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Add traversals Signed-off-by: Sanchayan Maity <maitysanchayan@gmail.com>
2020-02-08 11:23:57 +01:00
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"<style>/* Styles used for the Hoogle display in the pager */\n",
".hoogle-doc {\n",
"display: block;\n",
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"</style><div class=\"suggestion-name\" style=\"clear:both;\">Unused LANGUAGE pragma</div><div class=\"suggestion-row\" style=\"float: left;\"><div class=\"suggestion-warning\">Found:</div><div class=\"highlight-code\" id=\"haskell\">{-# LANGUAGE TemplateHaskell #-}</div></div><div class=\"suggestion-row\" style=\"float: left;\"><div class=\"suggestion-warning\">Why Not:</div><div class=\"highlight-code\" id=\"haskell\"></div></div><div class=\"suggestion-name\" style=\"clear:both;\">Unused LANGUAGE pragma</div><div class=\"suggestion-row\" style=\"float: left;\"><div class=\"suggestion-warning\">Found:</div><div class=\"highlight-code\" id=\"haskell\">{-# LANGUAGE TypeApplications #-}</div></div><div class=\"suggestion-row\" style=\"float: left;\"><div class=\"suggestion-warning\">Why Not:</div><div class=\"highlight-code\" id=\"haskell\"></div></div><div class=\"suggestion-name\" style=\"clear:both;\">Unused LANGUAGE pragma</div><div class=\"suggestion-row\" style=\"float: left;\"><div class=\"suggestion-warning\">Found:</div><div class=\"highlight-code\" id=\"haskell\">{-# LANGUAGE OverloadedStrings #-}</div></div><div class=\"suggestion-row\" style=\"float: left;\"><div class=\"suggestion-warning\">Why Not:</div><div class=\"highlight-code\" id=\"haskell\"></div></div>"
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"Line 1: Unused LANGUAGE pragma\n",
"Found:\n",
"{-# LANGUAGE TemplateHaskell #-}\n",
"Why not:\n",
"Line 6: Unused LANGUAGE pragma\n",
"Found:\n",
"{-# LANGUAGE TypeApplications #-}\n",
"Why not:\n",
"Line 9: Unused LANGUAGE pragma\n",
"Found:\n",
"{-# LANGUAGE OverloadedStrings #-}\n",
"Why not:"
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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",
"{-# LANGUAGE AllowAmbiguousTypes #-}\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"
]
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"<style>/* Styles used for the Hoogle display in the pager */\n",
".hoogle-doc {\n",
"display: block;\n",
"padding-bottom: 1.3em;\n",
"padding-left: 0.4em;\n",
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".hoogle-code {\n",
"display: block;\n",
"font-family: monospace;\n",
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".hoogle-text {\n",
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".suggestion-name {\n",
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"</style><span class='get-type'>both :: forall (r :: * -> * -> *) (f :: * -> *) a b. (Bitraversable r, Applicative f) => (a -> f b) -> r a a -> f (r b b)</span>"
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"both :: forall (r :: * -> * -> *) (f :: * -> *) a b. (Bitraversable r, Applicative f) => (a -> f b) -> r a a -> f (r b b)"
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"text/plain": [
"[\"Bubbles\",\"Buttercup\"]"
]
},
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"text/plain": [
"(\"Bubbles!\",\"Buttercup!\")"
]
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"text/plain": [
"(\"Blossom\",\"Blossom\")"
]
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"data": {
"text/plain": [
"(7,9)"
]
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"data": {
"text/plain": [
"(10,20,30)"
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"text/plain": [
"[10,20,30]"
]
},
