The call type( expr, 'partition' ) returns true if expr is a partition of a positive integer, and returns false otherwise.

A partition of a positive integer $n$ is a list [ $k_1,\mathrm{...},k_r$]. of positive integers $k_i$, whose sum is equal to $n$, and which is non-decreasing, that is, which satisfies $\mathrm{add}\left(k_i\,i=1..r\right)=n$ and $k_i\le k_{i+1}$, for $i$ in $1..r-1$.

$\mathrm{type}\left(\left\{\left\{1\,2\right\}\,\left\{3\,4\right\}\right\}\,'\mathrm{partition}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left[1\,2\,\frac{2}{3}\right]\,'\mathrm{partition}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left[1\,-2\,3\right]\,'\mathrm{partition}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left[1\,2\,3\right]\,'\mathrm{partition}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\left[1\,2\,3\,3\,4\right]\,'\mathrm{partition}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\left[1\,2\,3\,3\,2\right]\,'\mathrm{partition}'\right)$

$\mathrm{false}$