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haskell-notebooks/folds.ipynb
Sanchayan Maity e3beb5ea1d Add folds chapter 
Some exercises we need to finish and some we also need to revisit.

Signed-off-by: Sanchayan Maity <maitysanchayan@gmail.com>
2020-01-26 21:23:28 +05:30

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"{-# LANGUAGE TemplateHaskell #-}\n",
"{-# LANGUAGE FlexibleInstances #-}\n",
"{-# LANGUAGE FlexibleContexts #-}\n",
"{-# LANGUAGE RankNTypes #-}\n",
"{-# LANGUAGE ScopedTypeVariables #-}\n",
"{-# LANGUAGE TypeApplications #-}\n",
"{-# LANGUAGE TypeFamilies #-}\n",
"{-# LANGUAGE InstanceSigs #-}\n",
"{-# LANGUAGE OverloadedStrings #-}\n",
"\n",
"import Control.Lens\n",
"import Numeric.Lens\n",
"import Data.Bits.Lens\n",
"import Data.Data.Lens\n",
"\n",
"import Control.Applicative\n",
"import Data.Char as C\n",
"import qualified Data.Map as M\n",
"import qualified Data.Set as S\n",
"import qualified Data.Text as T\n",
"import qualified Data.List as L\n",
"\n",
"data Role\n",
" = Gunner\n",
" | PowderMonkey\n",
" | Navigator\n",
" | Captain\n",
" | FirstMate\n",
" deriving (Show, Eq, Ord)\n",
" \n",
"data CrewMember =\n",
" CrewMember { _name :: String\n",
" , _role :: Role\n",
" , _talents :: [String]\n",
" } deriving (Show, Eq, Ord)\n",
" \n",
"makeLenses ''CrewMember\n",
"\n",
"roster :: S.Set CrewMember\n",
"roster = S.fromList\n",
" [ CrewMember \"Grumpy Roger\" Gunner [\"Juggling\", \"Arbitrage\"]\n",
" , CrewMember \"Long-John Bronze\" PowderMonkey [\"Origami\"]\n",
" , CrewMember \"Salty Steve\" PowderMonkey [\"Charcuterie\"]\n",
" , CrewMember \"One-eyed jack\" Navigator []\n",
" ]"
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"<interactive>:1:11: error:\n • No instance for (Monoid CrewMember) arising from a use of ‘crewMembers’\n • In the second argument of ‘(^.)’, namely ‘crewMembers’\n In the expression: roster ^. crewMembers\n In an equation for ‘it’: it = roster ^. crewMembers"
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"rosterRoles :: Fold (S.Set CrewMember) Role\n",
"rosterRoles = undefined\n",
"\n",
"crewMembers :: Fold (S.Set CrewMember) CrewMember\n",
"crewMembers = folded\n",
"\n",
":t folded\n",
"\n",
"-- folded :: Foldable f => Fold (f a) a\n",
"\n",
"roster ^. crewMembers"
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"[CrewMember {_name = \"Grumpy Roger\", _role = Gunner, _talents = [\"Juggling\",\"Arbitrage\"]},CrewMember {_name = \"Long-John Bronze\", _role = PowderMonkey, _talents = [\"Origami\"]},CrewMember {_name = \"One-eyed jack\", _role = Navigator, _talents = []},CrewMember {_name = \"Salty Steve\", _role = PowderMonkey, _talents = [\"Charcuterie\"]}]"
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":t toListOf\n",
":t (^..)\n",
"\n",
"-- toListOf :: Fold s a -> s -> [a]\n",
"-- (^..) :: s -> Fold s a -> [a]\n",
"\n",
"toListOf crewMembers roster"
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{
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"[\"Buried Treasure\"]"
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"[]"
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"[\"Cutlass\"]"
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"text/plain": [
"[\"Gold\"]"
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"[\"Captain\",\"First Mate\"]"
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"Just \"Buried Treasure\" ^.. folded\n",
"\n",