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"data": {
"text/plain": [
"\"HERE'S JOHNNY\""
]
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"ename": "",
"evalue": "",
"output_type": "error",
"traceback": [
"<interactive>:1:43: error:\n • Couldn't match type ‘Int’ with ‘Char’ arising from a use of ‘each’\n • In the first argument of ‘(.~)’, namely ‘each’\n In the second argument of ‘(&)’, namely ‘each .~ (22 :: Int)’\n In the expression: (\"Houston we have a problem\" :: T.Text) & each .~ (22 :: Int)"
]
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"source": [
"-- both is a traversal which focuses both sides of a tuple if it has the same type in each side\n",
"\n",
"-- Specialized to tuples\n",
"-- both :: Traversal (a, a) (b, b) a b\n",
"\n",
"-- General\n",
"-- both :: Bitraversable r => Traversal (r a a) (r b b) a b\n",
"\n",
":t both\n",
"\n",
"(\"Bubbles\", \"Buttercup\") ^.. both\n",
"\n",
"(\"Bubbles\", \"Buttercup\") & both %~ (++ \"!\")\n",
"\n",
"(\"Bubbles\", \"Buttercup\") & both .~ \"Blossom\"\n",
"\n",
"(\"Bubbles\", \"Buttercup\") & both %~ length\n",
"\n",
"(1, 2, 3) & each %~ (*10)\n",
"\n",
"[1, 2, 3] & each %~ (*10)\n",
"\n",
"(\"Here's Johnny\" :: T.Text) & each %~ C.toUpper\n",
"\n",
"(\"Houston we have a problem\" :: T.Text) & each .~ (22 :: Int)"
]
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"metadata": {},
"outputs": [
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"data": {
"text/plain": [
"[10,20,30,4,5]"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"[1,2,3,40,50]"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"\"ONCE UPON A TIME - optics became mainstream\""
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"[1,20,3,40,5]"
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},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"(\"short\",\"gnol yllaer\")"
]
},
"metadata": {},
"output_type": "display_data"
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"source": [
"[1, 2, 3, 4, 5] & taking 3 traversed *~ 10\n",
"\n",
"[1, 2, 3, 4, 5] & dropping 3 traversed *~ 10\n",
"\n",
"-- focus characters until '-'\n",
"\"once upon a time - optics became mainstream\" & takingWhile (/= '-') traversed %~ toUpper\n",
"\n",
"-- filter can be used to filter focuses from a traversal\n",
"\n",
"-- Multiply all even numbers by 10\n",
"[1, 2, 3, 4, 5] & traversed . filtered even *~ 10\n",
"\n",
"-- Reverse only the long strings\n",
"(\"short\", \"really long\") & both . filtered ((> 5) . length) %~ reverse"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"### Traversal Combinators"
]
},
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"execution_count": 23,
"metadata": {},
"outputs": [
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".hoogle-doc {\n",
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".suggestion-name {\n",
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"</style><span class='get-type'>traversed :: forall (p :: * -> * -> *) (f1 :: * -> *) (f2 :: * -> *) a b. (Indexable Int p, Traversable f1, Applicative f2) => p a (f2 b) -> f1 a -> f2 (f1 b)</span>"
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"traversed :: forall (p :: * -> * -> *) (f1 :: * -> *) (f2 :: * -> *) a b. (Indexable Int p, Traversable f1, Applicative f2) => p a (f2 b) -> f1 a -> f2 (f1 b)"
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"[10,20,30]"
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"text/plain": [
"(\"Batman\",\"Sup\")"
]
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"data": {
"text/plain": [
"fromList [(\"Gohan\",\"710\"),(\"Goku\",\"Over 9000\"),(\"Krillin\",\"5000\"),(\"Piccolo\",\"408\")]"
]
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"data": {
