Dict Typing

Solving the Haskell record problem with Data.Constraint.Dict and implicit parameters

Soares Chen

Haskell SG Meetup - June 2018

The Haskell Record Problem

The Extensible Record Problem

  • Functions working around an environment / name arguments

  • Problems with concrete type Env

    • Hard to extend

    • Extension affects all code globally

    • Hard to break down into smaller parts

    • etc

data Env = Env { foo :: String, ... }

myApp :: Env -> Result

myApp :: Reader Env Result

myApp :: ReaderT Env (IO Result)

myApp :: MonadReader Env m => m Result

Non Haskell Solutions

Row Polymorphism

Subtyping

Dynamic Typing

Duct Typing

etc

Haskell Solutions

https://www.reddit.com/r/haskell/comments/8g8ojm/lets_create_a_comparison_table_of_all_the_haskell/

Ad Hoc Solutions

The Has* / ReaderT design patterns

class HasFoo a where
  getFoo :: a -> String

class Has a ctx where
  get :: ctx -> a

class HasField (x :: Symbol) r a | x r -> a where
  getField :: Proxy# x -> r -> a

Problems with Existing Solutions

  • Manual instance declaration

    • Limited support on auto instance declarations

    • Hard to create new types that extends concrete types

  • Interoperability issues

    • Libraries have to commit to specific type classes / record framework

  • Hard to compose functions with complex constraints

    • Require explicit type annotation

    • MultiParamTypeClasses causes ambiguity in intermediate type variables

  • Easily get into typeclass language extensions hell

    • FlexibleInstances, OverlappingInstances, IncoherentInstances,  
      AllowAmbiguousTypes, FunctionalDependencies, UndecidableInstances, etc

  • Limitations on nested constraint resolution

    • Record contains field with flexible type, satisfying some other constraint

    • Manipulation of record object turning into other types

Dict Typing

Yet Another Solution to the Record Problem

  • Data.Constraint.Dict

  • Implicit Parameters

Introducing

Constraint Dictionary

https://hackage.haskell.org/package/constraints-0.10/docs/Data-Constraint.html

 

Type Classes vs. the World - https://www.youtube.com/watch?v=hIZxTQP1ifo

data Dict :: Constraint -> * where
  Dict :: p => Dict p

showStringDict :: Dict (Show String)
showStringDict = Dict

Implicit Parameters

  • Dynamic scoping

  • Act like local constraints

  • Restriction: only one type per named parameter

    • Problematic when consuming multiple environments with similar parameters

  • Dictionary stores accessors, not values

handleFooLike :: forall a
  . (?getFoo :: a -> String) 
  => a -> Result

data Env = Env { foo :: String }

result = let
  ?getFoo = foo
in
  handleFooLike $ Env { foo = "fooValue" }

Dictionary of Implicit Parameters

  • Can “instantiate” abstract functions by partially applying dictionaries to functions

  • No runtime overhead

  • No complicated type class constraint resolution

handleFooLike :: forall a
  . Dict (?getFoo :: a -> String) 
  -> a -> Result

data Env = Env { foo :: String }

envDict :: Dict (?getFoo :: a -> String)
envDict = let ?getFoo = foo in Dict

handleEnv :: Env -> Result
handleEnv = handleFooLike envDict

result = handleEnv $ Env { foo = "fooValue" }

Dict Typing plays well with Lenses

  • Have to use WithLens data wrapper to work around lack of impredicative polymorphism

  • Remaining slides focus on getters only for simplicity

data WithLens s a = WithLens { getLens :: Lens' s a }

handleFooLike :: forall a
  . Dict (?fooLens :: WithLens a String) 
  -> a -> Result

data Env = Env { _foo :: String }
makeLenses ''Env

handleEnv :: Env -> Result
handleEnv = let
  ?fooLens = WithLens foo
in
  handleFooLike Dict

result = handleEnv $ Env { _foo = "fooValue" }

Type checking problems with Dict

  • For any constraint p q, Dict (p, q), Dict (q, p) and Dict p are different types!

handleFooLike :: forall a
  . Dict (?getFoo :: a -> String) 
  -> a -> Result

data Env = Env { foo :: String, bar :: String }

envDict :: Dict (
  ?getFoo :: a -> String, 
  ?getBar :: a -> String)
envDict = let
  ?getFoo = foo
  ?getBar = bar
in
  Dict