"Nothing ^.. folded\n",
"\n",
"Identity \"Cutlass\" ^.. folded\n",
"\n",
"(\"Rubies\", \"Gold\") ^.. folded\n",
"\n",
"M.fromList [(\"Jack\", \"Captain\"), (\"Will\", \"First Mate\")] ^.. folded"
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":t role\n",
"\n",
"crewRole :: Fold CrewMember Role\n",
"crewRole = role\n",
"\n",
"let jerry = CrewMember \"Jerry\" PowderMonkey [\"Ice Cream Making\"]\n",
"\n",
"jerry ^.. crewRole\n",
"\n",
"-- Lens' s a\n",
"-- becomes\n",
"-- Fold s a\n",
"\n",
"roster ^.. folded . role\n",
"\n",
"-- folded :: Fold (S.Set CrewMember) CrewMember\n",
"-- role :: Fold CrewMember Role"
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"[\"Leo\",\"Libra\"]"
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":t both\n",
"\n",
"-- both :: Bitraversable r => Traversal (r a a) (r b b) a b\n",
"-- both :: Bitraversable r => Fold (r a a) a\n",
"\n",
"(\"Gemini\", \"Leo\") ^.. both\n",
"\n",
"Left \"Albuquerque\" ^.. both\n",
"\n",
"Right \"Yosemite\" ^.. both\n",
"\n",
"(\"Gemini\", \"Leo\", \"Libra\") ^.. both"
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":t each\n",
"\n",
"-- each :: Each s t a b => Traversal s t a b\n",
"-- each :: Each s s a a => Fold s a\n",
"\n",
":t traverse\n",
"\n",
"(1, 2, 3, 4, 5) ^.. each\n",
"\n",
"[1, 2, 3, 4, 5] ^.. each\n",
"\n",
"(\"Made him an offer he couldn't refuse\" :: T.Text) ^.. each"
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"### Exercises"
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"[(3,\"Sirens\"),(882,\"Kraken\"),(92,\"Ogopogo\")]"
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"\"SirensKrakenOgopogo\""
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"[\"Captain\",\"First Mate\"]"
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"text/plain": [
"[\"Why\",\"So\",\"Serious?\"]"
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"text/plain": [
"\"HelloIt's me\""
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"[(\"Why\",\"So\",\"Serious?\"),(\"This\",\"is\",\"SPARTA\")]"
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"[1,2,3]"
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"[\"Light\"]"
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"\"DarkSad\""
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"[\"Bond\",\"James\",\"Bond\"]"
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"-- 1.\n",
"\n",
"beastSizes :: [(Int, String)]\n",
"beastSizes = [(3, \"Sirens\"), (882, \"Kraken\"), (92, \"Ogopogo\")]\n",
"\n",
"beastSizes ^.. folded\n",
"\n",
"beastSizes ^.. folded . folded\n",
"\n",
"beastSizes ^.. folded . folded . folded\n",
"\n",
"beastSizes ^.. folded . _2\n",
"\n",
"toListOf (folded . folded) [[1, 2, 3], [4, 5, 6]]\n",
"\n",
"toListOf (folded . folded) (S.fromList [(\"Jack\", \"Captain\"), (\"Will\", \"First Mate\")])\n",
"\n",
"(\"Why\", \"So\", \"Serious?\") ^.. each\n",
"\n",
"(\"Hello\" :: String, \"It's me\" :: String) ^.. both . folded\n",
"\n",
"quotes :: [(T.Text, T.Text, T.Text)]\n",
"quotes = [(\"Why\", \"So\", \"Serious?\"), (\"This\", \"is\", \"SPARTA\")]\n",
"\n",
"quotes ^.. each\n",
"quotes ^.. each . each\n",
"quotes ^.. each . each . each\n",
"\n",
"-- 3.\n",
"\n",
"[1, 2, 3] ^.. each\n",
"\n",
"(\"Light\" :: String, \"Dark\" :: String) ^.. _1\n",
"\n",
"[(\"Light\", \"Dark\"), (\"Happy\", \"Sad\")] ^.. each . each\n",
"\n",
"[(\"Light\", \"Dark\"), (\"Happy\", \"Sad\")] ^.. each . _1\n",
"\n",
