Wolfram: Principles

Principle of Wolfram Language Syntax

• Everything is a Expression.
• Expression is either an atom, or a list of atoms in the form a[b, c, etc], arbitrarily nested.
• Atom is a number (3.4), a Symbol (x), a string ("cat"), or special character (\[Pi]).
• There are many short syntax for function or function call. e.g. List[1,2,3] can be written as {1,2,3}, and Set[x,2] can be written as x=2, and Plus[1,2] can be written as 1+2. WolframEngine transform any short syntax to the fully nested form a[b, c, etc] internally before computation. 〔see Wolfram: Syntax, Operators Cheatsheet〕

• WolframLang code is just a sequence of expressions, practically just function calls. Knowing what function to call is the essence of coding WolframLang. 〔see Wolfram: Find Function by Name〕

How Does Wolfram Language Do Computation

There are 2 ways WolframLang does computation.

• Function call. Either builtin or user defined. e.g. Plus[3, 2], Sin[3], Range[5], If[3 > 2, "yes", "no"]
• Syntactical transformation by pattern matching and replacement. (aka term rewriting system)