Data.Diverse.Which

Re-export Which without the constructor

Which type

data Which xs

A Which is an anonymous sum type (also known as a polymorphic variant, or co-record) which can only contain one of the types in the typelist. This is essentially a typed version of Dynamic.

The following functions are available can be used to manipulate unique types in the typelist

• constructor: pick
• destructor: trial
• injection: diversify and reinterpret
• catamorphism: which or switch

These functions are type specified. This means labels are not required because the types themselves can be used to access the Which. It is a compile error to use those functions for duplicate fields.

For duplicate types in the list of possible types, Nat-indexed version of the functions are available:

• constructor: pickN
• destructor: trialN
• inejction: diversifyN and reinterpretN
• catamorphism: whichN or switchN

Encoding: The variant contains a value whose type is at the given position in the type list. This is the same encoding as Haskus.Util.Variant and Data.Hlist.Variant.

The constructor is only exported in the Data.Diverse.Which.Internal module

Instances

Reduce (Which ((:) Type x xs)) (Switcher CaseEqWhich Bool ((:) Type x xs)) => Eq (Which ((:) Type x xs))

Two Whiches are only equal iff they both contain the equivalnet value at the same type index.

Methods

(==) :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Bool

(/=) :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Bool

Eq (Which ([] Type))

(zilch == zilch) == True

Methods

(==) :: Which [Type] -> Which [Type] -> Bool

(/=) :: Which [Type] -> Which [Type] -> Bool

(Reduce (Which ((:) Type x xs)) (Switcher CaseEqWhich Bool ((:) Type x xs)), Reduce (Which ((:) Type x xs)) (Switcher CaseOrdWhich Ordering ((:) Type x xs))) => Ord (Which ((:) Type x xs))

A Which with a type at smaller type index is considered smaller.

Methods

compare :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Ordering

(<) :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Bool

(<=) :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Bool

(>) :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Bool

(>=) :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Bool

max :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Which ((Type ': x) xs)

min :: Which ((Type ': x) xs) -> Which ((Type ': x) xs) -> Which ((Type ': x) xs)

Ord (Which ([] Type))

(compare zilch zilch) == EQ

Methods

compare :: Which [Type] -> Which [Type] -> Ordering

(<) :: Which [Type] -> Which [Type] -> Bool

(<=) :: Which [Type] -> Which [Type] -> Bool

(>) :: Which [Type] -> Which [Type] -> Bool

(>=) :: Which [Type] -> Which [Type] -> Bool

max :: Which [Type] -> Which [Type] -> Which [Type]

min :: Which [Type] -> Which [Type] -> Which [Type]

WhichRead (Which_ ((:) Type x xs)) => Read (Which ((:) Type x xs))

This Read instance tries to read using the each type in the typelist, using the first successful type read.

Methods

readsPrec :: Int -> ReadS (Which ((Type ': x) xs))

readList :: ReadS [Which ((Type ': x) xs)]

readPrec :: ReadPrec (Which ((Type ': x) xs))

readListPrec :: ReadPrec [Which ((Type ': x) xs)]

Read (Which ([] Type))

Reading a 'Which '[]' value is always a parse error, considering 'Which '[]' as a data type with no constructors.

Methods

readsPrec :: Int -> ReadS (Which [Type])

readList :: ReadS [Which [Type]]

readPrec :: ReadPrec (Which [Type])

readListPrec :: ReadPrec [Which [Type]]

Reduce (Which ((:) Type x xs)) (Switcher CaseShowWhich ShowS ((:) Type x xs)) => Show (Which ((:) Type x xs))

show (pick' 'A') == "pick 'A'"

Methods

showsPrec :: Int -> Which ((Type ': x) xs) -> ShowS

show :: Which ((Type ': x) xs) -> String

showList :: [Which ((Type ': x) xs)] -> ShowS

Show (Which ([] Type))

Methods

showsPrec :: Int -> Which [Type] -> ShowS

show :: Which [Type] -> String

showList :: [Which [Type]] -> ShowS

Generic (Which ((:) Type x ((:) Type x' xs)))

A Generic instance encoded as either the x value (:+:) or the diversify0ed remaining 'Which xs'. The C1 and S1 metadata are not encoded.

