# How to prove that this function is primitive recursive [closed]

How can I solve the following problem:

$f, \pi, g$ accept one, two and three arguments respectively. If you know that $f, \pi, g$ are primitive recursive functions prove that $h$ defined as:

$\begin{array}{lcl} h(0, y) \simeq f(y) \newline h(x + 1, y) \simeq g(x, y, h(x, \pi(x, y))) \end{array}$ is also primitive recursive function.

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This seems oddly like homework. –  Igor Rivin Nov 23 '11 at 21:25
I voted to re-open, since the critical comments and answers below seem to have overlooked the function $\pi$. A direct instance of primtive recursion would provide $h(x+1,y)$ in terms of $x,y$ and $h(x,y)$, rather than $h(x,\pi(x,y))$ as here. –  Joel David Hamkins Nov 24 '11 at 1:14
Joel is right to point out that this is not just the definition of primitive recursion. Nevertheless, it still looks like homework to me. –  Andreas Blass Nov 24 '11 at 1:29
What resources do you allow yourself? I could mention hints and sources, but if that would "cheapen the grade", I'd rather not say anything. Gerhard "Ask Me About System Design", 2011.11.23 –  Gerhard Paseman Nov 24 '11 at 2:04