diff --git a/Data/QuadTree.hs b/Data/QuadTree.hs new file mode 100644 --- /dev/null +++ b/Data/QuadTree.hs @@ -0,0 +1,479 @@ +{-# OPTIONS_HADDOCK show-extensions #-} + +{-# LANGUAGE Safe #-} + +{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE ScopedTypeVariables #-} + +{-| +Module : QuadTree +Description : Region quadtrees with Lens support. +Copyright : (c) Ashley Moni, 2014 +License : GPL-3 +Maintainer : Ashley Moni +Stability : Experimental +Portability : Rank 2 Types, Scoped Type Variables + +The purpose of this module is to provide discrete region quadtrees +that can be used as simple functional alternatives to 2D arrays, +with lens support. + +@ +test = set ('atLocation' (0,0)) \'d\' $ + set ('atLocation' (5,5)) \'c\' $ + set ('atLocation' (3,2)) \'b\' $ + set ('atLocation' (2,4)) \'a\' $ + 'makeTree' (6,6) \'.\' +@ + +>>> printTree id test +d..... +...... +...b.. +...... +..a... +.....c +-} + +module Data.QuadTree ( + -- * Data Type & Constructor + QuadTree, makeTree, + -- * Index access + -- $locations + Location, getLocation, setLocation, atLocation, + -- * Functor + fuseTree, tmap, + -- * Foldable + -- $foldables + filterTree, sortTreeBy, + -- ** Tiles + -- $tiles + Region, Tile, + -- ** Tile functions + -- $tileuse + tile, expand, foldTiles, + filterTiles, sortTilesBy, + -- * Printers + showTree, printTree, + -- * Miscellaneous helpers + outOfBounds, treeDimensions, regionArea, inRegion ) where + +import Control.Lens.Type (Lens') +import Control.Lens.Lens (lens) +-- import Control.Lens.Setter (set) + +import Data.List (find, sortBy) +import Data.Maybe (fromJust) +import Data.Function (on) +import Data.Composition ((.:)) + +-- Foldable: +import Data.Foldable (Foldable, foldr) +import Prelude hiding (foldr) + +---- Structures: + +-- |Tuple corresponds to (X, Y) co-ordinates. + +type Location = (Int, Int) + +-- |The eponymous data type. +-- +-- 'QuadTree' is itself a wrapper around an internal tree structure +-- along with spatial metadata about the boundaries and depth of the +-- 2D area it maps to. + +data QuadTree a = Wrapper { wrappedTree :: Quadrant a + , treeLength :: Int + , treeWidth :: Int + , treeDepth :: Int } + deriving (Show, Read) + +instance Functor QuadTree where + fmap fn = onQuads $ fmap fn + +instance Foldable QuadTree where + foldr = foldTree + +-- + +data Quadrant a = Leaf a + | Node (Quadrant a) + (Quadrant a) + (Quadrant a) + (Quadrant a) + deriving (Show, Read) + +instance Functor Quadrant where + fmap fn (Leaf x) = Leaf (fn x) + fmap fn (Node a b c d) = Node (fmap fn a) + (fmap fn b) + (fmap fn c) + (fmap fn d) + +---- Index access: + +-- $locations +-- This provides an array-style interface to the 'QuadTree', albeit +-- with an O(log n) lookup and insertion speed. This is both faster +-- and slower than an actual array (O(1) lookup and O(n) insertion +-- respectively). +-- +-- The user can imagine a two dimensional grid that can be modified +-- or queried via co-ordinate pair indices. + + +-- |Lens for accessing and manipulating data at a specific +-- location. +-- +-- This is simply 'getLocation' and 'setLocation' wrapped into a lens. +atLocation :: Eq a => Location -> Lens' (QuadTree a) a +atLocation index = lens (getLocation index) (setLocation index) + +-- |Getter for the value at a given location for a 'QuadTree'. +getLocation :: Location -> QuadTree a -> a +getLocation index tree + | outOfBounds tree index = + error "Location index out of QuadTree bounds." + | otherwise = + go (offsetIndex tree index) (treeDepth tree) (wrappedTree tree) + where + go :: Location -> Int -> Quadrant a -> a + go _ _ (Leaf x) = x + go _ 0 _ = error "Wrapped tree is deeper than tree depth." + go (x,y) n (Node a b c d) = + go (x `mod` mid, y `mod` mid) (n - 1) node + where mid = 2 ^ (n - 1) + node | y < mid = if x < mid then a + else b + | otherwise = if x < mid then c + else d + +-- |Setter for the value at a given location for a 'QuadTree'. +-- +-- This automatically compresses the 'QuadTree' nodes if possible with +-- the new value. +setLocation :: forall a. Eq a => Location -> QuadTree a -> a -> QuadTree a +setLocation index tree new + | outOfBounds tree index = + error "Location index out of QuadTree bounds." + | otherwise = + onQuads (go (offsetIndex tree index) (treeDepth tree)) tree + where + go :: Eq a => Location -> Int -> Quadrant a -> Quadrant a + go (x,y) n (Leaf old) + | old == new = Leaf old + | n == 0 = Leaf new + | otherwise = go (x,y) n (Node l l l l) + where l = Leaf old + go _ 0 _ = error "Wrapped tree is deeper than tree depth." + go (x,y) n (Node a b c d) = fusedNode + where fusedNode = fuse newNode + newNode + | y < mid = if x < mid then Node (recurse a) b c d + else Node a (recurse b) c d + | otherwise = if x < mid then Node a b (recurse c) d + else Node a b c (recurse d) + recurse = go (x `mod` mid, y `mod` mid) (n - 1) + mid = 2 ^ (n - 1) + +---- Helpers: + +-- |Checks if a 'Location' is outside the boundaries of a 'QuadTree'. + +outOfBounds :: QuadTree a -> Location -> Bool +outOfBounds tree (x,y) = x < 0 || y < 0 + || x >= treeLength tree + || y >= treeWidth tree + +-- |Dimensions of a 'QuadTree', as an Int pair. + +treeDimensions :: QuadTree a + -> (Int, Int) -- ^ (Length, Width) +treeDimensions tree = (treeLength tree, treeWidth