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  "body": "\n## Summary\n\nKleene's T predicate is a [[primitive recursive|5NVA2JRHPV]] relation $T(e, x, c)$ about computations.\nIt says that $c$ codes a halting computation of the program with index $e$ on input $x$.\nTogether with a primitive recursive function $U$ that reads off the output, it gives Kleene's normal form theorem.\nEvery partial [[computable function|KZSB5E471K]] has the form $x \\mapsto U(\\mu c \\, T(e, x, c))$ for some $e$.\nSo a single unbounded search is enough for any computation.\n\n## Explanations\n\n### L1 human\n\nChecking that a given record of a computation is correct is easy: you go through it step by step.\nThe T predicate is exactly this check, done for every program and every input at once.\nFinding a correct record may be impossible, because the program may never stop.\nSo every computation is \"search for a valid record, then read the answer from it\".\nFor instance, the halting set is the set of $e$ for which some $c$ satisfies $T(e, e, c)$.\n",
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