A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
Filters
Self-Formalisation of Higher-Order Logic
2016
Journal of automated reasoning
Preserved Fulltext
Soundness of the logic extends to soundness of a theorem prover, because we also show that a synthesised implementation of the kernel in CakeML refines the inference system. ...
Our semantics supports defined constants directly via a context, and we find this approach cleaner than our previous work formalising Wiedijk's Stateless HOL. ...
We are grateful to John Harrison and Freek Wiedijk for providing inspiration for this project. We also thank the anonymous reviewers for carefully reading our submission and suggesting improvements. ...
doi:10.1007/s10817-015-9357-x
fatcat:3dcm7pdklzcrhc37yryjzm3f7u
A Mechanized Theory of Regular Trees in Dependent Type Theory
[chapter]
2015
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Proof assistants are tools developed by computer scientists in order to ease formal reasoning. In this sense, they provide a framework to express statements and properties. ...
Then, by using the proof rules of the underlying logic, theorems are proved and mechanically checked by the machine. ...
First, we give a short introduction to the dependent type theory that serves as the theoretical foundation of all definitions and results presented in the subsequent chapters. ...
doi:10.1007/978-3-319-22102-1_27
fatcat:yoldarn4rbflph37rh3wvwfjy4
To be or not to be constructive, that is not the question
2018
Indagationes mathematicae
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
2017 pre-print arXiv:1704.00462v5 fatcat:pvtvs2xg2vbdtj5dctueaijjveOther Versions
Out of intuitionism grew intuitionistic logic and the associated Brouwer-Heyting-Kolmogorov interpretation by which 'there exists x' intuitively means 'an algorithm to compute x is given'. ...
To this end, we identify a part of classical mathematics, namely classical Nonstandard Analysis, and show it inhabits the twilight-zone between the constructive and non-constructive. ...
An example involving Transfer .
4.3.1. Introduction. ...
doi:10.1016/j.indag.2017.05.005
fatcat:ssfs6tio7vfxdpbhxz4ka5gcsy
A Refinement of de Bruijn's Formal Language of Mathematics
2004
Journal of Logic, Language and Information
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We provide a syntax and a derivation system for a formal language of mathematics called Weak Type Theory (WTT). We give the metatheory of WTT and a number of illustrative examples. ...
The derivation system allows one to establish that a book written in WTT is well-formed following the syntax of WTT, and has great resemblance with ordinary mathematics books. ...
, a set theory (ZF? FM?), etc. The choice of the proof checker: Automath [14] , Isabelle [15] , Coq [2] , PVS [18] , Mizar [17] , etc. ...
doi:10.1023/b:jlli.0000028393.47593.b8
fatcat:4fvkefihbngpddqzcjc5qb7q7a
Computability in constructive type theory
[article]
2022
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We give a formalised and machine-checked account of computability theory in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. ...
Since then, my journey through academia has brought me to many great places and introduced me to many great people. ...
He verifies a universal term and proves Rice's theorem. Forster and Smolka [83] formalise the weak call-by-value λ-calculus in Coq. ...
doi:10.22028/d291-35758
fatcat:deb5muacebhsnnmk5p25mgc7ia
Change actions: from incremental computation to discrete derivatives
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in the analytic sense, that is to say, to provide a common definition of derivative of which ...
To this end we define and explore the notions of change actions and differential maps between change actions and show how these notions relate to incremental computation through the concrete example of ...
On the other hand, a causal map f is ε-linear if and only if it is a group homomorphism in every component except the first. zf ([a i ] + [b i ]) = zf ([a i ]) + zf ([b i ]). ...
arXiv:2002.05256v2
fatcat:o6zzymbz5rcgbgamuqve2fkyou
Evidence for Set-Theoretic Truth and the Hyperuniverse Programme
[chapter]
2017
The Hyperuniverse Project and Maximality
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
For example, the formalisation in Coq of ever more abstract mathematics has turned out to require a deep revision of the concept of identity in Martin-Löf type theory. ...
A widely used proof assistant is Coq, named after Coquand. For formalising mathematics proof theory is indispensable. ...
This is not immediately obvious since it appears we need induction up to ψ θ (ε Ω+1 ), which we do not have access to in KP(P). ...
doi:10.1007/978-3-319-62935-3_4
fatcat:kqy4pyoxtzepjejot5cxup3qtu
LIPIcs, Volume 39, TYPES'14, Complete Volume
[article]
2015
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
I also thank the anonymous referees for their many suggestions that led to major improvements in this paper. This research was partially supported by French ANR project COQUAS (12 JS02 006 01). ...
I want to thank the referees, especially the first one for numerous pertinent and helpful remarks and suggestions.
Typeful Normalization by Evaluation Acknowledgements. ...
We show that ZF ε is a conservative extension of ZF, and that the model N satisfies the axioms of ZF ε , which means that each one of these axioms is realized by a proof-like term. ...
doi:10.4230/lipics.types.2014
fatcat:3zwqtan44jcxfheghkucefqbh4
Organization Programme Committee Organizing Committee
2015
21st International Conference on Types for Proofs and Programs TYPES 2015
unpublished
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
The TYPES meetings are a forum to present new and ongoing work in all aspects of type theory and its applications, especially in formalized and computer assisted reasoning and computer programming. ...
The TYPES conferences are of open and informal character. Selection of contributed talks is based on short abstracts; reporting work in progress and work presented or published elsewhere is welcome. ...
This work was supported by IUT20-56 "Computational models for Estonian", the Swedish Institute, and the European Regional Development Fund through the Estonian Center of Excellence in Computer Science, ...
fatcat:ej5sa3lm7bc6tdhhjd3w3hwos4