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  "body": "\n## Summary\n\nA primitive recursive function is a function on the [[natural numbers|0MWKJ44V5A]] built from zero, successor and projections by composition and primitive recursion.\nPrimitive recursion defines $f(n + 1)$ from $f(n)$, like a for-loop whose number of steps is fixed in advance.\nEvery primitive recursive function is total and [[computable|KZSB5E471K]], and most functions met in ordinary number theory are primitive recursive.\nNot every total computable function is primitive recursive; the [[Ackermann function|N470JF7ZJX]] is the classical example.\n\n## Explanations\n\n### L1 human\n\nStart with the simplest functions: the constant $0$, adding one, and picking one argument out of a list.\nThen allow two ways of building new functions: plugging functions into each other, and defining a value at $n + 1$ from the value at $n$.\nAddition comes from adding one repeatedly, multiplication from adding repeatedly, and powers from multiplying repeatedly.\nEvery function obtained this way can be computed by a program whose loops have a bound known before the loop starts.\n",
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