grid 4.1 → 5.0

raw patch · 5 files changed

+416/−96 lines, 5 filesdep ~QuickCheckPVP ok

version bump matches the API change (PVP)

Dependency ranges changed: QuickCheck

API changes (from Hackage documentation)

Files

• grid.cabal +2/−2
• src/Math/Geometry/Grid.hs +41/−5
• src/Math/Geometry/GridInternal.hs +118/−3
• src/Math/Geometry/GridMap.hs +7/−3
• test/Math/Geometry/GridQC.hs +248/−83

@@ -1,5 +1,5 @@ name:           grid-version:        4.1+version:        5.0 synopsis:       Tools for working with regular grids (graphs, lattices). description:    Provides tools for working with regular arrangements                 of tiles, such as might be used in a board game or some@@ -42,7 +42,7 @@   build-depends:   base ==4.*,                    exact-combinatorics ==0.2.*,                    test-framework-quickcheck2 ==0.3.*,-                   QuickCheck ==2.4.* || ==2.5.*,+                   QuickCheck ==2.4.* || ==2.5.* || ==2.6.*,                    test-framework ==0.8.*,                    grid,                    base-unicode-symbols ==0.2.*

@@ -12,9 +12,34 @@ -- The userguide is available at  -- <https://github.com/mhwombat/grid/wiki>. --+-- In this package, tiles are called \"triangular\", \"square\", etc.,+-- based on the number of /neighbours/ they have.+-- For example, a square tile has four neighbours, and a hexagonal+-- tile has six.+-- There are only three regular polygons that can tile a plane:+-- triangles, squares, and hexagons.+-- Of course, other plane tilings are possible if you use irregular +-- polygons, or curved shapes, or if you combine tiles of different +-- shapes.+--+-- When you tile other surfaces, things get very interesting.+-- Octagons will tile a /hyperbolic/ plane.+-- (Alternatively, you can think of these as squares on a board game+-- where diagonal moves are allowed.)+--+-- For a board game, you probably want to choose the grid type based+-- on the number of /directions/ a player can move, rather than the+-- number of sides the tile will have when you display it.+-- For example, for a game that uses square tiles and allows the user+-- to move diagonally as well as horizontally and vertically,+-- consider using one of the grids with /octagonal/ tiles to model the+-- board.+-- You can still /display/ the tiles as squares, but for internal+-- calculations they are octagons.+-- -- NOTE: Version 4.0 uses associated (type) synonyms instead of  -- multi-parameter type classes.-+-- -- NOTE: Version 3.0 changed the order of parameters for many functions. -- This makes it easier for the user to write mapping and folding -- operations.@@ -25,6 +50,8 @@  module Math.Geometry.Grid   (+    -- * Example+    -- $Example     -- * The Grid class     Grid(..),     FiniteGrid(..),@@ -61,9 +88,16 @@     hexHexGrid,     -- ** Parallelogram-shaped grid with hexagonal tiles     ParaHexGrid,-    paraHexGrid-    -- * Example-    -- $Example+    paraHexGrid,+    -- * Grids with octagonal tiles+    -- ** Unbounded grid with octagonal tiles+    UnboundedOctGrid,+    -- ** Rectangular grid with octagonal tiles+    RectOctGrid,+    rectOctGrid,+    -- ** Toroidal grid with octagonal tiles+    TorOctGrid,+    torOctGrid   ) where  import Math.Geometry.GridInternal (Grid(..), FiniteGrid(..), @@ -71,7 +105,9 @@   ParaTriGrid, paraTriGrid, RectTriGrid, rectTriGrid,    TorTriGrid, torTriGrid, UnboundedSquareGrid,    RectSquareGrid, rectSquareGrid, TorSquareGrid, torSquareGrid, -  UnboundedHexGrid, HexHexGrid, hexHexGrid, ParaHexGrid, paraHexGrid)+  UnboundedHexGrid, HexHexGrid, hexHexGrid, ParaHexGrid, paraHexGrid, +  UnboundedOctGrid, RectOctGrid, rectOctGrid, TorOctGrid, torOctGrid)+  {- $Example    Create a grid.