Associated Types

type Rep (Which ((:) Type x ((:) Type x' xs))) :: * -> *

Methods

from :: Which ((Type ': x) ((Type ': x') xs)) -> Rep (Which ((Type ': x) ((Type ': x') xs))) x

to :: Rep (Which ((Type ': x) ((Type ': x') xs))) x -> Which ((Type ': x) ((Type ': x') xs))

Generic (Which ((:) Type x ([] Type)))

A terminating Generic instance for one type encoded with pick'. The C1 and S1 metadata are not encoded.

Associated Types

type Rep (Which ((:) Type x ([] Type))) :: * -> *

Methods

from :: Which ((Type ': x) [Type]) -> Rep (Which ((Type ': x) [Type])) x

to :: Rep (Which ((Type ': x) [Type])) x -> Which ((Type ': x) [Type])

Generic (Which ([] Type))

A terminating Generic instance for no types encoded as a zilch. The C1 and S1 metadata are not encoded.

Associated Types

type Rep (Which ([] Type)) :: * -> *

Methods

from :: Which [Type] -> Rep (Which [Type]) x

to :: Rep (Which [Type]) x -> Which [Type]

Semigroup (Which ([] Type))

Methods

(<>) :: Which [Type] -> Which [Type] -> Which [Type]

sconcat :: NonEmpty (Which [Type]) -> Which [Type]

stimes :: Integral b => b -> Which [Type] -> Which [Type]

(NFData x, NFData (Which ((:) Type x' xs))) => NFData (Which ((:) * x ((:) Type x' xs)))

Methods

rnf :: Which ((* ': x) ((Type ': x') xs)) -> ()

NFData x => NFData (Which ((:) * x ([] *)))

Methods

rnf :: Which ((* ': x) [*]) -> ()

NFData (Which ([] Type))

Methods

rnf :: Which [Type] -> ()

(Case (c r) ((:) Type x ([] Type)), (~) * r (CaseResult * Type (c r) x)) => Reduce (Which ((:) Type x ([] Type))) (Switcher c r ((:) Type x ([] Type)))

Terminating case of the loop, ensuring that a instance of Case '[] with an empty typelist is not required. You can't reduce zilch

Methods

reduce :: Switcher c r ((Type ': x) [Type]) -> Which ((Type ': x) [Type]) -> Reduced (Switcher c r ((Type ': x) [Type]))

(Case (c r) ((:) Type x ((:) Type x' xs)), Reduce (Which ((:) Type x' xs)) (Switcher c r ((:) Type x' xs)), Reiterate (c r) ((:) Type x ((:) Type x' xs)), (~) * r (CaseResult * Type (c r) x)) => Reduce (Which ((:) Type x ((:) Type x' xs))) (Switcher c r ((:) Type x ((:) Type x' xs)))

trial0 each type in a Which, and either handle the case' with value discovered, or reiterate trying the next type in the type list.

Methods

reduce :: Switcher c r ((Type ': x) ((Type ': x') xs)) -> Which ((Type ': x) ((Type ': x') xs)) -> Reduced (Switcher c r ((Type ': x) ((Type ': x') xs)))

Reduce (Which ([] Type)) (Switcher c r ([] Type))

Allow 'Which '[]' to be reinterpret'ed or diversifyed into anything else This is safe because Which '[] is uninhabited, and this is already something that can be done with impossible

Methods

reduce :: Switcher c r [Type] -> Which [Type] -> Reduced (Switcher c r [Type])

(Case (c r n) ((:) Type x ([] Type)), (~) * r (CaseResult * Type (c r n) x)) => Reduce (Which ((:) Type x ([] Type))) (SwitcherN c r n ((:) Type x ([] Type)))

Terminating case of the loop, ensuring that a instance of Case '[] with an empty typelist is not required. You can't reduce zilch

Methods

reduce :: SwitcherN c r n ((Type ': x) [Type]) -> Which ((Type ': x) [Type]) -> Reduced (SwitcherN c r n ((Type ': x) [Type]))

(Case (c r n) ((:) Type x ((:) Type x' xs)), Reduce (Which ((:) Type x' xs)) (SwitcherN c r ((+) n 1) ((:) Type x' xs)), ReiterateN (c r) n ((:) Type x ((:) Type x' xs)), (~) * r (CaseResult * Type (c r n) x)) => Reduce (Which ((:) Type x ((:) Type x' xs))) (SwitcherN c r n ((:) Type x ((:) Type x' xs)))

trial0 each type in a Which, and either handle the case' with value discovered, or reiterateN trying the next type in the type list.

