Btukfyl

2 $begingroup$ I'm currently working through a few books on computability and I am having a little bit of trouble with the primitive recursive scheme. When defining the primitive recursive scheme for unary functions most authors give something like the following: $text{For function $h$ which is primitive recursive, the function $f$ defined by}$ $$f(0)=m $$ $$f(n+1)=h(n,f(n))$$ is primitive recursive where $m$ is a zero-ary constant function and where $h$ is a binary function. My question is can we view $h$ as a unary function since it seems to depend on only $n$ ? I feel like I could define $g(n)=h(n,f(n))$ where g is unary. This would then violate the requirement that the arity of $h$ be $k+1$ if the arity of $f$ is $k$ . I'm just a little confused about how the arity requirement works in the...