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 ...

A nominal syntax for internal parametricity

▷ We don't know how to compute refl= a0 a1 a2. Ambrus Kaposi (University of Nottingham) A nominal syntax for internal parametricity. May 22, ...

[POPL'24] Internal parametricity, without an interval - YouTube

In previous theories with internal parametricity, either an explicit syntax for higher cubes is present or the theory is extended with a new ...

Internalizing Parametricity - Chalmers Publication Library

In the first one we introduce a de- pendent type theory with special syntax for hypercubes. In the second proposal we outline a colored type theory, which ...

(PDF) Internal parametricity, without an interval - ResearchGate

Parametricity is a property of the syntax of type theory implying e.g. that there is only one function having the type of the polymorphic ...

arXiv:2307.06448v2 [cs.LO] 15 Nov 2023

In this paper we define a theory with internal parametricity which does not have explicit geometry in the syntax. Compared to previous theories ...

Towards a cubical type theory without an interval∗ - Ambrus Kaposi

This is in line with Bernardy and Moulin's earlier work on internal parametricity. In this paper we present a naive syntax for internal parametricity and by ...

Higher Inductive Types and Internal Parametricity for Cubical Type ...

I thank my committee for their time, and Dan in particular for suggesting a modal parametric type theory. I thank my many friends at CMU and in ...

Internal Parametricity for Cubical Type Theory - DROPS

Robert Atkey, Neil Ghani, and Patricia Johann. A relationally parametric model of dependent type theory. In The 41st Annual ACM SIGPLAN-SIGACT ...

Ambrus Kaposi

A nominal syntax for internal parametricity: TYPES, Tallinn, 21 May 2015: abstract · Bevezetés a homotópia-típuselméletbe: Eötvös Kollégium, Budapest, 7 Jan ...

Internal Parametricity for Cubical Type Theory - Evan Cavallo

In syntax, we would like to write “H(ah0/xi)(ah1/xi)(λ2x.a)@x”. This does not quite make sense: a is a variable, so ah0/xi = a. We ...

Internal Parametricity for Cubical Type Theory - arXiv

Reynolds translated this apparently syntactic property—the lack of constructs for inspecting types—into a semantic one: if we take a term in ...

(PDF) A dependent nominal type theory - ResearchGate

Internal Parametricity for Cubical Type Theory ... Finally, we apply this syntax to guarded recursion and parametricity. View. Show abstract ... However, in nominal ...

Graduality and Parametricity: Together Again for the First Time

We then show that by modifying the syntax of universal and existential types to make the type name generation explicit, we remove the need for type-directed ...

Nominal Syntax at the Interfaces - Cambridge Scholars Publishing

and Modification, and internal Merge, which is due to the recursive nature of language. ... micro-parametric variation typical of inflectional morphology.

Representing Syntax with Binding using Parametricity - Bob Atkey

To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity.

[PDF] Syntax and models of Cartesian cubical type theory

Internal Parametricity, without an Interval ... Proc. ACM Program. Lang. 2024. TLDR. A gluing model is ...

Parametricity and Local Variables - Internet Archive Scholar

As is well known, re exive graphs in CAT can be equivalently viewed as internal categories in a category of (large enough) re exive graphs. Parametric functors ...

Internal and Observational Parametricity for Cubical Agda - Lirias

f , 𝜆x → f (Agda syntax) or sometimes just x.f . Logical relations between e.g.. x0 and x1 are typically denoted with a postfix r notation xr. Bridges and paths ...

A Parametric Analysis of Nominal Arguments in Classifier Languages

The first type lacks the functional category D in the syntax as well as the lexical intransitivization rule of classifiers (i.e., [-D, -ClINTR] ClLs); this type ...