Methods

reduce :: SwitcherN c r n ((Type ': x) ((Type ': x') xs)) -> Which ((Type ': x) ((Type ': x') xs)) -> Reduced (SwitcherN c r n ((Type ': x) ((Type ': x') xs)))

type Rep (Which ((:) Type x ((:) Type x' xs)))

type Rep (Which ((:) Type x ((:) Type x' xs))) = (:+:) (Rec0 x) (Rec0 (Which ((:) Type x' xs)))

type Rep (Which ((:) Type x ([] Type)))

type Rep (Which ((:) Type x ([] Type))) = Rec0 x

type Rep (Which ([] Type))

type Rep (Which ([] Type)) = V1

Single type

Construction

impossible :: Which '[] -> a

Analogous to absurd. Renamed impossible to avoid conflicts.

Since 'Which '[]' values logically don't exist, this witnesses the logical reasoning tool of "ex falso quodlibet", ie "from falsehood, anything follows".

A 'Which '[]' is a Which with no alternatives, which may occur as a Left-over from trialing a Which '[x] with one type. It is an uninhabited type, just like Void

pick :: forall x xs. UniqueMember x xs => x -> Which xs

Lift a value into a Which of possibly other types xs. xs can be inferred or specified with TypeApplications. NB. forall is used to specify xs first, so TypeApplications can be used to specify xs first

pick 'A' @_ @'[Int, Bool, Char, Maybe String] :: Which '[Int, Bool, Char, Maybe String]

pick0 :: x -> Which (x ': xs)

A variation of pick into a Which where x is the first type.

pick0 'A' :: Which '[Char, Int, Bool]

pickOnly :: x -> Which '[x]

A variation of pick into a Which of a single type.

pickOnly 'A' :: Which '[Char]

pickL :: forall l xs proxy x. (UniqueLabelMember l xs, x ~ KindAtLabel l xs) => proxy l -> x -> Which xs

A variation of pick where x is specified via a label

let y = pickL @Foo Proxy (Tagged (5 :: Int)) :: Which '[Bool, Tagged Foo Int, Tagged Bar Char]
    x = trialL @Foo Proxy y
x shouldBe (Right (Tagged 5))

pickN :: forall n xs proxy x. MemberAt n x xs => proxy n -> x -> Which xs

Lift a value into a Which of possibly other (possibley indistinct) types, where the value is the n-th type.

pickN (Proxy @4) (5 :: Int) :: Which '[Bool, Int, Char, Bool, Int, Char]

Destruction

obvious :: Which '[a] -> a

It is obvious what value is inside a Which of one type.

let x = pick' 'A' :: Which '[Char]
obvious x `shouldBe` 'A'

trial :: forall x xs. UniqueMember x xs => Which xs -> Either (Which (Remove x xs)) x

trial a type in a Which and Either get the Right value or the Left-over possibilities.

let x = pick 'A' @'[Int, Bool, Char, Maybe String] :: Which '[Int, Bool, Char, Maybe String]
trial @Char x `shouldBe` Right 'A'
trial @Int x `shouldBe` Left (pick 'A') :: Which '[Bool, Char, Maybe String]

trial' :: forall x xs. UniqueMember x xs => Which xs -> Maybe x

Variation of trial which returns a Maybe

trial0 :: forall x xs. Which (x ': xs) -> Either (Which xs) x

A variation of a Which trial which trials the first type in the type list.

let x = pick 'A' @'[Int, Bool, Char, Maybe String] :: Which '[Int, Bool, Char, Maybe String]
trial0 x `shouldBe` Left (pick 'A') :: Which '[Bool, Char, Maybe String]

trial0' :: forall x xs. Which (x ': xs) -> Maybe x

Variation of trial0 which returns a Maybe

trialL :: forall l xs proxy x. (UniqueLabelMember l xs, x ~ KindAtLabel l xs) => proxy l -> Which xs -> Either (Which (Remove x xs)) x

