This repository contains accompanying code for my (upcoming) Bachelor's thesis.
Weak timeline :
- Combinatory Algebras
- Applicative Structures
- Feferman structure on an AS
- Combinatorial completeness
- Computation rule for
$\lambda*$ - Combinators
- Identity, booleans, if-then-else, pairs, projections, B combinator, some Curry numerals
- Computation rule for pairs
- Fixpoint combinators and primitive recursion combinator
- Category of Assemblies
- Define assemblies
- Define the category
$\mathsf{Asm}$ - Cartesian closure and similar structure
- Binary products
- Binary coproducts
- Universal property
- Equalisers
- Exponentials
- Initial and terminal objects
-
$\mathsf{Asm}$ is regular
You will need Agda >= 2.6.3 and a custom fork 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.