  We define polynomial tangle invariants $\nabla_T^s$ via Kauffman states and
Alexander codes and investigate some of their properties. In particular, we
prove symmetry relations for $\nabla_T^s$ of 4-ended tangles and deduce that
the multivariable Alexander polynomial is invariant under Conway mutation. The
invariants $\nabla_T^s$ can be interpreted naturally via Heegaard diagrams for
tangles. This leads to a categorified version of $\nabla_T^s$: a Heegaard Floer
homology $\widehat{\operatorname{HFT}}$ for tangles, which we define as a
bordered sutured invariant. We discuss a bigrading on
$\widehat{\operatorname{HFT}}$ and prove symmetry relations for
$\widehat{\operatorname{HFT}}$ of 4-ended tangles that echo those for
$\nabla_T^s$.
