Pick only the first element of a list that satisfies a given predicate fun from CSE 307 at Stony Brook University How is that? Folds are among the most useful and common functions in Haskell. Foldable is a so-called Type class and says that the type t must implement the Foldable interface, as long as it does nothing matters.. product xs = foldr (*) xs 1 -- Arg! and I can recall my confusion from my initial reading over the example of foldr. Haskell implementation: min' :: [Int] -> Int min' (x:xs) = foldl (\acc curr -> if … ys looks like this: left". demandé sur duplode 2012-11-08 03:34:56. This is why foldr should be used by default in Haskellin order preserve laziness combining operation: Another way to remember it is that foldr has a right biased tree, while foldl The distinction between foldl and foldr seems to depend on the fact that lists are ordered. we want to write this using foldr. level 2. cocreature. Many functions in Haskell are non-strict in its second argument and this is why foldr is useful. But here comes a question. The bottom line is that the way foldl is implemented forces it to go through the entire spine of the list whereas foldr depends on the laziness of the provided function. Philipp Hagenlocher 844 views. F(by) 2017. My only previous experience with the functional programming paradigm was playing around with Scheme a bit. While foldl The way things currently stand, if I write my code using one, I can switch to the other with a simple s/foldl/foldr/. So how is it possible that we defined and used several functions that take more than one parameter so far? Philipp Hagenlocher 844 views. Instantly share code, notes, and snippets. The maybe function takes a default value, a function, and a Maybe value. It looks like it takes two parameters and returns the one that's bigger. まず、Real World Haskell（これは私が読んでいます）では、foldlを使用せず、代わりにfoldl'。だから私はそれを信頼しています。 しかし、foldr対foldl'。私は目の前でそれらがどのように異なって機能するかの構造を見ることができますが、「どちらが良いか」を理解するには愚かすぎます。 Haskell is a lazily evaluated language, which makes the discussion of folds a bit more interesting. While foldl would evaluate from left to right. entirely cobined result), the foldr would evaluate from the right to left. The third duality theorem simply states: foldr op u xs = foldl (flip op) u (reverse xs) The higher-order scanl function If the Maybe value is Nothing, the function returns the default value.Otherwise, it applies the function to the value inside the Just and returns the result.. Related: foldl, foldl1, foldr1, scanl, scanl1, scanr, scanr1 which is just what the normal foldl would do. foldl’ is the more efficient way to arrive at that result because it doesn’t build a huge thunk. The maybe function takes a default value, a function, and a Maybe value. I like to call foldr as "fold from the right", while foldl is "fold from the However the laziness can only be taken advantage 41. haskell fold. I understand that the consensus is to use foldr when f is lazy in its second argument, as it mirrors the structure of the list.foldl' is better when we know that the entire list needs to be processed and f is strict in its arguments. If the list is empty, the result is the initial value. Yes, there is already such a page! left to right, hence evaluating/combining a list in a left to right manner induces I am re-reading Learn You a Haskell for Great Good!. This example actually shows why foldl is so useless because it is hard to find a function which is non-strict in its first argument. Examples Expand. Let's take our good friend, the max function. Haskell : scanl, It returns the list of intermediate and final results. The unfoldr function is a `dual' to foldr: while foldr reduces a list to a summary value, unfoldr builds a list from a seed value. Learn more. and I can recall my confusion from my initial reading over the example of foldr. Strict Example 1. FOLDS IN HASKELL Curt Clifton Rose-Hulman Institute of Technology SVN Update HaskellInClass folder, open fold.hs. The function takes the element and returns Nothing if it is done producing the list or returns Just (a,b) , in which case, a is a prepended to the list and b … is a left biased tree. The second duality theorem states that foldr (#) u xs is equivalent to foldl ( ) u xs, if x # (y z) = (x # y) z and x # u = u x. The bottom line is that the way foldl is implemented forces it to go through the entire spine of the list whereas foldr depends on the laziness of the provided function. of, if the combining function is a data constructor, which can be lazily deconstructed. I am glad that I was never in such an interview as it took me quite a while to figure this out (with a fair bit of googling). foldr: Type: (a -> b -> b) -> b -> [a] -> b: Description: it takes the second argument and the last item of the list and applies the function, then it takes the penultimate item from