There are many evaluation strategies for tensor contractions; naively translating into nested for loops and then doing direct random-access arithmetic is just one approach. If you like numpy's einsum, a drop in replacement is https://optimized-einsum.readthedocs.io/en/stable/. In general, it's an open question as to how to best "compile" a tensor contraction expression into something executable, for several reasons (there are a lot of possible orderings for the contractions, if one wishes to rely on BLAS routines for efficient primitives one will find that they don't exactly fit the problem of tensor contraction like a glove, and so on).