tree) + +offsetIndex :: QuadTree a -> Location -> Location +offsetIndex tree (x,y) = (x + xOffset, y + yOffset) + where (xOffset, yOffset) = offsets tree + +offsets :: QuadTree a -> (Int, Int) +offsets tree = (xOffset, yOffset) + where xOffset = (dimension - treeLength tree) `div` 2 + yOffset = (dimension - treeWidth tree) `div` 2 + dimension = 2 ^ treeDepth tree + +fuse :: Eq a => Quadrant a -> Quadrant a +fuse (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d)) + | a == b && b == c && c == d = Leaf a +fuse oldNode = oldNode + +---- Functor: + +onQuads :: (Quadrant a -> Quadrant b) -> QuadTree a -> QuadTree b +onQuads fn tree = tree {wrappedTree = fn (wrappedTree tree)} + +-- |Cleanup function for use after any 'Control.Monad.fmap'. +-- +-- When elements of a 'QuadTree' are modified by 'setLocation' (or +-- the 'atLocation' lens), it automatically compresses identical +-- adjacent nodes into larger ones. This keeps the 'QuadTree' from +-- bloating over constant use. +-- +-- 'Control.Monad.fmap' does not do this. If you wish to treat the +-- 'QuadTree' as a 'Control.Monad.Functor', you should compose this +-- function after to collapse it down to its minimum size. +-- +-- Example: +-- @ +-- 'fuseTree' $ 'Control.Monad.fmap' fn tree +-- @ +-- This particular example is reified in the function below. + +fuseTree :: Eq a => QuadTree a -> QuadTree a +fuseTree = onQuads fuseQuads + +fuseQuads :: Eq a => Quadrant a -> Quadrant a +fuseQuads (Node a b c d) = fuse $ Node (fuseQuads a) + (fuseQuads b) + (fuseQuads c) + (fuseQuads d) +fuseQuads leaf = leaf + +-- |tmap is simply 'Control.Monad.fmap' with 'fuseTree' applied after. +-- +-- prop> tmap fn tree == fuseTree $ fmap fn tree +tmap :: Eq b => (a -> b) -> QuadTree a -> QuadTree b +tmap = fuseTree .: fmap + +---- Foldable: + +-- $foldables +-- 'QuadTree's can be folded just like lists. If you simply replace +-- the "Prelude" fold functions with "Data.Foldable" ones... +-- +-- @ +-- import "Data.Foldable" +-- import "Prelude" hiding (foldr, foldl, any, sum, find...) +-- @ +-- +-- ... Then you can directly call then on 'QuadTree's without +-- qualification. No list functionality will be lost since the +-- "Data.Foldable" functions also work exactly like the "Prelude" +-- folds for list processing. +-- +-- In addition you also get some extras like 'Data.Foldable.toList'. + + +-- $tiles +-- Directly folding a 'QuadTree' will expand it into a sequence of +-- elements that are then folded over. For some types of operations +-- this can be incredibly inefficient; it may be faster to simply +-- manipulate a sequence of leaves and then later decompose the +-- results into a list of elements. +-- +-- For these operations, we can use 'Tile's. 'Tile's are simply +-- blocks of elements, represented by a tuple of the leaf data and +-- some information on the spatial location and dimensions of the +-- block. + + +-- $tileuse +-- The bread and butter method of manipulating 'Tile's is to first +-- decompose a 'QuadTree' with 'tile', process the intermediate +-- representation, and then decompose it into a final list of elements +-- with 'expand'. +-- +-- @ +-- 'expand' . fn . 'tile' $ tree +-- @ + +-- |Rectangular area, represented by a tuple of four Ints. +-- +-- They correspond to (X floor, Y floor, X ceiling, Y ceiling). +-- +-- The co-ordinates are inclusive of all the rows and columns in all +-- four Ints. +-- +-- prop> regionArea (x, y, x, y) == 1 + +type Region = (Int, Int, Int, Int) + +-- |Each 'Tile' is a tuple of an element from a 'QuadTree' and the +-- 'Region' it subtends. + +type Tile a = (a, Region) + +foldTree :: (a -> b -> b) -> b -> QuadTree a -> b +foldTree fn z = foldr fn z . expand . tile + +-- |Takes a list of 'Tile's and then decomposes them into a list of +-- all their elements, properly weighted by 'Tile' size. + +expand :: [Tile a] -> [a] +expand = concatMap decompose + where decompose :: Tile a -> [a] + decompose (a, r) = replicate (regionArea r) a + +-- |Returns a list of 'Tile's. The block equivalent of +-- 'Data.Foldable.toList'. + +tile :: QuadTree a -> [Tile a] +tile = foldTiles (:) [] + +-- |Decomposes a 'QuadTree' into its constituent 'Tile's, before +-- folding a 'Tile' consuming function over all of them. + +foldTiles :: forall a b. (Tile a -> b -> b) -> b -> QuadTree a -> b +foldTiles fn z tree = go (treeRegion tree) (wrappedTree tree) z + where go :: Region -> Quadrant a -> b -> b + go r (Leaf a) = fn (a, normalizedIntersection) + where normalizedIntersection = + (interXl - xOffset, interYt - yOffset, + interXr - xOffset, interYb - yOffset) + (interXl, interYt, interXr, interYb) = + treeIntersection r + go (xl, yt, xr, yb) (Node a b c d) = + go (xl, yt, midx, midy) a . + go (midx + 1, yt, xr, midy) b . + go (xl, midy + 1, midx, yb) c . + go (midx + 1, midy + 1, xr, yb) d + where midx = (xr + xl) `div` 2 + midy = (yt + yb) `div` 2 + + (xOffset, yOffset) = offsets tree + treeIntersection = regionIntersection $ boundaries tree + +treeRegion :: QuadTree a -> Region +treeRegion tree = (0, 0, limit, limit) + where limit = (2 ^ treeDepth tree) - 1 + +boundaries :: QuadTree a -> Region +boundaries tree = (left, top, right, bottom) + where (left, top) = offsetIndex tree (0,0) + (right, bottom) = offsetIndex tree (treeLength tree - 1, + treeWidth tree - 1) + +regionIntersection :: Region -> Region -> Region +regionIntersection (xl , yt , xr , yb ) + (xl', yt', xr', yb') = + (max xl xl', max yt yt', + min xr xr', min yb yb') + +-- |Simple helper function that lets you calculate the area of a +-- 'Region', usually for 'Data.List.replicate' purposes. + +regionArea :: Region -> Int +regionArea (xl,yt,xr,yb) = (xr + 1 - xl) * (yb + 1 - yt) + +-- |Does the region contain this location? + +inRegion :: Location -> Region -> Bool +inRegion (x,y) (xl,yt,xr,yb) = xl <= x && x <= xr && + yt <= y && y <= yb + +---- Foldable extras: + +-- |'Data.List.filter's a list of the 'QuadTree' 's elements. + +filterTree :: (a -> Bool) -> QuadTree a -> [a] +filterTree fn = expand . filterTiles fn . tile + +-- |'Data.List.sortBy's a list of the 'QuadTree' 's elements. + +sortTreeBy :: (a -> a -> Ordering) -> QuadTree a -> [a] +sortTreeBy fn = expand . sortTilesBy fn . tile + +-- |'Data.List.filter's a list of the 'Tile's of a 'QuadTree'. + +filterTiles :: (a -> Bool) -> [Tile a] -> [Tile a] +filterTiles _ [] = [] +filterTiles fn ((a,r) : rs) + | fn a = (a,r) : filterTiles fn rs + | otherwise = filterTiles fn rs + +-- |'Data.List.sortBy's a list of the 'Tile's of a 'QuadTree'. + +sortTilesBy :: (a -> a -> Ordering) -> [Tile a] -> [Tile a] +sortTilesBy fn = sortBy (fn `on` fst) + +---- Constructor: + +-- |Constructor that generates a 'QuadTree' of the given dimensions, +-- with all cells filled with a default value. + +makeTree :: (Int, Int) -- ^ (Length, Width) + -> a -- ^ Initial element to fill + -> QuadTree a +makeTree (x,y) a + | x <= 0 || y <= 0 = error "Invalid dimensions for tree." + | otherwise = Wrapper { wrappedTree = Leaf a + , treeLength = x + , treeWidth = y + , treeDepth = fst . fromJust $ + find ((>= max x y) . snd) $ + zip [0..] (iterate (*2) 1) } + + +---- Sample Printers: + +-- |Generates a newline delimited string representing a 'QuadTree' as +-- a 2D block of characters. +-- +-- Note that despite the word 'show' in the function name, this does +-- not 'Text.show' the 'QuadTree'. It pretty prints it. The name +-- is simply a mnemonic for its @'QuadTree' -> String@ behaviour. + +showTree :: (a -> Char) -- ^ Function to generate characters for each + -- 'QuadTree' element. + -> QuadTree a -> String +showTree printer tree = breakString (treeLength tree) string + where string = map printer grid + grid = [getLocation (x,y) tree | + y <- [0 .. treeWidth tree - 1], + x <- [0 .. treeLength tree - 1]] + breakString :: Int -> String -> String + breakString _ [] = [] + breakString n xs = a ++ "\n" ++ breakString n b + where (a,b) = splitAt n xs + +-- |As 'showTree' above, but also prints it. + +printTree :: (a -> Char) -- ^ Function to generate characters for each + -- 'QuadTree' element. + -> QuadTree a -> IO () +printTree = putStr .: showTree + + +--------- Test: + +-- x' :: QuadTree Int +-- x' = Wrapper { treeLength = 6 +-- , treeWidth = 5 +-- , treeDepth = 3 +-- , wrappedTree = y' } + +-- y' :: Quadrant Int +-- y' = Node (Leaf 0) +-- (Node (Leaf 2) +-- (Leaf 3) +-- (Leaf 4) +-- (Leaf 5)) +-- (Leaf 1) +-- (Leaf 9) + +-- basic :: QuadTree Int +-- basic = Wrapper {treeLength = 4, treeWidth = 5, treeDepth = 3, +-- wrappedTree = Node (Leaf 0) +-- (Leaf 1) +-- (Leaf 2) +-- (Leaf 3)} + +-- x5 = set (atLocation (2,3)) 1 (makeTree (5,7) 0) +-- x6 = set (atLocation (2,3)) 1 (makeTree (6,7) 0) +-- p n = printTree (head . show) n + +-- test = set (atLocation (0,0)) 'd' $ +-- set (atLocation (5,5)) 'c' $ +-- set (atLocation (3,2)) 'b' $ +-- set (atLocation (2,4)) 'a' $ +-- makeTree (6,6) '.' diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,675 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. You can apply it to +your programs, too. + + When we speak of free software, we are referring to freedom, not +price. Our General Public Licenses are designed to make sure that you +have the freedom to distribute copies of free software (and charge for +them if you wish), that you receive source code or can get it if you +want it, that you can change the software or use pieces of it in new +free programs, and that you know you can do these things. + + To protect your rights, we need to prevent others from denying you +these rights or asking you to surrender the rights. Therefore, you have +certain responsibilities if you distribute copies of the software, or if +you modify it: responsibilities to respect the freedom of others. + + For example, if you distribute copies of such a program, whether +gratis or for a fee, you must pass on to the recipients the same +freedoms that you received. You must make sure that they, too, receive +or can get the source code. And you must show them these terms so they +know their rights. + + Developers that use the GNU GPL protect your rights with two steps: +(1) assert copyright on the software, and (2) offer you this License +giving you legal permission to copy, distribute and/or modify it. + + For the developers' and authors' protection, the GPL clearly explains +that there is no warranty for this free software. For both users' and +authors' sake, the GPL requires that modified versions be marked as +changed, so that their problems will not be attributed erroneously to +authors of previous