absolute-was called into doubt, the more difficult it was for the human being to embrace a cosmic meaning system. But meaning systems cannot be relinquished without some substitute. Perhaps we can forgo the answer to the question, Why do we live? but it is not easy to postpone the question, How shall we live? Modern secular humans face the task of finding some direction to life without an exter...

Elementarily free groups are the finitely generated groups with the same elementary theory as free groups. We prove that elementarily free groups are subgroup separable, answering a question of Zlil Sela. Limit groups arise naturally in the study of the set of homomorphisms to free groups and, in the guise of fully residually free groups, have long been studied in connection with the first-orde...

Abstract datatypes can be typed conveniently using existential types. Even though it is a powerful abstraction mechanism, current type inference systems based on Hindley-Milner do not allow existential types as first-class citizens – every existential type must be explicitly declared, packed, and unpacked using a data constructor. We present an extension of theMLF type system with first-class e...

We integrate existential types into a strongly typed C-like language. In particular, we show how a bad combination of existential types, mutation, and aliasing can cause a subtle violation of type safety. We explore two independent ways to strengthen the type system to restore safety. One restricts the mutation of existential packages. The other restricts the types of aliases of existential pac...