@@ -37,7 +37,12 @@     HexHexGrid,     hexHexGrid,     ParaHexGrid,-    paraHexGrid+    paraHexGrid,+    UnboundedOctGrid,+    RectOctGrid,+    rectOctGrid,+    TorOctGrid,+    torOctGrid,   ) where  import Prelude hiding (null)@@ -49,7 +54,7 @@ import Data.Ord.Unicode ((≤), (≥))  -- | A regular arrangement of tiles.---   Minimal complete definition: @indices@ and @distance@.+--   Minimal complete definition: @Index@, @indices@ and @distance@. class Grid g where   type Index g @@ -225,6 +230,9 @@ -- Triangular tiles -- +-- | An unbounded grid with triangular tiles.+--   The grid and its indexing scheme are illustrated in the user guide,+--   available at <https://github.com/mhwombat/grid/wiki>. data UnboundedTriGrid = UnboundedTriGrid deriving Show  instance Grid UnboundedTriGrid where@@ -453,6 +461,9 @@ -- Square tiles -- +-- | An unbounde grid with square tiles.+--   The grid and its indexing scheme are illustrated in the user guide,+--   available at <https://github.com/mhwombat/grid/wiki>. data UnboundedSquareGrid = UnboundedSquareGrid deriving Show  instance Grid UnboundedSquareGrid where@@ -540,7 +551,7 @@ --      [((x-1) `mod` c,y), (x,(y+1) `mod` r), ((x+1) `mod` c,y),  --        (x,(y-1) `mod` r)]   neighbours g = nub . map (normalise g) . neighbours UnboundedSquareGrid-  distance g@(TorSquareGrid (r,c) _) (x1, y1) (x2, y2) =+  distance g@(TorSquareGrid (r,c) _) (x1, y1) (x2, y2) = -- TODO redo     if g `contains` (x1, y1) && g `contains` (x2, y2)       then min adx (abs (c-adx)) + min ady (abs (r-ady))       else undefined @@ -555,6 +566,18 @@   normalise g (x,y) = (x `mod` c, y `mod` r)     where (r, c) = size g +denormaliseTor+  :: (FiniteGrid g, Index g ~ (Int, Int), (Int, Int) ~ Size g) =>+     g -> Index g -> [Index g]+denormaliseTor g (x,y) = nub [(x2,y1), (x,y1), (x1,y1), +                              (x2,y),  (x,y),  (x1,y),+                              (x2,y2), (x,y2), (x1,y2)]+  where (r, c) = size g+        x1 = x + c+        y1 = y + r+        x2 = x - c+        y2 = y - r+ -- | @'torSquareGrid' r c@ returns a toroidal grid with @r@  --   rows and @c@ columns, using square tiles. If @r@ and @c@ are  --   both nonnegative, the resulting grid will have @r*c@ tiles. Otherwise, @@ -566,6 +589,9 @@ -- Hexagonal tiles -- +-- | An unbounded grid with hexagonal tiles+--   The grid and its indexing scheme are illustrated in the user guide,+--   available at <https://github.com/mhwombat/grid/wiki>. data UnboundedHexGrid = UnboundedHexGrid deriving Show  instance Grid UnboundedHexGrid where@@ -656,4 +682,93 @@ paraHexGrid ∷ Int → Int → ParaHexGrid paraHexGrid r c =    ParaHexGrid (r,c) [(x, y) | x ← [0..c-1], y ← [0..r-1]]+++--+-- Octagonal tiles+--++-- | An unbounded grid with octagonal tiles.+--   The grid and its indexing scheme are illustrated in the user guide,+--   available at <https://github.com/mhwombat/grid/wiki>.+data UnboundedOctGrid = UnboundedOctGrid deriving Show++instance Grid UnboundedOctGrid where+  type Index UnboundedOctGrid = (Int, Int)+  indices _ = undefined+  neighbours _ (x,y) = [(x-1,y+1), (x,y+1), (x+1,y+1), (x+1,y), +                        (x+1,y-1), (x,y-1), (x-1,y-1), (x-1,y)]+  distance _ (x1, y1) (x2, y2) = max (abs (x2-x1)) (abs (y2-y1))+  contains _ _ = True++--+-- Rectangular grids with octagonal tiles+--++-- | A rectangular grid with octagonal tiles.+--   The grid and its indexing scheme are illustrated in the user guide,+--   available at <https://github.com/mhwombat/grid/wiki>.+data RectOctGrid = RectOctGrid (Int, Int) [(Int, Int)] deriving Eq++instance Show RectOctGrid where +  show (RectOctGrid (r,c) _) = +    "rectOctGrid " ++ show r ++ " " ++ show c++instance Grid RectOctGrid where+  type Index RectOctGrid = (Int, Int)+  indices (RectOctGrid _ xs) = xs+  neighbours = neighboursBasedOn UnboundedOctGrid+  distance = distanceBasedOn UnboundedOctGrid++instance FiniteGrid RectOctGrid where+  type Size RectOctGrid = (Int, Int)+  size (RectOctGrid s _) = s++instance BoundedGrid RectOctGrid where+  tileSideCount _ = 4+  boundary g = cartesianIndices . size $ g+  centre g = cartesianCentre . size $ g++-- | @'rectOctGrid' r c@ produces a rectangular grid with @r@ rows+--   and @c@ columns, using octagonal tiles. If @r@ and @c@ are both +--   nonnegative, the resulting grid will have @r*c@ tiles. Otherwise, +--   the resulting grid will be null and the list of indices will be +--   null.