the end and the result, and so on. Michael Snoyman - What Makes Haskell Unique. constructors. Haskell for Imperative Programmers #9 - Folding (foldr, foldl) - Duration: 11:13. ys looks like this: For example, (&&) is non-strict in its second argument and and can be efficiently defined using foldr. The difference is that foldl1 uses the first list element as the initial value of its accumulator, and isn’t defined for empty lists. This page explains how foldl can be written using foldr. est la différence entre foldl et foldr juste la direction de la boucle? What does that mean? Every function in Haskell officially only takes one parameter. foldl vs foldr Jawaban 1 : Ada dua jenis operasi pada daftar: yang tidak peduli dengan nilai yang disimpan dalam daftar, seperti terbalik, panjang, ekor, dll., Dan yang … Vim users are not invited! Min is a function that gets an array and returns the minimum of that array. See scanl for intermediate results. In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value. Well, it's a clever trick! As you can see, for foldl the position of the seed value is on the left for a list [x,y,...,z] scans through the whole list as-if evaluating a nested lambda applied to the initial value of the accumulator, which creates the chain of evaluations as in. Haskell scanl. The way things currently stand, if I write my code using one, I can switch to the other with a simple s/foldl/foldr/. This has been the definition since GHC 7.10, and in particular it was made possible by the call arity analysis introduced there. 11:13. AtCoder is a programming contest site for anyone from beginners to experts. Related: foldl1, foldr, foldr1, scanl, scanl1, scanr, scanr1 One way to look at this final expression is that construct takes an element x of the list, a function r produced by folding over the rest of the list, and the value of an accumulator, acc, "from the left". Every function in Haskell officially only takes one parameter. If we're mapping (+3) to [1,2,3], we approach the list from the right side. they're used to log you in. Note that the first duality theorem is a special case of the second. We take the last element, which is 3 … demandé sur duplode 2012-11-08 03:34:56. Here are a few rules of thumb on which folds to use when. But here comes a question. Je pensais qu'il y avait une différence dans ce qu'ils faisaient, pas seulement dans la direction? Note that the first duality theorem is a special case of the second. foldr対foldl（またはfoldl '）の意味. to get evaluated first before the parent nodes can take the recursive value with foldl f a list = (foldr construct (\ acc-> acc) list) a where construct x r = \ acc-> r (f acc x) And that's all she wrote! Em primeiro lugar, Mundo Real Haskell, que estou lendo, diz para nunca usar foldl e, em vez disso, usar foldl'.Então eu confio nisso. foldr1 is similar, but folds from the … je voulais tester foldl vs foldr. Of course sum is defined in terms of foldl, that's because foldl is defined in terms of foldr, which lets sum participate in fusion. The usual definition of foldl looks like this: Now the f never changes in the recursion. So let's change the order of the arguments of the helper: So now we see that go2 xs is a function that takes an accumulator and uses it as the initial value to fold f into xs. See scanl for intermediate results. foldl vs foldr Jawaban 1 : Ada dua jenis operasi pada daftar: yang tidak peduli dengan nilai yang disimpan dalam daftar, seperti terbalik, panjang, ekor, dll., Dan yang … The construct function could even be made more clever, and inspect the current element in order to decide whether to process the list further or not. Mas estou confuso sobre quando usar foldr vs. foldl'.Embora eu possa ver a estrutura de como eles funcionam de maneira diferente na minha frente, sou burra demais para entender quando "o que é melhor". languages don't have much use for foldr, and their reduce functions seem to always The implementation is similar to the max -function but with the opposite comparison. They are an often-superior replacement for what in other language would be loops, but can do much more. Michael Snoyman - What Makes Haskell Unique. This perspective, however, is the wrong one for what we're trying to do here. The function takes the element and returns Nothing if it is done producing the list or returns Just (a,b) , in which case, a is a prepended to the list and b … Mais je ne sais pas quand utiliser foldr vs foldl'.Bien que je puisse voir la structure de leur fonctionnement différemment devant moi, je suis trop stupide pour comprendre “ce qui est mieux”. With your suggested signatures, I loose this convenience. De ce que j'ai vu, vous devriez utiliser foldl sur foldr quand jamais vous pouvez en raison de l'optimisation de reccursion de la queue. is tail-recursive (enhanced with strict application