diff options
Diffstat (limited to 'libraries/base/Data/Function.hs')
| -rw-r--r-- | libraries/base/Data/Function.hs | 25 |
1 files changed, 23 insertions, 2 deletions
diff --git a/libraries/base/Data/Function.hs b/libraries/base/Data/Function.hs index c5ded4cda5..ccc58c74ac 100644 --- a/libraries/base/Data/Function.hs +++ b/libraries/base/Data/Function.hs @@ -32,13 +32,28 @@ infixl 1 & -- | @'fix' f@ is the least fixed point of the function @f@, -- i.e. the least defined @x@ such that @f x = x@. +-- +-- For example, we can write the factorial function using direct recursion as +-- +-- >>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5 +-- 120 +-- +-- This uses the fact that Haskell’s @let@ introduces recursive bindings. We can +-- rewrite this definition using 'fix', +-- +-- >>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5 +-- 120 +-- +-- Instead of making a recursive call, we introduce a dummy parameter @rec@; +-- when used within 'fix', this parameter then refers to 'fix'' argument, hence +-- the recursion is reintroduced. fix :: (a -> a) -> a fix f = let x = f x in x --- | @(*) \`on\` f = \\x y -> f x * f y@. +-- | @((==) \`on\` f) x y = f x == f y@ -- -- Typical usage: @'Data.List.sortBy' ('compare' \`on\` 'fst')@. --- + -- Algebraic properties: -- -- * @(*) \`on\` 'id' = (*)@ (if @(*) ∉ {⊥, 'const' ⊥}@) @@ -95,6 +110,12 @@ on :: (b -> b -> c) -> (a -> b) -> a -> a -> c -- convenience. Its precedence is one higher than that of the forward -- application operator '$', which allows '&' to be nested in '$'. -- +-- >>> 5 & (+1) & show +-- "6" +-- -- @since 4.8.0.0 (&) :: a -> (a -> b) -> b x & f = f x + +-- $setup +-- >>> import Prelude |