"text/plain": [
"Node {rootLabel = \"sneL\", subForest = [Node {rootLabel = \"dloF\", subForest = []},Node {rootLabel = \"lasrevarT\", subForest = []}]}"
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"-- Errors out\n",
"-- [1, 2, 3] & folded %~ (*10)\n",
"\n",
"-- Simplified\n",
"-- traversed :: Traversable f => Traversal (f a) (f b) a b\n",
"\n",
"-- A bit more complex\n",
"-- traversed :: Traversable f => IndexedTraversal Int (f a) (f b) a b\n",
"\n",
"-- Actual\n",
":t traversed\n",
"\n",
"[1, 2, 3] & traversed *~ 10\n",
"\n",
"-- Tuples are traversable over their last slot\n",
"(\"Batman\", \"Superman\") & traversed %~ take 3\n",
"\n",
"let powerLevels = M.fromList [ (\"Gohan\", 710), (\"Goku\", 9001), (\"Krillin\", 5000), (\"Piccolo\", 408) ]\n",
"\n",
"powerLevels & traversed %~ \\n -> if n > 9000 then \"Over 9000\" else show n\n",
"\n",
"import Data.Tree\n",
"\n",
"let opticsTree = Node \"Lens\" [Node \"Fold\" [], Node \"Traversal\" []]\n",
"\n",
"opticsTree & traversed %~ reverse"
]
},
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"cell_type": "markdown",
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"source": [
"### More Combinators"
]
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"text/plain": [
"[\"I'll\",\"be\",\"back!\"]"
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"data": {
"text/plain": [
"[\"Run\",\"Forrest\",\"Run\"]"
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"text/plain": [
"\"*blue* *suede* *shoes*\""
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"text/plain": [
"\"Blue Suede Shoes\""
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"\"#blue\\n#suede\\n#shoes\""
]
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"metadata": {},
"output_type": "display_data"
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"text/plain": [
"\"blue suede shoes\""
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"source": [
"-- worded :: Traversal' String String\n",
"-- lined :: Traversal' String String\n",
"\n",
":t worded\n",
":t lined\n",
"\n",
"\"I'll be back!\" ^.. worded\n",
"\n",
"\"Run\\nForrest\\nRun\" ^.. lined\n",
"\n",
"-- Surround each word with '*'s\n",
"\"blue suede shoes\" & worded %~ \\s -> \"*\" ++ s ++ \"*\"\n",
"\n",
"-- Capitalize each word\n",
"\"blue suede shoes\" & worded %~ \\(x:xs) -> C.toUpper x : xs\n",
"\n",
"-- Add a \"#\" to the start of each line:\n",
"\"blue\\nsuede\\nshoes\" & lined %~ ('#':)\n",
"\n",
"-- Mapping the identity function still has the\n",
"-- white-space collapsing side-effects of `unwords`\n",
"\"blue \\n suede \\n \\n shoes\" & worded %~ id"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Traversing multiple paths at once"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[\"T-Rex\",\"Stegosaurus\"]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[1,2,3,4,5,6,7]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[\"T-Rex\",\"Ankylosaurus\",\"Stegosaurus\"]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"(\"COWABUNGA\",[\"LET'S\",\"ORDER\",\"PIZZA\"])"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"Left (-1,-2)"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"Right [-3,-4]"
]
},
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"source": [
"-- beside :: Traversal s t a b -> Traversal s' t' a b -> Traversal (s, s') (t, t') a b\n",
"\n",
"-- beside :: Lens s t a b -> Lens s' t' a b -> Traversal (s, s') (t, t') a b\n",
"-- beside :: Fold s a -> Fold s' a -> Fold (s, s') a\n",
"\n",
"let dinos = (\"T-Rex\", (42, \"Stegosaurus\"))\n",
"\n",
"dinos ^.. beside id _2\n",
"\n",
"let numbers = ([(1, 2), (3, 4)], [5, 6, 7])\n",
"\n",
"numbers ^.. beside (traversed . both) traversed\n",
"\n",
