Symbolic programming

Wolfram Language itself comes with a vast standard library, which is suitable for most problem solving, where Python or Julia are used.

The complexity for some utility tasks such as plotting data in the a given range might even be comparable with a level of Microsoft Excel.

Wolfram Language is symbolic programming language, which is in a nutshell

code and data are expressions
computations are executed by applying rules
what you see is one of the forms of interpretation

Introduction

Let us have a look at an example

Integer numbers are so-called atoms of the language on which we can apply any transformation rule. Or we can use more general pattern

Here what you see

\frac{1}{2}

is actually written in the code editor as

raw text
(*FB[*)((1)(*,*)/(*,*)(2))(*]FB*)

Looking closely on it, we can se that the it is still a normal (1/2) expression like in any other programming language. However, it is wrapped with some special comment blocks, that tells an editor how to render it. One can go quite far with it

Any output expression is editable and can be reevaluated as well

One can go even further in exploring the idea of symbolics and syntax sugar of our editor by applying more complicated rule

As one can see, Wolfram Language does not differentiate what you are entering: a color, a function, a number. All of them are normal Wolfram Language expressions.

There are also built-in expression used for styling the output

here % means to use the previous output

Or something more complicated

this expression will make an array of numbers and highlight primes

If you try to evaluate it, all decorations will be gone and you get a normal-looking Wolfram Language array with numbers up to 20.

The same symbolic features count for Graphics. For example

One might think, that this is an image, but not

info

Everything is a set of Wolfram Expressions covered with a decoration. Underneath there is still a working code than can be copied

info

Most symbols are abstract objects that represent ideas, which, then can be interpreted in many ways.

This is also valid for 3D graphics

This is all a question of interpretation

What you see is only one form, however, taking the same symbol of Cuboid, we can treat it as a an abstract object that represents a corresponding geometric object, i.e.

Raster images are also expressions. Try to drag and drop your image to an editor

What can you do with it? Anything! For instance

or analyze a color distribution in LAB space

If you like math like me, you will probably find it useful to work in MatrixForm

And it is still fine to work with it like if it was a normal list of lists (matrix)

tip

Use Command palette for easy matrix drawing

Or combining it with other syntax sugar, one can do quite weird things

Syntax sugar and decorations also serves the purpose of abstracting classical OOP objects providing a short summary

which is still a normal symbol, which can be copied somewhere else.

For instance DateObject is rendered as a date

Time-series has also its own representation

tip

Introduction​

Introduction