John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church–Rosser theorem in lambda calculus.
He was part of the mathematics department at Cornell University from 1936 to 1963, chairing it several times.
In 1936, he proved Rosser's trick, a stronger version of Gödel's first incompleteness theorem, showing that the requirement for ω-consistency may be weakened to consistency.
The Kleene–Rosser paradox showed that the original lambda calculus was inconsistent.
Rosser died of an aneurysm September 5, 1989, at his home in Madison, Wisconsin.