  We present a simple model for an associating liquid in which polymorphism and
density anomaly are connected. Our model combines a two dimensional lattice gas
with particles interacting through a soft core potential and orientational
degrees of freedom represented through thermal \char`\"{}ice
variables\char`\"{} . The competition between the directional attractive forces
and the soft core potential leads to a phase diagram in which two liquid phases
and a density anomaly are present. The coexistence line between the low density
liquid and the high density liquid has a positive slope contradicting the
surmise that the presence of a density anomaly implies that the high density
liquid is more entropic than the low density liquid.