"[(\"Light\", \"Dark\") :: (String, String), (\"Happy\", \"Sad\") :: (String, String)] ^.. each . _2 . each\n",
"\n",
"(\"Bond\", \"James\", \"Bond\") ^.. each"
]
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"## Custom Folds"
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"newtype Name = Name\n",
" { getName :: String\n",
" } deriving Show\n",
" \n",
"data ShipCrew = ShipCrew\n",
" { _shipName :: Name\n",
" , _captain :: Name\n",
" , _firstMate :: Name\n",
" , _conscripts :: [Name]\n",
" } deriving (Show)\n",
" \n",
"makeLenses ''ShipCrew\n",
"\n",
"-- folding :: Foldable f => (s -> f a) -> Fold s a\n",
":t folding\n",
"\n",
"collectCrewMembers :: ShipCrew -> [Name]\n",
"collectCrewMembers crew =\n",
" [_captain crew, _firstMate crew] ++ _conscripts crew\n",
" \n",
"crewMembers :: Fold ShipCrew Name\n",
"crewMembers = folding collectCrewMembers\n",
"\n",
"myCrew :: ShipCrew\n",
"myCrew =\n",
" ShipCrew\n",
" { _shipName = Name \"Purple Pearl\"\n",
" , _captain = Name \"Grumpy Roger\"\n",
" , _firstMate = Name \"Long-John Breeze\"\n",
" , _conscripts = [Name \"One-eyed jack\", Name \"Filthy Frank\"]\n",
" }\n",
" \n",
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"### Mapping over folds"
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"\"TWO-FACED TONY\""
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":t to\n",
"\n",
"-- Map the end of our fold\n",
"-- to :: (s -> a) -> Fold s a\n",
"\n",
"-- Technically to is actually a Getter rather than a fold, a Getter is just a fold which has this 1-to-1\n",
"-- mapping property, it’s basically the “getter” half of a lens. A Getter can ALWAYS transform an input\n",
"-- into an output. A pure function s -> a shouldn’t ever fail, so we can make this stronger guarantee.\n",
"-- Since we’re guaranteed an output from to we can use it with view or ^. directly.\n",
"\n",
"Name \"Two-faced Tony\" ^. to getName\n",
"\n",
"Name \"Two-faced Tony\" ^. to getName . to (fmap C.toUpper)\n",
"\n",
"Name \"Two-faced Tony\" ^. to (fmap C.toUpper . getName)\n",
"\n",
"myCrew ^.. crewMembers . to getName"
]
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"### Combining multiple folds"
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":t shipName\n",
":t captain\n",
":t firstMate\n",
":t conscripts\n",
"\n",
"crewNames :: Fold ShipCrew Name\n",
"crewNames =\n",
" folding (\\s -> s ^.. captain\n",
" <> s ^.. firstMate\n",
" <> s ^.. conscripts . folded)\n",
" \n",
"myCrew ^.. crewNames . to getName"
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"## Exercises - Custom Folds"
]
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"\"YerawizardHarry\""
]
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"text/plain": [
"[1,2,4,5]"
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"[[1,2],[4,5]]"
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"[\"bob\",\"otto\",\"hannah\"]"
]
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"data": {
"text/plain": [
"\"cbafed\""
]
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"text/plain": [
"[100,200,300,400,500]"
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"[1,2]"
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"[\"one\",\"two\"]"
]
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"[1,2,3]"
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"[2]"
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"[1,2,3,4,5,6,7,8]"
