QuadTree 0.10.1 → 0.11.0

raw patch · 5 files changed

+720/−1050 lines, 5 filesdep +QuickCheckdep ~basedep ~compositiondep ~lensPVP ok

version bump matches the API change (PVP)

Dependencies added: QuickCheck

Dependency ranges changed: base, composition, lens

API changes (from Hackage documentation)

Files

• Data/QuadTree.hs +6/−372
• Data/QuadTree/Internal.hs +409/−0
• LICENSE +21/−673
• QuadTree.cabal +11/−5
• Test/quadtree-tests.hs +273/−0

@@ -6,10 +6,10 @@ {-# LANGUAGE ScopedTypeVariables #-}  {-|-Module      : QuadTree+Module      : Data.QuadTree Description : Region quadtrees with lens support.-Copyright   : (c) Ashley Moni, 2014-License     : GPL-3+Copyright   : (c) Ashley Moni, 2015+License     : BSD3 Maintainer  : Ashley Moni <ashley.moni1@gmail.com> Stability   : Stable @@ -39,7 +39,7 @@   QuadTree, makeTree,   -- * Index access   -- $locations-  Location, getLocation, setLocation, atLocation,+  Location, atLocation, getLocation, setLocation, mapLocation,   -- * Functor   fuseTree, tmap,   -- * Foldable@@ -57,61 +57,9 @@   -- * Miscellaneous helpers   outOfBounds, treeDimensions, regionArea, inRegion ) where -import Control.Lens.Type (Lens')-import Control.Lens.Lens (lens)--- import Control.Lens.Setter (set)+import Data.QuadTree.Internal -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@@ -122,130 +70,6 @@ -- 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...@@ -255,7 +79,7 @@ -- import "Prelude" hiding (foldr, foldl, any, sum, find...) -- @ ----- ... Then you can directly call then on 'QuadTree's without+-- ... Then you can directly call them 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.@@ -286,193 +110,3 @@ -- '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) '.'

