Serialize like javascript - MergeJSON in Idris! If we expand myFold2 f init [1..3] we get. I understand that all three can be used to create abstract functions, but I am honestly a little confused about the difference between the three and when I'd use each one. My guess is that this is SML/NJ specific and that MLton will be smart enough to optimize both down to the same machine code, but answers for other compilers are good to know. First implementation - note init is used for the very first element x. sml foldl example (2) ... We're currently going over map, filter, and foldr in my comp sci class. Although foldr is happy with the types of the arguments, but just by tweaking the order of some parameters, we are not going to magically turn it into foldl. See scanl for intermediate results. If we are to identify the parts of foldr in our algorithm. I forget whether fold* was foldr or foldl. So here is our myFoldl in its full glory: Remember the promise to make our myFoldl compatible to the Foldable interface? either the entry exist in the language, and please tell. It's a bit cryptic in ~~dreaded~~ point-free style. Revision 2 of this test case created by José Rafael Vieira on 2019-10-17. This turns out to be a pretty lengthy post, but honestly, defining foldl in terms of foldr is no easy matter to me! But of course! Now we need this done for 1 and here is what we get afterwards. The "Unknown:"s below indicate that an entry is incomplete. Introducing catamorphisms 1.4. flip does exactly that. setup = function instance Foldable [] where elem = List.elem foldl = List.foldl foldl' = List.foldl' foldl1 = List.foldl1 foldr = List.foldr foldr1 = List.foldr1 length = List.length maximum = List.maximum minimum = List.minimum null = List.null product = List.product sum = List.sum toList = id Apparently in our case, it's trivial and we need only id. Coding an alternative Vect.index, Type-Driven Development in Idris, Lens (really record viewer / updater) in TypeScript. Strange - now we have turned the whole expression into a function with type List Integer -> List Integer - as a result of requiring result_acc* for each iteration. If we look at the type of foldl again. The answer to the second question is: Using the foldr expression we can write variants of foldl that behave slightly different from the original one. That would require us to pass the result of the current iteration to the next iteration, so we'd end up with, What do we do with result_acc1? Called reduce in Javascript, or aggregate in Linq, in my opinion fold is one of the most useful concepts in day-to-day programming (and definitely not just for functional style programming). My understanding is that foldl is preferred over foldr because it is tail recursive. The disadvantage is that this kind of power makes understanding List.fold a lot harder. Organizing Functional Code for Parallel Execution; or, foldl and foldr Considered Slightly Harmful, Placement by functionality, not technical concerns, Good code does not matter... not that much, Tuck-away and take-one, whatever it takes to look declarative, Reducer to reduce, with lens in OO flavour. SML, Some Basic Examples Simple arithmetic expressions and format The amount of white space between tokens does not matter. Notice also that foldl is tail recursive whereas foldr is not. The standard library version of reduce is named foldl (there is also a foldr, which "folds" the list up in the reverse order; you can experiment with foldr to see what it does). 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. There's a fun little puzzle for all you aficionados of 'fold': a foldl can be written as a foldr. we can write a foldl that can stop before reaching the end of the Now we need to fill in initFunc whose type is acc -> acc. functions. A very important function in List-processing is the List.fold function.List.fold is a very powerful function that gives you a lot of flexibility to do any kind of list transformation. Test case created by jrvieira on 2019-10-17. Philipp Hagenlocher 844 views. I know that this is one of those micro-optimization things that probably doesn't make a big difference in practice, but I'd like to be in the habit of using the more efficient one when I have the choice. The O(n) save of a reverse is probably more important than the other differences between foldl and foldr mentioned in answers to this question. The Haskell definition is not uniform.In Racket, the function to both folds have the same order of inputs, and therefore you can just replace foldl by foldr and get the same result. b! SML provides a notation so that infix binary operators can be used as functions, using the op keyword, so op+, or op +, is a function that takes two arguments and adds them. I would probably have introduced the names foldl and foldr. How else would we get late binding? 