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"[Left 1,Right 2,Left 3,Right 4]"
]
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"[1,2,3,4,5,6]"
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"-- 1.\n",
"\n",
"-- folding :: Foldable f => (s -> f a) -> Fold s a\n",
"-- Map the end of our fold\n",
"-- to :: (s -> a) -> Fold s a\n",
"\n",
"([\"Yer\", \"a\", \"wizard\", \"Harry\"] :: [String]) ^.. folded . each\n",
"-- ([\"Yer\", \"a\", \"wizard\", \"Harry\"] :: [String]) ^.. folded . folded\n",
"\n",
"[[1, 2, 3], [4, 5, 6]] ^.. folded . folding (take 2)\n",
"\n",
"[[1, 2, 3], [4, 5, 6]] ^.. folded . to (take 2)\n",
"\n",
"[\"bob\", \"otto\", \"hannah\"] ^.. folded . to reverse\n",
"\n",
"(\"abc\", \"def\") ^.. folding (\\(a, b) -> [a, b]). to reverse . folded\n",
"\n",
"-- 2.\n",
"\n",
"[1..5] ^.. folded . to (* 100)\n",
"\n",
"(1, 2) ^.. both\n",
"\n",
"[(1, \"one\"), (2, \"two\")] ^.. folded . _2\n",
"\n",
"(Just 1, Just 2, Just 3) ^.. each . _Just\n",
"\n",
"[Left 1, Right 2, Left 3] ^.. each . _Right\n",
"\n",
"[([1, 2], [3, 4]), ([5, 6], [7, 8])] ^.. folded . each . folded\n",
"\n",
"[1, 2, 3, 4] ^.. folded . to (\\x -> if even x then Right x else Left x)\n",
"\n",
"[(1, (2, 3)), (4, (5, 6))] ^.. folded . folding (\\(a, (b, c)) -> [a, b, c])\n",
"\n",
"-- Couldn't think of these last three by myself :( :(\n",
"\n",
"[(Just 1, Left \"one\"), (Nothing, Right 2)] ^.. folded . folding (\\(a, b) -> a ^.. folded <> b ^.. folded)\n",
"\n",
"[(1, \"one\"), (2, \"two\")] ^.. folded . folding (\\(a, b) -> [Left a, Right b])\n",
"\n",
"S.fromList [\"apricots\", \"apples\"] ^.. folded . folding reverse\n",
"\n",
"-- 3. Bonus\n",
"\n",
"-- [(12, 45, 66), (91, 123, 87)] ^.. _\n",
"-- \"54321\"\n",
"\n",
"-- [(1, \"a\"), (2, \"b\"), (3, \"c\"), (4, \"d\")] ^.. _\n",
"-- [\"b\", \"d\"]"
]
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"source": [
"### Fold Actions"
]
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"True"
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"False"
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"Just 4"
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"elemOf folded 3 [1,2,3,4]\n",
"\n",
"elemOf folded 99 [1,2,3,4]\n",
"\n",
"anyOf folded even [1,2,3,4]\n",
"\n",
"anyOf folded (> 10) [1,2,3,4]\n",
"\n",
"allOf folded even [1,2,3,4]\n",
"\n",
"allOf folded (> 10) [1,2,3,4]\n",
"\n",
"findOf folded even [1, 2, 3, 4]\n",
"\n",
"findOf folded even [1, 2, 3, 4]\n",
"\n",
"has folded []\n",
"\n",
"has folded [1, 2]\n",
"\n",
"hasn't folded []\n",
"\n",
"hasn't folded [1, 2]\n",
"\n",
"lengthOf folded [1, 2, 3, 4]\n",
"\n",
"sumOf folded [1, 2, 3, 4]\n",
"\n",
"productOf folded [1, 2, 3, 4]\n",
"\n",
"firstOf folded []\n",
"\n",
"firstOf folded [1, 2, 3, 4]\n",
"\n",
"preview folded [1, 2, 3, 4]\n",
"\n",
"[1, 2, 3, 4] ^? folded\n",
"\n",
"lastOf folded [1, 2, 3, 4]\n",
"\n",
"minimumOf folded [2, 1, 4, 3]\n",
"\n",
"maximumOf folded [2, 1, 4, 3]\n",
"\n",
"minimumOf folded []\n",
"\n",
"maximumOf folded []"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"### Queries case study"
]
},
{
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"execution_count": 107,
"metadata": {},
"outputs": [],
"source": [
"data Actor =\n",
" Actor { _name :: String\n",
" , _birthYear :: Int \n",
" } deriving (Show, Eq)\n",
"makeLenses ''Actor\n",
"\n",
"data TVShow =\n",
" TVShow { _title :: String\n",
" , _numEpisodes :: Int\n",
