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Pascal Voitot mandubian

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mandubian / function1_closed.scala
Created November 12, 2017 22:11
implicit val Function1ClosedCartesianCat: ClosedCartesianCat[Function1] = new ClosedCartesianCat[Function1] {
def id[A]: A => A = identity
def ○[A, B, C]: (B => C) => (A => B) => (A => C) = f => g => f compose g
def ⨂[A, C, D]: (A => C) => (A => D) => (A => (C, D)) = f => g => (a => (f(a), g(a)))
def exl[A, B]: ((A, B)) => A = _._1
def exr[A, B]: ((A, B)) => B = _._2
def it[A]: A => Unit = _ => ()
@mandubian
mandubian / closed.scala
Created November 12, 2017 22:06
trait ClosedCartesianCat[->[_, _]] extends CartesianCat[->] {
def it[A]: A -> Unit
def ap[A, B]: ((A -> B), A) -> B
def curry[A, B, C]: ((A, B) -> C) => (A -> (B :=> C))
def uncurry[A, B, C]: (A -> (B -> C)) => ((A, B) -> C)
}
@mandubian
mandubian / terminal.scala
Created November 12, 2017 21:20
def it[A]: A -> Unit
@mandubian
mandubian / ap.scala
Last active November 12, 2017 21:13
def ap[A, B]: (A -> B, A) -> B
@mandubian
mandubian / cartesian_cat.scala
Created November 12, 2017 13:37
trait CartesianCat[->[_, _]] extends Cat[->] {
def ⨂[A, C, D]: (A -> C) => (A -> D) => (A -> (C, D))
def exl[A, B]: (A, B) -> A
def exr[A, B]: (A, B) -> B
}
@mandubian
mandubian / product_lambda.hs
Last active November 12, 2017 13:38
// lambda calculus augmented with cartesian product (A x B) and 2 projections from (A x B) to A and B
// projection1 from (A x B) to A
𝚷1(a:A, b:B) = a:A
// projection1 from (A x B) to B
𝚷2(a:A, b:B) = b:B
// cartesian product expressed in terms of the 2 projections
(𝚷1(c:A ⨂ B), 𝚷2(c: A ⨂ B)) = (c: A ⨂ B)
@mandubian
mandubian / translate.scala
Last active November 12, 2017 13:02
// simple identity function
def f: A => A = identity
// if I have an implicit Cat[=>] in my scope
val K = implicitly[Cat[Function1]]
// I can rewrite f into the language of categories
def f = K.id[A]
// Both are equivalent by the CHL isomorphism...
@mandubian
mandubian / id_compose.scala
Last active November 12, 2017 12:59
// in the context of a Category
def f: A => B = ???
// ≌ representing isomorphism
f ○ Id ≌ Id ○ f ≌ f
// associativity
(h ○ g) ○ f ≌ h ○ (g ○ f)
@mandubian
mandubian / chou_farci.md
Created November 12, 2017 11:38
  • Prendre un petit chou sinon tu en manges pendant 1 semaine :D
  • le blanchir entier dans eau salée (+bicarbonate pour la couleur et éviter les gaz) 10-15mn mais sans que les feuilles soit molles
  • bien égoutter
  • écarter les feuilles jusqu'au coeur (les feuilles bien blanches/jaunes)
  • enlever la boule de feuiles du coeur
  • les ciseler finement et les ajouter à la farce ci-dessous
  • préparer une farce de porc (type chair à saucisse) 500gr voire moins sinon il t'en restera
  • prendre de la mie de pain rassi et la mouiller avec un peu de lait et l'écraser (pas du pain de mie dégueu harry's, c'est trop sucré)
  • mélanger la mie à la farce
  • faire jaunir un oignon haché assez finement mais pas au mixeur de préférence et l'ajouter à la farce
@mandubian
mandubian / Function1Cat.scala
Created November 11, 2017 20:21
implicit val Function1Cat: Cat[Function1] = new Cat[Function1] {
def id[A]: A => A = identity
def ○[A, B, C]: (B => C) => (A => B) => (A => C) = f => g => f compose g
}