versions. + + Some devices are designed to deny users access to install or run +modified versions of the software inside them, although the manufacturer +can do so. This is fundamentally incompatible with the aim of +protecting users' freedom to change the software. The systematic +pattern of such abuse occurs in the area of products for individuals to +use, which is precisely where it is most unacceptable. Therefore, we +have designed this version of the GPL to prohibit the practice for those +products. If such problems arise substantially in other domains, we +stand ready to extend this provision to those domains in future versions +of the GPL, as needed to protect the freedom of users. + + Finally, every program is threatened constantly by software patents. +States should not allow patents to restrict development and use of +software on general-purpose computers, but in those that do, we wish to +avoid the special danger that patents applied to a free program could +make it effectively proprietary. To prevent this, the GPL assures that +patents cannot be used to render the program non-free. + + The precise terms and conditions for copying, distribution and +modification follow. + + TERMS AND CONDITIONS + + 0. Definitions. + + "This License" refers to version 3 of the GNU General Public License. + + "Copyright" also means copyright-like laws that apply to other kinds of +works, such as semiconductor masks. + + "The Program" refers to any copyrightable work licensed under this +License. Each licensee is addressed as "you". "Licensees" and +"recipients" may be individuals or organizations. + + To "modify" a work means to copy from or adapt all or part of the work +in a fashion requiring copyright permission, other than the making of an +exact copy. The resulting work is called a "modified version" of the +earlier work or a work "based on" the earlier work. + + A "covered work" means either the unmodified Program or a work based +on the Program. + + To "propagate" a work means to do anything with it that, without +permission, would make you directly or secondarily liable for +infringement under applicable copyright law, except executing it on a +computer or modifying a private copy. Propagation includes copying, +distribution (with or without modification), making available to the +public, and in some countries other activities as well. + + To "convey" a work means any kind of propagation that enables other +parties to make or receive copies. Mere interaction with a user through +a computer network, with no transfer of a copy, is not conveying. + + An interactive user interface displays "Appropriate Legal Notices" +to the extent that it includes a convenient and prominently visible +feature that (1) displays an appropriate copyright notice, and (2) +tells the user that there is no warranty for the work (except to the +extent that warranties are provided), that licensees may convey the +work under this License, and how to view a copy of this License. If +the interface presents a list of user commands or options, such as a +menu, a prominent item in the list meets this criterion. + + 1. Source Code. + + The "source code" for a work means the preferred form of the work +for making modifications to it. "Object code" means any non-source +form of a work. + + A "Standard Interface" means an interface that either is an official +standard defined by a recognized standards body, or, in the case of +interfaces specified for a particular programming language, one that +is widely used among developers working in that language. + + The "System Libraries" of an executable work include anything, other +than the work as a whole, that (a) is included in the normal form of +packaging a Major Component, but which is not part of that Major +Component, and (b) serves only to enable use of the work with that +Major Component, or to implement a Standard Interface for which an +implementation is available to the public in source code form. A +"Major Component", in this context, means a major essential component +(kernel, window system, and so on) of the specific operating system +(if any) on which the executable work runs, or a compiler used to +produce the work, or an object code interpreter used to run it. + + The "Corresponding Source" for a work in object code form means all +the source code needed to generate, install, and (for an executable +work) run the object code and to modify the work, including scripts to +control those activities. However, it does not include the work's +System Libraries, or general-purpose tools or generally available free +programs which are used unmodified in performing those activities but +which are not part of the work. For example, Corresponding Source +includes interface definition files associated with source files for +the work, and the source code for shared libraries and dynamically +linked subprograms that the work is specifically designed to require, +such as by intimate data communication or control flow between those +subprograms and other parts of the work. + + The Corresponding Source need not include anything that users +can regenerate automatically from other parts of the Corresponding +Source. + + The Corresponding Source for a work in source code