" , _numSeasons :: Int\n",
" , _criticScore :: Double\n",
" , _actors :: [Actor]\n",
" } deriving (Show, Eq)\n",
" \n",
"makeLenses ''TVShow\n",
"\n",
"howIMetYourMother :: TVShow\n",
"howIMetYourMother = TVShow\n",
" { _title = \"How I Met your mother\"\n",
" , _numEpisodes = 208\n",
" , _numSeasons = 9\n",
" , _criticScore = 83\n",
" , _actors =\n",
" [ Actor \"Josh Radnor\" 1974\n",
" , Actor \"Cobie Smulders\" 1982\n",
" , Actor \"Neil Patrick Harris\" 1973\n",
" , Actor \"Alyson Hannigan\" 1974\n",
" , Actor \"Jason Segel\" 1980\n",
" ]\n",
" }\n",
" \n",
"buffy :: TVShow\n",
"buffy = TVShow\n",
" { _title = \"Buffy the Vampire Slayer\"\n",
" , _numEpisodes = 144\n",
" , _numSeasons = 7\n",
" , _criticScore = 81\n",
" , _actors =\n",
" [ Actor \"Sarah Michelle Gellar\" 1977\n",
" , Actor \"Alysson Hannigan\" 1974\n",
" , Actor \"Nicholas Brendon\" 1971\n",
" , Actor \"David Boreanaz\" 1969\n",
" , Actor \"Anthony Head\" 1954\n",
" ]\n",
" }\n",
" \n",
"tvShows :: [TVShow]\n",
"tvShows = [ howIMetYourMother\n",
" , buffy\n",
" ]"
]
},
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"sumOf (folded . numEpisodes) tvShows\n",
"\n",
"maximumOf (folded . criticScore) tvShows\n",
"\n",
"-- maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a\n",
"-- maximumByOf :: Fold s a -> (a -> a -> Ordering) -> s -> Maybe a\n",
"\n",
":t maximumByOf\n",
"\n",
"import Data.Ord (comparing)\n",
"\n",
"_title <$> maximumByOf folded (comparing _criticScore) tvShows\n",
"\n",
"minimumByOf (folded . actors . folded) (comparing _birthYear) tvShows\n",
"\n",
"comparingOf :: Ord a => Lens' s a -> s -> s -> Ordering\n",
"comparingOf l = comparing (view l)\n",
"\n",
"minimumByOf (folded . actors . folded) (comparingOf birthYear) tvShows"
]
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"cell_type": "markdown",
"metadata": {},
"source": [
"### Folding with Effects"
]
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"cell_type": "code",
"execution_count": 121,
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"Josh Radnor: 56\n",
"Cobie Smulders: 48\n",
"Neil Patrick Harris: 57\n",
"Alyson Hannigan: 56\n",
"Jason Segel: 50\n",
"Sarah Michelle Gellar: 53\n",
"Alysson Hannigan: 56\n",
"Nicholas Brendon: 59\n",
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"Anthony Head: 76"
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"-- traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()\n",
"-- for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()\n",
"\n",
":t traverseOf_\n",
":t forOf_\n",
"\n",
"-- traverseOf_ :: Functor f => Fold s a -> (a -> f r) -> s -> f ()\n",
"-- forOf_ :: Functor f => Fold s a -> s -> (a -> f r) -> f ()\n",
"\n",
"calcAge :: Actor -> Int\n",
"calcAge actor = 2030 - _birthYear actor\n",
"\n",
"showActor :: Actor -> String\n",
"showActor actor = _name actor <> \": \" <> show (calcAge actor)\n",
"\n",
"traverseOf_ (folded . actors . folded . to showActor) putStrLn tvShows"
]
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{
"cell_type": "markdown",
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"### Combining fold results"
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"-- foldOf :: Monoid a => Fold s a -> s -> a\n",
"-- foldMapOf :: Monoid r => Fold s a -> (a -> r) -> s -> r\n",
"\n",
":t foldOf\n",
":t foldMapOf\n",
"\n",
"import Data.Monoid\n",
"\n",
"ageSummary :: Actor -> (Sum Int, Sum Int)\n",
