Researchtype theorydependent typeslambda calculus
Lambda Cube Formalizes Type Dependency Dimensions
4.8
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.
Key Points
- 1Defines cube classifying eight typed lambda calculi by three orthogonal dependency dimensions
- 2Illustrates how dependency combinations change logical expressiveness and computational power across systems
- 3Guides language designers and practitioners on dependent-type features, polymorphism, and proof assistant foundations
Scoring Rationale
Moderate foundational relevance across programming-language theory, limited novelty, and reliance on a secondary source reduces immediate impact.
Sources
Public references used for this report.
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