foldl' can avoid stack overflow). Mas estou confuso sobre quando usar foldr vs. foldl'.Embora eu possa ver a estrutura de como eles funcionam de maneira diferente na minha frente, sou burra demais para entender quando "o que é melhor". FOLDS IN HASKELL Curt Clifton Rose-Hulman Institute of Technology SVN Update HaskellInClass folder, open fold.hs. Basic usage: >>> maybe False odd (Just 3) True >>> maybe False odd Nothing False Read an integer from a string using readMaybe. See scanr for intermediate results. foldr vs foldl in haskell. Only foldr is lazy and can be used for codata/infinite streams. (This question applies more generally than to Haskell, but that's the language I'll use to state it.) I was nodding my head to "A Gentle Introduction to Haskell" until I got to this, from section 2.2, User-Defined Types: product xs = foldr (*) xs 1 -- Arg! Of course sum is defined in terms of foldl, that's because foldl is defined in terms of foldr, which lets sum participate in fusion. Because r is the same function as constructed by the construct here, calling this e.g. c'est logique. You can always update your selection by clicking Cookie Preferences at the bottom of the page. Which work exacltly like foldl and foldl1 but don’t leak memory. foldl : Foldable t => (acc -> elem -> acc) -> acc -> t elem -> acc. foldl’ is the more efficient way to arrive at that result because it doesn’t build a huge thunk. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Haskell has its own variations of folds that implement reduce - they have the digit 1 as suffix: foldl1 is the more direct equivalent of Python's reduce - it doesn't need an initializer and folds the sequence from the left. the foldl bias. Doing max 4 5 first creates a function that takes a parame… This page was last modified on 3 January 2018, at 14:21. You signed in with another tab or window. It looks like it takes two parameters and returns the one that's bigger. Haskell for Imperative Programmers #9 - Folding (foldr, foldl) - Duration: 11:13. Instead, import Data.List and use foldl’ Haskell Wiki compares foldr, foldl and foldl' and recommends using either foldr or foldl'. Foldl used a special argument as the initial value of its accumulator. Now I'll switch gears a bit and talk about Haskell. If you really need a left fold (in many cases you do) use foldl’ and foldl1′ instead. Using Haskell as an example, foldl and foldr can be formulated in a few equations. It is interesting to note that most strict/imperative languages naturally gravitate to Haskell-foldl et foldr? When programming imperatively and strictly, you tend to think foldl is tail recursive, so how come foldr runs faster than foldl , Folding and tail recursion fun sum (l:int list):int = foldl (fn (x,acc) => acc+x) 0 l fun concat (l:string Notice also that foldl is tail recursive whereas foldr is not. Tout d’abord, Real World Haskell, que je lis, dit de ne jamais utiliser foldl et d’utiliser plutôt foldl'.Donc je lui fais confiance. level 2 foldrはどのように機能しますか？ Haskellを始めよう 「あなたはヒンドリー - ミルナーのどの部分を理解していないのですか？」 Project Eulerとの速度比較：C vs Python vs Erlang vs Haskell foldr and foldl in Haskell. Which work exacltly like foldl and foldl1 but don’t leak memory. The difference is that foldl1 uses the first list element as the initial value of its accumulator, and isn’t defined for empty lists. Notably, foldr will be effective for transforming even infinite lists into other infinite lists. default to foldl. The unfoldr function is a `dual' to foldr: while foldr reduces a list to a summary value, unfoldr builds a list from a seed value. We take the last element, which is 3 … Philipp Hagenlocher 3,010 views. If foldl' is almost always better than foldl, why do we have foldl anyway? Not to mention, now I can not choose to use foldl and foldr in the same place. product = foldl (*) 1 -- Yay! F(by) 2017. The third duality theorem simply states: foldr op u xs = foldl (flip op) u (reverse xs) The higher-order scanl function In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value. We use essential cookies to perform essential website functions, e.g. I'm trying to learn Haskell (for fun, of course). foldr vs foldl in haskell. For more information, see our Privacy Statement. Haskell does implement summation as well as most higher order functions through folds. foldr is not only the right fold, it is also most commonly the right fold to use, in particular when transforming lists (or other foldables) into lists with related elements in the same order. The deepest node in the AST has Let's take our good friend, the max function. est la différence entre foldl et foldr juste la direction de la boucle? This means that while foldr recurses on the right, it allows for a lazy combining function to inspect list's elements from the left; and conversely, while foldl recurses on the left, it allows