A variation of trial where x is specified via a label

let y = pickL @Foo Proxy (Tagged (5 :: Int)) :: Which '[Bool, Tagged Foo Int, Tagged Bar Char]
    x = trialL @Foo Proxy y
x shouldBe (Right (Tagged 5))

trialL' :: forall l xs proxy x. (UniqueLabelMember l xs, x ~ KindAtLabel l xs) => proxy l -> Which xs -> Maybe x

Variation of trialL which returns a Maybe

trialN :: forall n xs proxy x. MemberAt n x xs => proxy n -> Which xs -> Either (Which (RemoveIndex n xs)) x

trialN the n-th type of a Which, and get Either the Right value or the Left-over possibilities.

let x = pick 'A' @_ @'[Int, Bool, Char, Maybe String] :: Which '[Int, Bool, Char, Maybe String]
trialN @_ @1 Proxy x `shouldBe` Left (pick 'A') :: Which '[Int, Char, Maybe String]

trialN' :: forall n xs proxy x. MemberAt n x xs => proxy n -> Which xs -> Maybe x

Variation of trialN which returns a Maybe

Multiple types

Injection

type Diversify branch tree = Reduce (Which branch) (Switcher (CaseDiversify branch tree) (Which tree) branch)

A friendlier constraint synonym for diversify.

diversify :: forall branch tree. Diversify branch tree => Which branch -> Which tree

Convert a Which to another Which that may include other possibilities. That is, branch is equal or is a subset of tree.

This can also be used to rearrange the order of the types in the Which.

It is a compile error if tree has duplicate types with branch.

NB. Use TypeApplications with _ to specify tree@.

let a = pick' (5 :: Int) :: Which '[Int]
    b = diversify @_ @[Int, Bool] a :: Which '[Int, Bool]
    c = diversify @_ @[Bool, Int] b :: Which '[Bool, Int]

diversify' :: forall branch tree. (Diversify branch tree, SameLength branch tree) => Which branch -> Which tree

A restricted version of diversify which only rearranges the types

diversify0 :: forall x xs. Which xs -> Which (x ': xs)

A simple version of diversify which add another type to the front of the typelist.

diversifyL :: forall ls branch tree proxy. (Diversify branch tree, branch ~ KindsAtLabels ls tree, UniqueLabels ls tree, IsDistinct ls) => proxy ls -> Which branch -> Which tree

A variation of diversify where branchis additionally specified by a labels list.

let y = pickOnly (5 :: Tagged Bar Int)
    y' = diversifyL @'[Bar] Proxy y :: Which '[Tagged Bar Int, Tagged Foo Bool]
    y'' = diversifyL @'[Bar, Foo] Proxy y' :: Which '[Tagged Foo Bool, Tagged Bar Int]
switch y'' (CaseFunc @Typeable (show . typeRep . (pure @Proxy))) `shouldBe` "Tagged * Bar Int"

type DiversifyN indices branch tree = (Reduce (Which branch) (SwitcherN (CaseDiversifyN indices) (Which tree) 0 branch), KindsAtIndices indices tree ~ branch)

A friendlier constraint synonym for diversifyN.

diversifyN :: forall indices branch tree proxy. DiversifyN indices branch tree => proxy indices -> Which branch -> Which tree

A variation of diversify which uses a Nat list indices to specify how to reorder the fields, where

indices[branch_idx] = tree_idx

This variation allows tree to contain duplicate types with branch since the mapping is specified by indicies.

let y = pickOnly (5 :: Int)
    y' = diversifyN @'[0] @_ @[Int, Bool] Proxy y
    y'' = diversifyN @[1,0] @_ @[Bool, Int] Proxy y'
switch y'' (CaseFunc @Typeable (show . typeRep . (pure @Proxy))) `shouldBe` "Int"

Inverse Injection

type Reinterpret branch tree = Reduce (Which tree) (Switcher (CaseReinterpret branch tree) (Either (Which (Complement tree branch)) (Which branch)) tree)

A friendlier constraint synonym for reinterpret.

reinterpret :: forall branch tree. Reinterpret branch tree => Which tree -> Either (Which (Complement tree branch)) (Which branch)

Convert a Which into possibly another Which with a totally different typelist. Returns either a Which with the Right value, or a Which with the Leftover compliment types.