form is that +same work. + + 2. Basic Permissions. + + All rights granted under this License are granted for the term of +copyright on the Program, and are irrevocable provided the stated +conditions are met. This License explicitly affirms your unlimited +permission to run the unmodified Program. The output from running a +covered work is covered by this License only if the output, given its +content, constitutes a covered work. This License acknowledges your +rights of fair use or other equivalent, as provided by copyright law. + + You may make, run and propagate covered works that you do not +convey, without conditions so long as your license otherwise remains +in force. You may convey covered works to others for the sole purpose +of having them make modifications exclusively for you, or provide you +with facilities for running those works, provided that you comply with +the terms of this License in conveying all material for which you do +not control copyright. Those thus making or running the covered works +for you must do so exclusively on your behalf, under your direction +and control, on terms that prohibit them from making any copies of +your copyrighted material outside their relationship with you. + + Conveying under any other circumstances is permitted solely under +the conditions stated below. Sublicensing is not allowed; section 10 +makes it unnecessary. + + 3. Protecting Users' Legal Rights From Anti-Circumvention Law. + + No covered work shall be deemed part of an effective technological +measure under any applicable law fulfilling obligations under article +11 of the WIPO copyright treaty adopted on 20 December 1996, or +similar laws prohibiting or restricting circumvention of such +measures. + + When you convey a covered work, you waive any legal power to forbid +circumvention of technological measures to the extent such circumvention +is effected by exercising rights under this License with respect to +the covered work, and you disclaim any intention to limit operation or +modification of the work as a means of enforcing, against the work's +users, your or third parties' legal rights to forbid circumvention of +technological measures. + + 4. Conveying Verbatim Copies. + + You may convey verbatim copies of the Program's source code as you +receive it, in any medium, provided that you conspicuously and +appropriately publish on each copy an appropriate copyright notice; +keep intact all notices stating that this License and any +non-permissive terms added in accord with section 7 apply to the code; +keep intact all notices of the absence of any warranty; and give all +recipients a copy of this License along with the Program. + + You may charge any price or no price for each copy that you convey, +and you may offer support or warranty protection for a fee. + + 5. Conveying Modified Source Versions. + + You may convey a work based on the Program, or the modifications to +produce it from the Program, in the form of source code under the +terms of section 4, provided that you also meet all of these conditions: + + a) The work must carry prominent notices stating that you modified + it, and giving a relevant date. + + b) The work must carry prominent notices stating that it is + released under this License and any conditions added under section + 7. This requirement modifies the requirement in section 4 to + "keep intact all notices". + + c) You must license the entire work, as a whole, under this + License to anyone who comes into possession of a copy. This + License will therefore apply, along with any applicable section 7 + additional terms, to the whole of the work, and all its parts, + regardless of how they are packaged. This License gives no + permission to license the work in any other way, but it does not + invalidate such permission if you have separately received it. + + d) If the work has interactive user interfaces, each must display + Appropriate Legal Notices; however, if the Program has interactive + interfaces that do not display Appropriate Legal Notices, your + work need not make them do so. + + A compilation of a covered work with other separate and independent +works, which are not by their nature extensions of the covered work, +and which are not combined with it such as to form a larger program, +in or on a volume of a storage or distribution medium, is called an +"aggregate" if the compilation and its resulting copyright are not +used to limit the access or legal rights of the compilation's users +beyond what the individual works permit. Inclusion of a covered work +in an aggregate does not cause this License to apply to the other +parts of the aggregate. + + 6. Conveying Non-Source Forms. + + You may convey a covered work in object code form under the terms +of sections 4 and 5, provided that you also convey the +machine-readable Corresponding Source under the terms of this License, +in one of these ways: + + a) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by the + Corresponding Source fixed on a durable physical medium + customarily used for software interchange. + + b) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by a + written offer, valid for at least three years and valid for as + long as you offer spare parts or customer support