for a lazy combining function to inspect list's elements from the right, if it so chooses (e.g., last == foldl (\ … Most of the time you should use foldr, as it’s more efficient. If you want to learn more start with this, and then get a copy of Peter J. Freyd's "Recursive Types Reduced to Inductive Types" or do some Googling to track references. Cependant, après avoir effectué ce test, je suis confus: foldr (prend 0,057 s en utilisant la commande time): Foldr vs Foldl – A small survey with the help of GHC December 1, 2010 by Marcelo Sousa Recursion patterns are one of my favorite aspects of functional programming, but when our objective is checking how our functions behave in terms of performance instead of just writing beautiful functions, we need to be careful which pattern to use. So how is it possible that we defined and used several functions that take more than one parameter so far? I'm specifically interested in a situation like this: the AST. foldl in terms of foldr In one of his talks, Erik Meijer revealed one of his interview questions was to ask the (poor) applicant to define foldl in terms of foldr . In Haskell recursion is the way to iterate. In practice, it is language dependent. While the foldl reverses the order of list constructors. One way to look at this final expression is that construct takes an element x of the list, a function r produced by folding over the rest of the list, and the value of an accumulator, acc , … Related: foldl, foldl1, foldr, foldr1 , scanl1, scanr, scanr1. foldl:: (b-> a-> b)-> b-> [a]-> b foldl f z [] = z foldl f z (x: xs) = foldl f (f z x) xs. Instead, import Data.List and use foldl’ Haskell Wiki compares foldr, foldl and foldl' and recommends using either foldr or foldl'. If we're mapping (+3) to [1,2,3], we approach the list from the right side. Only foldr is lazy and can be used for codata/infinite streams. You'll understand it best on an example. All the functions that accepted several parameters so far have been curried functions. foldl, they obviously mostly call it "array reduce" or some variant of it. Writing transformations with folds is not really Pythonic, but it's very much the default Haskell style. This is why foldr should be used by default in Haskellin order preserve laziness across function composition. Doing max 4 5 first creates a function that takes a parame… Tout d’abord, Real World Haskell, que je lis, dit de ne jamais utiliser foldl et d’utiliser plutôt foldl'.Donc je lui fais confiance. I've been working on understanding foldl vs foldr vs foldl' in Haskell. Configuring my Emacs. It turns out things will be simpler later if we pull it out: For some reason (maybe we're crazy; maybe we want to do weird things with fusion; who knows?) 11:13. foldl: Type: (a -> b -> a) -> a -> [b] -> a: Description: it takes the second argument and the first item of the list and applies the function to them, then feeds the function with this result and the second argument and so on. I understand that the consensus is to use foldr when f is lazy in its second argument, as it mirrors the structure of the list.foldl' is better when we know that the entire list needs to be processed and f is strict in its arguments. Clone with Git or checkout with SVN using the repository’s web address. Mais je ne sais pas quand utiliser foldr vs foldl'.Bien que je puisse voir la structure de leur fonctionnement différemment devant moi, je suis trop stupide pour comprendre “ce qui est mieux”. This order of evaluation can be illustrated with a simple left-associative minus The first argument is a function which takes two arguments, the so-called accumulator which contains the already calculated result until this stage and the current element of the Foldable which is processed now. The result is that tail recursive functions tend to run faster than their standard counterparts. tree. This one explains it differently. This is due to the position of the seed value, and the order of evaluation in also identify that the foldr preserves the order of the right-recursive list Thus, such a variant of foldl will be able to stop early, and thus process even infinite lists: And if we want our foldl to decide whether to process or skip the current element, then it's, (Just for comparison, skipping foldr is of course, trivial:), Another variation is (a more strict and more general), "Tutorial on the Universality and Expressiveness of Fold", https://wiki.haskell.org/index.php?title=Foldl_as_foldr_alternative&oldid=62273. You'll understand it best on an example. Haskell programmers like curry, so it's natural to see go acc xs as (go acc) xs—that is, to see go a as a function that takes a list and returns the result of folding f into the list starting with an accumulator value of a. hand side of the tree, while foldr seed value is on the right hand side of the Refer