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Description | |||||||||||||||||||||||||||||||||

This modules provides a convienient way to access and update the elements of a structure.
It is very similar to Data.Accessors, but a bit more generic and has fewer dependencies.
I particularly like how cleanly it handles nested structures in state monads.
A brief tutorial to get started: To create a lense, you can use fromGetSet (although usually you would just derive them using templat haskell and deriveLenses from Data.Lenses.Template): lense = fromGetSet getField setField The lense has type: lense :: (MonadState r m) => StateT a m b -> m b Where r is the type of the record, and a is the type of the field, (b can be any type you choose, more on that latter). Though it may help to think of it as: lense :: State a b -> State r b Which is not entirely accurate, but emphasises how the lense works. You can think of it as "pass in an action that operates on the field, and you get an action that operates on the record". So say we pass in get (with a more specific type for clarity): get :: State a a lense get :: State r a We get out a state monad that we can run on our record to fetch our field. fieldValue = lense get `evalState` record This module has a special function fieldValue = record `fetch` lense You can also pass in put :: a -> State a () lense (put someValue) :: State r () Now we have a state monad that we can run on our record to update our field. updatedRecord = lense (put someValue) `execState` record This module has a special function updatedRecord = (record `update` lense) someValue To aid in clarity and to deal with the actual types of the lenses this module provides The lenses are especially convienient if you have nested structures. Lense composition is just function composition. data Point = Point { x_ :: Float, y_ :: Float } deriving (Show) $( deriveLenses ''Point ) data Triangle = Triangle { pa_ :: Point, pb_ :: Point, pc_ :: Point } deriving (Show) $( deriveLenses ''Triangle ) a_y :: (MonadState Triangle m) => StateT Float (StateT Point m) b -> m b a_y = pa . y a_y is now a lense that can operate on the y coordinate of point "a" inside a triangle. We can use a_y to fetch the coordinate or update it, on whatever triangle we choose. someTriangle = Triangle (Point 5 3) (Point 0 1) (Point 10 6) ayValue = someTriangle `fetch` a_y -- ayValue == 3 updatedTriangle = (someTriangle `update` a_y) 7 -- updatedTriangle == Triangle (Point 5 7) (Point 0 1) (Point 10 6) Or we could apply our lense to an action and pass it into (someTriangle `update` a_y) 7 == execIn someTriangle (a_y (put 7)) We can also chain actions together: a_x :: (MonadState Triangle m) => StateT Float (StateT Point m) b -> m b a_x = pa . x c_y :: (MonadState Triangle m) => StateT Float (StateT Point m) b -> m b c_y = pc . y updatedTriangle = execIn someTriangle $ a_y (put 7) >> a_x (put 1) >> c_y (put 9) -- updatedTriangle == Triangle (Point 1 7) (Point 0 1) (Point 10 9) What if we wanted to put the value of c_y into a_x? Can do! updatedTriangle = execIn someTriangle $ do cy <- c_y get a_x $ put cy -- updatedTriangle == Triangle (Point 6 3) (Point 0 1) (Point 10 6) Or if the order really bugs you, you can use the updatedTriangle = execIn someTriangle $ do cy <- get $% c_y put cy $% a_x -- updatedTriangle == Triangle (Point 6 3) (Point 0 1) (Point 10 6) Or you can use the updatedTriangle = execIn someTriangle $ do cy <- c_y get a_x $= cy Or more concisely: updatedTriangle = execIn someTriangle $ (c_y get >>= a_x . put) Or say we want to put the value of c_y into a_x, but want to throw an error if c_y is zero. We can do that as well! updatdeTriangle :: Either String Triangle updatdeTriangle = execInT someTriangle $ do cy <- c_y get when (cy == 0) $ throwError "Something bad happend" a_x $ put cy -- updatedTriangle == Right $ Triangle (Point 6 3) (Point 0 1) (Point 10 6) -- if cy had equaled 0 then we would have gotten this: -- updatedTriangle == Left "Something bad happend" Note that Yay for monad transformers! This module has one last feature that allows you to convert a function that fetches data from a structure to a function that modifies it! For an example see the documentation for One final note: Due to the generality of the lenses you might end up accidentally running into the monomorphism restriction. So if get a type error like: Couldn't match expected type `SomeMonad SomeStructureType' against inferred type `Control.Monad.Identity.Identity SomeStructureType' and nothing appears to be wrong with your code, try turning the restriction off with -XNoMonomorphismRestriction and see if it goes away. If it does then you probably need to add some explicit type signatures somewhere. I whipped out this documentation in a hurry, so if you spot any errors, or think I should explain something better, | |||||||||||||||||||||||||||||||||

Synopsis | |||||||||||||||||||||||||||||||||

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Basic functions to create lenses and use them | |||||||||||||||||||||||||||||||||