-- Type Error!
handleEnv :: Env -> Result
handleEnv = handleFooLike envDict

Dict Entailment

  • Dict of set of constraints always entails:

    • Dict of subset of constraints

    • Dict of different order of constraints

  • mapDict = “cast” operator for dictionaries

newtype a :- b = Sub (a => Dict b)

-- example
ordToEq :: forall a. Ord a :- Eq a
ordToEq = Sub Dict

mapDict :: (a :- b) -> Dict a -> Dict b
mapDict (Sub q) Dict = q

handleEnv :: Env -> Result
handleEnv = handleFooLike $ mapDict (Sub Dict) envDict

(Safe) Dict Casting

  • (someDict <-> Dict) boilerplates

    • Necessary evil to make dict typing work

    • Abuse? Ugly hacks?

    • Opportunity for GHC extension?

infixr 7 <->
(<->) :: forall p q. Dict p -> (p => Dict q) -> Dict q
(<->) Dict dict = dict

handleEnv :: Env -> Result
handleEnv = handleFooLike $ envDict <-> Dict


-- More verbose alternative
handleEnv = case envDict of Dict -> handleFooLike Dict

Dict Typing + Combinator Patterns

composeHandler :: forall p q a r
  . Monoid r 
  => (Dict p -> a -> r) -> (Dict q -> a -> r)
  -> Dict (p, q) -> a -> r
composeHandler f g dict =
  let
    f' = f (dict <-> Dict)
    g' = g (dict <-> Dict)
  in
    \x -> (f' x) <> (g' x)

handleFooLike :: forall a. Dict (?getFoo :: a -> String) -> a -> String
handleBarLike :: forall a. Dict (?getBar :: a -> String) -> a -> String

-- handleFooBarLike :: forall a
--   . Dict (?getFoo :: a -> String, ?getBar :: a -> String)
--   -> a -> String
handleFooBarLike = composeHandler handleFooLike handleBarLike

Higher Order Dictionaries

  • Dict + Implicit Parameters > Implicit Parameters
  • Semi-structural typing
  • Ability to bind accessors through partial application
  • Ability to return implicit parameters as values
  • Functions can generate dictionaries based on other dictionaries

Default Values

infixr 8 &-&
(&-&) :: forall p q. Dict p -> Dict q -> Dict (p, q)
(&-&) Dict Dict = Dict

defaultDict :: forall a. Dict (
  ?getFoo :: a -> String, ?getBar :: a -> String)
defaultDict = let
  ?getFoo = \_ -> "default-foo"
  ?getBar = \_ -> "default-bar"
in Dict

data Env = Env { foo :: String }

envDict1 :: Dict (?getFoo :: a -> String)
envDict1 = let ?getFoo = foo in Dict

envDict2 :: Dict (
  ?getFoo :: Env -> String, 
  ?getBar :: Env -> String)
envDict2 = fooBarDict &-& (defaultDict @Env) <-> Dict

handleFooBarLike :: forall a
  . Dict (?getFoo :: a -> String, ?getBar :: a -> String) 
  -> a -> Result

-- handleFooBarLike sees: foo = "foo-value", bar = "default-bar"
-- ... or maybe not. (GHC Bug?)
result = handleFooBarLike envDict2 $ Env { foo = "foo-value" }

Dict Casting bug in GHC?

dict1 :: Dict (?a :: String, ?b :: String, ?c :: String)
dict1 = let ?a = "a1"; ?b = "b1"; ?c = "c1" in Dict

dict2 :: Dict (?c :: String, ?b :: String, ?a :: String)
dict2 = let ?a = "a2"; ?b = "b2"; ?c = "c2" in Dict

dict3 = dict1 &-& dict2

showDict :: Dict (?a :: String, ?b :: String, ?c :: String) -> String
showDict Dict = ?a ++ " " ++ ?b ++ " " ++ ?c

-- castResult1 = "a1 b1 c1"
castResult1 = showDict $ ((dict3 <-> Dict)
  :: Dict (?a :: String, ?b :: String, ?c :: String)) <-> Dict

