https://github.com/sstucki/f-omega-int-agda

F-omega with interval kinds mechanized in Agda
https://github.com/sstucki/f-omega-int-agda

agda agda-mechanization interval-kinds proofs semantics subtypes

Last synced: 23 days ago
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F-omega with interval kinds mechanized in Agda

• Host: GitHub
• URL: https://github.com/sstucki/f-omega-int-agda
• Owner: sstucki
• License: mit
• Created: 2017-06-13T14:04:47.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2024-08-01T09:35:51.000Z (4 months ago)
• Last Synced: 2024-08-01T10:56:45.884Z (4 months ago)
• Topics: agda, agda-mechanization, interval-kinds, proofs, semantics, subtypes
• Language: Agda
• Size: 448 KB
• Stars: 13
• Watchers: 2
• Forks: 3
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
f-omega-int-agda – Fω with interval kinds mechanized in Agda

=============================================================

A mechanized type safety proof for Fω extended with interval kinds.

The code in this repository contains an Agda mechanization of the type system Fω extended with *interval kinds* ("F omega int").  An interval kind `A..B` represents a type interval bounded by a pair of types `A`, `B`.  It is inhabited by all proper types `C : A..B` that are both supertypes of `A` and subtypes of `B`.  Interval kinds are flexible enough to express various features found in other type systems, such as

 * F-<:-style bounded polymorphism,

 * bounded type operators,

 * singleton kinds and first-class type definitions.

The mechanization includes a small-step operational call-by-value semantics, declarative and canonical presentations of typing and kinding, along with (syntactic) proofs of various meta-theoretic properties, such as

 * weak normalization of types (and kinds) via hereditary substitution,

 * subject reduction for types (w.r.t. full β-reduction),

 * type safety (progress & preservation) w.r.t. to the CBV semantics,

 * undecidability of subtyping.

The metatheory of Fω with interval kinds is described in our [ICFP'21 paper _A Theory of Higher-Order Subtyping with Type Intervals_](https://doi.org/10.1145/3473574) and, in more detail, in my [PhD dissertation](https://doi.org/10.5075/epfl-thesis-8014).

The Agda mechanization

----------------------

The file `src/README.agda` contains a detailed overview of the formalization.

The theory has been mechanized in [Agda](https://github.com/agda/agda) and makes heavy use of the [Agda standard library](https://github.com/agda/agda-stdlib).  The code in this repository has been type-checked using Agda 2.6.4.3 and version 2.0 of the Agda standard library.  The latest versions of the Agda distribution and standard library, along with setup instructions, can be found at

 * https://github.com/agda/agda

 * https://github.com/agda/agda-stdlib

The easiest way to check all the code is to compile the `README.agda` file from the `src/` directory.  Run

    agda src/README.agda

in the console, or simply open the file using the [Agda Emacs mode](https://agda.readthedocs.io/en/latest/tools/emacs-mode.html) and type `C-c C-l`.

Source code

-----------

The Agda sources are freely available on GitHub:

 * https://github.com/sstucki/f-omega-int-agda

License and copyright

---------------------

The source code is released under the MIT License.  See the `LICENSE` file for details.

------------------------------------------------------------------------

Sandro Stucki — Copyright (c) 2017–2021 EPFL, Sandro Stucki