From 33ef8139751bfc9188be1198881e0dd1638aa621 Mon Sep 17 00:00:00 2001 From: Juan Manuel Gimeno Illa Date: Wed, 16 May 2018 12:35:58 +0200 Subject: [PATCH] Introlenses (16 May 2018) --- introlenses/introlenses.html | 97 +++++++++++++++++++----------------- introlenses/introlenses.lhs | 95 ++++++++++++++++------------------- 2 files changed, 95 insertions(+), 97 deletions(-) diff --git a/introlenses/introlenses.html b/introlenses/introlenses.html index b861373..d4f4860 100644 --- a/introlenses/introlenses.html +++ b/introlenses/introlenses.html @@ -295,7 +295,7 @@

Same again... using a lens to view

view :: Lens' s a -> s -> a view ln s = getConst (ln Const s) 
view :: Lens' s a -> s -> a
@@ -316,9 +316,7 @@ 
From Lens to LensR

 
 lensToLensR :: Lens' s a -> LensR s a
 LensToLensR ln = L { viewR = view ln, setR = set ln }
- -
-

Exercise

+

Exercise

@@ -339,19 +337,17 @@

Let's create a Lens

name elt_fn (P n s) = fmap (\n' -> P n' s) (elt_fn n)
-
name elt_fn (P n s)  = (\n' -> P n' s) <$> (elt_fn n)

Using lens

@@ -376,7 +372,7 @@

How on earth does this work?

= "Fred"
@@ -404,7 +400,7 @@

Composing and using lenses

ln1 . ln2 :: (a -> f a) -> s1 -> f s1
@@ -548,8 +544,8 @@

Fumbling in deep data structures

Traversals

type Lens' s a = forall f. Functor f => (a -> f a) -> s -> f s
type Traversal' s a = forall f. Applicative f => (a -> f a) -> s -> f s
class Applicative f => Monad m where
   return :: a -> m a
   (>>=)  :: m a -> (a -> m b) -> m b
pure = return
 mf <*> mx = do { f <- mf; x <- mx; return (f x)}
@@ -614,34 +610,33 @@

Using Traversals

over :: Lens' s a => (a -> a) -> s -> s
 over ln f = runIdentity . ln (Identify . f)
over :: Traversal' s a -> (a -> a) -> s -> s
 over ln f = runIdentity . ln (Identity . f)
ghci> let fredA = A "71 Humberstone Rd" "Cambridge" "CB4 1JD"
 ghci> over addr_strs toLower fredA
 A "71 humberstone rd" "cambridge" "CB4 1JD"
-
-

...more plase... try 'view'

+
+

...more please... try 'view'

view :: Lens' s a -> s -> a
 view ln s = getConst (ln Const s)
    -
  • Try replacing Lens with Traversal
    • +
  • Try replacing Lens with Traversal
view :: Traversal' s a -> s -> a
 view ln s = getConst (ln Const s)
    -

  • This absolutely can't work! (Why not?)

    • -

  • We need Const to be an instance of Applicative

    • +

  • This absolutely can't work!

    +
      +
    • We need Const to be an instance of Applicative
      • +
-
class Functor f => Applicative f where
-  pure  :: a -> f a
-  (<*>) :: f (a -> b) -> f a -> f b
newtype Const v a = Const v
 
 getConst :: Const v a -> v
@@ -654,8 +649,11 @@ 
...more plase... try 'view'

 instance Monoid a => Applicative (Const a) where
   pure x = Const mempty
   (Const vf) <*> (Const va) = Const (vp `mappend` va)
+
+
+

View on Traversals

    -
  • So 'view' on Traversals does a kind of fold
    • +
  • So view on Traversals does a kind of fold
instance Monoid [a] where
   mempty = []
@@ -663,11 +661,9 @@ 
...more plase... try 'view'

 
ghci> let fredA = A "71 Humberstone Rd" "Cambridge" "CB4 1JD"
 ghci> view addr_strs fredA
 "71 Humberstone RdCambridge"

-
-
-

Non-uniform traversals

+

Non-uniform traversals

    -

  • The foci of a traversal can be highlu selective

    • +

  • The foci of a traversal can be highly selective

  • Every alternate element of a list

  • All the even elements of a tree

  • The 'name' fields of all records in a table whose 'salary' field is > £20,100

    • @@ -675,6 +671,9 @@

    Non-uniform traversals

Composing Traversals

+
    +
  • Traversals and Lenses compose !!!
    • +
type Lens'      s a = forall f. Functor f
                     => (a -> f a) -> s -> f s
 type Traversal' s a = forall f. Applicative f
@@ -700,7 +699,8 @@ 
Unusually for a library, lenses are not abstract

                        => (a -> f a) -> s -> f s)

  • Lenses and traversals would not compose (or would require lots of different functions to do so)

    • -

  • BUT: the inner workings are more exposed

    • +

  • The inner workings are more exposed

    • +

  • But you don't need the lenses library to create lenses (they're only rank-2 functions !!!)

