  We present a comprehensive set of stellar evolution models for Procyon A in
an effort to guide future measurements of both traditional stellar parameters
and seismic frequencies towards constraining the amount of core overshoot in
Procyon A and possibly other stars. Current observational measurements of
Procyon A when combined with traditional stellar modeling only place a large
upper limit on overshoot of alphaOV < 1.1. By carrying out a detailed pulsation
analysis, we further demonstrate, how p- and g-mode averaged spacings can be
used to gain better estimates of the core size. For both p- and g-modes, the
frequency spacings for models without overshoot are clearly separated from the
models with overshoot. In addition, measurements of the l=0 averaged small
p-mode spacings could be used to establish Procyon A's evolutionary stage. For
a fixed implementation of overshoot and under favorable circumstances, the
g-mode spacings can be used to determine the overshoot extent to an accuracy of
+-0.05 Hp. However, we stress that considerable confusion is added due to the
unknown treatment of the overshoot region. This ambiguity might be removed by
analyzing many different stars. A simple non-local convection theory developed
by Kuhfuss is implemented in our stellar evolution code and contrasted with the
traditional approaches. We show that this theory supports a moderate increase
of the amount of convective overshoot with stellar mass of Delta(alphaOV) =
+0.10 between 1.5 Msun and 15 Msun. This theory places an upper limit on
Procyon A's core overshoot extent of ~0.4 Hp which matches the limit imposed by
Roxburgh's integral criterion.