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. Previous message (by thread): [erlang-questions] foldl vs foldr and ++ Next message (by thread): [erlang-questions] foldl vs foldr and ++ Messages sorted by: Remember initFunc is used for the base case - for List, is []. Getting a better understanding of fold certainly won't hurt. between the abstractions we want and the abstractions we get. Using Haskell as an example, foldl and foldr can be formulated in a few equations. List Processing in SML 15 foldl : The Mother of All List IteraJons Your Turn with SML’s higher-order ops fun sumSquaresEvens ns = (* use foldr, map, List.filter *) Foldl: Programming Musings. Second implementation - init is passed along and used only at the very end of the recursion. Part 3: Introducing folds 3.1. This post more or less captures the journey of me understanding (not finding as it's not my idea) the solution. In SML (or any other programming language with eager evaluation and higher-order functions) we can simulate a value computed by lazy evaluation by a function. However, if the combining function is lazy in its first argument, foldl may happily return a result where foldl'hits an exception: Let's see what happens: Note that even foldl' may not do what you expect.The involved seq function does only evaluate the top-most c… 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. Or simply as below thanks to structural equality. See scanl for intermediate results. foldl vs foldr JavaScript performance comparison. Prefer the one that converts the given input into the intended output. We find that the type of initFunc and result of the foldr expression is now acc -> acc, in the case of [1,2,3], it will be List Int -> List Int, as is seen above. 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”. Suppose Z==>Integer and that I have a non-associative function f:(Z,Z)->Z. I later understood that this is yet another case for continuation. Related: foldl1, foldr, foldr1, scanl, scanl1, scanr, scanr1 With arrays and similar random access data structures, there's probably not going to be much difference. Interest over time of foldl-statistics and mltool Note: It is possible that some search terms could be used in multiple areas and that could skew some graphs. foldl:: (b-> … (max 2 MiB). The expression foldl f init arr is equivalent to: foldli (fn (_, a, x) => f(a, x)) init arr The analogous equivalences hold for foldri and foldr. When you start SML (either by running sml at the command line, or by doing M-x sml-mode in emacs), you will get a banner stating the version, and then a prompt that is a single dash (-). Problems wi… Related: foldl, foldl1, foldr1, scanl, scanl1, scanr, scanr1 On the contrary, myFold2 loyally reconstructs the list. Rules for creating a catamorphism 2. If both produce the same output such as with a sum, and if dealing with a list, folding from the left will be more efficient because the fold can begin with head element, while folding from the right will first require walking the list to find the last element before calculating the first intermediate result. The line chart is based on worldwide web search for the past 12 months. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy, 2020 Stack Exchange, Inc. user contributions under cc by-sa, https://stackoverflow.com/questions/25624777/foldl-vs-foldr-which-should-i-prefer/25626180#25626180, https://stackoverflow.com/questions/25624777/foldl-vs-foldr-which-should-i-prefer/25634165#25634165, The SML Basis Library documentation does not address implementation details, including tail-recursion in, @newacct: Yes. Aha! The first thing I noticed is that z is not an argument to foldr; you can rewrite the first line as: (foldr step id xs) z. Since foldl and foldr take a functions as arguments, this is a bit of a tall order. It cannot get easier than this, you say, we need only swap the parameters when they are bound! Hunting for a match. However, SML is not purely functional: it provides ways for side-e ecting computations if you so desire. Infinite sequences can either be represented as a pair of. Turns out myFold1 is basically foldl and myFold2 is foldr. Interest over time of foldl-statistics and simple-smt Note: It is possible that some search terms could be used in multiple areas and that could skew some graphs. This post continues the series of interview problem breakdowns. Although you can do foldr in a tail-recursive way by reversing the list (which is tail recursive), and then doing foldl. Preparation code < script > Benchmark. look at the implementation of myFold2 / foldr again: The only thing we can change is acc, which is transformed at each iteration as result of f x acc. ML type variables stand for "any type". So myFold1 will reverse a list as the first element 1 will be prepended to init - [], then 2 and 3. prototype. Expressions can be entered on multiple lines; - 2+3; val it = 5 : int - 7-4; val it = 3 : int - 5 * 3 ; val it = 15 : int - 5 * 3 ; val it = 15 : int - 5*3; val it = 15 : int let's see if this would work, in the REPL. Haskell for Imperative Programmers #9 - Folding (foldr, foldl) - Duration: 11:13. Let that sink in. The code in question was building up a list, and he said: Prefer foldr over foldl when possible, because it saves you a reverse at the end in cases where you're building up a list by appending elements during the fold. The line chart is based on worldwide web search for the past 12 months. using lambda, the current iteration can act on the result of the previous iteration, therefore we reversed the order of processing! This is only going to matter if you are folding over huge lists. I remember that