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Proof and computation

1993
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Annals of Pure and Applied Logic
*

Germany icians working in the fields of

doi:10.1016/0168-0072(93)90193-h
fatcat:2sthqrebordbbavxi45i2ugb7u
*computational*aspects of H. Schwichtenberg. Munich. Germany S S. Wainer, Lewis, United Kingdom*proofs*, logical systems,*and*algebraic specifications. ... Stembraggen, Munich, Gemtany The logical notion of a formal*proof*in various constructive systems can be viewed as a very explicit way to describe a*computation*procedure. ... t "*PROOF**AND**COMPUTATION*" July 20 to August 1, 1993 The "Marktoberdorf Summer School" is a course of two R. ...##
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Proof, understanding, and computers

2020
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Philosophical Problems of Information Technologies and Cyberspace
*

The role of understanding in two types of

doi:10.17726/philit.2020.1.5
fatcat:sschdqixjbdmbf3l2fhk7nkreq
*proof*-traditional conceptual*and**computer*-based-is considered. ... It is shown that the concept of understanding in the framework of the philosophy of mathematics for the case of*computer**proof*is most interesting in the works of the late Wittgenstein. ... Воеводский работал над процедурами проверки*proof*-checkers на основе унивалентных оснований, так чтобы все математические доказательства для публикации сопровождались их машинно-проверяемыми эквивалентами ...##
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Mixing Computations and Proofs

2014
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Journal of Formalized Reasoning
*

We examine the relationship between

doi:10.6092/issn.1972-5787/4552
dblp:journals/jfrea/Beeson16
fatcat:ieften5wunhnnesihejategbku
*proof**and**computation*in mathematics, especially in formalized mathematics. ... We compare the various approaches to*proofs*with a significant*computational*component, including (i) verifying the algorithms, (ii) verifying the results of the unverified algorithms,*and*(iii) trusting ... Mathematics consists of logic*and**computation*, interwoven in tapestries of*proofs*. ...##
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The Robbins problem: computer proofs and human proofs

2001
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Kybernetes
*

Introduction This paper is devoted to a discussion of the relation between

doi:10.1108/eum0000000005698
fatcat:2rkbqkdhrbg6xegqvwh2szmvvu
*computer**proof**and*human*proof*. It is a discussion of the relationship of persons*and*machines. ... In this sense, a*computer*does not , can not produce a*proof*. The*computer*is not convinced of anything. ... A direct*proof*of this fact would solve the Robbins problem by a result of Steve Winker [Winker, S. (1992) ]. ...##
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Proof and Computation in Geometry
[chapter]

2013
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Lecture Notes in Computer Science
*

We consider the relationships between algebra, geometry,

doi:10.1007/978-3-642-40672-0_1
fatcat:syvmbmvp7je7rpppujtew7jo7a
*computation*,*and**proof*.*Computers*have been used to verify geometrical facts by reducing them to algebraic*computations*. ... But this does not produce*computer*-checkable first-order*proofs*in geometry. ... Nevertheless, those*proofs*, if we could find them, would be*proofs**and*not just*computations*. ...##
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Proof nets, garbage, and computations
[chapter]

1997
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Lecture Notes in Computer Science
*

We study the problem of local

doi:10.1007/3-540-62688-3_36
fatcat:e7d5sctfkfcg5ih24rmieubd5a
*and*asynchronous*computation*in the context of multiplicative exponential linear logic (MELL)*proof*nets. ... The proposed reduction system is strongly normalizing*and*con uent. ... We plan to apply the proposed approach to the case of functional languages (pure*and*typed {calculi) both from a theoretical*and*practical (implementative) point of view AG97]. ...##
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Proof nets, garbage, and computations

2001
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Theoretical Computer Science
*

We study the problem of local

doi:10.1016/s0304-3975(00)00094-3
fatcat:eqte4g7d4zezhcpbaywtrgo2u4
*and*asynchronous*computation*in the context of multiplicative exponential linear logic (MELL)*proof*nets. ... The proposed reduction system is strongly normalizing*and*con uent. The*proofs*are all based on pure syntactical reasonings. ... Introduction*Computation*as rewriting is a fundamental paradigm in*computer*science, rooted in the analysis of*computation*of the early days of*computability*theory. ...##
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Proof Theory and Computational Analysis

1997
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BRICS Report Series
*

In this survey paper we start with a discussion how functionals of finite type can be used for the

doi:10.7146/brics.v4i30.18956
fatcat:q2kvu7ah6fhoxky2o6uykd6mvq
*proof*-theoretic extraction of numerical data (e.g. effective<br />uniform bounds*and*rates of convergence ... ) from non-constructive*proofs*in numerical analysis. ...*Proof*: It is clear from the usual*proofs*in analysis that 1)-5) are true. ...##
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Proof theory and computational analysis

