Primitive recursive functional

In <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, the primitive recursive functionals are a generalization of <a href="/facts/Primitive_recursive_functions/4z97gRnl">primitive recursive functions</a> into higher <a href="/facts/Type_theory/xj0xzVqI">type theory</a>. They consist of a collection of functions in all pure finite types.
The primitive recursive functionals are important in <a href="/facts/Proof_theory/kopBdQn9">proof theory</a> and <a href="/facts/Constructive_mathematics/1VtNuLwT">constructive mathematics</a>. They are a central part of the <a href="/facts/Dialectica_interpretation/WPfbFVmL">Dialectica interpretation</a> of intuitionistic arithmetic developed by <a href="/facts/Kurt_G%C3%B6del/P14DqKqK">Kurt Gödel</a>.
In <a href="/facts/Recursion_theory/cqDfXwdf">recursion theory</a>, the primitive recursive functionals are an example of higher-type computability, as primitive recursive functions are examples of Turing computability.

Primitive recursive functional open-in-new

Primitive recursive functional