It is a compile error if branch or compliment has duplicate types with tree.

NB. forall used to specify branch first, so TypeApplications can be used to specify branch first.

    let a = pick @[Int, Char, Bool] (5 :: Int) :: Which '[Int, Char, Bool]
    let  b = reinterpret [String, Char] y
    b `shouldBe` Left (pick (5 :: Int)) :: Which '[Int, Bool]
    let c = reinterpret [String, Int] a
    c `shouldBe` Right (pick (5 :: Int)) :: Which '[String, Int]

type Reinterpret' branch tree = Reduce (Which tree) (Switcher (CaseReinterpret' branch tree) (Maybe (Which branch)) tree)

A friendlier constraint synonym for reinterpret'.

reinterpret' :: forall branch tree. Reinterpret' branch tree => Which tree -> Maybe (Which branch)

Variation of reinterpret which returns a Maybe.

reinterpretL :: forall ls branch tree proxy. (Reinterpret branch tree, branch ~ KindsAtLabels ls tree, UniqueLabels ls tree, IsDistinct ls) => proxy ls -> Which tree -> Either (Which (Complement tree branch)) (Which branch)

A variation of reinterpret where the branch is additionally specified with a labels list.

let y = pick @[Tagged Bar Int, Tagged Foo Bool, Tagged Hi Char, Tagged Bye Bool] (5 :: Tagged Bar Int)
    y' = reinterpretL @[Foo, Bar] Proxy y
    x = pick @[Tagged Foo Bool, Tagged Bar Int] (5 :: Tagged Bar Int)
y' `shouldBe` Right x

reinterpretL' :: forall ls branch tree proxy. (Reinterpret' branch tree, branch ~ KindsAtLabels ls tree, UniqueLabels ls tree, IsDistinct ls) => proxy ls -> Which tree -> Maybe (Which branch)

Variation of reinterpretL which returns a Maybe.

type ReinterpretN' indices branch tree = (Reduce (Which tree) (SwitcherN (CaseReinterpretN' indices) (Maybe (Which branch)) 0 tree), KindsAtIndices indices tree ~ branch)

A friendlier constraint synonym for reinterpretN.

reinterpretN' :: forall indices branch tree proxy. ReinterpretN' indices branch tree => proxy indices -> Which tree -> Maybe (Which branch)

A limited variation of reinterpret which uses a Nat list n to specify how to reorder the fields, where

indices[branch_idx] = tree_idx

This variation allows tree to contain duplicate types with branch since the mapping is specified by indicies.

However, unlike reinterpert, in this variation, branch must be a subset of tree instead of any arbitrary Which. Also it returns a Maybe instead of Either.

This is so that the same indices can be used in narrowN.

Catamorphism

type Switch c r xs = Reduce (Which xs) (Switcher c r xs)

A friendlier constraint synonym for switch.

newtype Switcher c r xs

Switcher is an instance of Reduce for which reiterates through the possibilities in a Which, delegating handling to Case, ensuring termination when Which only contains one type.

Constructors

Switcher (c r xs)

Instances

(Case (c r) ((:) Type x ([] Type)), (~) * r (CaseResult * Type (c r) x)) => Reduce (Which ((:) Type x ([] Type))) (Switcher c r ((:) Type x ([] Type)))

Terminating case of the loop, ensuring that a instance of Case '[] with an empty typelist is not required. You can't reduce zilch

Methods

reduce :: Switcher c r ((Type ': x) [Type]) -> Which ((Type ': x) [Type]) -> Reduced (Switcher c r ((Type ': x) [Type]))

(Case (c r) ((:) Type x ((:) Type x' xs)), Reduce (Which ((:) Type x' xs)) (Switcher c r ((:) Type x' xs)), Reiterate (c r) ((:) Type x ((:) Type x' xs)), (~) * r (CaseResult * Type (c r) x)) => Reduce (Which ((:) Type x ((:) Type x' xs))) (Switcher c r ((:) Type x ((:) Type x' xs)))

trial0 each type in a Which, and either handle the case' with value discovered, or reiterate trying the next type in the type list.

