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• Procedural programming of the kind familiar to users of C or Fortran. The canonical constructs of this style are the Do and For loop and it is heavily relying on saving intermediate values into variables. This is the kind of programming most novice Mathematica users resort to, and it is usually the least efficient.
• Functional programming is considered more canonically "Mathematica-style". Familiar to uses of LISP. The typical constructs in functional programming are Map (/@), Apply (@@), MapThread and pure functions (Function) using Apply and Slot (#, &).
• Rule-based programming uses Mathematica's pattern-matching engine to match and rewrite expressions. A typical construction in this style is the replacement rule e.g. a -> b or a :> b, which is involved using Replace, ReplaceAll (/.) or ReplaceRepeated (//.).