Hierarchy Builder: algebraic hierarchies made easy in Coq with Elpi

C Cohen, K Sakaguchi, E Tassi - FSCD 2020-5th International …, 2020‏ - inria.hal.science
It is nowadays customary to organize libraries of machine checked proofs around
hierarchies of algebraic structures [2, 6, 8, 16, 18, 23, 27]. One influential example is the …

On algebraic hierarchies in mathematical repository of Mizar

A Grabowski, A Korniłowicz… - … on Computer Science …, 2016‏ - ieeexplore.ieee.org
Mathematics, especially algebra, uses plenty of structures: groups, rings, integral domains,
fields, vector spaces to name a few of the most basic ones. Classes of structures are closely …

Rapid prototy** formal systems in MMT: 5 case studies

D Müller, F Rabe - arxiv preprint arxiv:1910.10850, 2019‏ - arxiv.org
Logical frameworks are meta-formalisms in which the syntax and semantics of object logics
and related formal systems can be defined. This allows object logics to inherit …

Leveraging the information contained in theory presentations

J Carette, WM Farmer, Y Sharoda - … , CICM 2020, Bertinoro, Italy, July 26 …, 2020‏ - Springer
A theorem prover without an extensive library is much less useful to its potential users.
Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic …

A language feature to unbundle data at will (short paper)

M Al-hassy, J Carette, W Kahl - Proceedings of the 18th ACM SIGPLAN …, 2019‏ - dl.acm.org
Programming languages with sufficiently expressive type systems provide users with
different means of data 'bundling'. Specifically, in dependently-typed languages such as …

Diagram combinators in MMT

F Rabe, Y Sharoda - … : 12th International Conference, CICM 2019, Prague …, 2019‏ - Springer
Formal libraries, especially large ones, usually employ modularity to build and maintain
large theories efficiently. Although the techniques used to achieve modularity vary between …

Automatically proving equivalence by type-safe reflection

F Slama, E Brady - … : 10th International Conference, CICM 2017, Edinburgh …, 2017‏ - Springer
One difficulty with reasoning and programming with dependent types is that proof
obligations arise naturally once programs become even moderately sized. For example …

Simple Type Theory

B Farmer‏ - Springer
2 Answers to Readers' Questions 6 2.1 Why Logic?............................ 6 2.2 Why a Practical
Logic?..................... 6 2.3 Why Simple Type Theory?................... 7 2.4 Why not First-Order …