The problem:
Currently I have a type WorkConfig, which looks like this
data WorkConfig = PhaseZero_wc BuildConfig
| PhaseOne_wc BuildConfig Filename (Maybe XMLFilepath)
| PhaseTwo_wc String
| SoulSucker_wc String
| ImageInjector_wc String
| ESX_wc String
| XVA_wc String
| VNX_wc String
| HyperV_wc String
| Finish_wc String
deriving Show
(I'm using String from PhaseTwo_wc on as a placeholder for what will actually be used)
I have a function updateConfig that takes a WorkConfig as one of it's parameters.
The problem is that I want to be able to enforce which constructor is used.
For example in the function phaseOne I want to be able to guarantee that when updateConfig is invoked, only the PhaseTwo_wc constructor can be used.
In order to use a type class for this enforcement, I would have to make separate data constructors, for example:
data PhaseOne_wc = PhaseOne_wc BuildConfig Filename (Maybe XMLFilepath)
If I go this route, I have another problem to solve. I have other data types that have WorkConfig as a value, what would I do to address this? For example,
type ConfigTracker = TMVar (Map CurrentPhase WorkConfig)
How can I use the type system for the enforcement I would like, while keeping in mind what I mentioned above?
ConfigTracker would have to be able to know which data type I wanted.
* Clarification:
I'm looking to restrict which WorkConfig that updateConfig may take as a parameter.
Your question was a little vague, so I will answer in the general.
If you have a type of the form:
data MyType a b c d e f g = C1 a b | C2 c | C3 e f g
... and you want some function f that works on all three constructors:
f :: MyType a b c d e f g -> ...
... but you want some function g that works on just the last constructor, then you have two choices.
The first option is to create a second type embedded within C3:
data SecondType e f g = C4 e f g
... and then embed that within the original C3 constructor:
data MyType a b c d e f g = C1 a b | C2 c | C3 (SecondType e f g)
... and make g a function of SecondType:
g :: SecondType e f g -> ...
This only slightly complicates the code for f as you will have to first unpack C3 to access the C4 constructor.
The second solution is that you just make g a function of the values stored in the C3 constructor:
g :: e -> f -> g -> ...
This requires no modification to f or the MyType type.
To be more concrete and drive the discussion, how close does this GADT & Existential code get to what you want?
{-# LANGUAGE GADTs, KindSignatures, DeriveDataTypeable, ExistentialQuantification, ScopedTypeVariables, StandaloneDeriving #-}
module Main where
import qualified Data.Map as Map
import Data.Typeable
import Data.Maybe
data Phase0 deriving(Typeable)
data Phase1 deriving(Typeable)
data Phase2 deriving(Typeable)
data WC :: * -> * where
Phase0_ :: Int -> WC Phase0
Phase1_ :: Bool -> WC Phase1
deriving (Typeable)
deriving instance Show (WC a)
data Some = forall a. Typeable a => Some (WC a)
deriving instance Show Some
things :: [Some]
things = [ Some (Phase0_ 6) , Some (Phase1_ True) ]
do'phase0 :: WC Phase0 -> WC Phase1
do'phase0 (Phase0_ i) = Phase1_ (even i)
-- Simplify by using TypeRep of the Phase* types as key
type M = Map.Map TypeRep Some
updateConfig :: forall a. Typeable a => WC a -> M -> M
updateConfig wc m = Map.insert key (Some wc) m
where key = typeOf (undefined :: a)
getConfig :: forall a. Typeable a => M -> Maybe (WC a)
getConfig m = case Map.lookup key m of
Nothing -> Nothing
Just (Some wc) -> cast wc
where key = typeOf (undefined :: a)
-- Specialization of updateConfig restricted to taking Phase0
updateConfig_0 :: WC Phase0 -> M -> M
updateConfig_0 = updateConfig
-- Example of processing from Phase0 to Phase1
process_0_1 :: WC Phase0 -> WC Phase1
process_0_1 (Phase0_ i) = (Phase1_ (even i))
main = do
print things
let p0 = Phase0_ 6
m1 = updateConfig p0 Map.empty
m2 = updateConfig (process_0_1 p0) m1
print m2
print (getConfig m2 :: Maybe (WC Phase0))
print (getConfig m2 :: Maybe (WC Phase1))
print (getConfig m2 :: Maybe (WC Phase2))
Sorry, this is more of an extended comment than an answer. I'm a little confused. It sounds like you have some functions like
phaseOne = ...
