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2023•Unpublished venueOpen access

Encoding Dependently-Typed Constructions into Simple Type Theory

Anthony Bordg, Adrián Doña Mateo

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Abstract

In this article, we show how one can formalise in type theory mathematical objects, for which dependent types are usually deemed unavoidable, using only simple types. We outline a method to encode most of the terms of Lean's dependent type theory into the simple type theory of Isabelle/HOL. Taking advantage of Isabelle's automation, we illustrate our method with the formalisation in Isabelle/HOL of a mathematical notion developed in the 1980s: strict omega-categories.

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What this paper is about

In this article, we show how one can formalise in type theory mathematical objects, for which dependent types are usually deemed unavoidable, using only simple types. We outline a method to encode most of the terms of Lean's dependent type theory into the simple type theory of Isabelle/HOL. Taking advantage of Isabelle's automation, we illustrate our method with the formalisation in Isabelle/HOL of a mathematical notion developed in the 1980s: strict omega-categories.

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Available abstract

In this article, we show how one can formalise in type theory mathematical objects, for which dependent types are usually deemed unavoidable, using only simple types. We outline a method to encode most of the terms of Lean's dependent type theory into the simple type theory of Isabelle/HOL. Taking advantage of Isabelle's automation, we illustrate our method with the formalisation in Isabelle/HOL of a mathematical notion developed in the 1980s: strict omega-categories.

Key concepts: HOL, Type theory, Simple (philosophy), Computer science, Type (biology), Automation, Proof assistant, Programming language

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