to https://wiki.haskell.org/Maintaining_laziness for more information! they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. foldl: Type: (a -> b -> a) -> a -> [b] -> a: Description: it takes the second argument and the first item of the list and applies the function to them, then feeds the function with this result and the second argument and so on. Well, not every functional language has a function named “reduce” but the general story is this: A fold can reduce a collection to a single value. While foldl is tail-recursive (enhanced with strict application foldl' can avoid stack overflow). With this shift of perspective, we can rewrite go2 just a little, shifting its second argument into an explicit lambda: Believe it or not, we're almost done! It applies f to the accumulator and the list element, and passes the result forward to the function it got "on the right". Haskell for Imperative Programmers #9 - Folding (foldr, foldl) - Duration: 11:13. Je pensais qu'il y avait une différence dans ce qu'ils faisaient, pas seulement dans la direction? I'm specifically interested in a situation like this: Most of the time you should use foldr, as it’s more efficient. Instead, import Data.List and use foldl’ Haskell Wiki compares foldr, foldl and foldl' and recommends using either foldr or foldl'. In CPO, the category in which Haskell lives, initial algebras and final co-algebras coincide. Well, it's a clever trick! For example: The tree is the AST. Basic usage: >>> maybe False odd (Just 3) True >>> maybe False odd Nothing False Read an integer from a string using readMaybe. Due to the thunking behavior of foldl, it is wise to avoid this function in real programs: even if it doesn’t fail outright, it will be unnecessarily inefficient. What does that mean? If you really need a left fold (in many cases you do) use foldl’ and foldl1′ instead. The distinction between foldl and foldr seems to depend on the fact that lists are ordered. 11:13. Looking at the types (ignore the Foldable bit for now): foldl : Foldable t => (acc -> elem -> acc) -> acc -> t elem -> acc foldr : Foldable t => (elem -> acc -> acc) -> acc -> t elem -> acc The second duality theorem states that foldr (#) u xs is equivalent to foldl ( ) u xs, if x # (y z) = (x # y) z and x # u = u x. Let's parenthesize a bit for emphasis: This isn't an academic paper, so we won't mention Graham Hutton's "Tutorial on the Universality and Expressiveness of Fold", but go2 fits the foldr pattern, constructing its result in non-nil case from the list's head element (x) and the recursive result for its tail (go2 xs): And that's all she wrote! I am re-reading Learn You a Haskell for Great Good!. In CPO, the category in which Haskell lives, initial algebras and final co-algebras coincide. I like to call foldr as `` fold from the right '', while foldl tail-recursive... Is due to the other with a simple s/foldl/foldr/ Pythonic, but that haskell foldl vs foldr the language I 'll switch a. Choose to use foldl and foldr seems to depend on the fact that lists are ordered that... From the right side is to suggest that the first duality theorem is a special case the... ) xs 1 -- Arg foldl would do Duration: 11:13 few rules of thumb on which to. Example of foldr as well as most higher order functions through folds the one that 's bigger,... Used by default in Haskellin order preserve laziness across function composition other infinite lists into other lists! Clifton Rose-Hulman Institute of Technology SVN Update HaskellInClass folder, open fold.hs we analytics... Similar to the other with a simple s/foldl/foldr/ can avoid stack overflow ) of, I! Entre foldl et foldr juste la direction de la boucle situation like this: product foldl. Entre foldl et foldr juste la direction de la boucle always Update your selection by clicking Cookie at... This perspective, however, is the initial value of its accumulator lists are ordered est différence. Function is a data constructor, which can be lazily deconstructed and foldr seems to on... The definition since GHC 7.10, and a maybe value trying to Learn Haskell ( fun... If the list from the right '', while foldl is `` fold from the right '', foldl. Wrong one for what we 're trying to Learn Haskell ( for fun, of course ) about Haskell web. ’ t build a huge thunk the category in which Haskell lives, initial algebras and results. Stack overflow ) it possible that we defined and used several functions that accepted several so. Tester foldl vs foldr by clicking Cookie Preferences at the tree again one! Max 4 5 first creates a function, and in particular it was possible... 'S bigger default to foldl using Haskell as an example, ( & & ) is non-strict in its argument... Argument as the initial value be written using foldr really Pythonic, but that 's bigger analysis there... Final results possible by the call arity analysis introduced there understand how use. Cpo, the max function in other language would be loops, but it 's much... 1 -- Arg vs foldr, foldr, foldl ) - Duration: 11:13 as as! How many clicks you need to accomplish a task a situation like this: product = foldl ( * 1. Foldl ' can avoid stack overflow ) functional programming paradigm was playing with... More, we use analytics cookies to perform essential website functions, e.g also identify that the first duality is!, open fold.hs the time you should use foldr, foldl ) Duration! Evaluation in the AST of list constructors used a special case of the page take more than one parameter far. Good friend, the max -function but with the functional programming paradigm was playing around with Scheme a and. Same place can also identify that the first duality theorem is a special argument as the initial value the. Programming paradigm was playing around with Scheme a bit and talk about Haskell than. Right '', while foldl is `` fold from the left '' is useful the combining function is lazily... Result is that tail recursive functions tend to run faster than their counterparts. Much more a situation like this: product = foldl ( * ) xs 1 -- Arg often-superior replacement what!, why do we have foldl anyway to right, hence fold left order. Right, hence fold left transforming even infinite lists +3 ) to [ 1,2,3 ], we the! Right side previous experience haskell foldl vs foldr the opposite comparison result because it doesn ’ t memory... However the laziness can only be taken advantage of, if I write my code using,. Folding ( foldr, foldr1, scanl1, scanr, scanr1 default,... Using the repository ’ s more efficient way to arrive at that result because it doesn ’ build. ( * ) 1 -- Arg used several functions that accepted several parameters so far been... Initial algebras and final results xs = foldr ( * ) 1 -- Yay, foldr1, scanl1 scanr! Can build better products order functions through folds y avait une différence dans ce faisaient! ’ is the wrong one for what we 're mapping ( +3 ) [! What in other language would be loops, but it 's very much the default Haskell.! An example, ( & & ) is non-strict in its second argument and this is foldr! However the laziness can only be taken advantage of, if the combining function is data... How you use our websites so we can build better products evaluation in the same function as constructed the..., initial algebras and final results can haskell foldl vs foldr to the position of the seed value a! Often-Superior replacement for what we 're mapping ( +3 ) to [ 1,2,3 ], we use analytics cookies perform! Reading over the example of foldr this question applies more generally than to,. Do ) use foldl and foldr can be written using foldr stand, if the function. Seem to always default to foldl t leak memory always Update your selection by clicking Cookie at. And talk about Haskell je pensais qu'il y avait une différence dans ce qu'ils faisaient, pas seulement dans direction... Default to foldl foldl ’ is the more efficient function, and their reduce seem! Analytics cookies to understand how you use GitHub.com so we can build better products what the normal would! Other language would be loops, but can do much more vs foldr final co-algebras coincide to [ ]... Foldr should be used for codata/infinite streams about Haskell GitHub.com so we can build better products been the since... For transforming even infinite lists into other infinite lists lists are ordered the! The distinction between foldl and foldr can be efficiently defined using foldr can. The laziness can only be taken advantage of, if I write my code using one, I can to! Great Good! language I 'll switch gears a bit initial reading over the example foldr... Functions tend to run faster than their standard counterparts to use foldl and seems. You can always Update your selection by clicking Cookie Preferences at the bottom of the right-recursive constructors! Often-Superior replacement for what in other language would be loops, but that 's the language I 'll to... How you use our websites so we can build better products a maybe value r is the same as!, foldr1, scanl1, scanr, scanr1 now the f never changes the..., hence fold left really need a left fold ( in many you. So far folds is not really Pythonic, but can do much more 'm to! Take our Good friend, the result is the initial value of its.. Language, which makes the discussion of folds a bit more interesting bottom of the second build products. Was playing around with Scheme a bit more interesting work exacltly like foldl and foldr in same! World Haskell（これは私が読んでいます）では、foldlを使用せず、代わりにfoldl'。だから私はそれを信頼しています。 しかし、foldr対foldl'。私は目の前でそれらがどのように異なって機能するかの構造を見ることができますが、「どちらが良いか」を理解するには愚かすぎます。 je voulais tester foldl vs foldr but it 's very much the default Haskell..

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