@@ -0,0 +1,409 @@+{-# OPTIONS_HADDOCK show-extensions #-}++{-# LANGUAGE Safe #-}++{-# LANGUAGE Rank2Types #-}+{-# LANGUAGE ScopedTypeVariables #-}++{-|+Module      : Data.QuadTree.Internal+Description : Internals for the Data.QuadTree library.+Copyright   : (c) Ashley Moni, 2015+License     : BSD3+Maintainer  : Ashley Moni <ashley.moni1@gmail.com>+Stability   : Stable++The QuadTree.Internals library is a separately encapsulated subset of+the QuadTree library, strictly for the purpose of exposing inner+structure and functions to the testing suites.+|-}++module Data.QuadTree.Internal where++import Control.Lens.Type (Lens')+import Control.Lens.Setter (over, set)+import Control.Lens.Getter (view)++import Data.List (find, sortBy)+import Data.Function (on)+import Data.Composition ((.:))++---- 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, Eq)++-- |'QuadTree's are 'Functor's, and their elements can be fmapped over.+instance Functor QuadTree where+  fmap fn = onQuads $ fmap fn++-- |'QuadTree's are 'Foldable', though the traversal path is a complex+-- recursive enumeration of internal 'Quadrant's. Don't use folds that aren't+-- ordering agnostic.+instance Foldable QuadTree where+  foldr = foldTree++-- Quadrants:++-- |The internal data structure of a 'QuadTree'.+--+-- Each 'Quadrant' consists of either a terminating Leaf node, or+-- four further 'Quadrant's.++data Quadrant a = Leaf a+                | Node (Quadrant a)+                       (Quadrant a)+                       (Quadrant a)+                       (Quadrant a)+  deriving (Show, Read, Eq)++-- |'Quadrant's are 'Functor's. -- You can fmap all their recursive leaf node.+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)++---- Quadrant lenses:++-- |Lens for the top left 'Quadrant' of a node.+_a :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a)+_a f (Node a b c d) = fmap (\x -> fuse $ Node x b c d) (f a)+_a f leaf           = fmap embed (f leaf)+  where embed :: Quadrant a -> Quadrant a+        embed x | x == leaf = leaf+                | otherwise = Node x leaf leaf leaf++-- |Lens for the top right 'Quadrant' of a node.+_b :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a)+_b f (Node a b c d) = fmap (\x -> fuse $ Node a x c d) (f b)+_b f leaf           = fmap embed (f leaf)+  where embed :: Quadrant a -> Quadrant a+        embed x | x == leaf = leaf+                | otherwise = Node leaf x leaf leaf++-- |Lens for the bottom left 'Quadrant' of a node.+_c :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a)+_c f (Node a b c d) = fmap (\x -> fuse $ Node a b x d) (f c)+_c f leaf           = fmap embed (f leaf)+  where embed :: Quadrant a -> Quadrant a+        embed x | x == leaf = leaf+                | otherwise = Node leaf leaf x leaf++-- |Lens for the bottom right 'Quadrant' of a node.+_d :: forall a. Eq a => Lens' (Quadrant a) (Quadrant a)+_d f (Node a b c d) = fmap (fuse . Node a b c) (f d)+_d f leaf           = fmap embed (f leaf)+  where embed :: Quadrant a -> Quadrant a+        embed x | x == leaf = leaf+                | otherwise = Node leaf leaf leaf x++-- |Lens for a terminate leaf value of a node.+_leaf :: Lens' (Quadrant a) a+_leaf f (Leaf leaf) = Leaf <$> f leaf+_leaf _ _           = error "Wrapped tree is deeper than cached tree depth."++-- |Lens to zoom into the internal data structure of a 'QuadTree',+-- lensing past the metadata to reveal the 'Quadrant' inside.+_wrappedTree :: Lens' (QuadTree a) (Quadrant a)+_wrappedTree f qt = (\x -> qt {wrappedTree = x}) <$> f (wrappedTree qt)++-- |Unsafe sanity test lens that makes sure a given location index exists+-- within the relevant 'QuadTree'.+verifyLocation :: Location -> Lens' (QuadTree a) (QuadTree a)+verifyLocation index f qt+  | index `outOfBounds` qt = error "Location index out of QuadTree bounds."