"(\"T-Rex\", (\"Ankylosaurus\", \"Stegosaurus\")) ^.. beside id both\n",
"\n",
"-- both = beside id id\n",
"\n",
"-- We can modify all characters inside both halves of the tuple\n",
"(\"Cowabunga\", [\"let's\", \"order\", \"pizza\"])\n",
" -- Each half of the tuple has a different path to focus the characters\n",
" & beside traversed (traversed . traversed)\n",
" %~ toUpper\n",
" \n",
"-- beside both traversed :: Traversal' (Either (Int, Int) [Int]) Int\n",
"Left (1, 2) & beside both traversed %~ negate\n",
"\n",
"Right [3, 4] & beside both traversed %~ negate :: Either (Int, Int) [Int]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Focusing a specific traversal element"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
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{
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".suggestion-name {\n",
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"</style><span class='get-type'>element :: forall (p :: * -> * -> *) (t :: * -> *) (f :: * -> *) a. (Indexable Int p, Traversable t, Applicative f) => Int -> p a (f a) -> t a -> f (t a)</span>"
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"Just 2"
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"[0,1,200,3,4]"
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"-- element :: Traversable f => Int -> Traversal' (f a) a\n",
"\n",
":t element\n",
"\n",
"[0, 1, 2, 3, 4] ^? element 2\n",
"\n",
"[0, 1, 2, 3, 4] & element 2 *~ 100\n",
"\n",
"-- elementOf :: Traversal' s a -> Int -> Traversal' s a\n",
"-- elementOf :: Fold s a -> Int -> Fold s a\n",
"\n",
"-- `element` is basically `elementOf traversed`\n",
"[0, 1, 2, 3, 4] ^? elementOf traversed 2\n",
"\n",
"-- We can get a specific element from a composition of traversals\n",
"[[0, 1, 2], [3, 4], [5, 6, 7, 8]] ^? elementOf (traversed . traversed) 6\n",
"\n",
"-- Modify the 6th integer from within nested lists:\n",
"[[0, 1, 2], [3, 4], [5, 6, 7, 8]]\n",
" & elementOf (traversed . traversed) 6 *~ 100"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Composing Traversals"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\"Blue Suede Shoes\""
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"[\"short\",\"*really* *long*\"]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"((\"Rich Ritchie\",100000),(\"Archie\",32),(\"Rich Reggie\",4350))"
]
},
"metadata": {},
"output_type": "display_data"
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"source": [
"-- Capitalize the first char of every word\n",
"\"blue suede shoes\" & worded . taking 1 traversed %~ toUpper\n",
"\n",
"-- Find all strings longer than 5 chars\n",
"-- then surround each word in that string with '*'\n",
"[\"short\", \"really long\"]\n",
" & traversed\n",
" . filtered ((> 5) . length)\n",
" . worded\n",
" %~ \\s -> \"*\" ++ s ++ \"*\"\n",
" \n",
"-- Add \"Rich \" to the names of people with more than $1000\n",
"((\"Ritchie\", 100000), (\"Archie\", 32), (\"Reggie\", 4350))\n",
" & each\n",
" . filtered ((> 1000) . snd)\n",
" . _1\n",
" %~ (\"Rich \" ++)"
]
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises - Simple Traversals"
]
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{
"cell_type": "code",
"execution_count": 67,
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"outputs": [
{
"data": {
"text/plain": [
"(\"N/A\",\"N/A\")"
]
},
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{
"data": {
"text/plain": [
"(\"xxxxxxxx\",\"xxxx\")"
]
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"data": {
"text/plain": [
"(\"Mal\",[\"Kay\",\"Ina\",\"Jay\"])"
]
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"data": {
"text/plain": [
"(\"Malcolm\",[\"Kaylee\",\"River\",\"Jayne\"])"