-- castResult2 = "a2 b2 c2"
castResult2 = showDict $ ((dict3 <-> Dict)
  :: Dict (?c :: String, ?b :: String, ?a :: String)) <-> Dict

-- castResult3 = "a1 b1 c1"
castResult3 = showDict $ ((dict3 <-> Dict)
  :: Dict (?c :: String, ?a :: String, ?b :: String)) <-> Dict

-- castResult4 = "a1 b1 c1"
castResult4 = showDict $ ((dict3 <-> Dict)
  :: Dict (?b :: String, ?a :: String, ?c :: String)) <-> Dict

Dict Casting bug in GHC?

showParam2 :: (?c :: String, ?b :: String, ?a :: String) => String
showParam2 = ?a ++ " " ++ ?b ++ " " ++ ?c

-- castResult5 = "a1 b1 c1"
castResult5 = case dict3 of
  Dict -> showParam2

dict4 :: ((?a :: String, ?b :: String, ?c :: String),
          (?c :: String, ?b :: String, ?a :: String))
         => Dict (?c :: String, ?b :: String, ?a :: String)
dict4 = Dict

-- castResult6 = "a2 b2 c2"
castResult6 = showDict $ (dict3 <-> dict4) <-> Dict

Prototype Inheritance

Prototype Inheritance

data Prototype (p :: Constraint) e a where
  Prototype :: ((a -> e) -> Dict p) -> Prototype p e a

infixr 8 =&=
(=&=) :: forall p1 p2 e1 e2 a.
  Prototype p1 e1 a
  -> Prototype p2 e2 a
  -> Prototype (p1, p2) (e1, e2) a
(=&=) (Prototype makeDict1) (Prototype makeDict2) =
  Prototype $ \getElement ->
    (makeDict1 (fst . getElement)) &-&
    (makeDict2 (snd . getElement))

runProto :: forall p e. Prototype p e e -> Dict p
runProto (Prototype makeDict) = makeDict id

Prototype Inheritance

fooProto :: forall a. Prototype (?getFoo :: a -> String) Env a
fooProto = Prototype $ \getEnv ->
  let ?getFoo = foo . getEnv in Dict

barProto :: forall a. Prototype (?getBar :: a -> String) String a
barProto = Prototype $ \getBar ->
  let ?getBar = getBar in Dict

fooBarDict :: Dict (
  ?getFoo :: (String, Env) -> String, 
  ?getBar :: (String, Env) -> String)
fooBarDict = runProto $ barProto =&= fooProto

protoResult = handleFooBarLike fooBarDict
  ("injected-bar", Env { foo = "foo" })

The Case Against Dict Typing

  • Abuse? Ugly hacks? Code Smells?

    • Casting / Subtyping / Dynamic typing / Implicit parameters are bad

    • Breaks constraints of all type class have only one instance

  • Better alternatives exist

    • Constraints are enough, no need Dict

    • Ways to workaround typeclass restrictions

    • Extensible effects FTW!

  • Workaround for lack of advanced type features in Haskell

    • Quantified Constraints (now available)

    • Existential types

    • Impredicative polymorphism

The Case For Dict Typing

  • Using Dicts are not much different from using constraints

    • We already rely on Haskell’s implicit constraint merging / propagation all the time

  • Efficient and predictable performance

    • No type level linked lists

    • Easy to reason

  • Interoperable with third party libraries

    • Polymorphic record by convention

    • Decouples choice of interface vs implementation

    • No need to commit to specific record library

  • Flexible higher order dictionary generation

    • No need to mess with type class extensions

Dict Typing

Implicit parameters of kind Constraint

Constraint Tuple (,)

Dict (?getFoo :: String, p)

 

Dict Typing

Functions taking dictionaries

Dict type

Explicit dict casting

Implicit parameters in dict

Row Polymorphism

Row variables of kind #Type

class Union l r (u :: # Type)

Row (foo :: String | r)

 

ML Modules

ML functors

Signatures

Implicit signature matching

Structures

vs

vs

Summary

  • Dict Typing provides a controversial but efficient solution to the Haskell record problem
  • While non-conventional, Dict typing helps bridge the gap of introducing other programming paradigms to Haskell
  • Next step: publish library on Hackage?
  • Learn more: https://github.com/soareschen/dict-typing

Thank you!

Made with Slides.com