"ageSummary actor = (Sum 1, Sum (calcAge actor))\n",
"\n",
"computeAverage :: (Sum Int, Sum Int) -> Double\n",
"computeAverage (Sum count, Sum total) = fromIntegral total / fromIntegral count\n",
"\n",
"foldOf (folded . actors . folded . to ageSummary) tvShows\n",
"computeAverage $ foldOf (folded . actors . folded . to ageSummary) tvShows\n",
"\n",
"computeAverage $ foldMapOf (folded . actors . folded) ageSummary tvShows"
]
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"### Using view on folds"
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"\"do it\""
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"\"do it\""
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"\"\""
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"Just \"do it\" ^. folded\n",
"\n",
"-- Just (42 :: Int) ^. folded\n",
"\n",
"-- When there's a single focus, we just return it\n",
"Just \"do it\" ^. folded\n",
"\n",
"-- When there aren't any focuses, return 'mempty'\n",
"Nothing ^. folded :: String\n",
"\n",
"-- When there are multiple focuses, combine them with (<>).\n",
"(\"one\", \"two\", \"three\") ^. each\n",
"\n",
"-- If we want to fold all focusses together, use foldOf"
]
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"fromList [(\"Alyson Hannigan\",1),(\"Alysson Hannigan\",1),(\"Anthony Head\",1),(\"Cobie Smulders\",1),(\"David Boreanaz\",1),(\"Jason Segel\",1),(\"Josh Radnor\",1),(\"Neil Patrick Harris\",1),(\"Nicholas Brendon\",1),(\"Sarah Michelle Gellar\",1)]"
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":t foldByOf\n",
":t foldMapByOf\n",
":t foldrOf\n",
":t foldlOf\n",
"\n",
"foldMapByOf\n",
" (folded . actors . folded . name) -- Focus each actor's name\n",
" (M.unionWith (+)) -- Combine duplicate keys with addition\n",
" mempty -- start with the empty Map\n",
" (\\n -> M.singleton n 1) -- inject names into Maps with a count of 1\n",
" tvShows"
]
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"### Exercises - Fold Actions"
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"text/plain": [
"False"
]
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{
"data": {
"text/plain": [
"\"YoAdrian\""
]
},
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"True"
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"Just 2"
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"True"
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},
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{
"data": {
"text/plain": [
"Just \"racecar\""
]
},
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"text/plain": [
"True"
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"Just (3,\"Be\")"
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{
"data": {
"text/plain": [
"3"
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"Just \"there\""
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{
"data": {
"text/plain": [
"\"cba\""
]
},
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{
"data": {
"text/plain": [
"\"54321\""
]
},
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"data": {
"text/plain": [
"[\"b\",\"d\"]"
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"-- elemOf :: Eq a => Fold s a -> a -> s -> Bool\n",
"-- has :: Fold s a -> s -> Bool\n",
"-- lengthOf :: Fold s a -> s -> Int\n",
"-- sumOf :: Num n => Fold s n -> s -> n\n",
"-- productOf:: Num n => Fold s n -> s -> n\n",
"-- foldOf :: Monoid a => Fold s a -> s -> a\n",