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This function takes a getter and setter function and returns our lense. Usually you only need to use this if you don't want to use Template Haskell to derive your Lenses for you. With a structure Point: data Point = Point { x_ :: Float, y_ :: Float } deriving (Show) This (from Data.Lenses.Template): $( deriveLenses ''Point ) is equivalent to this: x :: (MonadState Point m) => StateT Float m b -> m b x = fromGetSet x_ (\a s -> s { x_ = a }) y :: (MonadState Point m) => StateT Float m b -> m b y = fromGetSet y_ (\a s -> s { y_ = a }) | |||||||||||||||||||||||||||||||||

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fetches a field from a structure using a lense: somePoint = Point 5 3 a = somePoint `fetch` x b = somePoint `fetch` y -- a == 5 -- b == 3 | |||||||||||||||||||||||||||||||||

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updates a field in a structure using a lense: somePoint = Point 5 3 newPoint = (somePoint `update` y) 15 -- newPoint == Point 5 15 | |||||||||||||||||||||||||||||||||

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alters a field in a structure using a lense and a function: somePoint = Point 5 3 newPoint = (somePoint `alter` y) (+1) -- newPoint == Point 5 4 | |||||||||||||||||||||||||||||||||

Lense evaluators | |||||||||||||||||||||||||||||||||

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Runs a state monad action on a structure and returns the value returned from the action and the updated structure. somePoint = Point 5 3 a = runOn somePoint $ x (modifyAndGet (+1)) -- a == (6, Point 6 3) | |||||||||||||||||||||||||||||||||

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Monad transformer version of runOn. Note that runOnT = runStateT.
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Runs a state monad action on a structure and returns the value returned from the action. Use it to fetch values from fields. someTriangle = Triangle (Point 5 3) (Point 0 1) (Point 10 6) a = evalFrom someTriangle $ pb . x get -- a == 0 note that: evalFrom someTriangle (pb . x get) == someTriangle `fetch` (pb . x) The advantage over evalFrom someTriangle $ pb . x (modifyAndGet (+1)) | |||||||||||||||||||||||||||||||||

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Monad transformer version of evalFrom. Note that evalFromT = flip evalStateT.
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Runs a state monad action on a structure and returns the updated structure Use it to update fields: somePoint = Point 5 3 a = execIn somePoint $ x (put 1) -- a == Point 1 3 note that: execIn somePoint (x (put 1)) == (somePoint `update` x) 1 The advantage over a = execIn somePoint $ x (modifyAndGet (+1)) -- a = Point 6 3 | |||||||||||||||||||||||||||||||||

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Monad transformer version of execIn. Note that execIn = flip execStateT.
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Structure lenses | |||||||||||||||||||||||||||||||||

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This function has the magical ability to convert a function that fetches elements from a structure, to a function that lets you modify the elements in the structure.
The catch is that the structure must be a member of So say you have a function that gets the diagonal of a list of lists: diagonal :: [[a]] -> [a] we can make a function that increments the diagonal like so: addOne :: State Int () addOne = modify (+1) incrementDiagonal :: [[a]] -> [[a]] incrementDiagonal xss = snd $ runSTLense (fmap ($ addOne) . diagonal) xss Of course there are some helper combinators to make this cleaner: incrementDiagonal xss = (addOne `to` diagonal) `from` xss
specialFunction :: (Traversable f, Traversable t) => f (State a b -> s) -> t s (collectedValues, updatedStructure) = runSTLense specialFunction originalStructure collectedAlmostValues = specialFunction processedOriginalStructure processedOriginalStructure has the same shape as originalStructure but every element has been replaced with a transformer function (State a b -> s). specialFunction needs to return the result of the application of the functions in processedOriginalStructure to a state monad. The state monad by definition will return a result and potentially update state. Getting state will get the value of the element in originalStructure. Updating state will update the value of the element in updatedStructure. The returned values are gathered in collectedValues. | |||||||||||||||||||||||||||||||||

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A helper combinator used for applying a monad to element collected by a fetching function. For example: everyOther :: [a] -> [a] everyOther [] = [] everyOther (x:[]) = [x] everyOther (x:y:xs) = x : everyOther xs addOne :: State Int () addOne = modify (+1) test :: [Int] test = (addOne `to` everyOther) `from` [1, 2, 9, 6, 7, 8, 4] -- test == [2, 2, 10, 6, 8, 8, 5] which is the same as: test = snd $ runSTLense (addOne `to` everyOther) [1, 2, 9, 6, 7, 8, 4] which is the same as: test = snd $ runSTLense (fmap ($ addOne) . everyOther) [1, 2, 9, 6, 7, 8, 4] | |||||||||||||||||||||||||||||||||

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Applies runSTLense to a function and a structure and returns the snd of the result.
See to for example of use.
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Generic helper functions | |||||||||||||||||||||||||||||||||

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Modifies the state in a state monad and returns the original value.
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Modifies the state in a state monad and returns the new value. | |||||||||||||||||||||||||||||||||

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An operator for assigning a value to the value referenced by a lense. (see the example near the end of the tutorial at the start of this module) | |||||||||||||||||||||||||||||||||

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Flipped version of '($)'. | |||||||||||||||||||||||||||||||||

Produced by Haddock version 2.4.2 |