squares 0.1.1 → 0.2

raw patch · 3 files changed

+76/−1 lines, 3 files

Files

• CHANGELOG.md +4/−0
• squares.cabal +2/−1
• src/Data/Functor/Kan/Square.hs +70/−0

@@ -1,5 +1,9 @@ # Revision history for squares +## 0.2 -- 2020-07-08++* Added `Data.Functor.Kan.Square`.+ ## 0.1.1 -- 2020-05-27  * Added `fromRight2`, `fromLeft2`, `toRight2` and `toLeft2` to `Data.Square`.

@@ -1,7 +1,7 @@ cabal-version:       >=1.10  name:                squares-version:             0.1.1+version:             0.2 synopsis:            The double category of Hask functors and profunctors description:         A library for working with natural transformations of type                      .@@ -34,6 +34,7 @@                        Data.Profunctor.Square                        Data.Traversable.Square                        Data.Functor.Adjunction.Square+                       Data.Functor.Kan.Square                        Data.Functor.Rep.Square   build-depends:       base >= 4.9 && < 5                      , profunctors == 5.*

@@ -0,0 +1,70 @@+{-# LANGUAGE DataKinds, RankNTypes, GADTs #-}+-----------------------------------------------------------------------------+-- |+-- Module      :  Data.Functor.Kan.Square+-- License     :  BSD-style (see the file LICENSE)+-- Maintainer  :  sjoerd@w3future.com+--+-----------------------------------------------------------------------------+module Data.Functor.Kan.Square where++import Data.Square+import Data.Profunctor+import Data.Profunctor.Composition+import Data.Functor.Compose.List++-- | The left Kan extension of a functor @f@ along a profunctor @j@.+--+-- The left Kan extension of a functor @f@ along a functor @g@ is @'Lan' ('Data.Profunctor.Costar' g) f@.+data Lan j f b = forall a. Lan (j a b) (f a)++-- |+-- > +--f--++-- > |  v  |+-- > j--@  |+-- > |  v  |+-- > +--L--++lanSquare :: Square '[j] '[] '[f] '[Lan j f]+lanSquare = mkSquare Lan++-- |+-- > +--f--++-- > |  v  |     +--L--++-- > j-\|  |     |  v  |+-- > |  @  | ==> h--@  |+-- > h-/|  |     |  v  |+-- > |  v  |     +--g--++-- > +--g--++--+-- Any square like the one on the left factors through 'lanSquare'.+-- 'lanFactor' gives the remaining square.+lanFactor :: (Profunctor h, IsFList gs) => Square '[j, h] '[] '[f] gs -> Square '[h] '[] '[Lan j f] gs+lanFactor sq = mkSquare $ \h (Lan j f) -> runSquare sq (Procompose h j) f++-- | The right Kan extension of a functor @f@ along a profunctor @j@.+--+-- The right Kan extension of a functor @f@ along a functor @g@ is @'Ran' ('Data.Profunctor.Star' g) f@.+newtype Ran j f a = Ran { runRan :: forall b. j a b -> f b }++-- |+-- > +--R--++-- > |  v  |+-- > j--@  |+-- > |  v  |+-- > +--g--++ranSquare :: Square '[j] '[] '[Ran j g] '[g]+ranSquare = mkSquare $ flip runRan++-- |+-- > +--f--++-- > |  v  |     +--f--++-- > h-\|  |     |  v  |+-- > |  @  | ==> h--@  |+-- > j-/|  |     |  v  |+-- > |  v  |     +--R--++-- > +--g--++--+-- Any square like the one on the left factors through 'ranSquare'.+-- 'ranFactor' gives the remaining square.+ranFactor :: (Profunctor j, IsFList fs) => Square '[h, j] '[] fs '[g] -> Square '[h] '[] fs '[Ran j g]+ranFactor sq = mkSquare $ \h f -> Ran $ \j -> runSquare sq (Procompose j h) f