Lifting swMATH ID: 21010 Software Authors: Brian Huffman, Ondřej Kunčar Description: Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL. Quotients, subtypes, and other forms of type abstraction are ubiquitous in formal reasoning with higher-order logic. Typically, users want to build a library of operations and theorems about an abstract type, but they want to write definitions and proofs in terms of a more concrete representation type, or “raw” type. Earlier work on the Isabelle Quotient package has yielded great progress in automation, but it still has many technical limitations. We present an improved, modular design centered around two new packages: the Transfer package for proving theorems, and the Lifting package for defining constants. Our new design is simpler, applicable in more situations, and has more user-friendly automation. Homepage: https://link.springer.com/chapter/10.1007/978-3-319-03545-1_9 Dependencies: Isabelle Related Software: Transfer; Isabelle/HOL; Archive Formal Proofs; Isabelle; HOL; Coq; Sledgehammer; Autoref; ML; Locales; HOL-Omega; Density Compiler; Mizar; Zoo Probabilistic Systems; pGCL; Nuprl; Berlekamp Zassenhaus; CeTA; Circus; Isabelle/UTP Cited in: 35 Publications all top 5 Cited by 45 Authors 9 Lochbihler, Andreas 4 Divasón, Jose 4 Foster, Simon 4 Thiemann, René 4 Traytel, Dmitry 3 Immler, Fabian 3 Kunčar, Ondřej 3 Popescu, Andrei 3 Schneider, Joshua P. 3 Woodcock, James C. P. 3 Yamada, Akihisa 2 Aransay, Jesús 2 Blanchette, Jasmin Christian 2 Bundy, Alan 2 Cavalcanti, Ana 2 Fürer, Basil 2 Grov, Gudmund 2 Joosten, Sebastiaan J. C. 2 Marić, Filip 2 Pease, Alison 2 Raggi, Daniel 2 Traut, Christoph 2 Zeyda, Frank 1 Basin, David A. 1 Boutry, Pierre 1 Bouzy, Aymeric 1 Canham, Samuel 1 Dunne, Ciarán 1 Fleury, Mathias 1 Guttmann, Walter 1 Hirata, Michikazu 1 Hölzl, Johannes 1 Huffman, Brian 1 Kamareddine, Fairouz D. 1 Lammich, Peter 1 Minamide, Yasuhiko 1 Nipkow, Tobias 1 Petrović, Danijela 1 Roßkopf, Simon 1 Sato, Tetsuya 1 Sefidgar, S. Reza 1 Simić, Danijela 1 Struth, Georg 1 Thiele, Bernhard 1 Wells, Joe B. all top 5 Cited in 7 Serials 14 Journal of Automated Reasoning 1 Theoretical Computer Science 1 Journal of Cryptology 1 Formal Aspects of Computing 1 Annals of Mathematics and Artificial Intelligence 1 Mathematics in Computer Science 1 Logical Methods in Computer Science all top 5 Cited in 17 Fields 34 Computer science (68-XX) 9 Mathematical logic and foundations (03-XX) 3 Commutative algebra (13-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Numerical analysis (65-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Information and communication theory, circuits (94-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Geometry (51-XX) 1 Probability theory and stochastic processes (60-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Citations by Year