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| author | Gabriel Lebec <glebec@gmail.com> | 2018-04-07 12:57:36 -0400 |
|---|---|---|
| committer | Ben Gamari <ben@smart-cactus.org> | 2018-04-07 13:30:15 -0400 |
| commit | 8b823f270e53627ddca1a993c05f1ab556742d96 (patch) | |
| tree | a9efc6f5a8bbbb97c9d295e86e38fa4c2c5a4dde /libraries | |
| parent | a5bfb7e143d826db310f5c632a90d39de62c7aa3 (diff) | |
| download | haskell-8b823f270e53627ddca1a993c05f1ab556742d96.tar.gz | |
docs(Data.Function): fix and augment `on` annotation
Diffstat (limited to 'libraries')
| -rw-r--r-- | libraries/base/Data/Function.hs | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/libraries/base/Data/Function.hs b/libraries/base/Data/Function.hs index ccc58c74ac..c54e81facc 100644 --- a/libraries/base/Data/Function.hs +++ b/libraries/base/Data/Function.hs @@ -50,18 +50,21 @@ infixl 1 & fix :: (a -> a) -> a fix f = let x = f x in x --- | @((==) \`on\` f) x y = f x == f y@ +-- | @'on' b u x y@ runs the binary function `b` /on/ the results of applying unary function `u` to two arguments `x` and `y`. From the opposite perspective, it transforms two inputs and combines the outputs. +-- +-- @((+) \``on`\` f) x y = f x + f y@ -- -- Typical usage: @'Data.List.sortBy' ('compare' \`on\` 'fst')@. - +-- -- Algebraic properties: -- --- * @(*) \`on\` 'id' = (*)@ (if @(*) ∉ {⊥, 'const' ⊥}@) +-- * @(*) \`on\` 'id' = (*) -- (if (*) ∉ {⊥, 'const' ⊥})@ -- -- * @((*) \`on\` f) \`on\` g = (*) \`on\` (f . g)@ -- -- * @'flip' on f . 'flip' on g = 'flip' on (g . f)@ - +on :: (b -> b -> c) -> (a -> b) -> a -> a -> c +(.*.) `on` f = \x y -> f x .*. f y -- Proofs (so that I don't have to edit the test-suite): -- (*) `on` id @@ -102,9 +105,6 @@ fix f = let x = f x in x -- = -- flip on (g . f) -on :: (b -> b -> c) -> (a -> b) -> a -> a -> c -(.*.) `on` f = \x y -> f x .*. f y - -- | '&' is a reverse application operator. This provides notational -- convenience. Its precedence is one higher than that of the forward |