Results 11 to 20 of about 1,174,960 (285)
Informal proof, formal proof, formalism [PDF]
The Review of Symbolic Logic, 2015 Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations.
Weir, Alan
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A FORMAL PROOF OF THE KEPLER CONJECTURE [PDF]
Forum of Mathematics, Pi, 2017 This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.
THOMAS HALES +21 more
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ONTOLOGICAL PURITY FOR FORMAL PROOFS
The Review of Symbolic Logic, 2023 AbstractPurity is known as an ideal of proof that restricts a proof to notions belonging to the ‘content’ of the theorem. In this paper, our main interest is to develop a conception of purity for formal (natural deduction) proofs. We develop two new notions of purity: one based on an ontological notion of the content of a theorem, and one based on the ...
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Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs
Studia Humana, 2020 The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics.
Krajewski Stanisław
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Studia Humana, 2020 Two crucial concepts of the methodology and philosophy of mathematics are considered: proof and truth. We distinguish between informal proofs constructed by mathematicians in their research practice and formal proofs as defined in the foundations of ...
Murawski Roman
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Automatic Formal Specification and Its Verification of Assembly-Level Sequential Statement Blocks [PDF]
Jisuanji gongcheng, 2019 Formal verification of software is an important means to guarantee the provability,reliability and security of software, but the generation process of traditional formal verification script is complex and requires a lot of manual verification of formal ...
QI Longyun, Lü Xiaoliang, LU Hong, HUANG Hao
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A formally verified compiler back-end [PDF]
, 2008 This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming ...
A Dold +85 more
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Lightweight Interactive Proving inside an Automatic Program Verifier [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 Among formal methods, the deductive verification approach allows establishing the strongest possible formal guarantees on critical software. The downside is the cost in terms of human effort required to design adequate formal specifications and to ...
Sylvain Dailler +2 more
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Isabelle’s Metalogic: Formalization and Proof Checker [PDF]
, 2021 AbstractIsabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an executable (but inefficient) proof term checker and prove its correctness w.r.t. the metalogic.
Tobias Nipkow, Simon Roßkopf
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Improving legibility of natural deduction proofs is not trivial [PDF]
Logical Methods in Computer Science, 2014 In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, but also the readability of the proofs that witness validity ...
Karol Pąk
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