Frederik Hanghøj Iversen
41e2d02c8d
By Andrea
The reason you cannot use cong in [1] is that §2-fromMonad result type
depends on the input, you need a dependent version of cong:
cong-d : ∀ {ℓ} {A : Set ℓ} {ℓ'} {B : A → Set ℓ'} {x y : A}
→ (f : (x : A) → B x)
→ (eq : x ≡ y)
→ PathP (\ i → B (eq i)) (f x) (f y)
cong-d f p = λ i → f (p i)
I attach a modified Voevodsky.agda.
Notice that the definition of "t" is still highlighted in yellow,
that's because it being a homogeneous path depends on the exact
definition of lem, see the comment with the two definitional equality
constraints.
|
||
|---|---|---|
| libs | ||
| proposal | ||
| report | ||
| src | ||
| .gitignore | ||
| .gitmodules | ||
| BACKLOG.md | ||
| cat.agda-lib | ||
| CHANGELOG.md | ||
| libraries | ||
| Makefile | ||
| README.md | ||
Description
This project aims to formalize some parts of category theory using cubical agda — an extension to agda permitting univalence. To learn more about this readthedocs.
This project draws a lot of inspiration from the HoTT-book.
Installation
Dependencies
To succesfully compile the following is needed:
- The Agda release candidate 2.5.41
- The experimental branch of Agda Standard Library
- Cubical
It's important to have the right version of these - but which one is the right is in constant flux. It's most likely the newest one.
I've used git submodules to manage dependencies. Unfortunately Agda does not allow specifying libraries to be used only as local dependencies. So the submodules are mostly used for documentation.
You can let Agda know about these libraries by appending them to your global libraries file like so: (NB!: There is a good reason this is not in a makefile. So please verify that you know what you are doing, you probably already have standard-library in you libraries)
AGDA_LIB=~/.agda
readlink -f libs/*/*.agda-lib | tee -a $AGDA_LIB/libraries
Anyways, assuming you have this set up you should be good to go.
-
At least version >=
707ce6042b6a3bdb26521f3fe8dfe5d8a8470a43↩︎