for that product + model, to give anyone who possesses the object code either (1) a + copy of the Corresponding Source for all the software in the + product that is covered by this License, on a durable physical + medium customarily used for software interchange, for a price no + more than your reasonable cost of physically performing this + conveying of source, or (2) access to copy the + Corresponding Source from a network server at no charge. + + c) Convey individual copies of the object code with a copy of the + written offer to provide the Corresponding Source. This + alternative is allowed only occasionally and noncommercially, and + only if you received the object code with such an offer, in accord + with subsection 6b. + + d) Convey the object code by offering access from a designated + place (gratis or for a charge), and offer equivalent access to the + Corresponding Source in the same way through the same place at no + further charge. You need not require recipients to copy the + Corresponding Source along with the object code. If the place to + copy the object code is a network server, the Corresponding Source + may be on a different server (operated by you or a third party) + that supports equivalent copying facilities, provided you maintain + clear directions next to the object code saying where to find the + Corresponding Source. Regardless of what server hosts the + Corresponding Source, you remain obligated to ensure that it is + available for as long as needed to satisfy these requirements. + + e) Convey the object code using peer-to-peer transmission, provided + you inform other peers where the object code and Corresponding + Source of the work are being offered to the general public at no + charge under subsection 6d. + + A separable portion of the object code, whose source code is excluded +from the Corresponding Source as a System Library, need not be +included in conveying the object code work. + + A "User Product" is either (1) a "consumer product", which means any +tangible personal property which is normally used for personal, family, +or household purposes, or (2) anything designed or sold for incorporation +into a dwelling. In determining whether a product is a consumer product, +doubtful cases shall be resolved in favor of coverage. For a particular +product received by a particular user, "normally used" refers to a +typical or common use of that class of product, regardless of the status +of the particular user or of the way in which the particular user +actually uses, or expects or is expected to use, the product. A product +is a consumer product regardless of whether the product has substantial +commercial, industrial or non-consumer uses, unless such uses represent +the only significant mode of use of the product. + + "Installation Information" for a User Product means any methods, +procedures, authorization keys, or other information required to install +and execute modified versions of a covered work in that User Product from +a modified version of its Corresponding Source. The information must +suffice to ensure that the continued functioning of the modified object +code is in no case prevented or interfered with solely because +modification has been made. + + If you convey an object code work under this section in, or with, or +specifically for use in, a User Product, and the conveying occurs as +part of a transaction in which the right of possession and use of the +User Product is transferred to the recipient in perpetuity or for a +fixed term (regardless of how the transaction is characterized), the +Corresponding Source conveyed under this section must be accompanied +by the Installation Information. But this requirement does not apply +if neither you nor any third party retains the ability to install +modified object code on the User Product (for example, the work has +been installed in ROM). + + The requirement to provide Installation Information does not include a +requirement to continue to provide support service, warranty, or updates +for a work that has been modified or installed by the recipient, or for +the User Product in which it has been modified or installed. Access to a +network may be denied when the modification itself materially and +adversely affects the operation of the network or violates the rules and +protocols for communication across the network. + + Corresponding Source conveyed, and Installation Information provided, +in accord with this section must be in a format that is publicly +documented (and with an implementation available to the public in +source code form), and must require no special password or key for +unpacking, reading or copying. + + 7. Additional Terms. + + "Additional permissions" are terms that supplement the terms of this +License by making exceptions from one or more of its conditions. +Additional permissions that are applicable to the entire Program shall +be treated as though they were included in this License, to the extent +that they are valid under applicable law. If additional permissions +apply only to part of the Program, that part may be used separately +under those permissions, but the entire Program remains governed by +this License without regard to the additional permissions. + + When