@@ -712,7 +712,8 @@

I have been lying throughout

type Lens s t a b = forall f. Functor f => (a -> f b) -> s -> f t
-

-- over :: Lens' s a -> (a -> a) -> s -> s > over :: Profunctor p => Setting p s t a b -> p a b -> s -> t

+
-- over :: Lens' s a -> (a -> a) -> s -> s
+over :: Profunctor p => Setting p s t a b -> p a b -> s -> t

  • Edward is deeply in thrall to abstractionitis

  • But his Haddocks give lots of instantiations of the incomprehensible most general type

    • @@ -726,28 +727,32 @@

    I have been lying throughout

    There is more. A lot more

    • Prisms (pattern matching)
      • +
    • Folding, traversing, and filtering
    • Indexed lenses
    • Generic programming
    • Interaction with state monads
      • -

    • Folding, traversing, and filtering

      • -
    • lens-3.9.1 has
      • +
    • lens-3.9.1 has +
      • 94 modules
      • 69 classes
      • 39 newtypes
      • 34 data types
        • -

      • 194 type synonyms

        • -

      • Bottom line: this is an idea that goes far

        • +
      • 194 type synonyms
        • +
      • +
    • Bottom line: this is an idea that goes far, very far ...

Take away thoughts

  • A hymn to the power of abstraction

    • -

  • Lenses, and their variants (notabli Traversals), as a composable first-class values, giver remarkable expressive power

    • -
  • It all rests on Haskell's abstraction facilities:
    • +

  • Lenses, and their variants (notably Traversals), as a composable first-class values, giver remarkable expressive power

    • +
  • It all rests on Haskell's abstraction facilities: +
    • Type classes
      • +
    • Higher kinded type variables
    • Higher rank types
      • -