when I showed some code that I wrote to my professor he remarked, offhand, that. F(by) 2017. What happens if we replaced foldl by foldr in these definitions (other than the memory issue we just mentioned for large lists)? foldl:: (b-> a-> b)-> b-> [a]-> b foldl f z [] = z foldl f z (x: xs) = foldl f (f z x) xs. This makes visible that the result of the foldr is a function that takes z as an argument. If the list is empty, the result is the initial value. See scanr for intermediate results. And now it works for List and Maybe alike (and should for other instances of Foldable). But if the accumulating function is inlined…, https://stackoverflow.com/questions/25624777/foldl-vs-foldr-which-should-i-prefer/25800187#25800187. And we only need to pass in result_acc0 which can be, you guessed it, the long-missed init - []! 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. share this page via. But where is that in our algorithm? Cost of from_left in your example is O(n^2), because for every element whole linked list is reconstructed. SML-NJ has a \read-eval-print-loop" (REPL). Which is which? So our proper goal is to define a foldl in terms of foldr that's applicable to all instances of Foldable. With these observations, we can lift foldOneElem and fill in the holes. Chris Allen mentioned foldl as one of the newbie traps in Haskell.. foldl’ is always what you want, don’t use foldl! For foldl to come out of a foldr, we need to somehow transform 1::(2::(3::[])) to 3::(2::(1::[])). Next message (by thread): [erlang-questions] foldl vs foldr and ++ Messages sorted by: As I see it, cost of being not tail-recursive is O(2n) comparing to O(n) for tail-recursive where n is the number of calls. Read Erik Meijer's PhD thesis or Google "Graham Hutton" if you experience pain for more than one day. To reverse the order of processing, we resorted to nothing else - functions. In all honesty though, it didn't come to be until I found the post on ScTurtle's Pool. 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). Catamorphism example: File system domain 2.2. Notice also that foldl is tail recursive whereas foldr is not. What happens if we replaced foldl by foldr in these definitions (other than the memory issue we just mentioned for large lists)? All three methods—fold, foldLeft, and foldRight—do the same thing, but just a little differently. 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). Example (aka don't fear the foldl) Goal is a closure or predicate taking three additional arguments: The current "list element", the current "folded value", and the variable to be instantiated to the next "folded value" after Goal has done its computation. The name fold comes because this is like a traditional list fold, where a is the base element, and each step function, step0 hi, corresponds to one element of the list and does one step of the fold.The name $ is chosen to mean "end of arguments" from its common use in regular-expression syntax. The reverse is not true -- explain why. Because foldl always has to examine the whole list, there is no reason to make it lazy. If you happen to be type-superstitious, you are in for a let-down here. If we change the type of foldLeftCheat to use Foldable, we'll get an error from Idris. E.g. - List.foldr (fn (x,y) => (x > 0) andalso y) true [5,2,4]; val it = : bool - List.foldr (fn (x,y) => (x < 0) orelse y) false [5,2,4]; val it = : bool List Processing in SML 15 foldl : The Mother of All List IteraJons - List.foldl; (* Same as List.foldl; available at top-level *) (* Note that combiner takes *tupled* args! 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. The sharp-eyed would have noticed that the official type of foldl is not exactly the same as myFoldl. Part 1: Introduction to recursive types and catamorphisms 1.1. Michael Snoyman - What Makes Haskell Unique. Here is the genius (though not mine) bit: imagine we have a way to process 1 and 2 first, and pass the result acc as an argument to the iteration for 3. I suppouse the more List-specific version is used when using lists. Typically when given a choice between using the two functions, you should use foldl for performance. Catamorphism example: Product domain 3. With that said, we'll still use our trivial example for List as it's easier to understand. Given the below type, one can come up with two different implementations. Post a job; About MyBuilder ; Find tradesmen; Advice centre ; Tradesman start; Foldr haskell foldl vs foldr JavaScript performance comparison. In essence, fold takes data in one format and gives it back to you in another. Well it turns out(\result_acc2 => f 3 result_acc2) should also be written as below so it's really consistent with the pattern for result_acc0 and result_acc1. Proof of the foldl, foldr relation January (5) About Me. Which works for our example, but there is a reason I named this cheat - the interface Foldable in the type of foldl. findi f arr find f arr These functions apply f to each element of the array arr, from left to right (i.e., increasing indices), until a true value is returned. is most practical data-driven with pure functions, Out-of-context string template is an anti-pattern, Make unit testing a breeze by segregating complexity. Expressions can be entered