you convey a copy of a covered work, you may at your option +remove any additional permissions from that copy, or from any part of +it. (Additional permissions may be written to require their own +removal in certain cases when you modify the work.) You may place +additional permissions on material, added by you to a covered work, +for which you have or can give appropriate copyright permission. + + Notwithstanding any other provision of this License, for material you +add to a covered work, you may (if authorized by the copyright holders of +that material) supplement the terms of this License with terms: + + a) Disclaiming warranty or limiting liability differently from the + terms of sections 15 and 16 of this License; or + + b) Requiring preservation of specified reasonable legal notices or + author attributions in that material or in the Appropriate Legal + Notices displayed by works containing it; or + + c) Prohibiting misrepresentation of the origin of that material, or + requiring that modified versions of such material be marked in + reasonable ways as different from the original version; or + + d) Limiting the use for publicity purposes of names of licensors or + authors of the material; or + + e) Declining to grant rights under trademark law for use of some + trade names, trademarks, or service marks; or + + f) Requiring indemnification of licensors and authors of that + material by anyone who conveys the material (or modified versions of + it) with contractual assumptions of liability to the recipient, for + any liability that these contractual assumptions directly impose on + those licensors and authors. + + All other non-permissive additional terms are considered "further +restrictions" within the meaning of section 10. If the Program as you +received it, or any part of it, contains a notice stating that it is +governed by this License along with a term that is a further +restriction, you may remove that term. If a license document contains +a further restriction but permits relicensing or conveying under this +License, you may add to a covered work material governed by the terms +of that license document, provided that the further restriction does +not survive such relicensing or conveying. + + If you add terms to a covered work in accord with this section, you +must place, in the relevant source files, a statement of the +additional terms that apply to those files, or a notice indicating +where to find the applicable terms. + + Additional terms, permissive or non-permissive, may be stated in the +form of a separately written license, or stated as exceptions; +the above requirements apply either way. + + 8. Termination. + + You may not propagate or modify a covered work except as expressly +provided under this License. Any attempt otherwise to propagate or +modify it is void, and will automatically terminate your rights under +this License (including any patent licenses granted under the third +paragraph of section 11). + + However, if you cease all violation of this License, then your +license from a particular copyright holder is reinstated (a) +provisionally, unless and until the copyright holder explicitly and +finally terminates your license, and (b) permanently, if the copyright +holder fails to notify you of the violation by some reasonable means +prior to 60 days after the cessation. + + Moreover, your license from a particular copyright holder is +reinstated permanently if the copyright holder notifies you of the +violation by some reasonable means, this is the first time you have +received notice of violation of this License (for any work) from that +copyright holder, and you cure the violation prior to 30 days after +your receipt of the notice. + + Termination of your rights under this section does not terminate the +licenses of parties who have received copies or rights from you under +this License. If your rights have been terminated and not permanently +reinstated, you do not qualify to receive new licenses for the same +material under section 10. + + 9. Acceptance Not Required for Having Copies. + + You are not required to accept this License in order to receive or +run a copy of the Program. Ancillary propagation of a covered work +occurring solely as a consequence of using peer-to-peer transmission +to receive a copy likewise does not require acceptance. However, +nothing other than this License grants you permission to propagate or +modify any covered work. These actions infringe copyright if you do +not accept this License. Therefore, by modifying or propagating a +covered work, you indicate your acceptance of this License to do so. + + 10. Automatic Licensing of Downstream Recipients. + + Each time you convey a covered work, the recipient automatically +receives a license from the original licensors, to run, modify and +propagate that work, subject to this License. You are not responsible +for enforcing compliance by third parties with this License. + + An "entity transaction" is a transaction transferring control of an +organization, or substantially all assets of one, or subdividing an +organization, or merging organizations. If propagation of a covered +work results from an entity transaction, each party to that +transaction who receives