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-# 2D Grid utilities
-
-Types and utilities for dealing with a 2D grid of things
-
-We base our `Grid` type on `Data.Seq.Sized` from `contrib`, a finger tree based
-collection that tracks its size in its type, since it provides somewhat
-efficient random access and updates.
-
-```idris
-module Grid
-
-import Data.Seq.Sized
-import Data.Fin
-import Data.Fin.Extra
-import Data.List.Lazy
-import Data.Zippable
-import Data.Vect
-import Data.String
-import Decidable.Equality
-
-%default total
-```
-
-## Coordinates
-
-A coordinate is a pair of numbers both less than their respective bounds.
-
-Since `Grid`s will always be non-empty in the contexts we will be using them in,
-this type alias adds one to each of the bounds to ensure non-emptyness
-
-```idris
-public export
-Coord : (rows, cols : Nat) -> Type
-Coord rows cols = (Fin (S rows), Fin (S cols))
-```
-
-### Coordinate utility functions
-
-Lazily generate all the coordinates for a given pair of bounds
-
-Uses an internal helper function to generate a lazy list of all the fins of a
-given bound in ascending order (`all`), and another to convert a lazy list of
-`Fin` into a lazy list of pairs of `Fin`s.
-
-The totality checker likes to go in the descending direction, since then it can
-reason about values getting structurally "smaller", so it has issues with `all'`
-moving in the ascending direction. We know this function is total because the
-`acc < last` check will always eventually be triggered, since `Fin`s only have a
-finite number of values.
-
-We pull out an `assert_smaller` to tell Idris that the argument to the recursive
-call is getting structurally smaller, which while not strictly correct, does
-convey to the compiler that we are getting closer to our recursive base case and
-that the function is thus total.
-
-```idris
-export
-allCords : {rows, cols : Nat} -> LazyList (Coord rows cols)
-allCords = concat . map row $ all
- where
- all : {n : Nat} -> LazyList (Fin (S n))
- all = FZ :: all' FZ
- where
- all' : {n : Nat} -> (acc : Fin (S n)) -> LazyList (Fin (S n))
- all' acc =
- if acc < last
- then finS acc :: all' (assert_smaller acc (finS acc))
- else []
- row : Fin (S rows) -> LazyList (Coord rows cols)
- row r = map (\c => (r, c)) all
-```
-
-Add a given vector to a coordinate, returning `Nothing` if we go off the ends of
-the bounds in the process.
-
-To keep this function simple and reasonably efficient, we perform the arithmetic
-in integer space, using `integerToFin` to fallably convert back to `Fin` space,
-making use of the `Maybe` monad to keep the code clean.
-
-```idris
-export
-step : {rows, cols : Nat} -> (input : Coord rows cols) -> (direction : (Integer, Integer))
- -> Maybe (Coord rows cols)
-step (row, col) (d_row, d_col) = do
- let (row, col) = (finToInteger row, finToInteger col)
- row <- integerToFin (row + d_row) (S rows)
- col <- integerToFin (col + d_col) (S cols)
- pure (row, col)
-```
-
-## Grid
-
-A grid is a `Seq` of `Seq`s with the given size bounds.
-
-The inner `Seq`s are kept opaque to maintain flexability in the implementation
-
-```idris
-export
-record Grid (rows, cols : Nat) (e : Type) where
- constructor MkGrid
- grid : Seq (S rows) (Seq (S cols) e)
-%name Grid grid, grid2, grid3
-```
-
-### Constructors
-
-Construct a `Grid` by filling every slot with identical copies of the provided
-element
-
-```idris
-export
-replicate : {rows, cols : Nat} -> (seed : e) -> Grid rows cols e
-replicate seed =
- let row = replicate (S cols) seed
- grid = replicate (S rows) row
- in MkGrid grid
-```
-
-Attempt to construct a `Grid` from a Foldable of Foldables. Will return
-`Nothing` if either the rows are of heterogeneous size, or if either the rows or
-columns are empty. Requires that the outer Foldable also be Traversable.
-
-We make heavy use of the `Maybe` monad to keep the code clean here.
