module Tools where

pair :: a -> b -> (a,b)
pair = (,)

singleton :: a -> [a]
singleton a = [a]

dup :: (a,r) -> ((a,r),r)
dup   ~(a,r) =  ((a,r),r)

assocpairl :: ( (a, b), c) -> (a, (b, c))
assocpairl   ~(~(a, b), c) =  (a, (b, c))

assocpairr :: (a,  (b, c)) -> ((a, b), c)
assocpairr   ~(a, ~(b, c)) =  ((a, b), c)

swap12     :: (s,  (a, b)) -> (a, (s, b))
swap12       ~(s, ~(a, b)) =  (a, (s, b))
           
swap23     :: ( (a, b), s) -> ((a, s), b)
swap23       ~(~(a, b), s) =  ((a, s), b)
           
rotl       :: ( (c, a), s) -> ((a, s), c)
rotl         ~(~(c, a), s) =  ((a, s), c)
           
rotr       :: ( (a, s), c) -> ((c, a), s)
rotr         ~(~(a, s), c) =  ((c, a), s)

eitherout :: (Either a a',s) -> Either (a,s) (a',s)
eitherout ~(x,s) = either (Left . (`pair` s)) (Right . (`pair` s)) x

eitherin :: Either (b,s) (b',s) -> (Either b b',s)    
eitherin = either (mapFst Left) (mapFst Right)

mapFst :: (a->b) -> (a,c) -> (b,c)
mapFst f = f `seq` \(~(a, t)) -> (f a, t)

mapSnd :: (a->b) -> (c,a) -> (c,b)
mapSnd f = f `seq` \(~(t, a)) -> (t, f a)

swap :: (a,b) -> (b,a)
swap   ~(x,y) =  (y,x)

bool2Either :: Bool -> a -> Either a a
bool2Either b = if b then Left else Right

-- strict composition
comp :: (a->b) -> (b->c) -> (a->c)
comp f g = f `seq` g `seq` (g.f)