Zobrazeno 1 - 10
of 38
pro vyhledávání: '"GRATZER, DANIEL"'
Simplicial type theory extends homotopy type theory with a directed path type which internalizes the notion of a homomorphism within a type. This concept has significant applications both within mathematics -- where it allows for synthetic (higher) c
Externí odkaz:
http://arxiv.org/abs/2407.09146
When working in Homotopy Type Theory and Univalent Foundations, the traditional role of the category of sets, Set, is replaced by the category hSet of homotopy sets (h-sets); types with h-propositional identity types. Many of the properties of Set ho
Externí odkaz:
http://arxiv.org/abs/2402.04893
We develop a denotational semantics for general reference types in an impredicative version of guarded homotopy type theory, an adaptation of synthetic guarded domain theory to Voevodsky's univalent foundations. We observe for the first time the prof
Externí odkaz:
http://arxiv.org/abs/2307.16608
Autor:
Gratzer, Daniel
We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding type check
Externí odkaz:
http://arxiv.org/abs/2301.11842
Autor:
Kavvos, G. A., Gratzer, Daniel
We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category. The logic
Externí odkaz:
http://arxiv.org/abs/2211.06217
We present a novel mechanism for controlling the unfolding of definitions in dependent type theory. Traditionally, proof assistants let users specify whether each definition can or cannot be unfolded in the remainder of a development; unfolding defin
Externí odkaz:
http://arxiv.org/abs/2210.05420
We contribute the first denotational semantics of polymorphic dependent type theory extended by an equational theory for general (higher-order) reference types and recursive types, based on a combination of guarded recursion and impredicative polymor
Externí odkaz:
http://arxiv.org/abs/2210.02169
Publikováno v:
Logical Methods in Computer Science, Volume 20, Issue 4 (December 12, 2024) lmcs:9266
In this paper we combine the principled approach to modalities from multimodal type theory (MTT) with the computationally well-behaved realization of identity types from cubical type theory (CTT). The result -- cubical modal type theory (Cubical MTT)
Externí odkaz:
http://arxiv.org/abs/2203.13000
Hofmann and Streicher famously showed how to lift Grothendieck universes into presheaf topoi, and Streicher has extended their result to the case of sheaf topoi by sheafification. In parallel, van den Berg and Moerdijk have shown in the context of al
Externí odkaz:
http://arxiv.org/abs/2202.12012
Based on Taylor's hereditarily directed plump ordinals, we define the directed plump ordering on W-types in Martin-L\"of type theory. This ordering is similar to the plump ordering but comes equipped with non-empty finite joins in addition to the usu
Externí odkaz:
http://arxiv.org/abs/2202.07329