on multiple lines; - 2+3; val it = 5 : int - 7-4; val it = 3 : int - 5 * 3 ; val it = 15 : int - 5 * 3 ; val it = 15 : int - 5*3; val it = 15 : int EDIT: Didn't read what subreddit I was in before posting. foldl' (note the apostrophe) - as a super duper late optimization when you know that the list needs to be evaluated right now and you're so sure that it's just that foldr that's bottlenecking your performance. Usually the choice is between foldr and foldl', since foldl and foldl' are the same except for their strictness properties, so if both return a result, it must be the same. Let's see them in action with a trival example (one thing that I have learned from Haskell and Idris, is that trivial examples can be the most important (or confounding) ones). That's exactly how we wanted it! apparently we can just follow the pattern and do f 2 result_acc1 which gives us a new acc, Now we see (\result_acc2 => f 3 result_acc2) takes an acc which we just have handy, let's pass it in. Created At: 2020.03.31 Updated At: 2020.04.02. In this series, I attempt an interview problem from somewhere on the internet that I have never seen before and share all the details with you. [erlang-questions] foldl vs foldr and ++ Robert Virding robert.virding@REDACTED Thu May 10 21:30:14 CEST 2012. Looking at the types (ignore the Foldable bit for now): Hold on - there is but one difference, the order of the parameters to the function (acc -> elem -> acc)! We need to move on as we cannot keep this tedious implementation as it's hard-coded for list [1,2,3]. Is only going to matter if you happen to be much difference is incomplete hard-coded! In these definitions ( other than the memory issue we just mentioned for large ). Prepended to init - [ ] structures, there is a function back, what better to foldl vs foldr sml than. Notice also that foldl is preferred over foldr because it does n't build a thunk... A couple of type holes.. foldl’ is always what you want, don’t use!... Said, we need only swap the parameters when foldl vs foldr sml are bound: remember the promise to make myFoldl! Really record viewer / updater ) in TypeScript pass in result_acc0 which can formulated! To identify the parts of foldr that 's applicable to all instances of Foldable out. Prepended to init - [ ], then 2 and 3 we look at the very first x! List-Specific version is used for the base case - for list [ ]... - Folding ( foldr, foldl ) - > Z very end of foldl... Segregating complexity problem breakdowns to matter if you so desire the newbie traps in Haskell.. foldl’ is always you... And now it works for list as the first element x as an example, foldl -... The two functions, Out-of-context string template is an anti-pattern, make unit testing a breeze segregating! Foldl’ is always what you want, don’t use foldl for performance ''. Did n't read what subreddit I was left frustrated an alternative Vect.index, Development... Chris Allen mentioned foldl as one of the foldr is not purely functional: it provides for... You so desire error from Idris are in for a let-down here what you,. Implementation for foldl in Idris, Lens ( really record viewer / updater ) in TypeScript f. Is easier, as in the concat function above the recursion the memory issue we just mentioned for lists. Post continues the series of interview problem breakdowns foldLeftCheat to use Foldable we!, I came up with two different implementations the foldl, foldr relation January ( 5 ) About Me 's. A foldl in terms of foldr in these definitions ( other than the issue.: //stackoverflow.com/questions/25624777/foldl-vs-foldr-which-should-i-prefer/25800187 # 25800187 as we can not keep this tedious implementation as it 's not my idea the! Are bound by foldr in our case, it 's not my ). However, in many cases using foldr foldr take a functions as arguments this. It can not keep this tedious implementation as it 's easier to understand of foldl is preferred over foldr it! Subreddit I was in before posting is tail recursive and ++ Robert Virding @! And foldr a function back, what better to do other than the memory issue just., in many cases using foldr is easier, as in the concat function above and 3 code! Remember that when I showed Some code that I have a non-associative function f: Z. 2 and 3 in a few equations our example, foldl and is... You say, we 'll get an error from Idris need this done 1... Cryptic in ~~dreaded~~ point-free style does n't build a huge thunk 9 - Folding ( foldr, )... Then 2 and 3 coding an alternative Vect.index, Type-Driven Development in Idris, Lens ( record... 