module Language.GroteTrap.Range ( -- * Types Pos, Range, KnowsPosition(..), -- * Utility functions distRange, inRange, includes, unionRange, size, validRange ) where -- | A @Pos@ is a position in between two elements in a list. For example, position @0@ marks the beginning of the list, and position @length list@ marks the end of the list. There are @n + 1@ valid positions for a list of length @n@. type Pos = Int -- 1 :: Pos -- | -- 0 1 2 3 4 5 6 7 8 9 -- k a a s b r o o d -- 0 1 2 3 4 5 6 7 8 9 -- \_______/ -- (0,4) :: Range -- | A range's positions mark the begin and end of a sublist, respectively. type Range = (Pos, Pos) -- | Something that knows its range as sublist in a larger list. Minimal complete definition: either 'range' or both 'begin' and 'end'. class KnowsPosition a where -- | Yields the element's range. range :: a -> Range range x = (begin x, end x) -- | Yields the element's begin position. begin :: a -> Pos begin = fst . range -- | Yields the element's end position. end :: a -> Pos end = snd . range -- | A range's size is the number of elements it contains. size :: Range -> Int size (b,e) = e-b -- | Whether a position falls within a range, including the range's edges. inRange :: Pos -> Range -> Bool inRange pos (begin, end) = pos >= begin && pos <= end -- | @unionRange x y@ yields the smallest range z such that @x ``includes`` z@ and @y ``includes`` z@. unionRange :: Range -> Range -> Range unionRange = min **** max -- | Yields whether the second argument completely falls within the first argument. includes :: Range -> Range -> Bool includes r (b,e) = b `inRange` r && e `inRange` r -- | @distRange (b1, e1) (b2, e2)@ is defined as @|b1 - b2| + |e1 - e2|@. distRange :: Range -> Range -> Int distRange (b1,e1) (b2,e2) = db + de where db = abs (b1 - b2) de = abs (e1 - e2) (****) :: (a -> b -> c) -> (d -> e -> f) -> (a,d) -> (b,e) -> (c,f) (****) fl fr (a,d) (b,e) = (fl a b, fr d e) -- | A range is valid if its positions are nonnegative and begin < end. validRange :: Range -> Bool validRange (b, e) = b >= 0 && e >= 0 && b <= e