]
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"text/plain": [
"[\"Die xxxxxxx Day\",\"Live xxx Let Die\",\"You xxxx Live Twice\"]"
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"-- 1.\n",
"\n",
"-- What type of optic do you get when you compose a traversal with a fold?\n",
"-- We get a fold\n",
"\n",
"-- Which of the optics we have learned can act as a traversal?\n",
"-- Lens or Traversal\n",
"\n",
"-- Which of the optics we have learned can act as a fold?\n",
"-- Lens, traversal and fold\n",
"\n",
"-- 2.\n",
"-- Fill in the blank to complete each expression:\n",
"\n",
"(\"Jurassic\", \"Park\") & each .~ \"N/A\"\n",
"\n",
"(\"Jurassic\", \"Park\") & both . traversed .~ 'x'\n",
"\n",
"(\"Malcolm\", [\"Kaylee\", \"Inara\", \"Jayne\"])\n",
" & beside id traversed %~ take 3\n",
"\n",
"(\"Malcolm\", [\"Kaylee\", \"Inara\", \"Jayne\"])\n",
" & _2 . element 1 .~ \"River\"\n",
"\n",
"[\"Die Another Day\", \"Live and Let Die\", \"You Only Live Twice\"]\n",
" & traversed . elementOf worded 1 . traversed .~ 'x'\n",
"\n",
":t each\n",
":t traversed\n",
"\n",
"((True, \"Strawberries\"), (False, \"Blueberries\"), (True, \"Blackberries\")) \n",
" & each . filtered fst . _2 . taking 5 traversed %~ C.toUpper\n",
" \n",
"((True, \"Strawberries\"), (False, \"Blueberries\"), (True, \"Blackberries\"))\n",
" & each %~ snd"
]
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"### Traversal Actions"
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"source": [
":t sequenceA\n",
"\n",
"\n",
"sequenceA [Just 1, Just 2, Just 3]\n",
"\n",
"sequenceA [Just 1, Nothing, Just 3]\n",
"\n",
"sequenceA $ Just (Left \"Whoops\")\n",
"\n",
"sequenceA ([pure 1, pure 2, pure 3] :: [IO Int]) >>= print\n",
"\n",
":t traverse\n",
"\n",
"import Text.Read (readMaybe)\n",
"\n",
":t readMaybe\n",
"\n",
"traverse readMaybe [\"1\", \"2\", \"3\"] :: Maybe [Int]\n",
"\n",
"traverse readMaybe [\"1\", \"snark\", \"3\"] :: Maybe [Int]\n",
"\n",
":t readFile\n",
"\n",
"let results = traverse readFile [\"file1.txt\", \"file2.txt\"]\n",
"\n",
":t results\n",
"\n",
"traverse (\\n -> [n * 10, n * 100]) (\"a\", 10)"
]
},
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"cell_type": "markdown",
"metadata": {},
"source": [
"### Traverse on Traversals"
]
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{
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"execution_count": 81,
"metadata": {},
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"Nothing"
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"[('a','b'),('a','B'),('A','b'),('A','B')]"
]
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"[(\"ab\",\"cd\"),(\"ab\",\"cD\"),(\"ab\",\"Cd\"),(\"ab\",\"CD\"),(\"aB\",\"cd\"),(\"aB\",\"cD\"),(\"aB\",\"Cd\"),(\"aB\",\"CD\"),(\"Ab\",\"cd\"),(\"Ab\",\"cD\"),(\"Ab\",\"Cd\"),(\"Ab\",\"CD\"),(\"AB\",\"cd\"),(\"AB\",\"cD\"),(\"AB\",\"Cd\"),(\"AB\",\"CD\")]"
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"source": [
"-- Specialized signature\n",
"-- traverseOf :: Traversal s t a b -> (a -> f b) -> s -> f t\n",
"\n",
"-- Real signature\n",
"-- traverseOf :: LensLike f s t a b -> (a -> f b) -> s -> f t\n",
"\n",
":t traverse\n",
":t traverseOf\n",
":t traverseOf traversed\n",
"\n",
"traverseOf both readMaybe (\"1\", \"2\") :: Maybe (Int, Int)\n",
"\n",
"traverseOf both readMaybe (\"not a number\", \"2\") :: Maybe (Int, Int)\n",
"\n",
"traverseOf both (\\c -> [toLower c, toUpper c]) ('a', 'b')\n",
"\n",
"traverseOf\n",
" (both . traversed)\n",
" (\\c -> [toLower c, toUpper c])\n",
" (\"ab\", \"cd\")"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Right [(\"Mike\",\"mike@tmnt.io\"),(\"Raph\",\"raph@tmnt.io\"),(\"Don\",\"don@tmnt.io\"),(\"Leo\",\"leo@tmnt.io\")]"