+rectOctGrid ∷ Int → Int → RectOctGrid+rectOctGrid r c = +  RectOctGrid (r,c) [(x,y) | x ← [0..c-1], y ← [0..r-1]]++--+-- Toroidal grids with octagonal tiles.+--++-- | A toroidal grid with octagonal tiles.+--   The grid and its indexing scheme are illustrated in the user guide,+--   available at <https://github.com/mhwombat/grid/wiki>.+data TorOctGrid = TorOctGrid (Int, Int) [(Int, Int)] deriving Eq++instance Show TorOctGrid where +  show (TorOctGrid (r,c) _) = "torOctGrid " ++ show r ++ " " ++ show c++instance Grid TorOctGrid where+  type Index TorOctGrid = (Int, Int)+  indices (TorOctGrid _ xs) = xs+  neighbours g = nub . map (normalise g) . neighbours UnboundedOctGrid+  distance g a b = minimum . map (distance UnboundedOctGrid a) $ bs+    where bs = denormaliseTor g b++instance FiniteGrid TorOctGrid where+  type Size TorOctGrid = (Int, Int)+  size (TorOctGrid s _) = s++instance WrappedGrid TorOctGrid where+  normalise g (x,y) = (x `mod` c, y `mod` r)+    where (r, c) = size g++-- | @'torOctGrid' r c@ returns a toroidal grid with @r@ +--   rows and @c@ columns, using octagonal tiles. If @r@ and @c@ are +--   both nonnegative, the resulting grid will have @r*c@ tiles. Otherwise, +--   the resulting grid will be null and the list of indices will be null.+torOctGrid ∷ Int → Int → TorOctGrid+torOctGrid r c = TorOctGrid (r,c) [(x, y) | x ← [0..c-1], y ← [0..r-1]] 

@@ -42,7 +42,7 @@ -- | A regular arrangement of tiles, having a value associated with --   each tile. --   Minimal complete definition: @toMap@, @toGrid@, @adjustWithKey@,---   @mapWithKey.+--   @mapWithKey@. -- --   Note: Some of the methods have an @Ord@ constraint on the grid  --   index. This is purely to make it easier to write implementations.@@ -101,12 +101,16 @@   elems = M.elems . toMap    -- | Map a function over all values in the map.-  map ∷ GridMap gm b ⇒ (v → b) → gm v → gm b+  map +    ∷ (GridMap gm v2, +        G.Index (BaseGrid gm v) ~ G.Index (BaseGrid gm v2)) ⇒ +    (v → v2) → gm v → gm v2   map f = mapWithKey (\_ v → f v)    -- | Map a function over all values in the map.   mapWithKey -    ∷ (k ~ G.Index (BaseGrid gm v), GridMap gm v2) ⇒ +    ∷ (k ~ G.Index (BaseGrid gm v), k ~ G.Index (BaseGrid gm v2), +        GridMap gm v2) ⇒        (k → v → v2) → gm v → gm v2  {- $Compare

@@ -31,6 +31,17 @@ pointAt g i = indices g !! (i `mod` n)   where n = (length . indices) g +minPathCount+  ∷ (Eq (Index g), Grid g) ⇒ g → Index g → Index g → Int+minPathCount g a b = length . minimalPaths g a $ b++minPathCount2+  ∷ (Eq (Index g), Grid g) ⇒ g → [Index g] → Index g → Int+minPathCount2 g as b = sum . map (\x → minPathCount g x b) $ as++neighbourCount ∷ ∀ g. Grid g ⇒ g → Index g → Int+neighbourCount g x = length . neighbours g $ x+ -- -- Tests that should apply to and are identical for all grids --@@ -61,10 +72,10 @@   sort (delete a (neighbours g a)) ≡ sort expected     where a = g `pointAt` i           expected = map fst $ filter (\p → 1 ≡ snd p) $ viewpoint g a--- Note: In a small grid, a tile can be its own neighbour. However, when--- we calculate the distance between a tile and itself, we get 0, not 1.--- That's why we have to delete the tile from its list before comparing --- to the result from the neighbours function.+-- Note: In a small but unbounded grid, a tile can be its own neighbour.+-- However, when we calculate the distance between a tile and itself, we+-- get 0, not 1. That's why we have to delete the tile from its list +-- before comparing to the result from the neighbours function.  