限制type 为mere propositions,就可以当作做ZFC使用。目前已经在agda ,coq中formalize.
ua : ∀ {i} {A B : Type i} → (A ≃ B) → A == B 对于 同构类型(A ≃ B),它能构造identity type.在agda里边是一条postulate,也就是如果你使用了ua然后编译为程序是无法运行的,因为只给出了类型而没有给出term. 有了ua以后就简单了,只需要把同构扔进ua,再transport一下,我们就得到了一...
EPIT 2020 - Spring School on Homotopy Type Theory TeX10311 M-typesM-typesPublic A formalization of M-types in Agda Agda322 coqcoqPublic Forked fromcoq/coq Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems ...
Brunerie, G., Licata, D., Lumsdaine, P.: Homotopy theory in type theory, lecture notes (2013), [dlicata.wescreates.wesleyan.edu/pubs/bll13homotopy/bll13homotopy.pdf] Brunerie, G., Ljungström, A., Mörtberg, A.: Synthetic Integral Cohomology in Cubical Agda. In: 30th EACSL Annual...
我能够重现计数外延证明以及我其中一个引理的证明,该引理表明您可以从等式两侧移除一个元素并保持等式不变。 这类似于这个:https://github.com/agda/cubical/blob/0d272ccbf6f3b142d1b723cead28209444bc896f/Cubical/HITs/FiniteMultiset/Properties.agda#L183 ...
Cubical type theory offers a solution to this in the form of a new type theory with native support for both univalence and higher inductive types. In this paper we show how the recent cubical extension of Agda can be used to formalize some of the major results of homotopy type theory in ...
This repository contains a development of homotopy type theory and univalent foundations in Agda. The structure of the source code is described below. Setup The code is loosely broken intohott-coreandhott-theoremsAgda libraries. You need Agda 2.5.3 and include at least the path tohott-core.ag...
Homotopy Type Theory的书也写得还可以（目前只看了前六章），看的时候可以配合agda做做证明。
With these extensions, type theory can be used to construct proofs of homotopy-theoretic theorems, in a way that is very amenable to computer-checked proofs in proof assistants such as Coq and Agda. In this paper, we give a computer-checked construction of Eilenberg-MacLane spaces. For an ...
Type U of codes. Coercion El : U →Type, plus operations like Pi : Πa : U, (Ela →U) →U El only respects these operations up to propositional equality: El(Piab) = Πx : Ela, El(bx) Q: higher topos from the syntax of type theory? (Kapulkin). Egbert Rijke, Bas Spitters ...