  We are performing a line survey of 8 planet-forming Class II disks in Taurus
with the IRAM NOrthern Extended Millimeter Array (NOEMA), as a part of the
MPG-IRAM Observatory Program PRODIGE (PROtostars and DIsks: Global Evolution;
PIs: P. Caselli and Th. Henning). Compact and extended disks around T Tauri
stars CI, CY, DG, DL, DM, DN, IQ Tau, and UZ Tau E are observed in ~80 lines
from >20 C-, O,- N-, and S-bearing species. The observations in four spectral
settings at 210-280 GHz with $1\sigma$ rms sensitivity of ~ 8-12 mJy/beam at
0.9" and 0.3 km/s resolution will be completed in 2024. The uv-visibilities are
fitted with the DiskFit model to obtain key stellar and disk properties. In
this paper, the combined $^{12}$CO, $^{13}$CO and C$^{18}$O $J = 2-1$ data are
presented. We find that the CO fluxes and disk masses inferred from dust
continuum tentatively correlate with the CO emission sizes. We constrain
dynamical stellar masses, geometries, temperatures, the CO column densities and
gas masses for each disk. The best-fit temperatures at 100 au are ~ 17-37 K,
and decrease radially with the power-law exponent q ~ 0.05-0.76. The inferred
CO column densities decrease radially with the power-law exponent p ~ 0.2-3.1.
The gas masses estimated from $^{13}$CO (2-1) are ~ $0.001-0.2 M_\textrm{Sun}$.
The best-fit CO column densities point to severe CO freeze-out in the disks.
The DL Tau disk is an outlier, and has either stronger CO depletion or lower
gas mass than the rest of the sample. The CO isotopologue ratios are roughly
consistent with the observed values in disks and the low-mass star-forming
regions.
