Things

flake.lock

@@ -0,0 +1,58 @@
+{
+  "nodes": {
+    "flake-parts": {
+      "inputs": {
+        "nixpkgs-lib": "nixpkgs-lib"
+      },
+      "locked": {
+        "lastModified": 1727826117,
+        "narHash": "sha256-K5ZLCyfO/Zj9mPFldf3iwS6oZStJcU4tSpiXTMYaaL0=",
+        "owner": "hercules-ci",
+        "repo": "flake-parts",
+        "rev": "3d04084d54bedc3d6b8b736c70ef449225c361b1",
+        "type": "github"
+      },
+      "original": {
+        "owner": "hercules-ci",
+        "repo": "flake-parts",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "lastModified": 1729880355,
+        "narHash": "sha256-RP+OQ6koQQLX5nw0NmcDrzvGL8HDLnyXt/jHhL1jwjM=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "18536bf04cd71abd345f9579158841376fdd0c5a",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixos-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "nixpkgs-lib": {
+      "locked": {
+        "lastModified": 1727825735,
+        "narHash": "sha256-0xHYkMkeLVQAMa7gvkddbPqpxph+hDzdu1XdGPJR+Os=",
+        "type": "tarball",
+        "url": "https://github.com/NixOS/nixpkgs/archive/fb192fec7cc7a4c26d51779e9bab07ce6fa5597a.tar.gz"
+      },
+      "original": {
+        "type": "tarball",
+        "url": "https://github.com/NixOS/nixpkgs/archive/fb192fec7cc7a4c26d51779e9bab07ce6fa5597a.tar.gz"
+      }
+    },
+    "root": {
+      "inputs": {
+        "flake-parts": "flake-parts",
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

flake.nix

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+{
+  inputs = {
+    flake-parts.url = "github:hercules-ci/flake-parts";
+    nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable";
+  };
+
+  outputs = inputs @ {flake-parts, ...}:
+    flake-parts.lib.mkFlake {inherit inputs;} {
+      systems = ["x86_64-linux"];
+      perSystem = {pkgs, ...}: {
+	devShells.default = pkgs.mkShell {
+	  packages = with pkgs; [
+	    cabal-install
+	    ghc
+	    haskell-language-server
+	  ];
+	};
+      };
+    };
+}

src/ApplicativeChapter.hs

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+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE InstanceSigs #-}
+{-# OPTIONS_GHC -Wno-unused-top-binds #-}
+
+module ApplicativeChapter () where
+
+import Data.Function (const)
+import GHC.Base ( id, Functor(..) )
+import Data.Maybe (Maybe(..))
+import Data.Function (($))
+import Data.List (zipWith)
+
+liftA2 :: ApplicativeChapter.Applicative f => (a -> b -> c) -> f a -> f b -> f c
+liftA2 f x = (<*>) (fmap f x)
+
+class Functor f => Applicative f where
+  pure :: a -> f a
+  infixl 4 <*>, *>
+  (<*>) :: f (a -> b) -> f a -> f b
+
+  (*>) :: f a -> f b -> f b
+  a1 *> a2 = (id <$ a1) <*> a2
+
+  (<*) :: f a -> f b -> f a
+  (<*) = liftA2 const
+
+-- ??
+
+-- Maybe is Applicative
+
+instance Applicative Maybe where
+  (<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b
+  (<*>) Nothing _ = Nothing
+  (<*>) (Just f) x = fmap f x
+
+  pure :: a -> Maybe a
+  pure = Just
+
+-- List can be Applicative in 2 different ways
+
+newtype ZipList a = ZipList { getZipList :: [a] }
+
+instance Applicative ZipList where
+  pure :: a -> ZipList a
+  pure a = ZipList [a]
+
+  (<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b
+  (ZipList gs) <*> (ZipList xs) = ZipList (zipWith ($) gs xs)

