    -- ------------------------------------------------------------

    {- |
       Module     : Control.Arrow.ArrowIf
       Copyright  : Copyright (C) 2005 Uwe Schmidt
       License    : MIT

       Maintainer : Uwe Schmidt (uwe\@fh-wedel.de)
       Stability  : experimental
       Portability: portable
       Version    : $Id: ArrowIf.hs,v 1.8 2006/05/04 14:17:53 hxml Exp $

    Conditionals for List Arrows

    This module defines conditional combinators for list arrows.

    The empty list as result represents False, none empty lists True.

    -}

    -- ------------------------------------------------------------

    module Control.Arrow.ArrowIf
        ( module Control.Arrow.ArrowIf
        )
    where

    import Control.Arrow
    import Control.Arrow.ArrowList

    import Data.List
        ( partition )

    -- ------------------------------------------------------------

    -- | The interface for arrows as conditionals.
    --
    -- Requires list arrows because False is represented as empty list, True as none empty lists.
    --
    -- Only 'ifA' and 'orElse' don't have default implementations

    class ArrowList a => ArrowIf a where

        -- | if lifted to arrows

        ifA                 :: a b c -> a b d -> a b d -> a b d

        -- | shortcut: @ ifP p = ifA (isA p) @

        ifP                 :: (b -> Bool) -> a b d -> a b d -> a b d
        ifP p               = ifA (isA p)

        -- | negation: @ neg f = ifA f none this @

        neg                 :: a b c -> a b b
        neg f               = ifA f none this

        -- | @ f \`when\` g @ : when the predicate g holds, f is applied, else the identity filter this

        when                :: a b b -> a b c -> a b b
        f `when` g          = ifA g f this

        -- | shortcut: @ f \`whenP\` p = f \`when\` (isA p) @

        whenP               :: a b b -> (b -> Bool) -> a b b
        f `whenP` g         = ifP g f this

        -- | @ f \`whenNot\` g @ : when the predicate g does not hold, f is applied, else the identity filter this

        whenNot             :: a b b -> a b c -> a b b
        f `whenNot` g       = ifA g this f

        -- | like 'whenP'

        whenNotP            :: a b b -> (b -> Bool) -> a b b
        f `whenNotP` g      = ifP g this f

        -- | @ g \`guards\` f @ : when the predicate g holds, f is applied, else none

        guards              :: a b c -> a b d -> a b d
        f `guards` g        = ifA f g none

        -- | like 'whenP'

        guardsP             :: (b -> Bool) -> a b d -> a b d
        f `guardsP` g       = ifP f g none

        -- | shortcut for @ f `guards` this @

        filterA             :: a b c -> a b b
        filterA f           = ifA f this none

        -- | @ f \`containing\` g @ : keep only those results from f for which g holds
        --
        -- definition: @ f \`containing\` g = f >>> g \`guards\` this @

        containing          :: a b c -> a c d -> a b c
        f `containing` g    = f >>> g `guards` this

        -- | @ f \`notContaining\` g @ : keep only those results from f for which g does not hold
        --
        -- definition: @ f \`notContaining\` g = f >>> ifA g none this @

        notContaining       :: a b c -> a c d -> a b c
        f `notContaining` g = f >>> ifA g none this

        -- | @ f \`orElse\` g @ : directional choice: if f succeeds, the result of f is the result, else g is applied
        orElse              :: a b c -> a b c -> a b c

        -- | generalisation of 'orElse' for multi way branches like in case expressions.
        --
        -- An auxiliary data type 'IfThen' with an infix constructor ':->' is used for writing multi way branches
        --
        -- example: @ choiceA [ p1 :-> e1, p2 :-> e2, this :-> default ] @
        choiceA             :: [IfThen (a b c) (a b d)] -> a b d
        choiceA             = foldr ifA' none
                              where
                              ifA' (g :-> f) = ifA g f

        -- | tag a value with Left or Right, if arrow has success, input is tagged with Left, else with Right
        tagA                :: a b c -> a b (Either b b)
        tagA p              = ifA p (arr Left) (arr Right)

        -- | split a list value with an arrow and returns a pair of lists.
        -- This is the arrow version of 'span'. The arrow is deterministic.
        --
        -- example: @ runLA (spanA (isA (\/= \'-\'))) \"abc-def\" @ gives @ [(\"abc\",\"-def\")] @ as result

        spanA               :: a b b -> a [b] ([b],[b])
        spanA p             = ifA ( arrL (take 1) >>> p )
                              ( arr head &&& (arr tail >>> spanA p)
                                >>>
                                arr (\ ~(x, ~(xs,ys)) -> (x : xs, ys))
                              )
                              ( arr (\ l -> ([],l)) )

        -- | partition a list of values into a pair of lists
        --
        -- This is the arrow Version of 'Data.List.partition'

        partitionA          :: a b b -> a [b] ([b],[b])
        partitionA  p       = listA ( arrL id >>> tagA p )
                              >>^
                              ( (\ ~(l1, l2) -> (unTag l1, unTag l2) ) . partition (isLeft) )
                              where
                              isLeft (Left _) = True
                              isLeft _        = False
                              unTag = map (either id id)

    -- ------------------------------------------------------------

    -- | an auxiliary data type for 'choiceA'

    data IfThen a b = a :-> b

    -- ------------------------------------------------------------