Inhabitance of Existential Types is Decidable in Negation-Product Fragment
Makoto Tatsuta, Ken-etsu Fujita, Ryu Hasegawa, Hiroshi Nakano · 2008
This paper shows the inhabitance in the lambda calculus with negation, product, and existential types is decidable. This is proved by showing existential quantification can be eliminated and reducing the problem to provability in intuitionistic propositional logic. By the same technique, this paper also shows existential quantification followed by negation can be replaced by a specific witness in both that system and the system with implication and bottom.