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update readme

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Rachel Lambda Samuelsson 2022-07-28 15:46:00 +02:00
parent 6db8a23d00
commit 7c24f93efc
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README.md
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@ -24,11 +24,13 @@ A dependently typed system
# TODO # TODO
* Universes * Universes (a la tarksi)
* Elaboration * Elaboration
* Implicit arguments * Implicit arguments
* Universe family application * Universe family application
* Syntax level russel universes
* Universe of all other universes? (universe polymorphism)
* Inductives * Inductives
* Indexed inductives * Indexed inductives

4
tests/id.pi
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@ -5,3 +5,7 @@ let transport : Π (A : Type) Π (f : A → Type) Π (x : A) Π (y : A)
let ap : Π (A : Type) Π (B : Type) Π (f : A → B) let ap : Π (A : Type) Π (B : Type) Π (f : A → B)
Π (x : A) Π (y : A) Id A x y → Id B (f x) (f y) Π (x : A) Π (y : A) Id A x y → Id B (f x) (f y)
≔ λA.λB.λf.λx.λy. J A x y (λa.λb.λ_. Id B (f a) (f b)) (refl B (f x)) ≔ λA.λB.λf.λx.λy. J A x y (λa.λb.λ_. Id B (f a) (f b)) (refl B (f x))
let cat : Π (A : Type) Π (x : A) Π (y : A) Π (z : A)
Id A x y → Id A y z → Id A x z
≔ λA.λx.λy.λz.λp.λq. J A y z (λa.λb.λr. Id A x b) (refl A y) q