, arrays, images, pure functions, whatever.

How does one read x=4 out loud?

“x equals 4”, or, more rarely, “assign x to 4”, or “give x the value 4”.

Use names that are specific and explicit. Don’t worry if they’re long; they’ll get autocompleted when you type. For “informal” names, start with lowercase letters. For more carefully thought out names, consider using capitalization like built-in functions do.

%% gives the next to last, %%% gives the next-to-next-to-last, etc. %n gives the result on line n (i.e. the result labeled Out[n]).

Yes. x=y=6 assigns both x and y to 6. {x, y}={3, 4} assigns x to 3 and y to 4. {x, y}={y, x} swaps the values of x and y.

What happens if a variable escapes from a Module without having been assigned a value?

Try it! You’ll find you’ll get a new variable that’s been given a unique name.

The Wolfram Language has those. Do is sometimes worth using, particularly when your objective is side effects, like assigning variables or exporting data. For is almost always a bad idea, and can almost always be replaced by much cleaner code using constructs such as Table.

Tech Notes

- The result of x=2+2 is just 4, but as a
*side effect*an assignment is made for x. - In pure functional programming, the only effect of any computation is to give the result. As soon as you’re assigning values, there’s effectively a hidden state that’s set up by those assignments.
- x=. is an alternative to Clear[x].
- Module does
*lexical scoping*, which means it effectively localizes the names of variables. Block does*dynamic scoping*, which means it localizes the values, but not the names, of variables. Both are useful in different circumstances. Table effectively uses Block. - x++ is equivalent to x=x+1. x+=n is equivalent to x=x+n. AppendTo[x, n] is equivalent to x=Append[x, n] or x=Join[x, {n}].