    • Higher kinded type variables

      • +
diff --git a/introlenses/introlenses.lhs b/introlenses/introlenses.lhs index 6d9c1fb..daeefd0 100644 --- a/introlenses/introlenses.lhs +++ b/introlenses/introlenses.lhs @@ -247,7 +247,7 @@ Same again... using a lens to view > view :: Lens' s a -> s -> a > view ln s = getConst (ln Const s) -* Here Const is, deduced by the type inferencer, a -> Const a a +* Here Const is `a -> Const a a`{.haskell} (which is deduced by the type system) * Or, as Edward would write it: @@ -272,7 +272,7 @@ From Lens to LensR > LensToLensR ln = L { viewR = view ln, setR = set ln } Exercise -======== +-------- * Write lensRToLens @@ -294,23 +294,14 @@ Let's create a Lens > name elt_fn (P n s) > = fmap (\n' -> P n' s) (elt_fn n) -* elt_fn - - String -> f String - - element function +* `elt_fn :: String -> f String`{.haskell} + - element function -* \n' -> P n' s - - String -> Person - - It's like a data structure with a hole in it - - It's the function that replaces the name of the given Person +* `(\n' -> P n' s) :: String -> Person`{.haskell} + - It's like a data structure with a hole in it + - It's the function that replaces the name of the given Person -* elt_fn n - - f String - -* fmap is needed to go from f String to f Person given String -> Person - -* I can express it using <$> from Data.Functor - -> name elt_fn (P n s) = (\n' -> P n' s) <$> (elt_fn n) +* `(elt_fn n) :: f String`{.haskell} Using lens ========== @@ -338,7 +329,7 @@ How on earth does this work? * The newtype has no runtime cost -* I just tell the "Functor f =>" which functor dictionary to pass to ln +* I just tell the "`Functor f =>`{.haskell}" which functor dictionary to pass to `ln`{.haskell} * The place where the fmap threw away the function was precisely where the wrapper (the reconstruction function) got discarded giving only the value @@ -370,7 +361,7 @@ Composing and using lenses > ln1 . ln2 :: (a -> f a) -> s1 -> f s1 -* So lens composition is simply function composition, namely (.) +* __So lens composition is simply function composition, namely `(.)`{.haskell}__ !!!! Making lenses easily ==================== @@ -527,9 +518,9 @@ Traversals > type Lens' s a = forall f. Functor f => (a -> f a) -> s -> f s -* We have seen that can instantiate 'f' in various ways +* We have seen that can instantiate `f`{.haskell} in various ways -* But what if we changed "Functor" ? +* But what if we changed `Functor`{.haskell} ? > type Traversal' s a = forall f. Applicative f => (a -> f a) -> s -> f s @@ -545,13 +536,13 @@ What on earth is Applicative? > pure :: a -> f a > (<*>) :: f (a -> b) -> f a -> f b -* A bit like Monad, but weaker +* A bit like `Monad`{.haskell}, but weaker > class Applicative f => Monad m where > return :: a -> m a > (>>=) :: m a -> (a -> m b) -> m b -* Every Monad is an Applicative +* Every `Monad`{.haskell} is an `Applicative`{.haskell} > pure = return > mf <*> mx = do { f <- mf; x <- mx; return (f x)} @@ -597,37 +588,33 @@ Using Traversals > over :: Lens' s a => (a -> a) -> s -> s > over ln f = runIdentity . ln (Identify . f) -* Imagine instead ln :: Traversal' s a, does that work? +* Imagine instead `ln :: Traversal' s a`{.haskell}, does that work? > over :: Traversal' s a -> (a -> a) -> s -> s > over ln f = runIdentity . ln (Identity . f) -* Yes, if Identity is an instance of Applicative, which it is. +* Yes, if `Identity`{.haskell} is an instance of `Applicative`{.haskell} (which it is) -* over in action +* `over`{.haskell} in action < ghci> let fredA = A "71 Humberstone Rd" "Cambridge" "CB4 1JD" < ghci> over addr_strs toLower fredA < A "71 humberstone rd" "cambridge" "CB4 1JD" -...more plase... try 'view' +...more please... try 'view' =========================== > view :: Lens' s a -> s -> a > view ln s = getConst (ln Const s) -* Try replacing Lens with Traversal +* Try replacing `Lens`{.haskell} with `Traversal`{.haskell} > view :: Traversal' s a -> s -> a > view ln s = getConst (ln Const s) -* This absolutely can't work! (Why not?) - -* We need Const to be an instance of Applicative +* This absolutely can't work! -> class Functor f => Applicative f where -> pure :: a -> f a -> (<*>) :: f (a -> b) -> f a -> f b + - We need `Const`{.haskell} to be an instance of `Applicative`{.haskell} > newtype Const v a = Const v > @@ -642,7 +629,10 @@ Using Traversals > pure x = Const mempty > (Const vf) <*> (Const va) = Const (vp `mappend` va) -* So 'view' on Traversals does a kind of fold +View on Traversals +================== + +* So `view`{.haskell} on `Traversals`{.haskell} does a kind of fold > instance Monoid [a] where > mempty = [] @@ -653,9 +643,9 @@ Using Traversals < "71 Humberstone RdCambridge" Non-uniform traversals -====================== +---------------------- -* The foci of a traversal can be highlu selective +* The foci of a traversal can be highly selective - Every alternate element of a list @@ -666,6 +656,8 @@ Non-uniform traversals Composing Traversals ==================== +* Traversals and Lenses compose !!! + > type Lens' s a = forall f. Functor f > => (a -> f a) -> s -> f s > type Traversal' s a = forall f. Applicative f @@ -694,7 +686,9 @@ Unusually for a library, lenses are not abstract * Lenses and traversals would not compose (or would require lots of different functions to do so) -* BUT: the inner workings are more exposed +* The inner workings are more exposed + +* But you don't need the lenses library to create lenses (they're only rank-2 functions !!!) I have been lying throughout ============================ @@ -706,7 +700,7 @@ I have been lying throughout > type Lens s t a b > = forall f. Functor f => (a -> f b) -> s -> f t --- over :: Lens' s a -> (a -> a) -> s -> s +> -- over :: Lens' s a -> (a -> a) -> s -> s > over :: Profunctor p => Setting p s t a b -> p a b -> s -> t * Edward is deeply in thrall to abstractionitis @@ -723,28 +717,27 @@ There is more. A lot more ========================= * Prisms (pattern matching) +* Folding, traversing, and filtering * Indexed lenses * Generic programming * Interaction with state monads -* Folding, traversing, and filtering - * lens-3.9.1 has - - 94 modules - - 69 classes - - 39 newtypes - - 34 data types - - 194 type synonyms + - 94 modules + - 69 classes + - 39 newtypes + - 34 data types + - 194 type synonyms -* Bottom line: this is an idea that goes far +* Bottom line: this is an idea that goes far, very far ... Take away thoughts ================== * A hymn to the power of abstraction -* Lenses, and their variants (notabli Traversals), as a composable first-class values, giver remarkable expressive power +* Lenses, and their variants (notably Traversals), as a composable first-class values, giver remarkable expressive power * It all rests on Haskell's abstraction facilities: - - Type classes - - Higher rank types - - Higher kinded type variables + - Type classes + - Higher kinded type variables + - Higher rank types