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| Control.Arrow.DeepArrow | | Portability | portable | | Stability | experimental | | Maintainer | conal@conal.net |
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| Description |
| "Deep arrows" as an Arrow subclass.
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| Synopsis |
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| class Arrow ~> => DeepArrow (~>) where | | result :: (b ~> b') -> (a -> b) ~> (a -> b') | | idA :: a ~> a | | dupA :: a ~> (a, a) | | fstA :: (a, b) ~> a | | sndA :: (a, b) ~> b | | funF :: (c -> a, b) ~> (c -> (a, b)) | | funS :: (a, c -> b) ~> (c -> (a, b)) | | funR :: (a -> c -> b) ~> (c -> a -> b) | | curryA :: ((a, b) -> c) ~> (a -> b -> c) | | uncurryA :: (a -> b -> c) ~> ((a, b) -> c) | | swapA :: (a, b) ~> (b, a) | | lAssocA :: (a, (b, c)) ~> ((a, b), c) | | rAssocA :: ((a, b), c) ~> (a, (b, c)) |
| | | funFirst :: DeepArrow ~> => (a ~> (d -> a')) -> (a, b) ~> (d -> (a', b)) | | | funSecond :: DeepArrow ~> => (b ~> (d -> b')) -> (a, b) ~> (d -> (a, b')) | | | funResult :: DeepArrow ~> => (b ~> (d -> b')) -> (a -> b) ~> (d -> a -> b') | | | inpF :: DeepArrow ~> => ((a, b) -> c) ~> (a -> b -> c) | | | inpS :: DeepArrow ~> => ((a, b) -> c) ~> (b -> a -> c) | | | inpFirst :: DeepArrow ~> => ((a -> c) ~> (d -> a' -> c)) -> ((a, b) -> c) ~> (d -> (a', b) -> c) | | | inpSecond :: DeepArrow ~> => ((b -> c) ~> (d -> b' -> c)) -> ((a, b) -> c) ~> (d -> (a, b') -> c) | | | flipA :: DeepArrow ~> => (a -> c -> b) ~> (c -> a -> b) | | | unzipA :: DeepArrow ~> => (a ~> (b, c)) -> (a ~> b, a ~> c) | | | class FunAble h => FunDble h where | | resultFun :: (h b -> h b') -> h (a -> b) -> h (a -> b') | | dupAFun :: h a -> h (a, a) | | fstAFun :: h (a, b) -> h a | | sndAFun :: h (a, b) -> h b | | funFFun :: h (c -> a, b) -> h (c -> (a, b)) | | funSFun :: h (a, c -> b) -> h (c -> (a, b)) | | funRFun :: h (a -> c -> b) -> h (c -> a -> b) | | curryAFun :: h ((a, b) -> c) -> h (a -> b -> c) | | uncurryAFun :: h (a -> b -> c) -> h ((a, b) -> c) | | swapAFun :: h (a, b) -> h (b, a) | | lAssocAFun :: h (a, (b, c)) -> h ((a, b), c) | | rAssocAFun :: h ((a, b), c) -> h (a, (b, c)) |
| | | (->|) :: (DeepArrow ~>, FunArr ~> w) => w (a -> b) -> w (b -> c) -> w (a -> c) |
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| The DeepArrow class
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Arrows for deep application. Most of these methods could be defined
using arr, but arr is not definable for some types. If your
DeepArrow instance has arr, you might want to use these
implementations
idA = arr id
fstA = arr fst
dupA = arr (\ x -> (x,x))
sndA = arr snd
funF = arr (\ (f,b) -> \ c -> (f c, b))
funS = arr (\ (a,f) -> \ c -> (a, f c))
funR = arr flip
curryA = arr curry
uncurryA = arr uncurry
swapA = arr (\ (a,b) -> (b,a))
lAssocA = arr (\ (a,(b,c)) -> ((a,b),c))
rAssocA = arr (\ ((a,b),c) -> (a,(b,c)))
If your DeepArrow instance does not have arr, you'll have to come up
with other definitions. In any case, I recommend the following
definitions, which mirror Arrow defaults while avoiding arr. Be sure
also to define arr or pure to yield an error message (rather than
ping-ponging infinitely between them via the Arrow default definitions).
