An Overview of the PureScript Type System

Transcript

1. AN OVERVIEW OF THE
   TYPE SYSTEM
   

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2. Intro
   “PureScript is a small strongly-typed programming language that
   compiles to JavaScript”
   ● Learn more at purescript.org or on #purescript
   ● Goals:
   ○ Build the language I want to use every day
   ○ Explore how types can improve web programming
   ○ Try out some new type system ideas
   ○ Provide a fun project for Haskell OSS newcomers
   

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3. Agenda
   ● Recap some Haskell extensions
   ● Talk about the implementation
   ● Demo some novel features
   ● Future work
   

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4. Some Haskell Extensions
   

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5. Type Classes
   class Eq a where
   eq :: a -> a -> Boolean
   instance eqBoolean :: Eq Boolean where
   eq True True = True
   eq False False = True
   eq _ _ = False
   instance eqList :: Eq a => Eq (List a) where
   ...
   

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6. Higher-kinded types
   data Free f a
   = Pure a
   | Impure (f (Free f a))
   class Functor f where
   map :: (a -> b) -> f a -> f b
   

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7. Functional Dependencies
   class MonadState s m | m -> s where
   state :: (s -> Tuple s a) -> m a
   data Z
   data S n -- Peano naturals
   class Add n m r | n m -> r
   instance addZ :: Add Z n n
   instance addS :: Add n m r => Add (S n) m (S r)
   

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8. Functional Dependencies
   Functional dependencies give us “type-level Prolog”
   Examples:
   ● purescript-generics-rep
   ● purescript-type-map by @LiamGoodacre
   ● purescript-type-lang by @LiamGoodacre
   

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9. Higher-rank polymorphism
   runST :: forall a. (forall h. ST h a) -> a
   hiding
   :: forall result
   . (forall impl. Interface impl => Proxy impl -> result)
   -> result
   

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10. Implementation Notes
    

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11. Phases of the type checker
    1. Check/infer types and gather constraints
    2. Solve constraints
    3. goto 2 until no more constraints can be solved
    4. Final cleanup pass and generalization
    

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12. Unification
    Types can be partially solved during type checking
    Unification happens when we learn that two (partially known) types must be
    equal
    (Example)
    

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13. Bidirectional type checking
    Separate the type checker into two modes: inference and checking
    In practice, there are several judgments:
    ● Inference
    ● Checking
    ● Function application
    ● Subsumption
    

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14. Skolemization
    When checking something has a polymorphic type, we need to generate a
    fresh type variable which does not unify with other types.
    These are called skolem constants.
    At the end of type checking, we need to check that no skolem constants
    escaped their scope.
    (Example)
    

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15. Type Classes
    When we apply a function which has type class constraints, we insert a
    placeholder for a dictionary into the expression.
    This is called elaboration or dictionary-passing.
    These placeholders will get replaced during the solving phase.
    (Example)
    

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16. Functional Dependencies
    Functional dependencies can cause new unifications to happen during solving.
    These unifications can cause more instances to become applicable, solving
    new constraints.
    So the solver loops until no new type information can be learned.
    (Example)
    

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17. Cleanup
    ● Check no skolems escaped
    ● Generalize any unsolved type variables
    ● Generalize over any unsolved constraints
    

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18. Novel Features
    

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19. Row Polymorphism: Extensible Records
    getter :: forall a r
    . { foo :: a | r }
    -> a
    getter rec = rec.foo
    setter :: forall a r
    . a
    -> { foo :: a | r }
    -> { foo :: a | r }
    setter a rec = rec { foo = a }
    

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20. Row Polymorphism: Extensible Effects
    getFromNetwork
    :: forall eff
    . Eff (network :: NETWORK | eff) X
    main :: Eff (console :: CONSOLE, network :: NETWORK) Unit
    main = do
    x logShow x
    

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21. Row Polymorphism: Implementation
    ● Rows are maps from labels to types
    (actually, association lists)
    ● Rows can have duplicate labels
    ● Unification of rows must ignore order of different labels but preserve order
    of duplicates
    ● “row of k”, spelled # k is a new kind for each kind k
    (Example)
    

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22. -- a magic type class
    class Union r1 r2 r3 | r1 r2 -> r3, r1 r3 -> r2
    merge :: forall r1 r2 r3.
    . Union r1 r2 r3
    => Record r1
    -> Record r2
    -> Record r3
    See purescript-records by @doolse, also Ermine
    Row Constraints: Unions
    

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23. Polymorphic Labels
    -- another magic type class
    class RowCons l a r1 r2 | l a r1 -> r2, l r1 r2 -> a
    prop :: forall l a r1 r2.
    . RowCons l a r1 r2
    => SProxy l
    -> Lens’ (Record r2) a
    See purescript-profunctor-lenses
    

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24. Polymorphic Labels: Variants
    ctor :: forall l a r1 r2.
    . RowCons l a r1 r2
    => SProxy l
    -> Prism’ (Variant r2) a
    See purescript-variants by @natefaubion
    

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25. Type-Directed Search
    flatten :: List (Maybe Int) -> Maybe (List Int)
    flatten = ?IForgot
    Hole 'IForgot' has the inferred type
    List (Maybe Int) -> Maybe (List Int)
    You could substitute the hole with one of these values:
    Data.Monoid.mempty :: forall m. Monoid m => m
    Data.Traversable.sequence :: forall a m t. Traversable t => Applicative m => t (m a) -> m (t a)
    

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26. Type-Directed Search: Implementation
    ● Brute-force search through the context
    ● Uses subsumption to test for compatibility
    See @kritzcreek’s thesis :)
    

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27. Future Work
    

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28. Instance Chains
    class TypeEq a b r | a b -> r
    instance typeEq :: TypeEq a a True
    instance typeNotEq :: TypeEq a b False -- ← overlapping!
    instances
    instance typeEq :: TypeEq a a True
    instance typeNotEq :: TypeEq a b False
    

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29. Constraint Kinds
    class MapRow (c :: Symbol -> Type -> Type -> Constraint)
    (r1 :: # Type)
    (r2 :: # Type)
    -- auto-generated instances
    instance mapEmpty :: MapRow c () ()
    instance mapNonEmpty
    :: (c l a b, MapRow xs ys) =>
    MapRow (l :: a | xs) (l :: a | ys)
    

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30. References
    

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31. Haskell 98
    ● Typing Haskell in Haskell
    Mark P. Jones
    

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32. Higher-rank Polymorphism
    ● Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism
    Joshua Dunfield and Neelakantan R. Krishnaswami
    ● HMF: Simple Type Inference for First-Class Polymorphism
    Daan Leijen
    

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33. Type Classes and Functional Dependencies
    ● How to make ad-hoc polymorphism less ad hoc
    Philip Wadler
    ● Type Classes with Functional Dependencies
    Mark P. Jones
    ● Instance Chains: Type Class Programming Without Overlapping Instances
    J. Garrett Morris and Mark P. Jones
    

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34. Extensible Records
    ● Row Polymorphism Isn’t Subtyping
    Brian McKenna
    ● Extensible records with scoped labels
    Daan Leijen
    ● First-class labels for extensible rows
    Daan Leijen
    ● Koka: Programming with Row Polymorphic Effect Types
    Daan Leijen
    ● Ermine compiler
    

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35. Questions?
    

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