]
},
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"data": {
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"Left \"missing '@': raph.io\""
]
},
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"<style>/* Styles used for the Hoogle display in the pager */\n",
".hoogle-doc {\n",
"display: block;\n",
"padding-bottom: 1.3em;\n",
"padding-left: 0.4em;\n",
"}\n",
".hoogle-code {\n",
"display: block;\n",
"font-family: monospace;\n",
"white-space: pre;\n",
"}\n",
".hoogle-text {\n",
"display: block;\n",
"}\n",
".hoogle-name {\n",
"color: green;\n",
"font-weight: bold;\n",
"}\n",
".hoogle-head {\n",
"font-weight: bold;\n",
"}\n",
".hoogle-sub {\n",
"display: block;\n",
"margin-left: 0.4em;\n",
"}\n",
".hoogle-package {\n",
"font-weight: bold;\n",
"font-style: italic;\n",
"}\n",
".hoogle-module {\n",
"font-weight: bold;\n",
"}\n",
".hoogle-class {\n",
"font-weight: bold;\n",
"}\n",
".get-type {\n",
"color: green;\n",
"font-weight: bold;\n",
"font-family: monospace;\n",
"display: block;\n",
"white-space: pre-wrap;\n",
"}\n",
".show-type {\n",
"color: green;\n",
"font-weight: bold;\n",
"font-family: monospace;\n",
"margin-left: 1em;\n",
"}\n",
".mono {\n",
"font-family: monospace;\n",
"display: block;\n",
"}\n",
".err-msg {\n",
"color: red;\n",
"font-style: italic;\n",
"font-family: monospace;\n",
"white-space: pre;\n",
"display: block;\n",
"}\n",
"#unshowable {\n",
"color: red;\n",
"font-weight: bold;\n",
"}\n",
".err-msg.in.collapse {\n",
"padding-top: 0.7em;\n",
"}\n",
".highlight-code {\n",
"white-space: pre;\n",
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"}\n",
".suggestion-warning { \n",
"font-weight: bold;\n",
"color: rgb(200, 130, 0);\n",
"}\n",
".suggestion-error { \n",
"font-weight: bold;\n",
"color: red;\n",
"}\n",
".suggestion-name {\n",
"font-weight: bold;\n",
"}\n",
"</style><span class='get-type'>sequenceAOf :: forall (f :: * -> *) s t b. LensLike f s t (f b) b -> s -> f t</span>"
],
"text/plain": [
"sequenceAOf :: forall (f :: * -> *) s t b. LensLike f s t (f b) b -> s -> f t"
]
},
"metadata": {},
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{
"data": {
"text/plain": [
"Just (\"Garfield\",\"Lasagna\")"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"Nothing"
]
},
"metadata": {},
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{
"data": {
"text/plain": [
"Just ([\"apples\"],[\"oranges\"])"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
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"Nothing"
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"source": [
"validateEmail :: String -> Either String String\n",
"validateEmail email | elem '@' email = Right email\n",
" | otherwise = Left (\"missing '@': \" <> email)\n",
" \n",
"traverseOf (traversed . _2) validateEmail\n",
" [ (\"Mike\", \"mike@tmnt.io\")\n",
" , (\"Raph\", \"raph@tmnt.io\")\n",
" , (\"Don\", \"don@tmnt.io\")\n",
" , (\"Leo\", \"leo@tmnt.io\")\n",
" ]\n",
" \n",
"traverseOf (traversed . _2) validateEmail\n",
" [ (\"Mike\", \"mike@tmnt.io\")\n",
" , (\"Raph\", \"raph.io\")\n",
" , (\"Don\", \"don@tmnt.io\")\n",
" , (\"Leo\", \"leo@tmnt.io\")\n",
" ]\n",
" \n",
"-- forOf :: Traversal s t a b -> s -> (a -> f b) -> f t\n",
":t forOf\n",
"\n",
"-- sequenceAOf :: Traversal s t (f a) a -> s -> f t\n",
":t sequenceAOf\n",
"\n",
"sequenceAOf _1 (Just \"Garfield\", \"Lasagna\")\n",
"\n",
"sequenceAOf _1 (Nothing, \"Lasagna\")\n",
"\n",
"sequenceAOf (both . traversed) ([Just \"apples\"], [Just \"oranges\"])\n",
"\n",
"sequenceAOf (both . traversed) ([Just \"apples\"], [Nothing])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"-- traverseOf :: Traversal s t a b -> (a -> f b) -> s -> f t\n",
