Implementation and Documentation
This commit is contained in:
commit
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1
.gitignore
vendored
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.gitignore
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.stack-work/
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11
CHANGELOG.md
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CHANGELOG.md
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# Changelog for `Infinitree`
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All notable changes to this project will be documented in this file.
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The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
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and this project adheres to the
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[Haskell Package Versioning Policy](https://pvp.haskell.org/).
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## Unreleased
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## 0.1.0.0 - YYYY-MM-DD
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36
Infinitree.cabal
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36
Infinitree.cabal
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cabal-version: 2.2
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-- This file has been generated from package.yaml by hpack version 0.38.0.
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--
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-- see: https://github.com/sol/hpack
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name: Infinitree
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version: 0.1.0.0
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synopsis: Infinitely deep trees for lazy stateless memoization
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description: Please see the README on GitHub at <https://github.com/githubuser/Infinitree#readme>
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author: VegOwOtenks
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maintainer: vegowotenks@jossco.de
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copyright: 2025 VegOwOtenks
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license: AGPL-3.0-or-later
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license-file: LICENSE
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build-type: Simple
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extra-source-files:
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README.md
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CHANGELOG.md
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library
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exposed-modules:
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Data.Infinitree
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Data.Infinitree.Examples
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other-modules:
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Paths_Infinitree
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autogen-modules:
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Paths_Infinitree
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hs-source-dirs:
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src
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ghc-options: -Wall -Wextra -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints
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build-depends:
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adjunctions
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, base >=4.7 && <5
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, distributive
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default-language: Haskell2010
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1
README.md
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1
README.md
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# Infinitree
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2
Setup.hs
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2
Setup.hs
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import Distribution.Simple
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main = defaultMain
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39
package.yaml
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39
package.yaml
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name: Infinitree
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version: 0.1.0.0
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license: AGPL-3.0-or-later
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author: "VegOwOtenks"
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maintainer: "vegowotenks@jossco.de"
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copyright: "2025 VegOwOtenks"
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extra-source-files:
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- README.md
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- CHANGELOG.md
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# Metadata used when publishing your package
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synopsis: Infinitely deep trees for lazy stateless memoization
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# category: Web
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# To avoid duplicated efforts in documentation and dealing with the
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# complications of embedding Haddock markup inside cabal files, it is
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# common to point users to the README.md file.
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description: Please see the README on GitHub at <https://github.com/githubuser/Infinitree#readme>
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dependencies:
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- base >= 4.7 && < 5
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- adjunctions
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- distributive
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ghc-options:
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- -Wall
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- -Wextra
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- -Wcompat
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- -Widentities
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- -Wincomplete-record-updates
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- -Wincomplete-uni-patterns
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- -Wmissing-export-lists
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- -Wmissing-home-modules
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- -Wpartial-fields
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- -Wredundant-constraints
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library:
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source-dirs: src
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182
src/Data/Infinitree.hs
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182
src/Data/Infinitree.hs
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{-# LANGUAGE DeriveFunctor #-}
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{-# LANGUAGE InstanceSigs #-}
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{-# LANGUAGE TypeFamilies #-}
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{-# LANGUAGE TypeApplications #-}
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{-# LANGUAGE BangPatterns #-}
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{-# LANGUAGE DeriveFoldable #-}
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{-# LANGUAGE RankNTypes #-}
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-- |
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-- Copyright: (c) Luca S. Jaekel
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-- License: AGPL3
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--
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-- Infinitrees are memoization trees, which can be used to avoid dealing with mutable caches.
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module Data.Infinitree
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-- export the structure and the instances but not any accessors because you're not meant to invalidate the Infinitree
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( Infinitree()
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-- * Identity trees
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, nats
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, ints
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, nums
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-- * Construction Functions
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, build
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, buildInt
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, buildNum
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)
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where
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-- Distributive is a typeclass which allows you to use the law of distribution on functors
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-- It is a superclass constraint for Representable, which is why I have to define it
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import Data.Distributive (Distributive (distribute))
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-- Representable functors allow indexing and construction from indices
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-- they have a index type (Rep :: Type -> Type)
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-- index takes an index and a structure, returns the element
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-- tabulate calls your function with every index to build the functor
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import Data.Functor.Rep (Representable, Rep, tabulate, index)
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-- Natural numbers are [0..]
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import Numeric.Natural (Natural)
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-- ternary operator of sorts
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import Data.Bool (bool)
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-- | This tree is infinite, it doesn't end anywhere.
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--
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-- You can index into it infitely.
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--
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-- It always has a left and a right branch. Every Branch also holds a value.