... (updateConfig ...) ...
phaseTwo = ...
... (updateConfig ...) ...
and you're trying to make sure that eg, inside the definition of phaseOne, this never appears:
phaseOne = ...
... (updateConfig $ PhaseTwo_wc ...) ...
But now I ask you: is updateConfig a pure (non-monadic) function? Because if it is, than phaseOne can easily be perfectly correct and still invoke updateConfig with a PhaseTwo_wc; ie it could just throw away the result (and even if it's monadic too):
phaseOne = ...
... (updateConfig $ PhaseTwo_wc ...) `seq` ...
In other words, I'm wondering if the constraint you're trying to enforce is really the actual property you are looking for?
But now, if we're thinking of monads, there is a common pattern that what you describe is sort of like: making "special" monads that limit the kind of actions that can be performed; eg
data PhaseOneMonad a = PhaseOnePure a | PhaseOneUpdate BuildConfig Filename (Maybe XMLFilepath) a
instance Monad PhaseOneMonad where ...
Is this maybe what you're getting at? Note also that PhaseOneUpdate doesn't take a WorkConfig; it just takes the constructor parameters it is interested in. This is another common pattern: you can't constrain which constructor is used, but you can just take the arguments directly.
Hm... still not sure though.
Related
I have a state machine where states are implemented using a sum type. Posting a simplified version here:
data State =
A { value :: Int }
| B { value :: Int }
| C { other :: String }
most of my functions are monadic consuming States and doing some actions based on the type. Something like (this code doesn't compile):
f :: State -> m ()
f st= case st of
s#(A | B) -> withValueAction (value s)
C -> return ()
I know that I could unroll constructors like:
f :: State -> m ()
f st= case st of
A v -> withValueAction v
B v -> withValueAction v
C _ -> return ()
But that's a lot of boilerplate and brittle to changes. If I change the parameters to the constructor I need to rewrite all case .. of in my codebase.
So how would you pattern match on a subset of constructors and access a shared element?
One way to implement this idiomatically is to use a slightly different value function:
value :: State -> Maybe Int
value (A v) = Just v
value (B v) = Just v
value _ = Nothing
Then you can write your case using a pattern guard like this:
f st | Just v <- value st -> withValueAction v
f C{} = return ()
f _ = error "This should never happen"
Or you can simplify this a bit further using view patterns and even more with pattern synonyms:
{-# LANGUAGE ViewPatterns, PatternSynonyms #-}
pattern V :: Int -> State
pattern V x <- (value -> Just v)
{-# COMPLETE V, C #-}
f (V x) = withValueAction x
f C{} = return ()
#Noughtmare's answer demonstrates how you can use view patterns to get the right "pattern matching syntax". To auto-generate the value function that selects a shared field from several constructors, you can use lens, though this kind of requires buying into the whole Lens ecosystem. After:
{-# LANGUAGE TemplateHaskell #-}
import Control.Lens
import Control.Lens.TH
data State =
A { _value :: Int }
| B { _value :: Int }
| C { _other :: String }
makeLenses ''State
you will have a traversal value that can be used to access the partially shared field:
f :: (Monad m) => State -> m ()
f st = case st ^? value of
Just v -> withValueAction v
Nothing -> return ()
This is the solution I've picked at the end. My two main requirements were:
"Or" pattern matching over constructors
Selection of a subset of fields shared by the pattern match
As reported by #Noughtmare 1 is not possible at the moment https://github.com/ghc-proposals/ghc-proposals/pull/522.
