13 lines
523 B
Markdown
13 lines
523 B
Markdown
Fix Composition (2/2)
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Goal, find: `◎ :: (b -> F c) -> (a -> F b) -> (a -> F c)`
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`f :: a -> F b`, `g :: b -> F c`, <span class="yellow">`f x :: F b`</span>:
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- Use `fmap :: (t -> u) -> (F t -> F u)`!
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- `(fmap g) :: F b -> F (F c)` ; (`t=b`, `u=F c`)
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- `(fmap g) (f x) :: F (F c)` it almost WORKS!
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- We lack an important component, `join :: F (F c) -> F c`
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- `(g ◎ f) x = join ((fmap g) (f x))` ☺
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◎ is the Kleisli composition; in Haskell: `<=<` (in `Control.Monad`).
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