Formalization of mathematics through proof assistants

Visual Mathematics: Diagrammatic Formalization and Proof

Diagrams have been used for centuries in the visualization of mathematical concepts and to aid the exploration and formalization of ideas. This is hardly surprising given the intuitive appeal of visual languages. Thus it seems very natural to establish how diagrams can play an integral part of mathematical formalization and reasoning, giving them the same status as the symbolic languages that t...

Formalization of Algorithms and Logical Inference Systems in Proof Assistants

Formalization of real analysis: a survey of proof assistants and libraries

interfaces are heavily used to ease statements and proofs (Krebbers and Spitters 2013). Thanks to type classes, the algebraic and order hierarchies (setoid, group, ring, and so on) easily benefit from inheritance. Finally, C-CoRN and Coq’s standard library are not entirely unrelated: Kaliszyk and O’Connor (2009) provide an equivalence lemma between both libraries, under the axioms of the standa...

Proof - assistants using Dependent

Algebraic Proof Assistants in HOL

We explore several ways to formalize the algebraic laws of CSP-like languages in HOL. The intent of the paper is to show how HOL can be tailored to acting as a proof assistant. The emphasis is therefore on the consequences of various choices to be made during the formalization for writing tactics. We end up with a proof assistant that allows a user to make steps of the granularity of an algebra...