Since for my problem the source of variability comes mostly from parameters in the constructors and not from the number of states, the solution I picked was to enable NamedFieldPuns extension, so the solution is something like:
f :: State -> m ()
f st= case st of
A {value} -> withValueAction value
B {value} -> withValueAction value
C {} -> return ()
It has some boilerplate enumerating constructors but at least it has none at the constructor parameters. I'll have a look at the view patterns maybe they are useful when the source of variability comes from the number of constructors and not the arguments.
I have some data that have different representations based on a type parameter, a la Sandy Maguire's Higher Kinded Data. Here are two examples:
wholeMyData :: MyData Z
wholeMyData = MyData 1 'w'
deltaMyData :: MyData Delta
deltaMyData = MyData Nothing (Just $ Left 'b')
I give some of the implementation details below, but first the actual question.
I often want to get a field of the data, usually via a local definition like:
let x = either (Just . Left . myDataChar) myDataChar -- myDataChar a record of MyData
It happens so often I would like to make a standard combinator,
getSubDelta :: ( _ -> _ ) -> Either a b -> Maybe (Either c d)
getSubDelta f = either (Just . Left . f) f
but filling in that signature is problematic. The easy solution is to just supply the record selector function twice,
getSubDelta :: (a->c) -> (b->d) -> Either a b -> Maybe (Either c d)
getSubDelta f g = either (Just . Left . f) g
but that is unseemly. So my question. Is there a way I can fill in the signature above? I'm assuming there is probably a lens based solution, what would that look like? Would it help with deeply nested data? I can't rely on the data types always being single constructor, so prisms? Traversals? My lens game is weak, so I was hoping to get some advice before I proceed.
Thanks!
Some background. I defined a generic method of performing "deltas", via a mix of GHC.Generics and type families. The gist is to use a type family in the definition of the data type. Then, depending how the type is parameterized, the records will either represent whole data or a change to existing data.
For instance, I define the business data using DeltaPoints.
MyData f = MyData { myDataInt :: DeltaPoint f Int
, myDataChar :: DeltaPoint f Char} deriving Generic
The DeltaPoints are implemented in the library, and have different forms for Delta and Z states.
data DeltaState = Z | Delta deriving (Show,Eq,Read)
type family DeltaPoint (st :: DeltaState) a where
DeltaPoint Z a = a
DeltaPoint Delta a = Maybe (Either a (DeltaOf a))
So a DeltaPoint Z a is just the original data, a, and a DeltaPoint Delta a, may or may not be present, and if it is present will either be a replacement of the original (Left) or an update (DeltaOf a).
The runtime delta functionality is encapsulated in a type class.
class HasDelta a where
type DeltaOf a
delta :: a -> a -> Maybe (Either a (DeltaOf a))
applyDeltaOf :: a -> DeltaOf a -> Maybe a
And with the use of Generics, I can usually get the delta capabilities with something like:
instance HasDelta (MyData Z) where
type (DeltaOf (MyData Z)) = MyData Delta
I think you probably want:
{-# LANGUAGE RankNTypes #-}
getSubDelta :: (forall f . (dat f -> DeltaPoint f fld))
-> Either (dat Z) (dat Delta)
-> Maybe (Either (DeltaPoint Z fld) (DeltaOf fld))
getSubDelta sel = either (Just . Left . sel) sel
giving:
x :: Either (MyData Z) (MyData Delta)
-> Maybe (Either (DeltaPoint Z Char) (DeltaOf Char))
x = getSubDelta myDataChar
-- same as: x = either (Just . Left . myDataChar) myDataChar
Suppose I have a type Thing with a state property A | B | C,
and legal state transitions are A->B, A->C, C->A.
I could write:
transitionToA :: Thing -> Maybe Thing
which would return Nothing if Thing was in a state which cannot transition to A.
But I'd like to define my type, and the transition functions in such a way that transitions can only be called on appropriate types.