prop_edges_cw_neighbours ∷ (Grid g, Ord (Index g)) ⇒ g → Int → Property prop_edges_cw_neighbours g i = nonNull g ==> @@ -182,9 +193,7 @@  prop_TriTriGrid_neighbour_count_in_bounds ∷ TriTriGrid → Int → Property prop_TriTriGrid_neighbour_count_in_bounds g i = nonNull g ==>-  if tileCount g ≡ 1-    then length (neighbours g x) ≡ 0-    else length (neighbours g x) `elem` [1,2,3]+  neighbourCount g x ≤ 3   where x = g `pointAt` i  prop_TriTriGrid_boundary_count_correct ∷ TriTriGrid → Property@@ -237,9 +246,7 @@  prop_ParaTriGrid_neighbour_count_in_bounds ∷ ParaTriGrid → Int → Property prop_ParaTriGrid_neighbour_count_in_bounds g i = nonNull g ==>-  if tileCount g ≡ 1-    then length (neighbours g x) ≡ 0-    else length (neighbours g x) `elem` [1,2,3]+  neighbourCount g x ≤ 3   where x = g `pointAt` i  prop_ParaTriGrid_boundary_count_correct ∷ ParaTriGrid → Property@@ -283,9 +290,7 @@  prop_RectTriGrid_neighbour_count_in_bounds ∷ RectTriGrid → Int → Property prop_RectTriGrid_neighbour_count_in_bounds g i = nonNull g ==>-  if tileCount g ≡ 1-    then length (neighbours g x) ≡ 0-    else length (neighbours g x) `elem` [1,2,3]+  neighbourCount g x ≤ 3   where x = g `pointAt` i  prop_RectTriGrid_boundary_count_correct ∷ RectTriGrid → Property@@ -330,9 +335,7 @@  prop_TorTriGrid_neighbour_count_in_bounds ∷ TorTriGrid → Int → Property prop_TorTriGrid_neighbour_count_in_bounds g i = nonNull g ==>-  if tileCount g ≡ 1-    then length (neighbours g x) ≡ 0-    else length (neighbours g x) `elem` [1,2,3]+  neighbourCount g x ≤ 3   where x = g `pointAt` i  --@@ -374,18 +377,14 @@  prop_RectSquareGrid_neighbour_count_in_bounds ∷    RectSquareGrid → Int → Property-prop_RectSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> f+prop_RectSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> +  neighbourCount g x ≤ 4   where x = g `pointAt` i-        neighbourCount = length (neighbours g x)-        (r, c) = size g-        f | tileCount g ≡ 1 = neighbourCount ≡ 0-          | r ≡ 1 || c ≡ 1  = neighbourCount `elem` [1,2]-          | otherwise       = neighbourCount `elem` [2,3,4]  prop_RectSquareGrid_num_min_paths_correct ∷    RectSquareGrid → Int → Int → Property prop_RectSquareGrid_num_min_paths_correct g i j = nonNull g ==>-  length (minimalPaths g a b) ≡ M.choose (deltaX+deltaY) deltaX+  minPathCount g a b ≡ M.choose (deltaX+deltaY) deltaX     where a = g `pointAt` i           b = g `pointAt` j           deltaX = abs $ fst b - fst a@@ -408,7 +407,7 @@   ----- Toroidal grids with square-ish tiles+-- Toroidal grids with square tiles --  -- We want the number of tiles in a test grid to be O(n)@@ -442,21 +441,14 @@           ps = indices g           a = head ps           b = last ps-          f | r ≡ 1 && c ≡ 1 = 0 -- zero-size torus+          f | r ≡ 1 && c ≡ 1 = 0 -- single-tile torus             | r ≡ 1 || c ≡ 1 = 1 -- a and b are the same             | otherwise      = 2  prop_TorSquareGrid_neighbour_count_in_bounds ∷ TorSquareGrid → Int → Property-prop_TorSquareGrid_neighbour_count_in_bounds g i = nonNull g ==> f+prop_TorSquareGrid_neighbour_count_in_bounds g i = nonNull g ==>+  neighbourCount g x ≤ 4   where x = g `pointAt` i-        neighbourCount = length . neighbours g $ x-        (r, c) = size g-        f | tileCount g ≡ 1                = neighbourCount ≡ 1-          | (r,c) ≡ (1,2) || (r,c) ≡ (2,1) = neighbourCount ≡ 2-          | (r,c) ≡ (2,2)                  = neighbourCount ≡ 2-          | r ≡ 1 || c ≡ 1                 = neighbourCount ≡ 3-          | r ≡ 2 || c ≡ 2                 = neighbourCount ≡ 3-          | otherwise                      = neighbourCount ≡ 4  -- -- Circular hexagonal grids   @@ -494,9 +486,7 @@  prop_HexHexGrid_neighbour_count_in_bounds ∷ HexHexGrid → Int → Property prop_HexHexGrid_neighbour_count_in_bounds g i = nonNull g ==> -  if tileCount g ≡ 1-    then length (neighbours g x) ≡ 0-    else length (neighbours g x) `elem` [2,3,4,5,6]+  neighbourCount g x ≤ 6   where x = g `pointAt` i  prop_HexHexGrid_boundary_count_correct ∷ HexHexGrid → Property@@ -549,13 +539,9 @@           (r, c) = size g  prop_ParaHexGrid_neighbour_count_in_bounds ∷ ParaHexGrid → Int → Property-prop_ParaHexGrid_neighbour_count_in_bounds g i = nonNull g ==> f+prop_ParaHexGrid_neighbour_count_in_bounds g i = nonNull g ==>+  neighbourCount g x ≤ 6   where x = g `pointAt` i-        neighbourCount = length (neighbours g x)-        (r, c) = size g-        f | tileCount g ≡ 1 = neighbourCount ≡ 0-          | r ≡ 1 || c ≡ 1  = neighbourCount `elem` [1,2]-          | otherwise       = neighbourCount `elem` [2,3,4,5,6]  prop_ParaHexGrid_boundary_count_correct ∷ ParaHexGrid → Property prop_ParaHexGrid_boundary_count_correct g = property $@@ -565,7 +551,110 @@ prop_ParaHexGrid_boundary_tiles_have_fewer_neighbours g = property $   all (5>) . map (numNeighbours g) . boundary $ g +--+-- Rectangular grids with octagonal tiles+-- +-- We want the number of tiles in a test grid to be O(n)+sizedRectOctGrid ∷ Int → Gen RectOctGrid+sizedRectOctGrid n = do+  let n' = min n 12 -- calculation time for these grids grows quickly!