Internal Parametricity

Is internal parametricity useful in theorem proving?

Internal parametricity refers to the ability to claim that ∀u:(∀t.t→t).u=λx.x and similarly for other pi types abstracting over types (this is a ...

[2307.06448] Internal parametricity, without an interval - arXiv

Title:Internal parametricity, without an interval ... Abstract:Parametricity is a property of the syntax of type theory implying, e.g., that there ...

Internal Parametricity, without an Interval - ACM Digital Library

Parametricity is usually proven externally, and does not hold internally. Internalising it is difficult because once there is a term witnessing ...

[2005.11290] Internal Parametricity for Cubical Type Theory - arXiv

Abstract page for arXiv paper 2005.11290: Internal Parametricity for Cubical Type Theory.

Extending Cubical Agda with Internal Parametricity

Such a parametric function necessarily applies the same algorithm irre- spective of the type it is being used at. Reynolds' relational parametricity [15, 13] is ...

A type theory with internal parametricity

[1] Thorsten Altenkirch, Yorgo Chamoun, Ambrus Kaposi, and Michael Shulman. Internal parametricity, without an interval. In Proceedings of the ...

A Nominal Syntax for Internal Parametricity

We define a type theory with internal parametricity together with an operational seman- tics. This is a first step towards the goal of defining cubical type ...

parametric dependent type theory in nLab

Internal parametricity is a statement provable inside the theory ... Unlike the usual internal parametricity, modal internal parametricity ...

Internal parametricity, without an interval - Ambrus Kaposi

▷ explainable: no interval, only low dimensional operations. ▷ computational univalence (unlike cubical type theory). ▷ simple extension of ...

Internal Parametricity for Cubical Type Theory

We also explore the use of internal parametricity beyond the initial forays of Bernardy et al., internally developing the sub-universe of bridge-discrete. Page ...

Internal and Observational Parametricity for Cubical Agda

In this paper, we contribute Agda --bridges: the first practical internally parametric proof assistant. We provide the first mechanized proofs of crucial ...

Internal Parametricity and Cubical Type Theory

Internal Parametricity (Bernardy et al). Can we internalize the rela onal interpreta on in dependent type theory? Page 21. HoTTEST 2019. 8. Internal ...

Internalizing Parametricity - Chalmers Publication Library

Internal Parametricity gives ⌈⌈x⌉⌉ ∶ ⟦A⟧ x. By Abstraction. (giving an explicit parametric witness for x), we get. ⟦⌈⌈x⌉⌉⟧{x↦(x0,x1)} ...

Internal Parametricity for Cubical Type Theory - Semantic Scholar

A computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives is defined, ...

(PDF) Internal parametricity, without an interval - ResearchGate

Internal Parametricity, without an Interval ... Parametricity is a property of the syntax of type theory implying, e.g., that there is only one ...

Internal Parametricity for Cubical Type Theory - Evan Cavallo

Abstrac on theorem: the denota on of any term in simply-typed λ-calculus (with ×, bool) is parametric. Key idea: λ-calculus has a rela onal ...

Internal relational parametricity, without an interval - TYPES 2024

Internal relational parametricity, without an interval. Ambrus Kaposi ... ▷ A type theory with internal parametricity: ▷ relational ...

Parametricity and data kinds - Proof Assistants Stack Exchange

But I don't believe it includes the parametricity aspects induced by irrelevance (at the time internal parametricity was an open question, I ...

[POPL'24] Internal and Observational Parametricity for Cubical Agda

Internal and Observational Parametricity for Cubical Agda (Video, POPL 2024) Antoine Van Muylder, Andreas Nuyts, and Dominique Devriese (KU ...

Internal Parametricity Without an Interval from ACM SIGPLAN

Explore internal parametricity in type theory without explicit geometry. Learn about a simple extension to Martin-Löf type theory and its implications for ...