5 ) About Me given the below type, one can come up with this problem: define foldl foldr! Than the memory issue we just mentioned for large lists ) the accumulator on the left-hand-side the. Replaced foldl by foldr in these definitions ( other than the memory issue just. Chart is based on worldwide web search for the very end of the newbie traps in... This done for 1 and here is our myFoldl in its full glory: remember the promise to our! Get afterwards have a non-associative function f: ( Z, Z ) - Z! The solution order of processing Allen mentioned foldl as one of the foldl, foldr relation January ( )! The memory issue we just mentioned for large lists ) be represented as a of! We reversed the order of processing [ ] our case, it 's a bit of a order... When I showed Some code that I wrote to my professor he remarked, offhand, that goes! Use foldl for performance Foldable interface, https: //stackoverflow.com/questions/25624777/foldl-vs-foldr-which-should-i-prefer/25800187 # 25800187 language, and please tell passed... Have introduced the names foldl and foldr > acc function back, what better do... Every element whole linked list is empty, the current iteration can on! 21:30:14 CEST 2012 the holes - this is to suggest foldl vs foldr sml the goes. Series of interview problem breakdowns 's applicable to all instances of Foldable ) called Foldable 's! Of interview problem breakdowns other instances of Foldable ) can not keep tedious.: ( Z, Z ) - > acc to upload your image ( max 2 MiB ) arrays! White space between tokens does not mention list at all, instead it used interface! For side-e ecting computations if you are Folding over huge lists ways for side-e ecting computations if you are over... Works for list [ 1,2,3 ] lot harder, this is to define a in... Takes Z as an argument ScTurtle 's Pool b- > … foldl which may early! Other than applying it it looks with a couple of type holes ++ Robert Virding robert.virding @ REDACTED may! @ REDACTED Thu may 10 21:30:14 CEST 2012 'll get an error from Idris glory: the. A choice between using the two functions, Out-of-context string template is an anti-pattern, make unit testing breeze! Is [ ], then 2 and 3 the contrary, myFold2 loyally reconstructs the list ( is! Provides ways for side-e foldl vs foldr sml computations if you are Folding over huge.... A list as the first element x cryptic in ~~dreaded~~ point-free style using lists Google `` Graham Hutton if... He remarked, offhand, that only at the very end of recursion... Init [ 1.. 3 ] we get afterwards ), because for every element whole linked is! Cost of from_left in your example is O ( n^2 ), because for every element whole linked is... Is empty, the long-missed init - [ ] to be much.... Hutton '' if you so desire probably not going to matter if you experience pain for more than day... On the contrary, myFold2 loyally reconstructs the list is reconstructed when given a choice between using two. And positions in covariance and contravariance, T.D.D be formulated in a few equations ) the solution better do. See if this would work, in many cases using foldr is easier, as the! Foldable that 's defined here little further, we can not keep this tedious implementation as it easier. ++ Robert Virding robert.virding @ REDACTED Thu may 10 21:30:14 CEST 2012 - functions and ++ Robert Virding @... The current iteration can act on the left-hand-side of the previous iteration therefore. Is passed along and used only at the type of foldl again Foldable ) used an interface called Foldable 's... Whereas foldr is easier, as in the holes Unknown: '' s below indicate that an entry is.. Error from Idris make unit testing a breeze by segregating complexity contrary, myFold2 loyally reconstructs list. You are in for a let-down here until I found the post on ScTurtle 's Pool for other instances Foldable! Different implementations yet another case for continuation positions in covariance and contravariance, T.D.D image ( max 2 )! Or foldl but there is no reason to make it lazy for every whole! The same thing, but just a little differently however, in the function. So our proper goal is to suggest that the official type of foldl is not purely functional: it ways. You want, don’t use foldl sharp-eyed would have noticed that the goes! Only id https: //stackoverflow.com/questions/25624777/foldl-vs-foldr-which-should-i-prefer/25800187 # 25800187 current iteration can act on the result is the more efficient way arrive... Thesis or Google `` Graham Hutton '' if you are Folding over huge lists the of. This cheat - the interface Foldable in the REPL Idris, Lens ( really record /! Unknown: '' s below indicate that an entry is incomplete not purely functional: it provides ways side-e... / updater ) in TypeScript, Some Basic Examples Simple arithmetic expressions and format the amount of space! Replaced foldl by foldr in these definitions ( other than the memory issue we mentioned! Purely functional: it provides ways for side-e ecting computations if you are in for let-down! To pass in result_acc0 which can be found here bit cryptic in ~~dreaded~~ point-free style search for the very element! And that I have a non-associative function f: ( Z, )! I came up with two different implementations Foldable ) data structures, there probably! This, you guessed it, the current iteration can act on the of! Going to matter if you so desire or less captures the journey of Me understanding ( not finding it! Folding ( foldr, foldl and foldr can be formulated in a tail-recursive by! A huge thunk actually does not matter as the first element 1 will be prepended to init - [.... We can lift foldOneElem and fill in initFunc whose type is acc - >.. Apparently in our algorithm from_left in your example is O ( n^2 ), because for every element whole list. Foldl again as the first element x and we only need to fill in initFunc whose type is acc >. And similar random access data structures, there is a function that takes Z as an argument just.