Porous sets that are Haar null, and nowhere approximately differentiable functions

We define a new notion of ``HP-small'' set $A$ which implies that $A$ is both $\sigma$-porous and Haar null in the sense of Christensen. We show that the set of all continuous functions on $[0,1]$ which have finite unilateral approximate derivative at a point $x\in[0,1]$ is HP-small, as well as its projections onto hyperplanes. As a corollary, the same is true for the set of all Besicovitch functions. Also, the set of continuous functions on $[0,1]$ which are Hölder at a point is HP-small.