Inferring Datatypes Ningning Xie HIW 2019.08.23 data Maybe a = - - PowerPoint PPT Presentation

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Inferring Datatypes Ningning Xie HIW 2019.08.23 data Maybe a = - - PowerPoint PPT Presentation

Jun 22, 2023 520 likes •844 views

Inferring Datatypes Ningning Xie HIW 2019.08.23 data Maybe a = Nothing | Just a data List a = Nil | Cons a ( List a) data Either a b = Left a | Right b Wh Which da datatype ype de declarations ns sh should be e ac accepted? Wh What ki

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Inferring Datatypes

Ningning Xie HIW 2019.08.23

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data Maybe a = Nothing | Just a data List a = Nil | Cons a (List a) data Either a b = Left a | Right b

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Wh Which da datatype ype de declarations ns sh should be e ac accepted?

Wh What ki kinds do do accep accepted ed da datatypes pes ha have? e?

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Haskell98

data AppInt f = Mk (f Int) AppInt :: ?

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Haskell98

data AppInt f = Mk (f Int) AppInt :: ? AppInt :: ∗ → ∗ → ∗

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data Q1 a = MkQ1 data Q2 = MkQ2 (Q1 Maybe)

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data Q1 a = MkQ1 data Q2 = MkQ2 (Q1 Maybe)

  • - Q1 ∷ ∗ → ∗
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data Q1 a = MkQ1 data Q2 = MkQ2 (Q1 Maybe)

  • - Q1 ∷ ∗ → ∗
  • - Rejected!
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data Q1 a = MkQ1 Q2 data Q2 = MkQ2 (Q1 Maybe)

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data Q1 a = MkQ1 Q2 data Q2 = MkQ2 (Q1 Maybe)

  • - Q1 ∷ (∗ → ∗) → ∗
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data Q1 a = MkQ1 Q2 data Q2 = MkQ2 (Q1 Maybe)

  • - Q1 ∷ (∗ → ∗) → ∗
  • - Accepted!
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Modern Haskell

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{-# LANGUAGE ExplicitForAll , PolyKinds , ExistentialQuantification , TypeInType , TypeApplications #-}

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data X :: forall a (b::*->*). a b -> * data Y :: forall (c :: Maybe Bool). X c -> *

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data X :: forall a (b::*->*). a b -> * data Y :: forall (c :: Maybe Bool). X c -> *

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data X :: forall a (b::*->*). a b -> * data Y :: forall (c :: Maybe Bool). X c -> * a :: (∗ → ∗) → ∗ Kind mismatch!

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data Q :: forall (a :: f b) (c :: k) . f c -> *

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data Q :: forall (a :: f b) (c :: k) . f c -> *

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data Q :: forall (a :: f b) (c :: k) . f c -> * data Q :: forall (f::?) (b::?) (k::?) forall (a :: f b) (c :: k) . f c -> *

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data Q :: forall (a :: f b) (c :: k) . f c -> * c :: k k :: *

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data Q :: forall (a :: f b) (c :: k) . f c -> * c :: k k :: * f :: k -> *

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data Q :: forall (a :: f b) (c :: k) . f c -> * c :: k k :: * f :: k -> * b :: k

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data Q :: forall (a :: f b) (c :: k) . f c -> * k :: * f :: k -> * b :: k

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data Q :: forall (a :: f b) (c :: k) . f c -> * data Q :: forall (f::?) (b::?) (k::?) forall (a :: f b) (c :: k) . f c -> *

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data Q :: forall (a :: f b) (c :: k) . f c -> * data Q :: forall (k::?) (f::?) (b::?) forall (a :: f b) (c :: k) . f c -> *

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data Q :: forall (a :: f b) (c :: k) . f c -> * data Q :: forall (k::*) (f::k->*) (b::k) forall (a :: f b) (c :: k) . f c -> *

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Inferring Datatypes

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Inferring Datatypes

  • If you are a type theorist…
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Inferring Datatypes

  • If you are a GHC hacker/developer…
  • Further language extensions
  • How our work relates to GHC