-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Alternative combinators for unorthodox function composition
--
-- Alternative combinators for unorthodox function composition
@package altcomposition
@version 0.2.1.0
-- | Compose functions with higher arity.
--
-- Ever tried something like this:
--
--
-- (length . (++)) stringA stringB
--
--
-- Only to find out that you can't? The second function takes two
-- parameters, and as such the simple function composition does not work.
--
-- A well known solution to this problem is this fun operator:
--
--
-- (.).(.) :: (c -> d) -> (a -> b -> c) -> (a -> b -> d)
--
--
-- And this is quite general:
--
--
-- ((.).(.).(.)) :: (d -> e) -> (a -> b -> c -> d) -> (a -> b -> c -> e)
--
--
-- See the following link to gain a intuition for how this works:
-- https://stackoverflow.com/questions/17585649/composing-function-composition-how-does-work
--
-- However, in real use these suffer from some problems, namely:
--
--
-- - They cannot be used infix, even with ticks (at least in
-- ghci).
-- - They are quite verbose.
--
--
-- Then, someone thought about using a new symbol instead:
--
--
-- (.:) :: (c -> d) -> (a -> b -> c) -> (a -> b -> d)
--
--
-- And for each new parameter, you would add a dot
--
--
-- (.:.) :: (d -> e) -> (a -> b -> c -> d) -> (a -> b -> c -> e)
--
--
-- And so on, to .::, .::., etc. This is the approach
-- taken by the composition package, which inspired this one. It
-- can be found at:
--
-- http://hackage.haskell.org/package/composition
--
-- This package is included in (and re-exported from) this
-- AltComposition.
--
-- So, why define a new package?
--
-- It does not scale well for other combinations. Let say I want (+)
-- . (*), a function that takes three parameters, uses the first two
-- in the multiplication, and then adds the third parameter with the
-- result. And what if I want to feed to the first binary function as the
-- second parameter of the second function?
--
-- The scheme proposed here is a little more verbose than the one from
-- the composition package, but it allows for a precise indication
-- of where the result of the first function is applied on the second
-- function using the % symbol (remember printf %). So,
-- the following operator:
--
--
-- *%*.**
--
--
-- Takes a binary function, and composes it with a ternary function,
-- aplying its result as the middle parameter.
--
-- Its all a matter of opinion, and I strongly recomend that you use
-- standard haskell syntax instead of these, for more portable code.
--
-- Also, many of these verbose operators have simpler counterparts. This
-- is either noted as Deprecation, or a single note.
--
-- However, I still find myself writing the *%.*** operators
-- myself, and I trust the deprecations to warn me about the simpler
-- alternatives.
--
-- If you need even higher arity, first check your code, then refactor
-- your code, and if you still need it, please send a pull request!
module Data.AltComposition
-- | Compose a binary function with a unitary function
--
-- Note: you should use idiomatic haskell instead
--
--
-- (.).(.) :: (c -> d) -> (a -> b -> c) -> (a -> b -> d)
--
--
--
-- (f %.** g) x y = f (g x y)
--
--
--
-- (f .: g) x y = f (g x y)
--
(%.**) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
-- | Compose a ternary function with a unitary function
--
-- Note: you should use idiomatic haskell instead
--
--
-- (.).(.).(.) :: (d -> e) -> (a -> b -> c -> d) -> (a -> b -> c -> e)
--
--
--
-- (f %.*** g) x y z = f (g x y z)
--
--
--
-- (f .:. g) x y z = f (g x y z)
--
(%.***) :: (d -> e) -> (a -> b -> c -> d) -> a -> b -> c -> e
-- | Compose a quaternary function with a unitary function
--
-- Note: you should use idiomatic haskell instead
--
--
-- (.).(.).(.).(.) :: (e -> f) -> (a -> b -> c -> d -> e) -> (a -> b -> c -> d -> f)
--
--
--
-- (f %.**** g) w x y z = f (g w x y z)
--
--
--
-- (f .:: g) w x y z = f (g w x y z)
--
(%.****) :: (e -> f) -> (a -> b -> c -> d -> e) -> a -> b -> c -> d -> f
-- | Compose a unary function with a binary function, applying the result
-- of the unary function as the first parameter of the binary function.
