Some Experiments with Undeenedness

We distinguish two kinds of undeenedness: undeenedness in existence versus undeenedness in information. We give several applications of the rst kind: a rst order formulation of the untyped lambda calculus and a Zermelo-Fraenkel style theory for partial functions which is equally powerful as ZF-Set Theory. We add the rst kind of unde-nedness to a typed lambda calculus, and show that identifying it to the second kind gives inconsistency. Finally, we use it to give an alternative approach to exception handling. A main goal of this paper is to argue that undeenedness is not a single concept which can be approached in diierent ways, but that there are diierent kinds of undeenedness, each having its speciic properties. Some of these kinds can be fruitfully used, and diierent kinds can be combined inside one formalism.