1998
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Electronical Notes in Theoretical Computer Science
*

In this survey paper we start with a discussion how functionals of nite type can be used for the

doi:10.1016/s1571-0661(05)80219-1
fatcat:ixrvz2n45jbjffobwhegqgyfxq
*proof*-theoretic extraction of numerical data (e.g. e ective uniform bounds*and*rates of convergence) from ... non-constructive*proofs*in numerical analysis. ... (n) : = 1 36(n+1) 2*and*thus the*computability*of the zero of cos in G 2 R ! ...##
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New Developments in Proofs and Computations
[chapter]

2008
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New Computational Paradigms
*

An example is Tait's

doi:10.1007/978-0-387-68546-5_14
fatcat:4z2kntxwqfbyhbiowa2zj5coey
*proof*of the existence of normal forms for the simply typed λ-calculus, which uses so-called*computability*predicates. ... One only needs to know that certain basic functionals are*computable*(including primitive recursion operators in finite types),*and*that the*computable*functionals are closed under composition. ... Instantiating x with y0*and*z with y1 gives |A(y0)| T x 1 ...xn(y0) y1 , which is ..xn s,y . Assume for simplicity that s is closed. ...##
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DATA INTEGRITY PROOF AND SECURE COMPUTATION IN CLOUD COMPUTING

2012
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Journal of Computer Science
*

This method is used to assure data integrity

doi:10.3844/jcssp.2012.1987.1995
fatcat:6ujwuho32jdr7dpukfelzcezle
*and*secured*computations*with reduced*computational**and*storage overhead of the client. ... One of the important concern is the integrity of data*and**computations*. ... Merkle Hash Tree Pre-*Computed*Tokens Science Publications JCS*Proof*Of Retrievability (POR) Problem Statement One of the important concern is the integrity of data*and**computation*. ...##
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Computer Runtimes and the Length of Proofs
[chapter]

2012
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Lecture Notes in Computer Science
*

It is suggested that theorem provers are subject to the same non-linear tradeoff between time

doi:10.1007/978-3-642-27654-5_17
fatcat:3sbujvawunaevox465jq66jp2m
*and*size as*computer*programs are, affording the possibility of determining optimal timeouts*and*waiting times ... Just as Calude*and*Stay suggest that most Turing machines are fully determined qua termination by a small number of*computational*steps,*and*that the error margin drops drastically, in [8] we have also ... Delahaye with whom I've undertaken related research [7] , studying the output distribution of abstract*computing*machines. ...##
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Herbrand Proofs and Expansion Proofs as Decomposed Proofs

2020
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Journal of Logic and Computation
*

In this paper we construct simple deep inference systems for first-order logic, both with

doi:10.1093/logcom/exaa052
fatcat:bpitzcjaivf4lgrbtb5ueld6ye
*and*without cut, such that 'decomposed'*proofs*—*proofs*where the contractive*and*non-contractive behaviour of the ... Translations between*proofs*in this system, expansion*proofs**and*Herbrand*proofs*are given, retaining much of the structure in each direction. ... the Engineering*and*Physical Sciences Research Council Project EP/K018868/1 Efficient*and*Natural*Proof*Systems*and*the Agence Nationale de la Recherche project FISP ANR-15-CE25-0014-01. ...##
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Program Development by Proof Transformation
[chapter]

1995
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Proof and Computation
*

.) | M ∀ c x A(x) r (∀ c ) − A(r ) (M ∀ c x A(x) r ) A(r ) Restrictions to → +

doi:10.1007/978-3-642-79361-5_1
fatcat:sueg46547ndrlo3hoywapfytda
*and*∀ + (non-*computational*) CV(M) := the set of "*computational*variables" of a derivation M, relative to a fixed assigment ... Seq(M) of a*proof*M consists of its context*and*end formula. ... Two*proofs*of the existence of a maximal end segment for n + 1 ∀ c n ∃ l j≤n+1 ∀ j ≤n+1 (seg(j , n + 1) ≤ seg(j, n + 1)). ...##
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Logic and computation—Interactive proof with Cambridge LCF

1988
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Science of Computer Programming
*

Sadly, sloppy

doi:10.1016/0167-6423(88)90007-x
fatcat:gc5rp3zc5fbtlnj3ga6quv2dne
*and*inaccurate accounts of supposed new results in logic, with inadequate*proofs*or no*proofs*at all, can easily be found in the*computer*science literature. ... Care is taken to present both the*computational*aspect (i.e. the implementation as ML functions)*and*the relation to the*proof*systems of the first part. ...*Proof*rules for some of the operations of the schema calculus are provided*and*are shown to be sound by reference to the semantics. ...
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