"-- (%%~) :: Traversal s t a b -> (a -> f b) -> s -> f t\n",
"\n",
"((\"1\", \"2\") & both %%~ readMaybe) :: Maybe (Int, Int)\n",
"\n",
"((\"not a number\", \"2\") & both %%~ readMaybe) :: Maybe (Int, Int)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises - Traversal Actions"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Nothing"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"ZipList {getZipList = [[1,3],[2,4]]}"
]
},
"metadata": {},
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"data": {
"text/plain": [
"ZipList {getZipList = [[('a',1),('b',3)],[('a',2),('b',4)]]}"
]
},
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"data": {
"text/plain": [
"(([1,2,3],(4,5)),5)"
]
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"source": [
"sequenceAOf _1 (Nothing, \"Rosebug\")\n",
"\n",
"-- sequenceAOf (traversed . _1) [(\"ab\", 1), (\"cd\", 2)]\n",
"\n",
"sequenceAOf traversed [ZipList [1, 2], ZipList [3, 4]]\n",
"\n",
"sequenceAOf (traversed . _2) [('a', ZipList [1, 2]), ('b', ZipList [3, 4])]\n",
"\n",
"import Control.Monad.State\n",
"let result = traverseOf (beside traversed both) (\\n -> modify (+n) >> get) ([1, 1, 1], (1, 1))\n",
"runState result 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Custom Traversals"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Deposit {_amount = 100},Withdrawal {_amount = 20},Withdrawal {_amount = 10}]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[100,20,10]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[10,30]"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"[Deposit {_amount = 100},Withdrawal {_amount = 20},Deposit {_amount = 300}]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"-- values :: Traversal [a] [b] a b\n",
"\n",
"-- values :: Applicative f => (a -> f b) -> [a] -> f [b]\n",
"\n",
"values :: Applicative f => (a -> f b) -> [a] -> f [b]\n",
"values _ [] = pure []\n",
"values handler (a : as) = liftA2 (:) (handler a) (values handler as)\n",
"\n",
"data Transaction =\n",
" Withdrawal { _amount :: Int }\n",
" | Deposit { _amount :: Int }\n",
" deriving Show\n",
" \n",
"makeLenses ''Transaction\n",
"\n",
"newtype BankAccount =\n",
" BankAccount\n",
" { _transactions :: [Transaction]\n",
" } deriving Show\n",
"makeLenses ''BankAccount\n",
"\n",
"let aliceAccount = BankAccount [Deposit 100, Withdrawal 20, Withdrawal 10]\n",
"\n",
"aliceAccount ^.. transactions . traversed\n",
"\n",
"aliceAccount ^.. transactions . traversed . amount\n",
"\n",
"-- deposits :: Traversal' [Transaction] Int\n",
"-- deposits :: Traversal [Transaction] [Transaction] Int Int\n",
"deposits :: Applicative f => (Int -> f Int) -> [Transaction] -> f [Transaction]\n",
"deposits _ [] = pure []\n",
"deposits handler (Withdrawal amt : rest) =\n",
" liftA2 (:) (pure (Withdrawal amt)) (deposits handler rest)\n",
"deposits handler (Deposit amt : rest) =\n",
" liftA2 (:) (Deposit <$> (handler amt)) (deposits handler rest)\n",
" \n",
"[Deposit 10, Withdrawal 20, Deposit 30] ^.. deposits\n",
"\n",
"[Deposit 10, Withdrawal 20, Deposit 30] & deposits *~ 10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercises - Custom Traversals"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [],
"source": [
"amountT :: Traversal' Transaction Int\n",
"amountT handler (Deposit n) = Deposit <$> handler n\n",
"amountT handler (Withdrawal n) = Withdrawal <$> handler n\n",
"\n",
"myBoth :: Traversal (a, a) (b, b) a b\n",
"myBoth handler (a, a') = liftA2 (,) (handler a) (handler a')\n",
"\n",
"transactionDelta :: Traversal' Transaction Int\n",
"transactionDelta handler (Deposit n) = Deposit <$> handler n\n",
"transactionDelta handler (Withdrawal n) = Withdrawal . negate <$> handler (negate n)\n",