An option is to create separate types AThing BThing CThing but that doesn't seem maintainable in complex cases.
Another approach is to encode each state as it's own type:
data A = A Thing
data B = B Thing
data C = C Thing
and
transitionCToA :: C Thing -> A Thing
This seems cleaner to me. But it occurred to me that A,B,C are then functors where all of Things functions could be mapped except the transition functions.
With typeclasses I could create somthing like:
class ToA t where
toA :: t -> A Thing
Which seems cleaner still.
Are there other preferred approaches that would work in Haskell and PureScript?
Here's a fairly simple way that uses a (potentially phantom) type parameter to track which state a Thing is in:
{-# LANGUAGE DataKinds, KindSignatures #-}
-- note: not exporting the constructors of Thing
module Thing (Thing, transAB, transAC, transCA) where
data State = A | B | C
data Thing (s :: State) = {- elided; can even be a data family instead -}
transAB :: Thing A -> Thing B
transAC :: Thing A -> Thing C
transCA :: Thing C -> Thing A
transAB = {- elided -}
transAC = {- elided -}
transCA = {- elided -}
You could use a type class (available in PureScript) along with phantom types as John suggested, but using the type class as a final encoding of the type of paths:
data A -- States at the type level
data B
data C
class Path p where
ab :: p A B -- One-step paths
ac :: p A C
ca :: p C A
trans :: forall a b c. p c b -> p b a -> p c a -- Joining paths
refl :: forall a. p a a
Now you can create a type of valid paths:
type ValidPath a b = forall p. (Path p) => p a b
roundTrip :: ValidPath A A
roundTrip = trans ca ac
Paths can only be constructed by using the one-step paths you provide.
You can write instances to use your paths, but importantly, any instance has to respect the valid transitions at the type level.
For example, here is an interpretation which calculates lengths of paths:
newtype Length = Length Int
instance pathLength :: Path Length where
ab = Length 1
ac = Length 1
ca = Length 1
trans (Length n) (Length m) = Length (n + m)
refl = Length 0
Since your goal is to prevent developers from performing illegal transitions, you may want to look into phantom types. Phantom types allow you to model type-safe transitions without leveraging more advanced features of the type system; as such they are portable to many languages.
Here's a PureScript encoding of your above problem:
foreign import data A :: *
foreign import data B :: *
foreign import data C :: *
data Thing a = Thing
transitionToA :: Thing C -> Thing A
Phantom types work well to model valid state transitions when you have the property that two different states cannot transition to the same state (unless all states can transition to that state). You can workaround this limitation by using type classes (class CanTransitionToA a where trans :: Thing a -> Thing A), but at this point, you should investigate other approaches.
If you want to store a list of transitions so that you can process it later, you can do something like this:
{-# LANGUAGE DataKinds, GADTs, KindSignatures, PolyKinds #-}
data State = A | B | C
data Edge (a :: State) (b :: State) where
EdgeAB :: Edge A B
EdgeAC :: Edge A C
EdgeCA :: Edge C A
data Domino (f :: k -> k -> *) (a :: k) (b :: k) where
I :: Domino f a a
(:>>:) :: f a b -> Domino f b c -> Domino f a c
infixr :>>:
example :: Domino Edge A B
example = EdgeAC :>>: EdgeCA :>>: EdgeAB :>>: I
You can turn that into an instance of Path by writing a concatenation function for Domino:
{-# LANGUAGE FlexibleInstances #-}
instance Path (Domino Edge) where
ab = EdgeAB :>>: I
ac = EdgeAC :>>: I
ca = EdgeCA :>>: I
refl = I
trans I es' = es'
trans (e :>>: es) es' = e :>>: (es `trans` es')
In fact, this makes me wonder if Hackage already has a package that defines "indexed monoids":
class IMonoid (m :: k -> k -> *) where
imempty :: m a a
imappend :: m a b -> m b c -> m a c
instance IMonoid (Domino e) where
imempty = I
imappend I es' = es'
imappend (e :>>: es) es' = e :>>: (es `imappend` es')
What's the best way to apply a transformation to a tree only once instead of everywhere using SYB? For instance, in the following simplified expression, there are several instances of Var "x", and I want to replace the first instance with Var "y" only.
data Exp = Var String
| Val Int
| Plus Exp Exp
|...
myExp = Val 5 `Plus` Var "x" `Plus` Val 5 `Plus` Var "x" ...