-
-```idris
-export
-fromFoldable : Traversable a => Foldable a => Foldable b => a (b e) ->
- Maybe (rows : Nat ** cols : Nat ** Grid rows cols e)
-fromFoldable xs = do
- -- First collect the number of rows from the outer foldable
- let (S rows) = foldl (\acc, e => acc + 1) 0 xs
- | _ => Nothing -- Return Nothing if there are no rows
- -- Get the number of columns in the largest row in the inner foldable
- let (S cols) = foldl (\acco, eo => max acco (foldl (\acci, ei => acci +1) 0 eo)) 0 xs
- | _ => Nothing -- Return Nothing if all the rows are empty
- -- Convert the rows by traversing our foldToSeq function over the outer foldable
- xs <- traverse (foldToSeq (S cols)) xs
- -- Reuse our foldToSeq helper function to convert the outer foldable
- xs <- foldToSeq (S rows) xs
- -- wrap it up and return
- pure (rows ** cols ** MkGrid xs)
- where
- -- Convert each row to a seq using an intermediate list
- foldToSeq : Foldable c => (n : Nat) -> c f -> Maybe (Seq n f)
- foldToSeq n x =
- let list = toList x
- -- Check to see if the list is of the correct length, then rewrite the
- -- output type to match if that's the case, otherwise return Nothing
- in case decEq (length list) n of
- Yes Refl => Just $ fromList list
- No _ => Nothing
-```
-
-Construct a `Grid` from a non-empty `Vect` of non-empty `Vect`s. To keep the
-function simple, we require that both the row and column dimension are known to
-be non-zero before calling this constructor.
-
-```idris
-export
-fromVect : Vect (S rows) (Vect (S cols) e) -> Grid rows cols e
-fromVect xs = MkGrid . fromVect . map fromVect $ xs
-```
-
-Construct `Grid` containing the coordinate of the location in each location
-
-```idris
-export
-coordinateGrid : {rows, cols : Nat} -> Grid rows cols (Coord rows cols)
-coordinateGrid =
- let row = fromVect $ allFins (S cols)
- grid = zip (fromVect $ allFins (S rows)) (replicate _ row)
- grid = map (\(x, xs) => map (x,) xs) grid
- in MkGrid grid
-```
-
-### Accessors and Mutators
-
-Get the value at a specific index in the grid
-
-```idris
-export
-index : Coord rows cols -> Grid rows cols e -> e
-index (row, col) grid =
- index' (index' grid.grid row) col
-```
-
-Replace the value at a specific index in the grid
-
-```idris
-export
-replaceAt : Coord rows cols -> e -> Grid rows cols e -> Grid rows cols e
-replaceAt (row, col) x (MkGrid grid) =
- let r = index' grid row
- r = update (finToNat col) x r @{elemSmallerThanBound col}
- grid = update (finToNat row) r grid @{elemSmallerThanBound row}
- in MkGrid grid
-```
-
-Update the value at a specific index in the grid
-
-```idris
-export
-updateAt : Coord rows cols -> (e -> e) -> Grid rows cols e -> Grid rows cols e
-updateAt (row, col) f (MkGrid grid) =
- let r = index' grid row
- r = adjust f (finToNat col) r @{elemSmallerThanBound col}
- grid = update (finToNat row) r grid @{elemSmallerThanBound row}
- in MkGrid grid
-```
-
-Lazily provide all the values in the grid as a flat collection
-
-```idris
-export
-flat : {rows, cols : Nat} -> Grid rows cols e -> LazyList e
-flat (MkGrid grid) =
- let grid = seqToLazy . map (seqToLazy {n = S cols}) $ grid
- grid = grid []
- in foldrLazy (\a, acc => a acc) [] grid
- where
- seqToLazy : {n : Nat} -> (seq : Seq n a) -> (rest : LazyList a) -> LazyList a
- seqToLazy {n = 0} seq rest = rest
- seqToLazy {n = (S k)} seq rest =
- let (head, tail) = viewl seq
- in head :: seqToLazy tail rest
-```
-
-### Interface Implementations
-
-#### Show
-
-```idris
-export
-{rows, cols : Nat} -> Show e => Show (Grid rows cols e) where
- show (MkGrid grid) =
- show . toVect . map toVect $ grid
-```
-
-#### Eq/Ord
-
-```idris
-export
-Eq e => Eq (Grid rows cols e) where
- (MkGrid grid_x) == (MkGrid grid_y) = grid_x == grid_y
-
-export
-Ord e => Ord (Grid rows cols e) where
- compare (MkGrid grid_x) (MkGrid grid_y) = compare grid_x grid_y
-```
-
-#### Functor
-
-```idris
-export
-Functor (Grid rows cols) where
- map f (MkGrid grid) =
- MkGrid . map (map f) $ grid
-```
-
-#### Foldable
-
-Cheeze it a little and use our `flat` function internally here.
