  Merging galaxy clusters often host spectacular diffuse radio synchrotron
sources. These sources can be explained by a non-thermal pool of relativistic
electrons accelerated by shocks and turbulence in the intracluster medium. The
origin of the pool and details of the cosmic ray transport and acceleration
mechanisms in clusters are still open questions. Due to the often extremely
steep spectral indices of diffuse radio emission, it is best studied at low
frequencies. However, the lowest frequency window available to ground-based
telescopes (10-30 MHz) has remained largely unexplored, as radio frequency
interference and calibration problems related to the ionosphere become severe.
Here, we present LOFAR observations from 16 to 168 MHz targeting the famous
cluster Abell 2256. In the deepest-ever images at decametre wavelengths, we
detect and resolve the radio halo, radio shock and various steep spectrum
sources. We measure standard single power-law behaviour for the radio halo and
radio shock spectra and find significant spectral index and curvature
fluctuations across the radio halo, indicating an inhomogeneous emitting
volume. In contrast to the straight power-law spectra of the large-scale
diffuse sources, the various AGN-related sources often show extreme steepening
towards higher frequencies and flattening towards low frequencies. We also
discover a new fossil plasma source with a steep spectrum between 23 and 144
MHz, with $\alpha=-1.9\pm 0.1$. Finally, by comparing radio and gamma-ray
observations, we rule out purely hadronic models for the radio halo origin in
Abell 2256, unless the magnetic field strength in the cluster is exceptionally
high, which is unsupportable by energetic arguments and inconsistent with the
knowledge of other cluster magnetic fields.