This can't be done using the everywhere combinator since it will try to transform all instances of Var "x" to Var "y".
EDIT (after posting): Looks like somewhere is what I am looking for.
Being a SYB beginner myself, my answer is more like a guess, but seems to work.
Combinator somewhere recommended by Neil Brown probably doesn't do exactly what you want. It's defined as
-- | Apply a monadic transformation at least somewhere
somewhere :: MonadPlus m => GenericM m -> GenericM m
-- We try "f" in top-down manner, but descent into "x" when we fail
-- at the root of the term. The transformation fails if "f" fails
-- everywhere, say succeeds nowhere.
--
somewhere f x = f x `mplus` gmapMp (somewhere f) x
where
-- | Transformation of at least one immediate subterm does not fail
gmapMp :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a
But we need to transform at most once. For this it seems that gmapMo will be better:
-- | Transformation of one immediate subterm with success
gmapMo :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a
So I made my own combinator:
{-# LANGUAGE DeriveDataTypeable, RankNTypes #-}
import Control.Monad
import Data.Maybe (fromMaybe)
import Data.Data
import Data.Typeable (Typeable)
import Data.Generics.Schemes
import Data.Generics.Aliases
-- | Apply a monadic transformation once.
once :: MonadPlus m => GenericM m -> GenericM m
once f x = f x `mplus` gmapMo (once f) x
If the substitution fails, it returns mzero, otherwise it returns the substituted result. If you don't care if the substitution fails (no matches), you could use something like
once' :: (forall a. Data a => a -> Maybe a) -> (forall a. Data a => a -> a)
once' f x = fromMaybe x (once f x)
With these, we can do some replacements:
data Exp = Var String | Val Int | Plus Exp Exp
deriving (Show, Typeable, Data)
myExp = Val 5 `Plus` Var "x" `Plus` Val 5 `Plus` Var "x"
replM :: (MonadPlus m) => Exp -> m Exp
replM (Var "x") = return $ Var "y"
replM t = mzero
main = do
-- `somewhere` doesn't do what we want:
print $ (somewhere (mkMp replM) myExp :: Maybe Exp)
-- returns `Just ..` if the substitution succeeds once,
-- Nothing otherwise.
print $ (once (mkMp replM) myExp :: Maybe Exp)
-- performs the substitution once, if possible.
print $ (once' (mkMp replM) myExp :: Exp)
-- Just for kicks, this returns all possible substitutions
-- where one `Var "x"` is replaced by `Var "y"`.
print $ (once (mkMp replM) myExp :: [Exp])
Yes, I think somewhere (mkMp mySpecificFunction) should do it, if you use a MonadPlus monad and make it succeed when it finds what you're looking for.
A flexible but hacky alternative is to use everywhereM with a State monad that can store a Boolean (or store Maybe MyFunc or whatever) and apply the transformation depending on the state being True or Just myFunc -- that way, when you are done (e.g. after applying the transformation once), you just alter the state to be False/Nothing.
Suppose I have
data Foo = A String Int | B Int
I want to take an xs :: [Foo] and sort it such that all the As are at the beginning, sorted by their strings, but with the ints in the order they appeared in the list, and then have all the Bs at the end, in the same order they appeared.
In particular, I want to create a new list containg the first A of each string and the first B.
I did this by defining a function taking Foos to (Int, String)s and using sortBy and groupBy.
Is there a cleaner way to do this? Preferably one that generalizes to at least 10 constructors.
Typeable, maybe? Something else that's nicer?
