Algorithm for type conversion / signature matching
I would suggest first solving the all-pairs shortest distance problem on the graph $T$ (or at least the single source version for each $p_i$ as the source) using standard approaches. Then, for each function signature $F_j=f_1,\dots,f_n$, compute $\sum_{i=1}^nd(p_i,f_i)$, where $d(p,f)$ is the distance between $p$ and $f$ (which can be infinite if $f$ is not reachable from $p$), then take the function that achieves the minimum. You should be able to do this in $O(|V|^3+nm)$ if you have $n$ parameters and $m$ functions.