Gradualizing the calculus of inductive constructions
M Lennon-Bertrand, K Maillard, N Tabareau… - ACM Transactions on …, 2022 - dl.acm.org
We investigate gradual variations on the Calculus of Inductive Construction (CIC) for swifter
prototyping with imprecise types and terms. We observe, with a no-go theorem, a crucial …
prototyping with imprecise types and terms. We observe, with a no-go theorem, a crucial …
Cubical models are cofreely parametric
H Moeneclaey - 2022 - theses.hal.science
A parametric model of type theory is defined as a model where any type comes with a
relation and any term respects these. Intuitively, this means that terms treat their inputs …
relation and any term respects these. Intuitively, this means that terms treat their inputs …
[PDF][PDF] Quotient inductive-inductive types in the setoid model
A Kaposi, Z Xie - 2021 - real.mtak.hu
Introduction. The setoid model of type theory provides a way to bootstrap functional
extensionality [1] and propositional extensionality [3]: the setoid model can be defined in an …
extensionality [1] and propositional extensionality [3]: the setoid model can be defined in an …
[HTML][HTML] A Proof Theoretic Redesign of the Calculus of Dependent Lambda Eliminations
A Marmaduke - 2024 - search.proquest.com
Abstract Language is a medium of expression, both artistic and technical. Like constrained
art, a programming language consists of self-imposed technical restrictions. These …
art, a programming language consists of self-imposed technical restrictions. These …
Internal Strict Propositions Using Point-Free Equations
I Donkó, A Kaposi - 27th International Conference on Types for …, 2022 - drops.dagstuhl.de
The setoid model of Martin-Löf's type theory bootstraps extensional features of type theory
from intensional type theory equipped with a universe of definitionally proof irrelevant (strict) …
from intensional type theory equipped with a universe of definitionally proof irrelevant (strict) …
[PDF][PDF] Bootstrapping extensionality
F Sestini - 2023 - core.ac.uk
Intuitionistic type theory is a formal system designed by Per Martin-Löf to be a full-fledged
foundation in which to develop constructive mathematics. One particular variant, intensional …
foundation in which to develop constructive mathematics. One particular variant, intensional …
[PDF][PDF] Canonicity and Decidability of Equality for Setoid Type Theory
I Donkó, A Kaposi - types22.inria.fr
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