"-- preview :: Fold s a => s -> Maybe a\n",
"-- lastOf :: Fold s a => s -> Maybe a\n",
"-- minimumOf:: Ord a => Fold s a -> s -> Maybe a\n",
"-- maximumOf:: Ord a => Fold s a -> s -> Maybe a\n",
"-- anyOf :: Fold s a -> (a -> Bool) -> s -> Bool\n",
"-- allOf :: Fold s a -> (a -> Bool) -> s -> Bool\n",
"-- findOf :: Fold s a -> (a -> Bool) -> s -> Maybe a\n",
"-- foldrOf :: Fold s a -> (a -> r -> r) -> r -> s -> r\n",
"-- foldMapOf:: Monoid r => Fold s a -> (a -> r) -> s -> r\n",
"\n",
"-- 1.\n",
"\n",
"has folded []\n",
"\n",
"foldOf both (\"Yo\", \"Adrian\")\n",
"\n",
"elemOf each \"phone\" (\"E.T\", \"phone\", \"home\")\n",
"\n",
"findOf folded even [5,7,2,3,13,17,11]\n",
"\n",
"lastOf folded [5,7,2,3,13,17,11]\n",
"\n",
"anyOf folded ((> 9) . length) [\"Bulbasaur\", \"Charmander\", \"Squirtle\"]\n",
"\n",
"findOf folded even [11, 22, 3, 5, 6]\n",
"\n",
"-- 2.\n",
"\n",
"findOf folded (\\xs -> xs == reverse xs) [\"umbrella\", \"olives\", \"racecar\", \"hammer\"]\n",
"\n",
"allOf each even (2, 4, 6)\n",
"\n",
"import Data.Function\n",
"\n",
"maximumByOf folded (compare `on` fst) [(2, \"I'll\"), (3, \"Be\"), (1, \"Back\")]\n",
"\n",
"getSum $ foldMapOf both Sum (1, 2)\n",
"\n",
"-- 3. Could not solve. Copied :(\n",
"\n",
"maximumByOf (folding words) (compare `on` (length . filter (`elem` \"aeiouy\"))) \"Do or do not, there is no try.\"\n",
"\n",
"foldByOf folded (flip (++)) \"\" [\"a\", \"b\", \"c\"]\n",
"\n",
"[(12, 45, 66), (91, 123, 87)] ^.. folded . _2 . to show . to reverse . folded\n",
"\n",
"[(1, \"a\"), (2, \"b\"), (3, \"c\"), (4, \"d\")] ^.. folded . folding (\\(a, b) -> if (even a) then return b else [])"
]
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"source": [
":t taking\n",
":t dropping\n",
"\n",
"-- taking :: Int -> Fold s a -> Fold s a \n",
"-- dropping :: Int -> Fold s a -> Fold s a\n",
"\n",
"[1, 2, 3, 4] ^.. taking 2 folded\n",
"\n",
"[1, 2, 3, 4] ^.. dropping 2 folded\n",
"\n",
"[[1, 2, 3], [10, 20, 30], [100, 200, 300]] ^.. folded . taking 2 folded\n",
"\n",
"(\"Albus\" :: String, \"Dumbledore\" :: String) ^.. both . taking 3 folded\n",
"\n",
"[[1, 2, 3], [10, 20, 30], [100, 200, 300]] ^.. taking 2 (folded . folded)\n",
"\n",
"(\"Albus\" :: String, \"Dumbledore\" :: String) ^.. taking 3 (both . folded)\n",
"\n",
"(\"Albus\" :: String, \"Dumbledore\" :: String) ^.. taking 3 both . folded\n",
"\n",
"[[1, 2, 3], [10, 20, 30], [100, 200, 300]] ^.. (taking 2 folded) . folded\n",
"\n",
"-- ([\"Albus\", \"Dumbledore\"], [\"Severus\", \"Snape\"]) ^.. taking 3 (both . folded)\n",
"\n",
"-- ([\"Albus\", \"Dumbledore\"], [\"Severus\", \"Snape\"]) ^.. taking 3 (both . folded) . folded\n",
" \n",
"[[1, 2, 3], [10, 20, 30], [100, 200, 300]] ^.. dropping 2 (folded . folded)\n",
" \n",
"[[1, 2, 3], [10, 20, 30], [100, 200, 300]] ^.. folded . dropping 2 folded\n",
" \n",
"[[1, 2, 3], [10, 20, 30], [100, 200, 300]] ^.. dropping 2 folded . folded\n",
" \n",
"-- (\"Albus\", \"Dumbledore\") ^.. both . dropping 2 folded\n",
" \n",
"-- (\"Albus\", \"Dumbledore\") ^.. dropping 2 (both . folded)\n",
"\n",
"-- backwards :: Fold s a -> Fold s a\n",
"\n",
":t backwards\n",
"\n",
"[1, 2, 3] ^.. backwards folded\n",
"\n",
"(\"one\", \"two\") ^.. backwards both\n",
"\n",
"[(1, 2), (3, 4)] ^.. backwards (folded . both)\n",
"\n",
"[(1, 2), (3, 4)] ^.. backwards folded . both\n",
"\n",
"[(1, 2), (3, 4)] ^.. folded . backwards both\n",
"\n",
