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you are splitting hair on definitions.

It is the pure function nature of functional programming that makes it easy for concurrent and parallel tasks. Recursion is neither here nor there

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It's not hair-splitting. As I understand it, functional shader languages are an active area of research. Mainstream shader languages such as HLSL are most certainly not functional.

Languages are functional if they support higher order functions, recursion, closures, etc.

Code is functional if it separates side-effects to small, clearly marked parts of the codebase.

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