-
-Also, `null` can statically return false, as `Grid` is structurally non-empty
-
-```idris
-export
-{rows, cols : Nat} -> Foldable (Grid rows cols) where
- foldr f acc grid = foldr f acc (flat grid)
- foldl f acc grid = foldl f acc (flat grid)
- null _ = False
- toList grid = toList (flat grid)
-```
-
-#### Applicative
-
-```idris
-export
-{rows, cols : Nat} -> Applicative (Grid rows cols) where
- pure a = replicate a
- (MkGrid f) <*> (MkGrid grid) =
- MkGrid . map (\(a,b) => a <*> b) . zip f $ grid
-```
-
-#### Traversable
-
-```idris
-export
-{rows, cols : Nat} -> Traversable (Grid rows cols) where
- traverse f (MkGrid grid) =
- map MkGrid . traverse (traverse f) $ grid
-```
-
-#### Zippable
-
-```idris
-export
-Zippable (Grid rows cols) where
- zipWith f (MkGrid grid_x) (MkGrid grid_y) =
- let xs = zip grid_x grid_y
- in MkGrid . map (\(a,b) => zipWith f a b) $ xs
- unzipWith f (MkGrid grid) =
- let (xs, ys) = unzip . map (unzipWith f) $ grid
- in (MkGrid xs, MkGrid ys)
- zipWith3 f (MkGrid as) (MkGrid bs) (MkGrid cs) =
- let xs = zip3 as bs cs
- in MkGrid . map (\(a, b, c) => zipWith3 f a b c) $ xs
- unzipWith3 f (MkGrid grid) =
- let (a, b, c) = unzip3 . map (unzipWith3 f) $ grid
- in (MkGrid a, MkGrid b, MkGrid c)
-```
-
-### Extra
-
-Extensions of the above functionality
-
-#### Indexing
-
-Convert this grid to one with both the index of the location and the element in
-each location
-
-```idris
-export
-indexed : {rows, cols : Nat} -> Grid rows cols e -> Grid rows cols (Coord rows cols, e)
-indexed grid = zip coordinateGrid grid
-```
-
-Same as `flat` above, but indexed
-
-```idris
-export
-flatIndexed : {rows, cols : Nat} -> Grid rows cols e -> LazyList (Coord rows cols, e)
-flatIndexed = flat . indexed
-```
-
-#### String functionality
-
-Attempts to convert a string, with newline delimited rows, to a grid of
-characters
-
-```idris
-export
-stringToGrid : String -> Maybe (rows : Nat ** cols : Nat ** Grid rows cols Char)
-stringToGrid = fromFoldable . map (unpack . trim) . lines . trim
-```
-
-Converts a grid of chars to a string, delimiting the rows with newlines
-
-```idris
-export
-gridToString : Grid rows cols Char -> String
-gridToString (MkGrid grid) = unlines . toList . map (pack . toList) $ grid
-```
-
-#### Conversion
-
-Convert a grid to a vect of vects
-
-```idris
-export
-toVects : {rows, cols : Nat} -> Grid rows cols e -> Vect (S rows) (Vect (S cols) e)
-toVects (MkGrid grid) = toVect . map toVect $ grid
-```
-
-Convert a grid to a list of lists
-
-```idris
-export
-toLists : Grid rows cols e -> List (List e)
-toLists (MkGrid grid) = toList . map toList $ grid
-```