  An effective equation of state (EoS) which generalizes the Lattimer-Swesty
equation for nuclear matter is presented for matter at supernuclear densities
including strange baryons. It contains an adjustable baryon potential energy
density, based on models of local potentials for the baryon-baryon
interactions. The features of the equation rely on the properties of nuclei for
the nucleon-nucleon interactions, and mainly on experimental data from
hypernuclei for the hyperon-nucleon and hyperon-hyperon interactions. The EoS
is used to calculate equilibrium compositions and thermodynamic properties of
high density matter with strangeness in two astrophysical contexts: neutron
star matter (transparent to neutrinos) and proto-neutron star matter (opaque to
neutrinos). The effective EoS reproduces typical properties of high density
matter found in theoretical microscopic models. Of these, the main result is
that hyperons appear in both types of matter at about twice the nuclear
saturation density, and that their appearance significantly softens the EoS.
The range of maximal masses of neutron stars found in a comprehensive parameter
survey is 1.4-1.7 $M_\odot$. Another typical result is that the maximal mass of
a proto-neutron star with strange baryons is higher than that of an evolved
neutron star (opposite to the case of nuclear matter), setting the stage for a
"delayed collapse" scenario.
