Effective support for custom proof automation is essential for large scale interactive proof development. However, existing languages for automation via *tactics* either (a) provide no way to specifyâ€¦ (More)

Most interactive theorem provers provide support for some form of user-customizable proof automation. In a number of popular systems, such as Coq and Isabelle, this automation is achieved primarilyâ€¦ (More)

During the last 20 years a new applied form of proof theory (sometimes referred to as â€˜proof miningâ€™) has been developed which uses proof-theoretic transformations to extract hidden quantitative andâ€¦ (More)

Coq supports a range of built-in tactics, which are engineered primarily to support backward reasoning. Starting from a desired goal, the Coq programmer can use these tactics to manipulate the proofâ€¦ (More)

This article is devoted to the presentation of Î» rex, an explicit substitution calculus with de Bruijn indexes and a simple notation. By being isomorphic to Î»ex â€“ a recent formalism with variableâ€¦ (More)

Unification is a core component of every proof assistant or programming language featuring dependent types. In many cases, it must deal with higher-order problems up to conversion. Since unificationâ€¦ (More)

Unification is a core component of every proof assistant or programming language featuring dependent types. In many cases, it must deal with higher-order problems up to conversion. Since unificationâ€¦ (More)

The Types Meeting is 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.â€¦ (More)

We provide formal semantics for a large subset of the Lua programming language, in its version 5.2. We validate our model by mechanizing it and testing it against the test suite of the referenceâ€¦ (More)