Kleene's T predicate

In <a href="/facts/Computability_theory/cqDfXwdf">computability theory</a>, the T predicate, first studied by mathematician <a href="/facts/Stephen_Cole_Kleene/sKSax2se">Stephen Cole Kleene</a>, is a particular <a href="/facts/Ternary_relation/m5wypU94">set of triples</a> of <a href="/facts/Natural_number/u65og8JE">natural numbers</a> that is used to represent <a href="/facts/Computable_function/dzwBlLGn">computable functions</a> within <a href="/facts/Theory_(mathematical_logic)/mYe5gQpI">formal theories</a> of <a href="/facts/Arithmetic/hvHwkbMV">arithmetic</a>. Informally, the T predicate tells whether a particular <a href="/facts/Computer_program/e38jH9N9">computer program</a> will halt when run with a particular input, and the corresponding U function is used to obtain the results of the computation if the program does halt. As with the <a href="/facts/Smn_theorem/gXQtSx65">smn theorem</a>, the original notation used by Kleene has become standard terminology for the concept.

Kleene's T predicate open-in-new

Kleene's T predicate