"-- takingWhile :: (a -> Bool) -> Fold s a -> Fold s a\n",
"-- droppingWhile :: (a -> Bool) -> Fold s a -> Fold s a\n",
"\n",
":t takingWhile\n",
":t droppingWhile\n",
"\n",
"[1..100] ^.. takingWhile (<10) folded\n",
"\n",
"[1, 5, 15, 5, 1] ^.. takingWhile (<10) folded\n",
"\n",
"[1..100] ^.. droppingWhile (<90) folded\n",
"\n",
"[1, 5, 15, 5, 1] ^.. droppingWhile (<10) folded"
]
},
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"### Filtering Folds"
]
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"</style><span class='get-type'>filtered :: forall (p :: * -> * -> *) (f :: * -> *) a. (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a</span>"
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"filtered :: forall (p :: * -> * -> *) (f :: * -> *) a. (Choice p, Applicative f) => (a -> Bool) -> Optic' p f a a"
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"[2,4]"
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"text/plain": [
"[\"passionfruit\",\"pomegranate\"]"
]
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"source": [
"-- filtered :: (s -> Bool) -> Fold s s\n",
"\n",
":t filtered\n",
"\n",
"[1, 2, 3, 4] ^.. folded . filtered even\n",
"\n",
"[\"apple\", \"passionfruit\", \"orange\", \"pomegranate\"] ^.. folded . filtered ((> 6) . length)\n",
"\n",
"data Card = \n",
" Card { _name :: String\n",
" , _aura :: Aura\n",
" , _holo :: Bool\n",
" , _moves :: [Move]\n",
" } deriving (Show, Eq)\n",
" \n",
"data Aura\n",
" = Wet\n",
" | Hot\n",
" | Spark\n",
" | Leafy\n",
" deriving (Show, Eq)\n",
"\n",
"data Move =\n",
" Move { _moveName :: String\n",
" , _movePower :: Int\n",
" } deriving (Show, Eq)\n",
" \n",
"makeLenses ''Card\n",
"makeLenses ''Move\n",
"\n",
"deck :: [Card]\n",
"deck = [ Card \"Skwortul\" Wet False [Move \"Squirt\" 20]\n",
" , Card \"Scorchander\" Hot False [Move \"Scord\" 20]\n",
" , Card \"Seedasaur\" Leafy False [Move \"Allergize\" 20]\n",
" , Card \"Kapichu\" Spark False [Move \"Poke\" 10, Move \"Zap\" 30]\n",
" , Card \"Elecdude\" Spark False [Move \"Asplode\" 50]\n",
" , Card \"Garydose\" Wet True [Move \"Gary's move\" 40]\n",
" , Card \"Moisteon\" Wet False [Move \"Soggy\" 3]\n",
" , Card \"Grasseon\" Leafy False [Move \"Leaf Cut\" 30]\n",
" , Card \"Spicyeon\" Hot False [Move \"Capsaicisize\" 40]\n",
" , Card \"Sparkeon\" Spark True [Move \"Shock\" 40, Move \"Battery\" 50]\n",
" ]"
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"5"
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"[\"Asplode\",\"Shock\",\"Battery\"]"
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"source": [
"lengthOf (folded . aura . filtered (== Spark)) deck\n",
"\n",
"lengthOf (folded . moves . folded . movePower . filtered (> 30)) deck\n",
"\n",
"deck ^.. folded . filtered (anyOf (moves . folded . movePower) (> 40)) . name\n",
"\n",
"lengthOf (folded . filtered ((== Spark) . _aura) . moves . folded) deck\n",
"\n",
"deck ^.. folded . filtered ((== Spark) . _aura) . moves . folded . filtered ((> 30) . _movePower) . moveName "
]
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"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"-- filteredBy requires lens-4.18.0 \n",
"\n",
"-- filteredBy :: Fold s a -> Fold s s\n",
"\n",
"-- filteredBy :: Fold s a -> IndexedTraversal' a s s\n",
"\n",
"-- filteredBy :: (Indexable i p, Applicative f) => Getting (First i) a i -> p a (f a) -> a -> f a"
]
}
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