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data Infinitree a = Branch
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{ left :: Infinitree a -- left branch, smaller number, the first left branch contains all odd numbers
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, leaf :: a -- current number, 0 for all intents and purposes
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, right :: Infinitree a -- right branch, bigger number, the first right branch contains all even numbers
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}
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instance Functor Infinitree where
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fmap :: (a -> b) -> Infinitree a -> Infinitree b
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fmap f tree = Branch (fmap f (left tree)) (f $ leaf tree) (fmap f (right tree))
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instance Applicative Infinitree where
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pure :: a -> Infinitree a
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pure e = Branch (pure e) e (pure e)
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(<*>) :: Infinitree (a -> b) -> Infinitree a -> Infinitree b
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(<*>) (Branch fl f fr) (Branch vl v vr) = Branch (fl <*> vl) (f v) (fr <*> vr)
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liftA2 :: (a -> b -> c) -> Infinitree a -> Infinitree b -> Infinitree c
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liftA2 f (Branch la va ra) (Branch lb vb rb) = Branch (liftA2 f la lb) (f va vb) (liftA2 f ra rb)
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(*>) :: Infinitree a -> Infinitree b -> Infinitree b
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(*>) = flip const
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(<*) :: Infinitree a -> Infinitree b -> Infinitree a
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(<*) = const
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-- >>> [1, 2] <* [1, 2]
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-- [1,1,2,2]
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-- I could not define a useful Foldable instance
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--
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-- instance Foldable Infinitree where
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-- foldMap :: Monoid m => (a -> m) -> Infinitree a -> m
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-- foldMap f (Branch l v r) = f v
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-- | This is a superclass constraint for representable, but it is entirely implementable from Representable
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--
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-- I now learned that I could have derived it via the Co newtype from Data.Functor.Rep
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--
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-- https://hackage-content.haskell.org/package/adjunctions-4.4.3/docs/Data-Functor-Rep.html#t:Co
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instance Distributive Infinitree where
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distribute :: Functor f => f (Infinitree a) -> Infinitree (f a)
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distribute f = tabulate (\ i -> fmap (flip index i) f)
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-- Representable allows indexing and construction
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instance Representable Infinitree where
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-- only natural numbers index into this structure
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type Rep Infinitree = Natural
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tabulate :: (Rep Infinitree -> a) -> Infinitree a
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tabulate f' = let
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-- build a tree structure of numbers, like this
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-- _0
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-- _/ \_
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-- _/ \_
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-- _/ \_
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-- / \
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-- _1 2_
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-- / \ / \
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-- / \ / \
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-- / \ / \
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-- 3 5 4 6
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-- / \ / \ / \ / \
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-- 7 11 9 13 8 12 10 14
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tabulate' :: (Rep Infinitree -> a) -> Rep Infinitree -> Natural -> Infinitree a
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tabulate' f !i !s = let -- keep the indices strict to avoid function application chains
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l = i + s
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r = l + s
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s' = 2 * s
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in Branch (tabulate' f l s') (f i) (tabulate' f r s')
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in tabulate' f' 0 1
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-- index into the tree structure recursively
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-- the current leaf always has value 0, the index will be adjusted along the way
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index :: Infinitree a -> Rep Infinitree -> a
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index t n = let
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-- inner recursive function
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index' !tree !0 = leaf tree
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index' !tree !i = index' subtree q
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where
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(!q, !r) = pred i `quotRem` 2 -- q is strict to avoid useless function application delays
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!subtree = bool right left (r == 0) $ tree
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in index' t n
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-- * Identity trees
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--
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-- These are probably not optimal for performance, since you always have two trees in memory if you `fmap` over them
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-- | a tree of natural numbers.
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--
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-- a use case would be to `fmap` over it to transform it.