src/FunctorChapter.hs

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+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE InstanceSigs #-}
+{-# OPTIONS_GHC -Wno-unused-top-binds #-}
+
+module FunctorChapter () where
+
+import Data.Either (Either(..))
+import Data.Function (($))
+import Data.Int
+import Data.Maybe ( Maybe, Maybe(..) )
+
+const :: a -> b -> a
+const a _ = a
+
+class Functor f where
+  fmap :: (a -> b) -> f a -> f b
+  (<$) :: a -> f b -> f a
+  {-# MINIMAL fmap #-}
+  (<$) a = fmap (const a)
+
+-- 1
+instance Functor (Either e) where
+  fmap :: (a -> b) -> Either e a -> Either e b
+  fmap f (Right ex) = Right $ f ex
+  fmap _ (Left x) = Left x
+
+(.) :: (b -> c) -> (a -> b) -> (a -> c)
+(.) fbc fab x = fbc (fab x)
+
+-- 1bis
+instance Functor ((->) e) where
+  fmap :: (a -> b) -> (e -> a) -> (e -> b)
+  fmap fab fea = fab . fea
+
+-- 2
+instance Functor ((,) e) where
+  fmap :: (a -> b) -> (e, a) -> (e, b)
+  fmap f (e, bx) = (e, f bx)
+
+data Pair a = Pair a a
+
+instance Functor Pair where
+  fmap :: (a -> b) -> Pair a -> Pair b
+  fmap f (Pair ax ay) = Pair (f ax) (f ay)
+
+-- Differences: Pair is a concrete type while ((,) e) isn't
+-- Moreover both the wrapped values in Pair have the same type
+-- and we have to wrap both if we want to return a Pair b
+-- Instead for ((,) e) we don't know anything about e so we
+-- cannot apply any function to it
+
+data ITree a = Leaf (Int -> a)
+             | Node [ITree a]
+
+-- 3
+
+instance Functor [] where
+  fmap :: (a -> b) -> [] a -> [] b
+  fmap fab (x:xs) = fab x : fmap fab xs
+  fmap _ [] = []
+
+instance Functor ITree where
+  fmap :: (a -> b) -> ITree a -> ITree b
+  fmap fab (Leaf fia) = Leaf $ fab . fia
+  fmap fab (Node ts) = Node (fmap (fmap fab) ts)
+
+-- 4 ???
+-- data Foo a = Foo
+
+-- instance Functor Foo where
+--   fmap :: (b -> c) -> Foo b -> Foo c
+--   fmap fbc (Foo) = Foo
+
+-- 5
+newtype ListMaybe a = ListMaybe [Maybe a]
+
+instance Functor Maybe where
+  fmap :: (a -> b) -> Maybe a -> Maybe b
+  fmap _ Nothing = Nothing
+  fmap fab (Just a) = Just $ fab a
+
+instance Functor ListMaybe where
+  fmap :: (a -> b) -> ListMaybe a -> ListMaybe b
+  fmap fab (ListMaybe ms) = ListMaybe (fmap (fmap fab) ms)
+
+-- 1
+
+data Maybe' a = Just' a | Nothing'
+
+instance Functor Maybe' where
+  fmap :: (a -> b) -> Maybe' a -> Maybe' b
+  fmap _ _ = Nothing'
+
+-- fmap id = \x -> Nothing' != id
+-- fmap f . fmap g = \x -> Nothing' = fmap (f . g)
+
+-- 2
+-- (evilFmap id) [1] = [1 1]
+-- then evilFmap id != id
+
+-- fmap id x:xs = 
+--   (id x):(id x):(fmap id xs) = # function application
+--   x:x:(fmap id xs) = # associativity 
+--   x:(  x:(fmap id xs)  ) = # definition (list, well defined Functor []): fmap id xs = x: fmap id xs 
+--   x:(  fmap id (x:xs) ) =
+--   x:(  id (x:xs) ) = # identity law substitution (fmap id = id)
+--   (x:) . (id $ (:) x xs) = # rewrite using composition (.)
+--   (x:) . id . (x:) xs = # rewrite using composition (.)
+--   (x:) . id . (x:) = # eta reduction
+--   != id

typeclassopedia.cabal

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+cabal-version:      3.0
+-- The cabal-version field refers to the version of the .cabal specification,
+-- and can be different from the cabal-install (the tool) version and the
+-- Cabal (the library) version you are using. As such, the Cabal (the library)
+-- version used must be equal or greater than the version stated in this field.
+-- Starting from the specification version 2.2, the cabal-version field must be
+-- the first thing in the cabal file.
+
+-- Initial package description 'typeclassopedia' generated by
+-- 'cabal init'. For further documentation, see:
+--   http://haskell.org/cabal/users-guide/
+--
+-- The name of the package.
+name:               typeclassopedia
+
+-- The package version.
+-- See the Haskell package versioning policy (PVP) for standards
+-- guiding when and how versions should be incremented.
+-- https://pvp.haskell.org
+-- PVP summary:     +-+------- breaking API changes
+--                  | | +----- non-breaking API additions
+--                  | | | +--- code changes with no API change
+version:            0.1.0.0
+
+-- A short (one-line) description of the package.
+-- synopsis:
+
+-- A longer description of the package.
+-- description:
+
+-- URL for the project homepage or repository.
+homepage:           https://github.com/aciceri/typeclassoopedia
+
+-- The license under which the package is released.
+license:            GPL-3.0-only
+
+-- The file containing the license text.
+license-file:       LICENSE
+
+-- The package author(s).
+author:             Andrea Ciceri
+
+-- An email address to which users can send suggestions, bug reports, and patches.
+maintainer:         andrea.ciceri@autistici.org
+
+-- A copyright notice.
+-- copyright:
+build-type:         Simple
+
+-- Extra doc files to be distributed with the package, such as a CHANGELOG or a README.
+extra-doc-files:    CHANGELOG.md
+
+-- Extra source files to be distributed with the package, such as examples, or a tutorial module.
+-- extra-source-files:
+
+common warnings
+    ghc-options: -Wall
+
+library
+    -- Import common warning flags.
+    import:           warnings
+
+    -- Modules exported by the library.
+    exposed-modules:  FunctorChapter, ApplicativeChapter
+
+    -- Modules included in this library but not exported.
+    -- other-modules:
+
+    -- LANGUAGE extensions used by modules in this package.
+    -- other-extensions:
+
+    -- Other library packages from which modules are imported.
+    build-depends:    base ^>=4.18.2.1
+
+    -- Directories containing source files.
+    hs-source-dirs:   src
+
+    -- Base language which the package is written in.
+    default-language: Haskell2010
+
+test-suite typeclassopedia-test
+    -- Import common warning flags.
+    import:           warnings
+
+    -- Base language which the package is written in.
+    default-language: Haskell2010
+
+    -- Modules included in this executable, other than Main.
+    -- other-modules:
+
+    -- LANGUAGE extensions used by modules in this package.
+    -- other-extensions:
+
+    -- The interface type and version of the test suite.
+    type:             exitcode-stdio-1.0
+
+    -- Directories containing source files.
+    hs-source-dirs:   test
+
+    -- The entrypoint to the test suite.
+    main-is:          Main.hs
+
+    -- Test dependencies.
+    build-depends:
+        base ^>=4.18.2.1,
+        typeclassopedia