--
-- Note: DO NOT USE. Equivalent to ..
--
--
-- (f %*.* g) x y = f (g x) y <=> f . g
--
-- | Deprecated: This is the same as just (.)
(%*.*) :: (b -> c -> d) -> (a -> b) -> a -> c -> d
-- | Compose a binary function with another binary function, applying the
-- result of the first binary function as the first parameter of the
-- second binary function.
--
-- Note: DO NOT USE. Equivalent to flip f . g.
--
--
-- (f %*.** g) x y z = f (g x y) z
--
-- | Deprecated: Use f %.** g or .: instead
(%*.**) :: (c -> d -> e) -> (a -> b -> c) -> a -> b -> d -> e
-- | Compose a ternary function with a binary function, applying the result
-- of the ternary function as the first parameter of the binary function.
--
--
-- (f %*.*** g) x y w z = f (g x y w) z
--
-- | Deprecated: Use f %.*** g or f .:. instead
(%*.***) :: (d -> e -> f) -> (a -> b -> c -> d) -> a -> b -> c -> e -> f
-- | Compose a unary function with a binary function, applying the result
-- of the unary function as the second parameter of the binary function.
--
-- Note: DO NOT USE. Equivalent to flip f . g.
--
--
-- (f *%.* g) x y = f y (g x)
--
(*%.*) :: (b -> c -> d) -> (a -> c) -> a -> b -> d
-- | Compose a binary function with another binary function, applying the
-- result of the first binary function as the second parameter of the
-- second binary function.
--
-- Note: DO NOT USE. Equivalent to flip f .: g or
-- flip f %.** g.
--
--
-- (f *%.** g) x y z = f z (g x y)
--
(*%.**) :: (c -> d -> e) -> (a -> b -> d) -> a -> b -> c -> e
-- | Compose a ternary function with a binary function, applying the result
-- of the ternary function as the second parameter of the binary
-- function.
--
-- Note: DO NOT USE. Equivalent to flip f .:. g or
-- flip f %.*** g.
--
--
-- (f *%.*** g) x y w z = f z (g x y w)
--
(*%.***) :: (d -> e -> f) -> (a -> b -> c -> e) -> a -> b -> c -> d -> f
-- | Compose a unary function with a ternary function, applying the result
-- of the unary function as the first parameter of the ternary function.
--
-- Note: DO NOT USE. Equivalent to ..
--
--
-- (f %**.* g) x y z = f (g x) y z
--
-- | Deprecated: This is the same as just (.)
(%**.*) :: (b -> c -> d -> e) -> (a -> b) -> a -> c -> d -> e
-- | Compose a binary function with a ternary function, applying the result
-- of the binary function as the first parameter of the ternary function.
--
--
-- (f %**.** g) x y w z = f (g x y) w z
--
-- | Deprecated: Use f %.** g or f .: instead
(%**.**) :: (c -> d -> e -> f) -> (a -> b -> c) -> a -> b -> d -> e -> f
-- | Compose a ternary function with another ternary function, applying the
-- result of the first ternary function as the first parameter of the
-- last ternary function.
--
--
-- (f %**.*** g) v w x y z = f (g v w x) y z
--
-- | Deprecated: Use f %.*** g or f .:. instead
(%**.***) :: (f -> d -> e -> g) -> (a -> b -> c -> f) -> a -> b -> c -> d -> e -> g
-- | Compose a unary function with a ternary function, applying the result
-- of the unary function as the second parameter of the ternary function.
--
--
-- (f *%*.* g) x y z = f y (g x) z
--
(*%*.*) :: (b -> c -> d -> e) -> (a -> c) -> a -> b -> d -> e
-- | Compose a binary function with a ternary function, applying the result
-- of the binary function as the second parameter of the ternary
-- function.
--
-- Note: DO NOT USE. Equivalent to flip f .: g or
-- flip f %.** g.
--
--
-- (f *%*.** g) x y w z = f w (g x y) z
--
-- | Deprecated: Use f *%.** g instead
(*%*.**) :: (c -> d -> e -> f) -> (a -> b -> d) -> a -> b -> c -> e -> f
-- | Compose a ternary function with another ternary function, applying the
-- result of the first ternary function as the second parameter of the
-- last ternary function.