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--
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-- >>> map (index nats) [0..15]
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-- [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
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nats :: Infinitree Natural
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nats = tabulate @Infinitree id
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-- | tree of integer numbers
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--
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-- in case you don't want to transform to integer for mapping
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ints :: Infinitree Integer
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ints = tabulate @Infinitree toInteger
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-- | a tree of generic numbers
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--
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-- if you need a specific number type, make sure you don't use a bounded type, the tree is infinite
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nums :: Num n => Infinitree n
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nums = tabulate @Infinitree fromIntegral
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-- * Construction functions
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-- | build using the infinitree indices
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build :: (Natural -> a) -> Infinitree a
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build = tabulate @Infinitree
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-- | build using arbitrary-width integers
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buildInt :: (Integer -> a) -> Infinitree a
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buildInt = tabulate @Infinitree . (. toInteger)
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-- | build using whatever num type you need
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buildNum :: Num n => (n -> a) -> Infinitree a
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buildNum = tabulate @Infinitree . (. fromIntegral)
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36
src/Data/Infinitree/Examples.hs
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36
src/Data/Infinitree/Examples.hs
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{-# LANGUAGE TypeApplications #-}
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-- |
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-- Copyright: (c) Luca S. Jaekel
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-- License: AGPL3
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--
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-- This is the example usage module, you're meant to look at the source code, feel free to click the `Source` link below
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module Data.Infinitree.Examples
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(fib)
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where
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import Data.Infinitree ( Infinitree )
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import qualified Data.Functor.Rep as Representable
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import Numeric.Natural (Natural)
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-- | This defines a convenience function
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-- users wouldn't have to call Representable.index fibonacci themselves
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-- This example is written to have you look at the source code for example usage.
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fib :: Natural -> Integer
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fib = Representable.index fibonacci
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-- | a tree of all fibonacci numbers
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--
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-- while this enables memoization it also adds a O(log n) overhead to every lookup
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fibonacci :: Infinitree Integer
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fibonacci = Representable.tabulate @Infinitree go
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-- `Representable.tabulate @Infinitree go` is equivalent to `fmap go nats` but more efficient because it doesn't maintain two trees
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where
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-- go is the fibonacci function, it will be called with every index
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go 0 = 0
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go 1 = 1
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-- sum the lower to fibonacci numbers from the tree
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go n = Representable.index fibonacci (n - 1) + Representable.index fibonacci (n - 2)
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66
stack.yaml
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stack.yaml
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# This file was automatically generated by 'stack init'
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#
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# Some commonly used options have been documented as comments in this file.
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# For advanced use and comprehensive documentation of the format, please see:
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# https://docs.haskellstack.org/en/stable/configure/yaml/
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# A 'specific' Stackage snapshot or a compiler version.
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# A snapshot resolver dictates the compiler version and the set of packages
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# to be used for project dependencies. For example:
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#
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# snapshot: lts-23.0
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# snapshot: nightly-2024-12-13
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# snapshot: ghc-9.8.4
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#
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# The location of a snapshot can be provided as a file or url. Stack assumes
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# a snapshot provided as a file might change, whereas a url resource does not.
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#
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# snapshot: ./custom-snapshot.yaml
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# snapshot: https://example.com/snapshots/2024-01-01.yaml
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snapshot: nightly-2025-04-09
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# User packages to be built.
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# Various formats can be used as shown in the example below.
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#
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# packages:
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# - some-directory
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# - https://example.com/foo/bar/baz-0.0.2.tar.gz
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# subdirs:
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# - auto-update
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# - wai
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packages:
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- .
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# Dependency packages to be pulled from upstream that are not in the snapshot.
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# These entries can reference officially published versions as well as
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# forks / in-progress versions pinned to a git hash. For example:
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#
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# extra-deps:
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# - acme-missiles-0.3
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# - git: https://github.com/commercialhaskell/stack.git
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# commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
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#
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# extra-deps: []
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# Override default flag values for project packages and extra-deps
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# flags: {}
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# Extra package databases containing global packages
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# extra-package-dbs: []
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# Control whether we use the GHC we find on the path
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# system-ghc: true
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#
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# Require a specific version of Stack, using version ranges
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# require-stack-version: -any # Default
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||||
# require-stack-version: ">=3.3"
|
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#
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||||
# Override the architecture used by Stack, especially useful on Windows
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# arch: i386
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# arch: x86_64
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#
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||||
# Extra directories used by Stack for building
|
||||
# extra-include-dirs: [/path/to/dir]
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# extra-lib-dirs: [/path/to/dir]
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||||
#
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||||
# Allow a newer minor version of GHC than the snapshot specifies
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# compiler-check: newer-minor
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12
stack.yaml.lock
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12
stack.yaml.lock
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@ -0,0 +1,12 @@
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# This file was autogenerated by Stack.
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||||
# You should not edit this file by hand.
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||||
# For more information, please see the documentation at:
|
||||
# https://docs.haskellstack.org/en/stable/topics/lock_files
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||||
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||||
packages: []
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||||
snapshots:
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||||
- completed:
|
||||
sha256: d129ed943d7204d72bbdf2c688d9c68030d901ee06a60223f52eae9c900ba976
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||||
size: 677117
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||||
url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/nightly/2025/4/9.yaml
|
||||
original: nightly-2025-04-09
|
||||
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