"\n",
"left :: Traversal (Either a b) (Either a' b) a a'\n",
"left f (Left a) = Left <$> f a\n",
"left _ (Right b) = pure (Right b)\n",
"\n",
"beside :: Traversal s t a b -> Traversal s' t' a b -> Traversal (s,s') (t,t') a b\n",
"beside left' right' handler (s, s') = liftA2 (,) (s & left' %%~ handler) (s' & right' %%~ handler)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"data": {
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"}\n",
".hoogle-code {\n",
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".mono {\n",
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".err-msg {\n",
"color: red;\n",
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"}\n",
"#unshowable {\n",
"color: red;\n",
"font-weight: bold;\n",
"}\n",
".err-msg.in.collapse {\n",
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"}\n",
".highlight-code {\n",
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"}\n",
".suggestion-warning { \n",
"font-weight: bold;\n",
"color: rgb(200, 130, 0);\n",
"}\n",
".suggestion-error { \n",
"font-weight: bold;\n",
"color: red;\n",
"}\n",
".suggestion-name {\n",
"font-weight: bold;\n",
"}\n",
"</style><span class='get-type'>partsOf :: forall (f :: * -> *) s t a. Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a]</span>"
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"partsOf :: forall (f :: * -> *) s t a. Functor f => Traversing (->) f s t a a -> LensLike f s t [a] [a]"
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"metadata": {},
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"data": {
"text/plain": [
"\"abc\""
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"text/plain": [
"[1,2,3]"
]
},
"metadata": {},
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{
"data": {
"text/plain": [
"[('c',1),('a',2),('t',3)]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[('l',1),('e',2),('o',3)]"
]
},
"metadata": {},
"output_type": "display_data"
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{
"data": {
"text/plain": [
"[('x',1),('b',2),('c',3)]"
]
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"data": {
"text/plain": [
"[('c',1),('b',2),('a',3)]"
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"metadata": {},
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"data": {
"text/plain": [
"[('f',1),('o',2),('o',3)]"
]
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"data": {
"text/plain": [
"[('o',1),('f',2),('f',3)]"
]
},
"metadata": {},
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"data": {
"text/plain": [
"(\"a a desk how is\",\" like r\",\"aven writing\")"
]
},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"-- partsOf :: Traversal' s a -> Lens' s [a]\n",
":t partsOf\n",
"\n",
"[('a', 1), ('b', 2), ('c', 3)] ^. partsOf (traversed . _1)\n",
"[('a', 1), ('b', 2), ('c', 3)] ^. partsOf (traversed . _2)\n",
"\n",
"[('a', 1), ('b', 2), ('c', 3)]\n",
" & partsOf (traversed . _1) .~ ['c', 'a', 't']\n",
" \n",
"-- Any 'extra' list elements are simply ignored\n",
"[('a', 1), ('b', 2), ('c', 3)]\n",
" & partsOf (traversed . _1) .~ ['l', 'e', 'o', 'p', 'a', 'r', 'd']\n",
" \n",
"-- Providing too few elements will keep the originals\n",
"[('a', 1), ('b', 2), ('c', 3)]\n",
" & partsOf (traversed . _1) .~ ['x']\n",
" \n",
"[('a', 1), ('b', 2), ('c', 3)]\n",
" & partsOf (traversed . _1) %~ reverse\n",
" \n",
"[('o', 1), ('o', 2), ('f', 3)]\n",
" & partsOf (traversed . _1) %~ L.sort\n",
" \n",
"[('o', 1), ('o', 2), ('f', 3)]\n",
" & partsOf (traversed . _1) %~ tail\n",
"\n",
"(\"how is a raven \", \"like a \", \"writing desk\")\n",
" & partsOf (each . traversed) %~ unwords . L.sort . words"
]
}
],
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