Lambda Cube Formalizes Type Dependency Dimensions

The lambda cube, introduced by Henk Barendregt, is a framework in type theory that classifies eight typed lambda calculi by three dependency dimensions (terms on terms, types on terms, types on types). It outlines syntax, β-reduction, typing rules and correspondences—λ→, λ2, λP, λω and λC—and explains expressiveness differences and relevance to language design and proof assistants like Coq.