Definitions
1.NounRecursion to a fixed depth.
2.NounThe operator
ρ
{\displaystyle \rho \,}
that creates a new function from two functions
g
{\displaystyle g\,}
and
h
{\displaystyle h\,}
such that:
ρ
(
g
,
h
)
(
0
,
x
1
,
…
,
x
k
)
=
g
(
x
1
,
…
,
x
k
)
ρ
(
g
,
h
)
(
y
+
1
,
x
1
,
…
,
x
k
)
=
h
(
y
,
ρ
(
g
,
h
)
(
y
,
x
1
,
…
,
x
k
)
,
x
1
,
…
,
x
k
)
{\displaystyle {\begin{aligned}\rho (g,h)(0,x_{1},\ldots ,x_{k})&=g(x_{1},\ldots ,x_{k})\\\rho (g,h)(y+1,x_{1},\ldots ,x_{k})&=h(y,\rho (g,h)(y,x_{1},\ldots ,x_{k}),x_{1},\ldots ,x_{k})\,\end{aligned}}}
.