--
-- Note: DO NOT USE. Equivalent to flip f .:. g or
-- flip f %.*** g.
--
--
-- (f *%*.*** g) v w x y z = f y (g v w x) z
--
-- | Deprecated: Use f *%.*** g instead
(*%*.***) :: (d -> f -> e -> g) -> (a -> b -> c -> f) -> a -> b -> c -> d -> e -> g
-- | Compose a unary function with a ternary function, applying the result
-- of the unary function as the third parameter of the ternary function.
--
--
-- (f **%.* g) x y z = f y z (g x)
--
(**%.*) :: (b -> c -> d -> e) -> (a -> d) -> a -> b -> c -> e
-- | Compose a binary function with a ternary function, applying the result
-- of the binary function as the third parameter of the ternary function.
--
--
-- (f **%.** g) x y w z = f w z (g x y)
--
(**%.**) :: (c -> d -> e -> f) -> (a -> b -> e) -> a -> b -> c -> d -> f
-- | Compose a ternary function with another ternary function, applying the
-- result of the first ternary function as the third parameter of the
-- last ternary function.
--
--
-- (f **%.*** g) v w x y z = f y z (g v w x)
--
(**%.***) :: (d -> e -> f -> g) -> (a -> b -> c -> f) -> a -> b -> c -> d -> e -> g
-- | Compose a unary function with a quaternary function, applying the
-- result of the first unary function as the first parameter of the
-- quaternary function.
--
--
-- (f %***.* g) w x y z = f (g w) x y z
--
-- | Deprecated: This is the same as just (.)
(%***.*) :: (f -> b -> c -> d -> g) -> (a -> f) -> a -> b -> c -> d -> g
-- | Compose a binary function with a quaternary function, applying the
-- result of the first binary function as the first parameter of the
-- quaternary function.
--
--
-- (f %***.** g) v w x y z = f (g v w) x y z
--
-- | Deprecated: This is the same as just %.** or .:
(%***.**) :: (f -> c -> d -> e -> g) -> (a -> b -> f) -> a -> b -> c -> d -> e -> g
-- | Conditional composition. Borrowed (and modified) from
-- http://hackage.haskell.org/package/cond-0.4.0.2 If the
-- predicate is False, id is returned instead of the second
-- argument. This function, for example, can be used to conditionally add
-- functions to a composition chain.
(?.) :: Category cat => Bool -> cat a a -> cat a a
-- | Slightly Lower fixity function composition for use with
-- ?..
(.$) :: (b -> c) -> (a -> b) -> (a -> c)
-- | Just like ($), but with higher precedence than
-- (<>), but still lower than
-- (.). Similar to Diagrams.Util '#', but
-- without flipped arguments.
(ยง) :: (a -> b) -> a -> b
-- | Group conditions with &&. Useful for filter.
--
-- Note: an easy mnemonic to remember is that operators ending in
-- \ (lambda) imply that their parameters are functions instead of values
-- (in this particular case, boolean tests)
--
--
-- (f &&\ g) x = f x && g x
--
(&&\) :: (a -> Bool) -> (a -> Bool) -> (a -> Bool)
-- | Group conditions with || Useful for filter.
--
-- Note: an easy mnemonic to remember is that operators ending in
-- \ (lambda) imply that their parameters are functions instead of values
-- (in this particular case, boolean tests)
--
--
-- (f ||\ g) x = f x || g x
--
(||\) :: (a -> Bool) -> (a -> Bool) -> (a -> Bool)
-- | fmap with its arguments reversed.
--
--
-- http://www.reddit.com/r/haskell/comments/qy990/suggestion_for_flip_map/
--
--
-- for = flip fmap
-- with = flip fmap
--
for :: Functor f => f a -> (a -> b) -> f b
-- | fmap with its arguments reversed.
--
--
-- http://www.reddit.com/r/haskell/comments/qy990/suggestion_for_flip_map/
--
--
-- for = flip fmap
-- with = flip fmap
--
with :: Functor f => f a -> (a -> b) -> f b