forked from orion/obsidian
79 lines
2.0 KiB
Markdown
79 lines
2.0 KiB
Markdown
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Generalizes [[Functor#map|map]] to [[Functions|functions]] with 2+ arguments; lifting functions `a -> b -> c` to `f a -> f b -> f c`
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```haskell
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class Functor f <= Apply f where
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apply :: forall a b. f (a -> b) -> f a -> f b
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infixl apply as <*>
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```
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> [!tip]
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> Apply often replaces the pattern of "building towards a final result"
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>
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> Consider a function that [[Tuple|tuple]]s together its arguments
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> ```haskell
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> mk3Tuple a b c = a /\ b /\ c
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> ```
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>
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> A common situation is wanting to build something like this 3-tuple from some components that are trapped in a context like [[Maybe]] or [[Either]], and we want to say "when all these things are ok, build it"; this is exactly what Apply lets us do:
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>
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> ```haskell
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> maybeMk3Tuple :: Maybe a -> Maybe b -> Maybe c -> Maybe (a /\ b /\ c)
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> maybeMk3Tuple ma mb mc = Just mk3Tuple <*> ma <*> mb <*> mc
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>
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> maybeMk3Tuple (Just 1) (Just 2) (Just 3)
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> -- Just (1 /\ 2 /\ 3)
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>
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> maybeMk3Tuple (Just "a") (Just 3) (Nothing)
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> -- Nothing
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>
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> maybeMk3Tuple Nothing Nothing Nothing
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> -- Nothing
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> ```
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> [!tip]
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> Obscure but occasionally usefully, Apply in collections lets us apply multiple functions to each element:
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> ```haskell
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> [(_ * 10), (_ * 20)] <*> [1, 2, 3]
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> -- [10, 20, 20, 40, 30, 60]
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>
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> [identity, const ", "] <*> ["a", "b", "c"]
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> -- ["a", ",", "b", ",", "c", ","]
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> ```
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### Examples
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lift `(a + b) / c` to [[Maybe]]
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```haskell
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f :: Number -> Number -> Number
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f a b c = (a + b) / c
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mf :: Maybe Number -> Maybe Number -> Maybe Number
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mf ma mb mc = pure f <*> ma <*> mb <*> mc
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```
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Build up a `Person` [[Record|record]] from Maybe fields; short-circuiting to `Nothing` if any fields are `Nothing`
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```haskell
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type PartialPerson =
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{ name :: Maybe String
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, email :: Maybe String
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, password :: Maybe String
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}
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type Person =
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{ name :: String
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, email :: String
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, password :: String
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}
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person :: PartialPerson -> Person
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person
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{ name: name'
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, email: email'
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, password: password'
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} =
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let
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buildPerson name email password = {name, email, password}
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in
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Just buildPerson <*> name' <*> email' <*> password'
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```
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