feat: Add function composition example and configure VS Code Haskell settings for Nix HLS.

Author: RyosukeDTomita

.vscode/settings.json

@@ -12,9 +12,11 @@
     "editor.defaultFormatter": "haskell.haskell",
     "editor.formatOnSave": true
   },
-  "haskell.manageHLS": "GHCup",
+  "haskell.manageHLS": "PATH", // nix
   "haskell.formattingProvider": "ormolu",
-  "haskell.ghcupExecutablePath": "~/.ghcup/bin/ghcup",
+  "haskell.ghcupExecutablePath": "",
+  "haskell.upgradeGHCup": false,
+  "haskell.serverExecutablePath": "haskell-language-server",
   "github.copilot.enable": {
     "haskell": false
   },
@@ -27,5 +29,5 @@
     "unlines",
     "zipWith",
     "elems"
-  ]
-}
+  ],
+}

WhyFunctionalProgrammingMatters/3_tree.hs

@@ -1,30 +1,42 @@
 -- https://www.sampou.org/haskell/article/whyfp.html より
-data Tree a = Node a [Tree a]
+-- Tree aはラベルaと自分自身(Tree a)のリストを持つデータ構造
+-- つまり木の構造を表す
+-- Node 1 [Node 2 [], Node 3 [Node 4 []]]
+data Tree a = Node a [Tree a] deriving (Show)
 
 -- 木のリストに対する畳み込み
 redtree ::
-  (a -> b -> b) -> -- f : node を潰す
-  (b -> b -> b) -> -- g : cons を潰す
-  b -> -- a : nil を潰す
+  (a -> c -> b) -> -- f : node を潰す
+  (b -> c -> c) -> -- g : cons を潰す
+  c -> -- a : nil を潰す
   Tree a ->
   b
 redtree f g a (Node label subtrees) =
   f label (redtree' f g a subtrees)
 
 -- ツリーのリストを処理する関数
 redtree' ::
-  (a -> b -> b) ->
-  (b -> b -> b) ->
-  b ->
+  (a -> c -> b) ->
+  (b -> c -> c) ->
+  c ->
   [Tree a] ->
-  b
+  c
 redtree' f g a (subtree : rest) =
   g
     (redtree f g a subtree) -- リストのサイズが1に分解して潰す --> f label (redtree' f g a [先頭の木]) ...という流れでredtree' _ _ a [] = aにたどりつく
     (redtree' f g a rest) -- 残りで再帰
 redtree' _ _ a [] =
   a
 
+sumtree :: (Num a) => Tree a -> a
+sumtree tree = redtree (+) (+) 0 tree
+
+labels :: (Num a) => Tree a -> [a]
+labels tree = redtree (:) (++) [] tree
+
+maptree :: (a -> b) -> Tree a -> Tree b
+maptree f tree = redtree (Node . f) (:) [] tree
+
 tree :: Tree Int
 tree =
   Node
@@ -40,15 +52,6 @@ tree =
         )
     )
 
-sumtree :: (Num a) => Tree a -> a
-sumtree tree = redtree (+) (+) 0 tree
-
-labels :: (Num a) => Tree a -> [a]
-labels tree = redtree (:) (++) [] tree
-
-maptree :: (a -> b) -> Tree a -> Tree b
-maptree f tree = redtree (\label subtrees -> Node (f label) subtrees) (:) [] tree
-
 main :: IO ()
 main = do
   print $ sumtree tree -- 10

math/newton/newtonRoot.hs …ionalProgrammingMatters/4_1newtonRoot.hsmath/newton/newtonRoot.hs renamed to WhyFunctionalProgrammingMatters/4_1newtonRoot.hs math/newton/newtonRoot.hs renamed to WhyFunctionalProgrammingMatters/4_1newtonRoot.hs

@@ -0,0 +1,4 @@
+main :: IO ()
+main = do
+  print $ (\input -> (+ 1) ((* 2) input)) 3 -- lambda式版
+  print $ ((+ 1) . (* 2)) 3 -- 関数合成のほうが完結に書ける 3*2+1

math/differential/differential.hs …nalProgrammingMatters/4_2differential.hsmath/differential/differential.hs renamed to WhyFunctionalProgrammingMatters/4_2differential.hs math/differential/differential.hs renamed to WhyFunctionalProgrammingMatters/4_2differential.hs

@@ -0,0 +1,18 @@
+# なぜ関数プログラミングは重要かのサンプルコード
+
+## ABOUT
+
+<https://www.sampou.org/haskell/article/whyfp.html>
+
+上記論文に登場するサンプルコードをHaskellで実装したもの
+
+---
+
+## INDEX
+
+- [3_list.hs](3_list.hs): 再帰によるリスト操作
+- [3_tree.hs](3_tree.hs): 再帰による木構造操作
+- [4_functionComposition.hs](4_functionComposition.hs): 関数合成
+- [4_1newtonRoot.hs](4_1newtonRoot.hs): ニュートンラフソン法
+- [4_2differential.hs](4_2differential.hs): 微分
+- [4_3integral.hs](4_3integral.hs): 積分

math/integrate/integrate.hs …ctionalProgrammingMatters/4_3integral.hsmath/integrate/integrate.hs renamed to WhyFunctionalProgrammingMatters/4_3integral.hs math/integrate/integrate.hs renamed to WhyFunctionalProgrammingMatters/4_3integral.hs

@@ -1,17 +1,5 @@
 # 数学ぽいやつ
 
-## フィボナッチ数列
-
-[fibonacci](./fibonacci/)
-
----
-
-## ニュートン法による平方根の近似
-
-[newton](./newton/)
-
----
-
 ## ユークリッドの互助法
 
 [euclidean](./euclidean/)