Combine sugar, flour, cornstarch, and salt.
Mix with cherries, adding extract.
Roll out pastry.
Use half to line a deep 9-inch pie pan; trim.
Pour in cherry mixture and dot with butter.
Cut remaining pastry into 5/8-inch strips.
Arrange pastry strips, lattice fashion, over all.
Seal edges with water.
If a glazed topping is desired, carefully brush lattice with evaporated milk or egg white.
Bake in preheated hot oven (425°F.) for 10 minutes; reduce heat to moderate (350° F.) and continue baking about 30 minutes longer, or until crust is well done.