Results 1 
3 of
3
Proofassistants using Dependent Type Systems
, 2001
"... this article we will not attempt to describe all the dierent possible choices of type theories. Instead we want to discuss the main underlying ideas, with a special focus on the use of type theory as the formalism for the description of theories including proofs ..."
Abstract

Cited by 47 (4 self)
 Add to MetaCart
this article we will not attempt to describe all the dierent possible choices of type theories. Instead we want to discuss the main underlying ideas, with a special focus on the use of type theory as the formalism for the description of theories including proofs
The Impact of the Lambda Calculus in Logic and Computer Science
 Bulletin of Symbolic Logic
, 1997
"... One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the represent ..."
Abstract

Cited by 23 (0 self)
 Add to MetaCart
One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand. Acknowledgement. The following persons provided help in various ways. Erik Barendsen, Jon Barwise, Johan van Benthem, Andreas Blass, Olivier Danvy, Wil Dekkers, Marko van Eekelen, Sol Feferman, Andrzej Filinski, Twan Laan, Jan Kuper, Pierre Lescanne, Hans Mooij, Robert Maron, Rinus Plasmeijer, Randy Pollack, Kristoffer Rose, Richard Shore, Rick Statman and Simon Thompson. Partial support came from the European HCM project Typed lambda calculus (CHRXCT920046), the Esprit Working Group Types (21900) and the Dutch NWO project WINST (612316607). 1. Introduction This paper is written to honor Church's gr...
Autarkic Computations in Formal Proofs
 J. Autom. Reasoning
, 1997
"... Formal proofs in mathematics and computer science are being studied because these objects can be verified by a very simple computer program. An important open problem is whether these formal proofs can be generated with an effort not much greater than writing a mathematical paper in, say, L A ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
Formal proofs in mathematics and computer science are being studied because these objects can be verified by a very simple computer program. An important open problem is whether these formal proofs can be generated with an effort not much greater than writing a mathematical paper in, say, L A T E X. Modern systems for proofdevelopment make the formalization of reasoning relatively easy. Formalizing computations such that the results can be used in formal proofs is not immediate. In this paper it is shown how to obtain formal proofs of statements like Prime(61) in the context of Peano arithmetic or (x + 1)(x + 1) = x 2 + 2x + 1 in the context of rings. It is hoped that the method will help bridge the gap between the efficient systems of computer algebra and the reliable systems of proofdevelopment. 1. The problem Usual mathematics is informal but precise. One speaks about informal rigor. Formal mathematics on the other hand consists of definitions, statements and proo...