EDIT: This is used for processing a list of Foos that is used elsewhere. There is already an Ord instance which is the normal ordering.
You can use
sortBy (comparing foo)
where foo is a function that extracts the interesting parts into something comparable (e.g. Ints).
In the example, since you want the As sorted by their Strings, a mapping to Int with the desired properties would be too complicated, so we use a compound target type.
foo (A s _) = (0,s)
foo (B _) = (1,"")
would be a possible helper. This is more or less equivalent to Tikhon Jelvis' suggestion, but it leaves space for the natural Ord instance.
To make it easier to build comparison function for ADTs with large number of constructors, you can map values to their constructor index with SYB:
{-# LANGUAGE DeriveDataTypeable #-}
import Data.Generics
data Foo = A String Int | B Int deriving (Show, Eq, Typeable, Data)
cIndex :: Data a => a -> Int
cIndex = constrIndex . toConstr
Example:
*Main Data.Generics> cIndex $ A "foo" 42
1
*Main Data.Generics> cIndex $ B 0
2
Edit:After re-reading your question, I think the best option is to make Foo an instance of Ord. I do not think there is any way to do this automatically that will act the way you want (just using deriving will create different behavior).
Once Foo is an instance of Ord, you can just use sort from Data.List.
In your exact example, you can do something like this:
data Foo = A String Int | B Int deriving (Eq)
instance Ord Foo where
(A _ _) <= (B _) = True
(A s _) <= (A s' _) = s <= s'
(B _) <= (B _) = True
When something is an instance of Ord, it means the data type has some ordering. Once we know how to order something, we can use a bunch of existing functions (like sort) on it and it will behave how you want. Anything in Ord has to be part of Eq, which is what the deriving (Eq) bit does automatically.
You can also derive Ord. However, the behavior will not be exactly what you want--it will order by all of the fields if it has to (e.g. it will put As with the same string in order by their integers).
Further edit: I was thinking about it some more and realized my solution is probably semantically wrong.
An Ord instance is a statement about your whole data type. For example, I'm saying that Bs are always equal with each other when the derived Eq instance says otherwise.
If the data your representing always behaves like this (that is, Bs are all equal and As with the same string are all equal) then an Ord instance makes sense. Otherwise, you should not actually do this.
However, you can do something almost exactly like this: write your own special compare function (Foo -> Foo -> Ordering) that encapsulates exactly what you want to do then use sortBy. This properly codifies that your particular sorting is special rather than the natural ordering of the data type.
You could use some template haskell to fill in the missing transitive cases. The mkTransitiveLt creates the transitive closure of the given cases (if you order them least to greatest). This gives you a working less-than, which can be turned into a function that returns an Ordering.
{-# LANGUAGE TemplateHaskell #-}
import MkTransitiveLt
import Data.List (sortBy)
data Foo = A String Int | B Int | C | D | E deriving(Show)
cmp a b = $(mkTransitiveLt [|
case (a, b) of
(A _ _, B _) -> True
(B _, C) -> True
(C, D) -> True
(D, E) -> True
(A s _, A s' _) -> s < s'
otherwise -> False|])
lt2Ord f a b =
case (f a b, f b a) of
(True, _) -> LT
(_, True) -> GT
otherwise -> EQ
main = print $ sortBy (lt2Ord cmp) [A "Z" 1, A "A" 1, B 1, A "A" 0, C]
Generates:
[A "A" 1,A "A" 0,A "Z" 1,B 1,C]
mkTransitiveLt must be defined in a separate module:
module MkTransitiveLt (mkTransitiveLt)
where
import Language.Haskell.TH
mkTransitiveLt :: ExpQ -> ExpQ
mkTransitiveLt eq = do
CaseE e ms <- eq
return . CaseE e . reverse . foldl go [] $ ms
where
go ms m#(Match (TupP [a, b]) body decls) = (m:ms) ++
[Match (TupP [x, b]) body decls | Match (TupP [x, y]) _ _ <- ms, y == a]
go ms m = m:ms