No description
Find a file
2026-04-29 11:08:50 +02:00
.gitignore Initial commit 2025-07-23 01:04:13 +02:00
cwf.agda Merge loic's changes 2026-04-29 11:08:50 +02:00
fibrancy.agda progress on the definition of the CwF 2026-04-26 21:37:45 +02:00
lib.agda progress on the definition of the CwF 2026-04-26 21:37:45 +02:00
nat.agda fix the natural numbers 2026-04-28 22:25:37 +02:00
observational.agda Merge loic's changes 2026-04-29 11:08:50 +02:00
prop.agda Advancing on cwf 2026-04-27 11:24:49 +02:00
README.md fix the natural numbers 2026-04-28 22:25:37 +02:00
setoids.agda progress on the definition of the CwF 2026-04-26 21:37:45 +02:00
typeformers.agda progress on the definition of the CwF 2026-04-26 21:37:45 +02:00
views.agda progress on the definition of the CwF 2026-04-26 21:37:45 +02:00

A strict, proof-relevant setoid model

Revisiting Hofmann's setoid model using PMP's strict presheaves.

  • lib.agda: preliminary definitions. In order to use PMP's construction, we need a definitionally proof-irrelevant equality type with a "strong J" eliminator. This is implemented by the rewrite rule transp-refl.
  • setoids.agda: definition of (PMP-style) setoids, and of the universe of small setoids.
  • typeformers.agda: definition of the setoid of natural numbers, dependent products of setoids, dependent sums, quotients (WIP)
  • views.agda: auxiliary definitions to help doing induction on the universe of small setoids. Proof that the setoid equality is reflexive and symmetric.
  • fibrancy.agda: definition of transitivity for the setoid equality, and type coercion.
  • cwf.agda: arranging all the pieces in a category with families. The resulting CwF supports Pi types (with η) and positive Σ types (without η)
  • nat.agda: adding natural numbers with large elimination to the CwF. Nat is in its own file because it is quite slow to typecheck.
  • observational.agda: adding observational features to the CwF. We define an observational equality which supports funext, propext, UIP. It computes via a cast operator, as in OTT.

TODO: quotients, choice principles, add a second universe level