+  | otherwise              = f qt++---- Index access:++-- |Lens for accessing and manipulating data at a specific+-- location.+atLocation :: forall a. Eq a => Location -> Lens' (QuadTree a) a+atLocation index fn qt = (verifyLocation index . _wrappedTree .+                          go (offsetIndex qt index) (treeDepth qt)) fn qt+  where+    go :: Eq a => Location -> Int -> Lens' (Quadrant a) a+    go _     0 = _leaf+    go (x,y) n | y < mid   = if x < mid then _a . recurse+                                        else _b . recurse+               | otherwise = if x < mid then _c . recurse+                                        else _d . recurse+      where recurse = go (x `mod` mid, y `mod` mid) (n - 1)+            mid = 2 ^ (n - 1)++-- |Getter for the value at a given location for a 'QuadTree'.+getLocation :: Eq a => Location -> QuadTree a -> a+getLocation = view . atLocation++-- |Setter for the value at a given location for a 'QuadTree'.+--+-- This automatically compresses the 'QuadTree' nodes if possible with+-- the new value.+setLocation :: Eq a => Location -> a -> QuadTree a -> QuadTree a+setLocation = set . atLocation++-- |Modifies value at a given location for a 'QuadTree'.+--+-- This automatically compresses the 'QuadTree' nodes if possible with+-- the new value.+mapLocation :: Eq a => Location -> (a -> a) -> QuadTree a -> QuadTree a+mapLocation = over . atLocation++---- Helpers:++-- |Checks if a 'Location' is outside the boundaries of a 'QuadTree'.+outOfBounds :: Location -> QuadTree a -> Bool+outOfBounds (x,y) tree = 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)++-- |Add offsets to a location index for the purpose of querying+-- the 'QuadTree' 's true reference frame.+offsetIndex :: QuadTree a -> Location -> Location+offsetIndex tree (x,y) = (x + xOffset, y + yOffset)+  where (xOffset, yOffset) = offsets tree++-- |Offsets added to a 'QuadTree' 's true reference frame+-- to reference elements in the centralized width and height.+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++-- |Merge 'Quadrant' into a leaf node if possible.+fuse :: Eq a => Quadrant a -> Quadrant a+fuse (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d))+  | allEqual [a,b,c,d] = Leaf a+fuse oldNode            = oldNode++-- |Test if all elements in a list are equal.+allEqual :: Eq a => [a] -> Bool+allEqual = and . (zipWith (==) <*> tail)++---- Functor:++-- |Apply a function to a 'QuadTree's internal 'Quadrant'.+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+  where 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:++-- |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)++-- |Foldr elements within a 'QuadTree', by first decomposing it into+-- 'Tile's and then decomposing those into lists of identical data values.++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++-- |The region denoting an entire 'QuadTree'.+treeRegion :: QuadTree a -> Region+treeRegion tree = (0, 0, limit, limit)+  where limit = (2 ^ treeDepth tree) - 1++-- |The boundary 'Region' of the internal 'QuadTree' 's true reference frame.+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)++-- |'Region' that's an intersection between two othe 'Region's.+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 = smallestDepth (x,y) }++-- |Find the smallest tree depth that would encompass a given width and height.+smallestDepth :: (Int, Int) -> Int+smallestDepth (x,y) = depth+  where (depth, _)         = smallestPower+        Just smallestPower = find bigEnough powersZip+        bigEnough (_, e)   = e >= max x y+        powersZip          = 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 :: Eq a => (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 :: Eq a => (a -> Char) -- ^ Function to generate characters for each+                                 -- 'QuadTree' element.+                  -> QuadTree a -> IO ()+printTree = putStr .: showTree

