DeepAI

On principal types and well-foundedness of terms in ECC

When we investigate a type system, it is helpful if we can establish the well-foundedness of types or terms with respect to a certain hierarchy, and the Extended Calculus of Constructions (called ECC, defined and studied comprehensively in [Luo, 1994]) is no exception. However, under a very natural hierarchy relation, the well-foundedness of terms does not hold generally. In this article, the well-foundedness are established for two natural families of terms (namely, types in a valid context and terms having normal forms). Also, we give an independent proof of the existence of principal types in ECC since it is used in the proof of well-foundedness of types in a valid context although it is often proved by utilizing the well-foundedness of terms, which would make our argument circular if adopted.

• 1 publication
• 1 publication
• 2 publications
• 1 publication
10/11/2017

Consistency of the Predicative Calculus of Cumulative Inductive Constructions (pCuIC)

In order to avoid well-know paradoxes associated with self-referential d...
03/07/2021

Reduction Free Normalisation for a proof irrelevant type of propositions

We show normalisation and decidability of convertibility for a type theo...
06/01/2018

The encodability hierarchy for PCF types

Working with the simple types over a base type of natural numbers (inclu...
11/15/2017

Statman's Hierarchy Theorem

In the Simply Typed λ-calculus Statman investigates the reducibility rel...
07/07/2020

The Vectorial Lambda Calculus Revisited

We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vec...
02/16/2019

Normalization by Evaluation for Call-by-Push-Value and Polarized Lambda-Calculus

We observe that normalization by evaluation for simply-typed lambda-calc...