Datatype-Generic Programming Meets Elaborator Reflection

Introduction

This repo contains

• representations for inductive families and generic programs,
• metaprograms and macros for translation between generic and native datatypes/functions,
• connections between generic and native definitions, and
• examples.

There are also highlighted and clickable HTML documents for traversing the modules in the html directory. The start page is Everything.html.

Requirement

• 6GB of memory or above.
• Agda 2.6.4 (or above, with the experimental syntax unquoteDecl data)

Check all modules

Type make to check all modules in the src directory with the patched Agda binary.

Details

src
├── Examples
│   ├── WithMacros
│   │   ├── Acc.agda ----------- Running examples in section 2, 3 and 4.
│   │   ├── List.agda ---------- Examples in section 6.2 and 6.3.
│   │   ├── BST.agda ----------- Examples in section 6.3.
│   │   └── ...
│   └── WithoutMacros
│       └── ...
├── Generics
│   ├── Algebra.agda ----------- Section 2.2 (^1)
│   ├── Description
│   │   └── FixedPoint.agda ---- Section 2.1.
│   ├── Description.agda ------- Section 3, 5.2, 5.3, Figure 1, 2 and 9(^2).
│   ├── Ornament --------------- Section 6.2.
│   │   ├── Algebraic.agda ----- Section 6.2(^3).
│   │   └── ...
│   ├── Recursion.agda --------- Section 3.2, 4.3, Figure 6 and 7(^2).
│   ├── RecursionScheme.agda --- Section 6.1.
│   ├── Reflection ------------- Section 4.
│   │   ├── Connection.agda
│   │   ├── Datatype.agda
│   │   ├── Recursion.agda ----- Section 4.3 and Figure 8(^2).
│   │   ├── Telescope.agda ----- Section 4.2.
│   │   └── Uncurry.agda ------- Section 4.3.
│   ├── SimpleContainer -------- Section 6.3 and Figure 11.
│   │   └── ...
│   └── Telescope.agda --------- Section 3.1, 5.1, Figure 3, 4, 5 and 10(^2).
└── Utils
    ├── Reflection
    │   ├── Print.agda --------- (*)
    │   ├── Tactic.agda -------- Section 4.2.
    │   └── ...
    └── ...

(^1): Alg is renamed to Algᶜˢ in the files.
(^2): Definitions in the main text before section 4 and those in figure 1 to 8 are not universe polymorphic, thus are different from their corresponding definitions in the files. See section 5 for their exact definitions.
(^3): Instead of AlgO and AlgD in section 3.2, an AlgOD that combines both is defined.

(*) To inspect the definition of a datatype D or a function F, import this module and normalise print D or print F (Ctrl+C Ctrl+N in agda mode), the definitions will be printed to the debug buffer(**).
(**) To open the debug buffer, select the *Agda Debug* buffer in Emacs, or execute Agda: Open Debug Buffer in the Command Palette of Visual Studio Code (see agda-mode).

Here's a list of definitions and their intended ways of generation:

	Expression	Declaration	Macro
Data type	N/A	defineByDataD	N/A
DataD			genDataD
DataC			genDataC
Data type wrapper			genDataT
Native Fold/Ind		defineFold defineInd
FoldP/IndP	fold-operator ind-operator	N/A	N/A
FoldC/IndC			genFoldC
Fold/Ind Wrapper			genFoldGT