Original address ：Haskell Study - Higher order function
Higher order function (higher-order function) A function that can operate a function , That is, the function can be used as a parameter , It can also be used as a return result . With these two characteristics ,haskell It can achieve many magical effects .
stay haskell All arithmetic operators in are functions ( Including the relationship between size and equal to, etc ), And their shortcuts can omit operands （ Parameters ）.
(+) 1 2 -- (+) Is a function that requires two operands
> 3 (+1) 2 -- (+1) Is a function that requires left operands
> 3 (3*) 3 -- (3*) It's a function that needs a right-hand operand
> 6 map (*2) [1,2,3] -- map All the elements *2 The operation of
> [2,4,6] filter (>3) [2,3,4,5] -- Filter >3 The elements of
haskell All functions in are prefix mode by default , That is to say ： Function name Parameters 1 Parameters 2 ... . But almost all functions with two parameters have infix patterns , Just wrap the function name in inverted quotation marks ： Parameters 1 ` Function name ` Parameters 2. Because infix functions are more readable in some cases , More in line with people's understanding habits .
5 `div` 3 -- Mod
> 1 9 `mod` 7 -- modulus
> 2 'f' `elem` ['a' .. 'z'] -- Does it include 'f'
Essentially ,Haskell All functions of have only one parameter , So what happened to our function with multiple parameters ? That's because all functions with multiple arguments are Curried functions. In fact, from the above example of arithmetic operation function , We can probably guess . And then use an example to verify ：
moreThen4 = max 4 -- The minimum is 4 Function of :t max -- Functions that require two comparable arguments
max :: Ord a => a -> a -> a :t moreThen4 -- A function that needs a comparable number
> moreThen4 :: (Ord a, Num a) => a -> a
By looking at the type of function, you can see that , Two parameters max Functions can actually be written as (max x) y .moreThen4 In fact, that is max Function is called with incomplete arguments , And create a new return function , The function is in the form of a single parameter .
We have a strange looking description of function types Num a => a -> a -> a , It's understandable . It means that the function takes a numeric parameter a after , Will return a need a Function of type parameter (Num a) => a -> a , The last function takes another parameter a after , Eventually it will be sent back a Result of type .
After removing the redundant parameters, the function is more concise ：
sum' xs = foldl (+) 0 xs
sum' = foldl (+) 0 -- Get rid of xs after maxNum x = foldr max 0 x
maxNum = foldr max 0 -- Get rid of x after
Write anonymous functions , So you don't have to create named functions . Because anonymous functions come from lambda From calculation , So anonymous functions are often called lambda function .
stay Haskell in , Anonymous functions are marked with backslashes \ Start , Followed by the parameters of the function （ You can include patterns ）, And the function body is defined in -> After the symbol .lambda The definition of a function can only have one statement , Cannot set multiple modes for one parameter at the same time , Such as  and (x:xs).
plusOne = \x -> x+1 checkZero = \x -> if x > 0 then " Greater than 0"
else if x<0 then " Less than 0"
else " be equal to 0"
Traversing lists is a very common requirement , Using folding function instead of explicit recursion for traversal is obviously easier to understand and implement . among foldl It's a combination of left and right ,foldr It's right combination , Generally, the right folding efficiency is relatively high , meanwhile foldr It can also be used for infinite lists , So try to use foldr.
Collapse function call format : fold Processing function Initial value ( Cumulative value ) The list that needs to be collapsed
In addition, it also provides and foldl/foldr alike foldl1/foldr1, They use the first item in the list as the initial value by default , So you can omit the initial value .
map' :: Foldable t1 => (t2 -> a) -> t1 t2 -> [a]
map' f = foldr (\x acc -> f x:acc)  filter' :: Foldable t => (a -> Bool) -> t a -> [a]
filter' f = foldr (\x acc -> if f x then x:acc else acc)  elem' :: (Foldable t, Eq a) => a -> t a -> Bool
elem' y = foldl (\acc x -> if y==x then True else acc) False and' :: Foldable t => t Bool -> Bool
and' = foldr1 (\x y->if not y then False else if not x then False else True) -- perform
map' (*2) [1,2]
> [2,4] filter (>2) [1,2,3,4]
> [3,4] elem' 1 [1,2,3]
> True and' [True,False,True]
And foldl and foldr alike scanl and scanr, They record all the states of the accumulated value to a List.
Also have scanl1 and scanr1.
scanl (+) 0 [3,5,2,1]
> [0,3,8,10,11] scanr (+) 0 [3,5,2,1]
also foldl' and foldl1' It's a strict version of their respective implementations . In use fold Deal with larger List when , Stack overflow is a common problem . And the culprit is fold The inertia of : In execution fold when , The value of the accumulator is not immediately updated , It's about being a " When necessary, it will achieve the desired results " Commitment . Every time I go through the accumulator , This behavior is repeated once . And all of this stuff " promise " It's going to end up filling your stack . Strict fold There would be no such problem , They don't do " promise ", Instead, we calculate the intermediate value directly and continue to execute it . If you use inertia fold Overflow errors are often encountered during the process , We should use their strict version instead .
（$) It's called function callers , It has the lowest priority .
f $ g x => f (g x) -- take >2 The list length of
length (filter (>2) [1,2,3,4])
length $ filter (>2) [1,2,3,4] -- Lower the priority, remove the brackets
(.) Function composition operator , It can combine functions , And generate new functions , Then pass it to other functions . Of course we can use lambda Realization , But most of the time , The use of function combinations is undoubtedly clearer .
(f . g) x => f(g x) -- Verify that the string is a number
not ( and ( map isDigit $ "12as"))
not . and . map isDigit $ "12as" -- Use a combination to remove parentheses
These two operators are the artifact of eliminating brackets , Have they , The readability of the code is greatly improved .
Let's reuse haskell Powerful pattern matching capabilities , Change the direction of the function , The effect after transformation is similar to unix/linux The pipe , Rewrite the above two expressions . Now even ($) (.) I don't need any more , It's a blast , Is there any
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