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@@ -10,7 +10,7 @@ -- PVP summary:      +-+------- breaking API changes --                   | | +----- non-breaking API additions --                   | | | +--- code changes with no API change-version:             0.10.1+version:             0.11.0  -- A short (one-line) description of the package. synopsis:            QuadTree library for Haskell, with lens support.@@ -20,7 +20,7 @@ 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+license:             BSD3  -- The file containing the license text. license-file:        LICENSE@@ -48,15 +48,21 @@   exposed-modules:     Data.QuadTree    -- Modules included in this library but not exported.-  -- other-modules:+  other-modules:       Data.QuadTree.Internal    -- Other library packages from which modules are imported.-  build-depends:       base >= 4.6 && <= 4.8,-                       lens >= 4.1 && <= 4.5,+  build-depends:       base >= 4.6 && < 4.10,+                       lens >= 4.1 && < 4.13,                        composition ==1.0.*    -- http://www.vex.net/~trebla/haskell/cabal-cabal.xhtml   default-language:    Haskell2010++Test-Suite quadtree-tests+  type: exitcode-stdio-1.0+  main-is: Test/quadtree-tests.hs+  build-depends: base, lens, composition, QuickCheck+  default-language: Haskell2010  source-repository head   type: git

@@ -0,0 +1,273 @@+{-# LANGUAGE TemplateHaskell #-}++{-# LANGUAGE ScopedTypeVariables #-}++module Main where++import Data.QuadTree.Internal++import Test.QuickCheck.Arbitrary (Arbitrary, arbitrary)+import Test.QuickCheck.Modifiers (Positive(..), NonNegative(..))+import Test.QuickCheck.Gen (Gen, choose, oneof, suchThat,+                            listOf, infiniteListOf)+import Test.QuickCheck.Property (Property, (==>))+import Test.QuickCheck.All (quickCheckAll)++import Text.Show.Functions ()+import System.Exit (exitSuccess, exitFailure)++import Control.Lens.Type (Lens')+import Control.Lens.Setter (set)+import Control.Lens.Getter (view)+import Control.Monad (replicateM)+import Data.Functor ((<$>))+import Data.Composition ((.:))++{- Structure++The QuadTree type has two structural invariants/constraints:++   1. The internal raw tree must not be deeper than its+   declared depth.++   2. No branch node can have four leaves that are identical.+   These need to be fused into a single leaf node by the algorithms.++We will acknowledge and manage these invariants by constructing+two separate Arbitrary generators for QuadTrees:++  1. The first generator will construct QuadTrees strictly using the+  exposed API (makeTree and setLocation). We'll use this to test if+  the invariant is consistently maintained across the subset of QuadTrees+  that the user can construct.++  2. The second generator will generate QuadTrees ex nihilo that obey+  the invariants. We'll use this for our primary testing purposes, since+  it can theoretically generate valid non-user-constructable trees and+  because it can generate large complex trees far far more efficiently.++-}++---- The API-constructable QuadTree generator++newtype APITree a = Constructed (QuadTree a)++instance Show a => Show (APITree a) where+  show (Constructed qt) = show qt++instance (Eq a, Arbitrary a) => Arbitrary (APITree a) where+  arbitrary = do+    Positive len <- arbitrary+    Positive wid <- arbitrary+    baseValue    <- arbitrary+    let baseTree = makeTree (len, wid) baseValue++    indices <- listOf $ generateIndexOf baseTree+    values  <- infiniteListOf arbitrary+    let setList = zip indices values++    return . Constructed $ foldr (uncurry setLocation) baseTree setList++-- Generates a random valid location index for a quadtree+generateIndexOf :: QuadTree a -> Gen Location+generateIndexOf qt = do+  x <- choose (0, treeLength qt - 1)+  y <- choose (0, treeWidth qt  - 1)+  return (x,y)+++---- Ex-nihilo QuadTree generator++newtype GenTree a = Generated (QuadTree a)++instance Show a => Show (GenTree a) where+  show (Generated qt) = show qt++instance (Eq a, Arbitrary a) => Arbitrary (GenTree a) where+  arbitrary = do+    Positive len <- arbitrary+    Positive wid <- arbitrary+    let depth = smallestDepth (len, wid)+    tree <- generateQuadrant depth++    return . Generated $ Wrapper { treeLength = len,+                                   treeWidth = wid,+                                   treeDepth = depth,+                                   wrappedTree = tree }++generateQuadrant :: (Eq a, Arbitrary a) => Int -> Gen (Quadrant a)+generateQuadrant 0 = generateLeaf+generateQuadrant n = oneof [generateLeaf, generateNode (n - 1)]++generateLeaf :: Arbitrary a => Gen (Quadrant a)+generateLeaf = Leaf <$> arbitrary++generateNode :: (Eq a, Arbitrary a) => Int -> Gen (Quadrant a)+generateNode n = do+  [a,b,c,d] <- replicateM 4 (generateQuadrant n) `suchThat` (not . equalLeaves)+  return (Node a b c d)+    where equalLeaves :: Eq a => [Quadrant a] -> Bool+          equalLeaves [Leaf a, Leaf b, Leaf c, Leaf d] = allEqual [a,b,c,d]+          equalLeaves _                                = False+++-- Ex-nihilo Quadrant generator++instance (Eq a, Arbitrary a) => Arbitrary (Quadrant a) where+  arbitrary = do+    NonNegative depth <- arbitrary+    generateQuadrant depth++---- General index generator++-- Ideally, we'd be able to generate random dimensionally valid lenses as+-- part of the arguments to property functions that take quadtrees.+-- But we'd need dependent types for that, so we're just going to generate+-- independent random lenses and only test the ones that would work with+-- the tree.++newtype Index = MkIndex (Int, Int)++instance Arbitrary Index where+  arbitrary = do+    NonNegative x <- arbitrary+    NonNegative y <- arbitrary+    return $ MkIndex (x,y)++instance Show Index where+  show (MkIndex index) = show index+++---- APITree structural tests++-- We use Bools here since they're the most trivial Eq type.+-- A QuadTree constructed with Bool insertions is the fastest way+-- to build/fuse up a complex set of nodes at various heights.++-- Inner tree representation cannot be deeper than defined depth+prop_APITreeDepth :: APITree Bool -> Bool+prop_APITreeDepth (Constructed qt) = go (treeDepth qt) (wrappedTree qt)+  where go :: Int -> Quadrant a -> Bool+        go _ (Leaf _)       = True+        go 0 _              = False+        go n (Node a b c d) = and $ fmap (go (n - 1)) [a,b,c,d]++-- Inner tree representation cannot have branches holding four equal leaves+prop_APITreeInequality :: APITree Bool -> Bool+prop_APITreeInequality (Constructed qt) = go $ wrappedTree qt+  where go :: Eq a => Quadrant a -> Bool+        go (Leaf _)            = True+        go (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d))+          | allEqual [a,b,c,d] = False+        go (Node a b c d)      = and $ fmap go [a,b,c,d]+++---- Ex Nihilo QuadTree tests++-- For completeness, we'll test the structural requirements here as well.+-- The requirements are baked into the generator, but this lets us test+-- that generator.++-- Inner tree representation cannot be deeper than defined depth+prop_treeDepth :: GenTree Bool -> Bool+prop_treeDepth (Generated qt) = go (treeDepth qt) (wrappedTree qt)+  where go :: Int -> Quadrant a -> Bool+        go _ (Leaf _)       = True+        go 0 _              = False+        go n (Node a b c d) = and $ fmap (go (n - 1)) [a,b,c,d]++-- Inner tree representation cannot have branches holding four equal leaves+prop_treeInequality :: GenTree Bool -> Bool+prop_treeInequality (Generated qt) = go $ wrappedTree qt+  where go :: Eq a => Quadrant a -> Bool+        go (Leaf _)            = True+        go (Node (Leaf a) (Leaf b) (Leaf c) (Leaf d))+          | allEqual [a,b,c,d] = False+        go (Node a b c d)      = and $ fmap go [a,b,c,d]++{- Functor laws++  fmap id = id+  fmap (f . g) = fmap f . fmap g -}++prop_functor1 :: Eq a => GenTree a -> Bool+prop_functor1 (Generated qt)     = fmap id qt == qt++prop_functor2 :: Eq c => GenTree a -> (b -> c) -> (a -> b) -> Bool+prop_functor2 (Generated qt) f g = fmap (f . g) qt == (fmap f . fmap g) qt++{- Lens laws++  view l (set l b a)  = b+  set l (view l a) a  = a+  set l c (set l b a) = set l c a -}++prop_lens1 :: Eq a => GenTree a -> a -> Index -> Property+prop_lens1 (Generated a) b (MkIndex location) =+  location `validIndexOf` a  ==>  view l (set l b a) == b+  where l :: Eq a => Lens' (QuadTree a) a+        l = atLocation location++prop_lens2 :: Eq a => GenTree a -> Index -> Property+prop_lens2 (Generated a) (MkIndex location) =+  location `validIndexOf` a  ==>  set l (view l a) a == a+  where l :: Eq a => Lens' (QuadTree a) a+        l = atLocation location++prop_lens3 :: Eq a => GenTree a -> a -> a -> Index -> Property+prop_lens3 (Generated a) b c (MkIndex location) =+  location `validIndexOf` a  ==>  set l c (set l b a) == set l c a+  where l :: Eq a => Lens' (QuadTree a) a+        l = atLocation location+++validIndexOf :: Location -> QuadTree a -> Bool+validIndexOf = not .: outOfBounds+++---- Collate and run tests:++return [] -- Template Haskell splice. See QuickCheck hackage docs.+runTests :: IO Bool+runTests = $quickCheckAll++main :: IO ()+main = do+  allClear <- runTests+  if allClear+    then exitSuccess+    else exitFailure++--------- Manual repl test fragments:++-- 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) '.'