diff --git a/README.org~ b/README.org~ deleted file mode 100644 index 8f2c425..0000000 --- a/README.org~ +++ /dev/null @@ -1,73 +0,0 @@ -# Experiments with Realizability in Univalent Type Theory - -This repository contains accompanying code for my (upcoming) Bachelor's thesis. I am studying categorical realisability through the lens of univalent type theory. - -This formalisation loosely follows my study (see the timeline below). Much of the development has been done inside Agda first, so it is convenient -for me to think using a cubical viewpoint, but most of the results should directly translate over to their Book HoTT analogues. - -This project is very much a work-in-progress, so the code is not very pretty - it is littered with `{!!}` and `--allow-unsolved-metas`. -Most of the holes have comments alongside them that explain how to fill that hole. - -I periodically clean and reorganise the code. - - -# Code Organisation - -- At the highest level, we have combinatory algebra machinery -- Most modules are parameterised by a combinatory algebra `ca : CombinatoryAlgebra A` -- There are modules on the category of assemblies in `Realizability.Assembly` -- Lemmas and stuff relating to the regularity of $\mathsf{Asm}$ is found in `Realizability.Assembly.Regular` -- Tripos modules are to be found in `Realizability.Tripos` - -# Writing - -There are some notes relating to the project on my [abstract non-sense](https://github.com/rahulc29/abstract-nonsense) repository. - -# Build Instructions - -You will need Agda >= 2.6.4 and a [custom fork](https://github.com/rahulc29/cubical/tree/rahulc29/realizability) of the Cubical library to build the code. - -The custom fork has a few additional definitions in the category theory modules. I will hopefully integrate them into the Cubical library. - -# Timeline - -Weak timeline : - -Upto November 2023: - -- [x] Combinatory Algebras - - [x] Applicative Structures - - [x] Feferman structure on an AS - - [x] Combinatorial completeness - - [ ] Computation rule for $\lambda*$ - - Combinators - - [x] Identity, booleans, if-then-else, pairs, projections, B combinator, some Curry numerals - - [x] Computation rule for pairs - - [ ] Fixpoint combinators and primitive recursion combinator -- [x] Category of Assemblies - - [x] Define assemblies - - [x] Define the category $\mathsf{Asm}$ - - [x] Cartesian closure and similar structure - - [x] Binary products - - [x] Binary coproducts - - [x] Universal property - - [x] Equalisers - - [x] Exponentials - - [x] Initial and terminal objects - - [x] Coequalisers (December 2023) - -December 2023: - -- [ ] $\mathsf{Asm}$ is regular - - [x] Kernel pairs of morphisms exist - - [x] Kernel pairs have coequalisers - - [ ] Regular epics stable under pullback -- [ ] Exact completion - - [x] Internal equivalence relations of a category - - [ ] Functional relations -- [ ] Tripos - - [x] Heyting-valued Predicates - - [x] $\forall$ and $\exists$ are adjoints - - [x] Beck-Chevalley condition - - [ ] Heyting prealgebra structure - - [ ] Interpret intuitionistic logic