a copy of the work also receives whatever +licenses to the work the party's predecessor in interest had or could +give under the previous paragraph, plus a right to possession of the +Corresponding Source of the work from the predecessor in interest, if +the predecessor has it or can get it with reasonable efforts. + + You may not impose any further restrictions on the exercise of the +rights granted or affirmed under this License. For example, you may +not impose a license fee, royalty, or other charge for exercise of +rights granted under this License, and you may not initiate litigation +(including a cross-claim or counterclaim in a lawsuit) alleging that +any patent claim is infringed by making, using, selling, offering for +sale, or importing the Program or any portion of it. + + 11. Patents. + + A "contributor" is a copyright holder who authorizes use under this +License of the Program or a work on which the Program is based. The +work thus licensed is called the contributor's "contributor version". + + A contributor's "essential patent claims" are all patent claims +owned or controlled by the contributor, whether already acquired or +hereafter acquired, that would be infringed by some manner, permitted +by this License, of making, using, or selling its contributor version, +but do not include claims that would be infringed only as a +consequence of further modification of the contributor version. For +purposes of this definition, "control" includes the right to grant +patent sublicenses in a manner consistent with the requirements of +this License. + + Each contributor grants you a non-exclusive, worldwide, royalty-free +patent license under the contributor's essential patent claims, to +make, use, sell, offer for sale, import and otherwise run, modify and +propagate the contents of its contributor version. + + In the following three paragraphs, a "patent license" is any express +agreement or commitment, however denominated, not to enforce a patent +(such as an express permission to practice a patent or covenant not to +sue for patent infringement). To "grant" such a patent license to a +party means to make such an agreement or commitment not to enforce a +patent against the party. + + If you convey a covered work, knowingly relying on a patent license, +and the Corresponding Source of the work is not available for anyone +to copy, free of charge and under the terms of this License, through a +publicly available network server or other readily accessible means, +then you must either (1) cause the Corresponding Source to be so +available, or (2) arrange to deprive yourself of the benefit of the +patent license for this particular work, or (3) arrange, in a manner +consistent with the requirements of this License, to extend the patent +license to downstream recipients. "Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Use with the GNU Affero General Public License. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU Affero General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the special requirements of the GNU Affero General Public License, +section 13, concerning interaction through a network will apply to the +combination as such. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + Each version is given a distinguishing version number. If the +Program specifies that a certain numbered version of the GNU General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. + diff --git a/QuadTree.cabal b/QuadTree.cabal new file mode 100644 --- /dev/null +++ b/QuadTree.cabal @@ -0,0 +1,59 @@ +-- Initial QuadTree.cabal generated by cabal init. For further +-- documentation, see http://haskell.org/cabal/users-guide/ + +-- The name of the package. +name: QuadTree + +-- The package version. See the Haskell package versioning policy (PVP) +-- for standards guiding when and how versions should be incremented. +-- http://www.haskell.org/haskellwiki/Package_versioning_policy +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.10.0 + +-- A short (one-line) description of the package. +synopsis: QuadTree library for Haskell, with lens support. + +-- A longer description of the package. +-- description: +description: The purpose of this package is to provide discrete region quadtrees that can be used as effective functional alternatives to 2D arrays, with lens support. + +-- The license under which the package is released. +license: GPL-3 + +-- The file containing the license text. +license-file: LICENSE + +-- The package author(s). +author: Ashley Moni + +-- An email address to which users can send suggestions, bug reports, and +-- patches. +maintainer: y30099923@gmail.com + +-- A copyright notice. +-- copyright: + +category: Data + +build-type: Simple + +-- Constraint on the version of Cabal needed to build this package. +cabal-version: >=1.8 + + +library + -- Modules exported by the library. + exposed-modules: Data.QuadTree + + -- Modules included in this library but not exported. + -- other-modules: + + -- Other library packages from which modules are imported. + build-depends: base ==4.6.*, lens ==4.0.*, composition ==1.0.* + + +source-repository head + type: git + location: git@github.com:AshleyMoni/QuadTree.git diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain