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An approach for a simple, general, and unified theory of effectivity on sets with cardinality not greater than that of the continuum is presented. A standard theory of effectivity on F = {f : N 3 N} has been developed in a previous paper. By representations 6: B-* M this theory is extended to other sets M. Topological and recursion theoretical properties of… (More)

- Xiaoming Liu, Christoph Kreitz, Robbert van Renesse, Jason Hickey, Mark Hayden, Kenneth P. Birman +1 other
- SOSP
- 1999

Although building systems from components has attractions, this approach also has problems. Can we be sure that a certain configuration of components is correct? Can it perform as well as a monolithic system? Our paper answers these questions for the Ensemble communication architecture by showing how, with help of the Nuprl formal system, configurations may… (More)

For twenty years the Nuprl (" new pearl ") system has been used to develop software systems and formal theories of computational mathematics. It has also been used to explore and implement computational type theory (CTT) – a formal theory of computation closely related to Martin-Löf's intuitionistic type theory (ITT) and to the calculus of inductive… (More)

- Jason Hickey, Aleksey Nogin, Robert L. Constable, Brian E. Aydemir, Eli Barzilay, Yegor Bryukhov +9 others
- TPHOLs
- 2003

MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCF-style tactic-based proof assistant, a logical… (More)

JProver is a first-order intuitionistic theorem prover that creates sequent-style proof objects and can serve as a proof engine in interactive proof assistants with expressive constructive logics. This paper gives a brief overview of JProver's proof technique, the generation of proof objects, and its integration into the Nuprl proof development system.

In previous papers we have presented a unified Type 2 theory of computability and continuity and a theory of representations. In this paper the concepts developed so far are used for the foundation of a new kind of constructive analysis. Different standard representations of the real numbers are compared. It turns out that the crucial differences are of… (More)

The Intuitionistic Logic Theorem Proving (ILTP) Library provides a platfom for testing and benchmarking theorem provers for first-order intuitionistic logic. It includes a collection of benchmark problems in a standardised syntax and performance results obtained by a comprehensive test of currently available intuitionistic theorem proving systems. These… (More)

The Nuprl system is a framework for reasoning about mathematics and programming. Over the years its design has been substantially improved to meet the demands of large-scale applications. Nuprl LPE, the newest release, features an open, distributed architecture centered around a flexible knowledge base and supports the cooperation of independent formal… (More)