Methods

reduce :: Switcher c r ((Type ': x) ((Type ': x') xs)) -> Which ((Type ': x) ((Type ': x') xs)) -> Reduced (Switcher c r ((Type ': x) ((Type ': x') xs)))

Reduce (Which ([] Type)) (Switcher c r ([] Type))

Allow 'Which '[]' to be reinterpret'ed or diversifyed into anything else This is safe because Which '[] is uninhabited, and this is already something that can be done with impossible

Methods

reduce :: Switcher c r [Type] -> Which [Type] -> Reduced (Switcher c r [Type])

type Reduced (Switcher c r xs)

type Reduced (Switcher c r xs) = r

which :: Switch c r xs => c r xs -> Which xs -> r

Catamorphism for Which. This is equivalent to flip switch.

switch :: Switch c r xs => Which xs -> c r xs -> r

A switch/case statement for Which. This is equivalent to flip which

Use Case instances like Cases to apply a Which of functions to a variant of values.

let y = pick (5 :: Int) :: Which '[Int, Bool]
switch y (
    cases (show @Bool
        ./ show @Int
        ./ nil)) `shouldBe` "5"

Or CaseFunc @Typeable to apply a polymorphic function that work on all Typeables.

let y = pick (5 :: Int) :: Which '[Int, Bool]
switch y (CaseFunc @Typeable (show . typeRep . (pure @Proxy))) `shouldBe` Int

Or you may use your own custom instance of Case.

type SwitchN c r n xs = Reduce (Which xs) (SwitcherN c r n xs)

A friendlier constraint synonym for switch.

newtype SwitcherN c r n xs

SwitcherN is a variation of Switcher which reiterateNs through the possibilities in a Which, delegating work to CaseN, ensuring termination when Which only contains one type.

Constructors

SwitcherN (c r n xs)

Instances

(Case (c r n) ((:) Type x ([] Type)), (~) * r (CaseResult * Type (c r n) x)) => Reduce (Which ((:) Type x ([] Type))) (SwitcherN c r n ((:) Type x ([] Type)))

Terminating case of the loop, ensuring that a instance of Case '[] with an empty typelist is not required. You can't reduce zilch

Methods

reduce :: SwitcherN c r n ((Type ': x) [Type]) -> Which ((Type ': x) [Type]) -> Reduced (SwitcherN c r n ((Type ': x) [Type]))

(Case (c r n) ((:) Type x ((:) Type x' xs)), Reduce (Which ((:) Type x' xs)) (SwitcherN c r ((+) n 1) ((:) Type x' xs)), ReiterateN (c r) n ((:) Type x ((:) Type x' xs)), (~) * r (CaseResult * Type (c r n) x)) => Reduce (Which ((:) Type x ((:) Type x' xs))) (SwitcherN c r n ((:) Type x ((:) Type x' xs)))

trial0 each type in a Which, and either handle the case' with value discovered, or reiterateN trying the next type in the type list.

Methods

reduce :: SwitcherN c r n ((Type ': x) ((Type ': x') xs)) -> Which ((Type ': x) ((Type ': x') xs)) -> Reduced (SwitcherN c r n ((Type ': x) ((Type ': x') xs)))

type Reduced (SwitcherN c r n xs)

type Reduced (SwitcherN c r n xs) = r

whichN :: SwitchN c r n xs => c r n xs -> Which xs -> r

Catamorphism for Which. This is equivalent to flip switchN.

switchN :: SwitchN c r n xs => Which xs -> c r n xs -> r

A switch/case statement for Which. This is equivalent to flip whichN

Use Case instances like CasesN to apply a Which of functions to a variant of values in index order.

let y = pickN @0 Proxy (5 :: Int) :: Which '[Int, Bool, Bool, Int]
switchN y (
    casesN (show @Int
        ./ show @Bool
        ./ show @Bool
        ./ show @Int
        ./ nil)) `shouldBe` "5"

Or you may use your own custom instance of Case.