منابع مشابه
Collections, sets and types
We give a rst order formulation of Church's type theory in which types are mere sets. This formulation is obtained by replacing -calculus by a language of combinators (skolemized comprehension schemes), introducing a distinction between propositions and their contents, relativizing quanti ers and at last replacing typing predicates by membership to some sets. The theory obtained this way has bo...
متن کاملSets in Types, Types in Sets
We present two mutual encodings, respectively of the Calculus of Inductive Constructions in Zermelo-Frrnkel set theory and the opposite way. More precisely, we actually construct two families of en-codings, relating the number of universes in the type theory with the number of inaccessible cardinals in the set theory. The main result is that both hierarchies of logical formalisms interleave w.r...
متن کاملTypes, Sets, and Categories
This essay is an attempt to sketch the evolution of type theory from its beginnings early in the last century to the present day. Central to the development of the type concept has been its close relationship with set theory to begin with and later its even more intimate relationship with category theory. Since it is effectively impossible to describe these relationships (especially in regard t...
متن کاملSets, Types and Type-checking
The underlying set theory of the Z-specification language is said to be a typed set theory. There are two interpretations of this to be found in the literature. One is based upon Simple Type theory and the other on set theory plus a type assignment system. We establish their equivalance.
متن کاملDirected Sets and Cofinal Types
We show that 1, w, ax, u x ux and ["iF" are the only cofinal types of directed sets of size S,, but that there exist many cofinal types of directed sets of size continuum. A partially ordered set D is directed if every two elements of D have an upper bound in D. In this note we consider some basic problems concerning directed sets which have their origin in the theory of Moore-Smith convergence...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 1999
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129598002680