second f = swapA >>> first f >>> swapA
f &&& g = dupA >>> f *** g
In a few cases, there are default methods, as noted below. The
defaults do not use arr.
| | | Methods | | result :: (b ~> b') -> (a -> b) ~> (a -> b') | Source |
| | Direct arrow into a function's result. Analogous to first and
second.
| | | | Identity.
| | | | Duplicate.
| | | | Extract first.
| | | | Extract second.
| | | funF :: (c -> a, b) ~> (c -> (a, b)) | Source |
| | Extract function from first element.
| | | funS :: (a, c -> b) ~> (c -> (a, b)) | Source |
| | Extract function from second element.
| | | funR :: (a -> c -> b) ~> (c -> a -> b) | Source |
| | Extract function from result.
| | | curryA :: ((a, b) -> c) ~> (a -> b -> c) | Source |
| | Curry arrow.
| | | uncurryA :: (a -> b -> c) ~> ((a, b) -> c) | Source |
| | Uncurry arrow.
| | | swapA :: (a, b) ~> (b, a) | Source |
| | Swap elements. Has default.
| | | lAssocA :: (a, (b, c)) ~> ((a, b), c) | Source |
| | Left-associate. Has default.
| | | rAssocA :: ((a, b), c) ~> (a, (b, c)) | Source |
| | Right-associate. Has default.
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| |  Instances | |
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| Composable function extractors
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| funFirst :: DeepArrow ~> => (a ~> (d -> a')) -> (a, b) ~> (d -> (a', b)) | Source |
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| Promote a function extractor into one that reaches into the first
element of a pair.
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| funSecond :: DeepArrow ~> => (b ~> (d -> b')) -> (a, b) ~> (d -> (a, b')) | Source |
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| Promote a function extractor into one that reaches into the second
element of a pair.
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| funResult :: DeepArrow ~> => (b ~> (d -> b')) -> (a -> b) ~> (d -> a -> b') | Source |
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| Promote a function extractor into one that reaches into the result
element of a function.
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| Composable input extractors
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| Extract the first component of a pair input.
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| Extract the second component of a pair input.
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| inpFirst :: DeepArrow ~> => ((a -> c) ~> (d -> a' -> c)) -> ((a, b) -> c) ~> (d -> (a', b) -> c) | Source |
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| Given a way to extract a d input from an a input, leaving an a'
residual input, inpFirst yields a way to extract a d input from an
(a,b) input, leaving an (a',b) residual input.
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| inpSecond :: DeepArrow ~> => ((b -> c) ~> (d -> b' -> c)) -> ((a, b) -> c) ~> (d -> (a, b') -> c) | Source |
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| Analogous to inpFirst.
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| Misc functions
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| Flip argument order
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| Like unzip but for DeepArrow arrows instead of lists.
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| DeepArrow instance helper
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| Support needed for a FunA to be a DeepArrow (as FunAble serves
Arrow).
| | | Methods | | resultFun :: (h b -> h b') -> h (a -> b) -> h (a -> b') | Source |
| | | dupAFun :: h a -> h (a, a) | Source |
| | | fstAFun :: h (a, b) -> h a | Source |
| | | sndAFun :: h (a, b) -> h b | Source |
| | | funFFun :: h (c -> a, b) -> h (c -> (a, b)) | Source |
| | | funSFun :: h (a, c -> b) -> h (c -> (a, b)) | Source |
| | | funRFun :: h (a -> c -> b) -> h (c -> a -> b) | Source |
| | | curryAFun :: h ((a, b) -> c) -> h (a -> b -> c) | Source |
| | | uncurryAFun :: h (a -> b -> c) -> h ((a, b) -> c) | Source |
| | | swapAFun :: h (a, b) -> h (b, a) | Source |
| | | lAssocAFun :: h (a, (b, c)) -> h ((a, b), c) | Source |
| | | rAssocAFun :: h ((a, b), c) -> h (a, (b, c)) | Source |
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| Some utilities
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| Compose wrapped functions
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| Produced by Haddock version 2.3.0 |