+  r ← choose (0,n')+  let c = n' `div` (r+1)+  return $ rectOctGrid r c++instance Arbitrary RectOctGrid where+  arbitrary = sized sizedRectOctGrid++prop_RectOctGrid_tile_count_correct ∷ RectOctGrid → Property+prop_RectOctGrid_tile_count_correct g = property $ +  tileCount g ≡ if r ≤ 0 || c ≤ 0 then 0 else r*c+    where (r, c) = size g++prop_RectOctGrid_distance_in_bounds ∷ RectOctGrid → Int → Int → Property+prop_RectOctGrid_distance_in_bounds g i j = nonNull g ==>+  distance g a b ≤ max r c+    where (r, c) = size g+          a = g `pointAt` i+          b = g `pointAt` j++-- If the ordering produced by rectOctGrid is ever changed, this+-- property may need to be changed too. It relies on the first and last +-- elements being at opposite corners.+prop_RectOctGrid_distance_corner_to_corner ∷ RectOctGrid → Property+prop_RectOctGrid_distance_corner_to_corner g = r > 0 && c > 0 ==> +  a ≡ b || distance g a b ≡ (max r c) - 1+    where (r, c) = size g+          ps = indices g+          a = head ps+          b = last ps++prop_RectOctGrid_neighbour_count_in_bounds ∷ +  RectOctGrid → Int → Property+prop_RectOctGrid_neighbour_count_in_bounds g i = nonNull g ==>+  neighbourCount g x ≤ 8+  where x = g `pointAt` i++prop_RectOctGrid_num_min_paths_correct ∷ +  RectOctGrid → Int → Int → Property+prop_RectOctGrid_num_min_paths_correct g i j = nonNull g ==>+  minPathCount g a b ≡+    if a ≡ b then 1 else minPathCount2 g att b+    where a = g `pointAt` i+          b = g `pointAt` j+          att = adjacentTilesToward g a b++prop_RectOctGrid_boundary_count_correct ∷ RectOctGrid → Property+prop_RectOctGrid_boundary_count_correct g = property $+  (length . boundary) g ≡ (cartesianBoundaryCount . size) g++prop_RectOctGrid_boundary_tiles_have_fewer_neighbours ∷ RectOctGrid → Property+prop_RectOctGrid_boundary_tiles_have_fewer_neighbours g = property $+  all (6>) . map (numNeighbours g) . boundary $ g+++--+-- Toroidal grids with octagonal tiles+--++-- We want the number of tiles in a test grid to be O(n)+sizedTorOctGrid ∷ Int → Gen TorOctGrid+sizedTorOctGrid n = do+  r ← choose (0,n)+  let c = n `div` (r+1)+  return $ torOctGrid r c++instance Arbitrary TorOctGrid where+  arbitrary = sized sizedTorOctGrid++prop_TorOctGrid_tile_count_correct ∷ TorOctGrid → Property+prop_TorOctGrid_tile_count_correct g = property $  +  tileCount g ≡ if r ≤ 0 || c ≤ 0 then 0 else r*c+    where (r, c) = size g++prop_TorOctGrid_distance_in_bounds ∷ TorOctGrid → Int → Int → Property+prop_TorOctGrid_distance_in_bounds g i j = nonNull g ==>+  distance g a b ≤ min r c + abs (r-c)+    where (r, c) = size g+          a = g `pointAt` i+          b = g `pointAt` j++-- If the ordering produced by torOctGrid is ever changed, this property+-- may need to be changed too.+prop_TorOctGrid_distance_corner_to_corner ∷ TorOctGrid → Property+prop_TorOctGrid_distance_corner_to_corner g = r > 0 && c > 0 ==> +  distance g a b ≡ if tileCount g ≡ 1 then 0 else 1+    where (r, c) = size g+          ps = indices g+          a = head ps+          b = last ps++prop_TorOctGrid_neighbour_count_in_bounds ∷ TorOctGrid → Int → Property+prop_TorOctGrid_neighbour_count_in_bounds g i = nonNull g ==>+  neighbourCount g x ≤ 8+  where x = g `pointAt` i++ test ∷ Test test = testGroup "Math.Geometry.GridQC"   [@@ -601,17 +690,17 @@     testProperty "prop_neighbours_cw_viewpoint - TriTriGrid"       (prop_neighbours_cw_viewpoint ∷ TriTriGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - TriTriGrid"-      ( prop_edges_cw_neighbours ∷ TriTriGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ TriTriGrid → Int → Property),     testProperty "prop_edges_are_adjacent - TriTriGrid"-      ( prop_edges_are_adjacent ∷ TriTriGrid → Property),+      (prop_edges_are_adjacent ∷ TriTriGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - TriTriGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            TriTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - TriTriGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            TriTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - TriTriGrid"-      ( prop_minimal_paths_are_valid ∷ TriTriGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ TriTriGrid → Int → Int → Property),      -- ParaTriGrid tests     testProperty "prop_ParaTriGrid_tile_count_correct"@@ -645,17 +734,17 @@     testProperty "prop_neighbours_cw_viewpoint - ParaTriGrid"       (prop_neighbours_cw_viewpoint ∷ ParaTriGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - ParaTriGrid"-      ( prop_edges_cw_neighbours ∷ ParaTriGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ ParaTriGrid → Int → Property),     testProperty "prop_edges_are_adjacent - ParaTriGrid"-      ( prop_edges_are_adjacent ∷ ParaTriGrid → Property),+      (prop_edges_are_adjacent ∷ ParaTriGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - ParaTriGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            ParaTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - ParaTriGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            ParaTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - ParaTriGrid"-      ( prop_minimal_paths_are_valid ∷ ParaTriGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ ParaTriGrid → Int → Int → Property),      -- RectTriGrid tests     testProperty "prop_RectTriGrid_tile_count_correct"@@ -687,17 +776,17 @@     testProperty "prop_neighbours_cw_viewpoint - RectTriGrid"       (prop_neighbours_cw_viewpoint ∷ RectTriGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - RectTriGrid"-      ( prop_edges_cw_neighbours ∷ RectTriGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ RectTriGrid → Int → Property),     testProperty "prop_edges_are_adjacent - RectTriGrid"-      ( prop_edges_are_adjacent ∷ RectTriGrid → Property),+      (prop_edges_are_adjacent ∷ RectTriGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - RectTriGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            RectTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - RectTriGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            RectTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - RectTriGrid"-      ( prop_minimal_paths_are_valid ∷ RectTriGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ RectTriGrid → Int → Int → Property),      -- TorTriGrid tests     testProperty "prop_TorTriGrid_tile_count_correct"@@ -715,17 +804,17 @@     testProperty "prop_neighbours_cw_viewpoint - TorTriGrid"       (prop_neighbours_cw_viewpoint ∷ TorTriGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - TorTriGrid"-      ( prop_edges_cw_neighbours ∷ TorTriGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ TorTriGrid → Int → Property),     testProperty "prop_edges_are_adjacent - TorTriGrid"-      ( prop_edges_are_adjacent ∷ TorTriGrid → Property),+      (prop_edges_are_adjacent ∷ TorTriGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - TorTriGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            TorTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - TorTriGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            TorTriGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - TorTriGrid"-      ( prop_minimal_paths_are_valid ∷ TorTriGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ TorTriGrid → Int → Int → Property),      -- RectSquareGrid tests     testProperty "prop_RectSquareGrid_tile_count_correct"@@ -759,17 +848,17 @@     testProperty "prop_neighbours_cw_viewpoint - RectSquareGrid"       (prop_neighbours_cw_viewpoint ∷ RectSquareGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - RectSquareGrid"-      ( prop_edges_cw_neighbours ∷ RectSquareGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ RectSquareGrid → Int → Property),     testProperty "prop_edges_are_adjacent - RectSquareGrid"-      ( prop_edges_are_adjacent ∷ RectSquareGrid → Property),+      (prop_edges_are_adjacent ∷ RectSquareGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - RectSquareGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            RectSquareGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - RectSquareGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            RectSquareGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - RectSquareGrid"-      ( prop_minimal_paths_are_valid ∷ RectSquareGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ RectSquareGrid → Int → Int → Property),     testProperty "prop_RectSquareGrid_num_min_paths_correct"       prop_RectSquareGrid_num_min_paths_correct, @@ -791,17 +880,17 @@     testProperty "prop_neighbours_cw_viewpoint - TorSquareGrid"       (prop_neighbours_cw_viewpoint ∷ TorSquareGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - TorSquareGrid"-      ( prop_edges_cw_neighbours ∷ TorSquareGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ TorSquareGrid → Int → Property),     testProperty "prop_edges_are_adjacent - TorSquareGrid"-      ( prop_edges_are_adjacent ∷ TorSquareGrid → Property),+      (prop_edges_are_adjacent ∷ TorSquareGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - TorSquareGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            TorSquareGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - TorSquareGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            TorSquareGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - TorSquareGrid"-      ( prop_minimal_paths_are_valid ∷ TorSquareGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ TorSquareGrid → Int → Int → Property),      -- HexHexGrid tests     testProperty "prop_HexHexGrid_tile_count_correct"@@ -835,17 +924,17 @@     testProperty "prop_neighbours_cw_viewpoint - HexHexGrid"       (prop_neighbours_cw_viewpoint ∷ HexHexGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - HexHexGrid"-      ( prop_edges_cw_neighbours ∷ HexHexGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ HexHexGrid → Int → Property),     testProperty "prop_edges_are_adjacent - HexHexGrid"-      ( prop_edges_are_adjacent ∷ HexHexGrid → Property),+      (prop_edges_are_adjacent ∷ HexHexGrid → Property),     testProperty "prop_adjacentTilesToward_moves_closer - HexHexGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            HexHexGrid → Int → Int → Property),     testProperty "prop_minimal_paths_have_min_length - HexHexGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            HexHexGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - HexHexGrid"-      ( prop_minimal_paths_are_valid ∷ HexHexGrid → Int → Int → Property),+      (prop_minimal_paths_are_valid ∷ HexHexGrid → Int → Int → Property),      -- ParaHexGrid tests     testProperty "prop_ParaHexGrid_tile_count_correct"@@ -879,16 +968,92 @@     testProperty "prop_neighbours_cw_viewpoint - ParaHexGrid"       (prop_neighbours_cw_viewpoint ∷ ParaHexGrid → Int → Property),     testProperty "prop_edges_cw_neighbours - ParaHexGrid"-      ( prop_edges_cw_neighbours ∷ ParaHexGrid → Int → Property),+      (prop_edges_cw_neighbours ∷ ParaHexGrid → Int → Property),     testProperty "prop_adjacentTilesToward_moves_closer - ParaHexGrid"-      ( prop_adjacentTilesToward_moves_closer ∷ +      (prop_adjacentTilesToward_moves_closer ∷            ParaHexGrid → Int → Int → Property),     testProperty "prop_edges_are_adjacent - ParaHexGrid"-      ( prop_edges_are_adjacent ∷ ParaHexGrid → Property),+      (prop_edges_are_adjacent ∷ ParaHexGrid → Property),     testProperty "prop_minimal_paths_have_min_length - ParaHexGrid"-      ( prop_minimal_paths_have_min_length ∷ +      (prop_minimal_paths_have_min_length ∷            ParaHexGrid → Int → Int → Property),     testProperty "prop_minimal_paths_are_valid - ParaHexGrid"-      ( prop_minimal_paths_are_valid ∷ ParaHexGrid → Int → Int → Property)+      (prop_minimal_paths_are_valid ∷ ParaHexGrid → Int → Int → Property),++    -- RectOctGrid tests+    testProperty "prop_RectOctGrid_tile_count_correct"+      prop_RectOctGrid_tile_count_correct,+    testProperty "prop_distance_reflexive - RectOctGrid"+      (prop_distance_reflexive ∷ RectOctGrid → Int → Property),+    testProperty "prop_distance_symmetric - RectOctGrid"+      (prop_distance_symmetric ∷ RectOctGrid → Int → Int → Property),+    testProperty "prop_minDistance_cw_distance - RectOctGrid"+      (prop_minDistance_cw_distance ∷ RectOctGrid → Int → [Int] → Property),+    testProperty "prop_grid_and_boundary_are_both_null_or_not - RectOctGrid"+      (prop_grid_and_boundary_are_both_null_or_not ∷ RectOctGrid → Property),+    testProperty "prop_boundary_in_grid - RectOctGrid"+      (prop_boundary_in_grid ∷ RectOctGrid → Property),+    testProperty "prop_boundary_tiles_have_fewer_neighbours - RectOctGrid"+      (prop_boundary_tiles_have_fewer_neighbours ∷ RectOctGrid → Int → Property),+    testProperty "prop_RectOctGrid_boundary_count_correct"+      prop_RectOctGrid_boundary_count_correct,+    testProperty "prop_RectOctGrid_boundary_tiles_have_fewer_neighbours"+      prop_RectOctGrid_boundary_tiles_have_fewer_neighbours,+    testProperty "prop_centres_equidistant_from_boundary - RectOctGrid"+      (prop_centres_equidistant_from_boundary ∷ RectOctGrid → Property),+    testProperty "prop_centres_farthest_from_boundary - RectOctGrid"+      (prop_centres_farthest_from_boundary ∷ RectOctGrid → Int → Property),+    testProperty "prop_RectOctGrid_distance_in_bounds"+      prop_RectOctGrid_distance_in_bounds,+    testProperty "prop_RectOctGrid_distance_corner_to_corner"+      prop_RectOctGrid_distance_corner_to_corner,+    testProperty "prop_RectOctGrid_neighbour_count_in_bounds"+      prop_RectOctGrid_neighbour_count_in_bounds,+    testProperty "prop_neighbours_cw_viewpoint - RectOctGrid"+      (prop_neighbours_cw_viewpoint ∷ RectOctGrid → Int → Property),+    testProperty "prop_edges_cw_neighbours - RectOctGrid"+      (prop_edges_cw_neighbours ∷ RectOctGrid → Int → Property),+    testProperty "prop_edges_are_adjacent - RectOctGrid"+      (prop_edges_are_adjacent ∷ RectOctGrid → Property),+    testProperty "prop_adjacentTilesToward_moves_closer - RectOctGrid"+      (prop_adjacentTilesToward_moves_closer ∷ +          RectOctGrid → Int → Int → Property),+    testProperty "prop_minimal_paths_have_min_length - RectOctGrid"+      (prop_minimal_paths_have_min_length ∷ +          RectOctGrid → Int → Int → Property),+    testProperty "prop_minimal_paths_are_valid - RectOctGrid"+      (prop_minimal_paths_are_valid ∷ RectOctGrid → Int → Int → Property),+    testProperty "prop_RectOctGrid_num_min_paths_correct"+      prop_RectOctGrid_num_min_paths_correct,++    -- TorOctGrid tests+    testProperty "prop_TorOctGrid_tile_count_correct"+      prop_TorOctGrid_tile_count_correct,+    testProperty "prop_distance_reflexive - TorOctGrid"+      (prop_distance_reflexive ∷ TorOctGrid → Int → Property),+    testProperty "prop_distance_symmetric - TorOctGrid"+      (prop_distance_symmetric ∷ TorOctGrid → Int → Int → Property),+    testProperty "prop_minDistance_cw_distance - TorOctGrid"+      (prop_minDistance_cw_distance ∷ TorOctGrid → Int → [Int] → Property),+    testProperty "prop_TorOctGrid_distance_in_bounds"+      prop_TorOctGrid_distance_in_bounds,+    testProperty "prop_TorOctGrid_distance_corner_to_corner"+      prop_TorOctGrid_distance_corner_to_corner,+    testProperty "prop_TorOctGrid_neighbour_count_in_bounds"+      prop_TorOctGrid_neighbour_count_in_bounds,+    testProperty "prop_neighbours_cw_viewpoint - TorOctGrid"+      (prop_neighbours_cw_viewpoint ∷ TorOctGrid → Int → Property),+    testProperty "prop_edges_cw_neighbours - TorOctGrid"+      (prop_edges_cw_neighbours ∷ TorOctGrid → Int → Property),+    testProperty "prop_edges_are_adjacent - TorOctGrid"+      (prop_edges_are_adjacent ∷ TorOctGrid → Property),+    testProperty "prop_adjacentTilesToward_moves_closer - TorOctGrid"+      (prop_adjacentTilesToward_moves_closer ∷ +          TorOctGrid → Int → Int → Property),+    testProperty "prop_minimal_paths_have_min_length - TorOctGrid"+      (prop_minimal_paths_have_min_length ∷ +          TorOctGrid → Int → Int → Property),+    testProperty "prop_minimal_paths_are_valid - TorOctGrid"+      (prop_minimal_paths_are_valid ∷ TorOctGrid → Int → Int → Property)  ]