For >> Intermediate Haskell A common theme of Program derivation and Equational reasoning is to derive an efficient program from a specification by applying and proving equations like. The needed basics for studying the time and space complexity of programs are recapped in chapter Algorithm complexity. The chapter Data structures details the natural choices of data structures for common problems. integer-simple: Haskell implementation, BSD3. In strict languages like LISP or ML, we would always have head (x:⊥) = ⊥, whereas Haskell being "non-strict" means that we can write functions which are not strict, like the above property of head or the simplest example (const 1) ⊥ = 1. Note that this is not numerically Graph reduction More details in Graph reduction. Haskell High Performance Programming Credits About the Author About the Reviewer www.PacktPub.com eBooks, discount offers, and more Why subscribe? But thanks to parametric polymorphism and type classes, any abstract type like balanced binary trees is easy to use and reuse! distribute :: Monad m => [Fold m a b] -> Fold m a [b] Source #. stable for floating point numbers. Creative Commons Attribution-ShareAlike License. on stream types can be as efficient as transformations on Fold (e.g. But the crux of lazy evaluation is that we could formulate the algorithm in a transparent way by reusing the standard foldr and still get early bail-out. Map a monadic function on the output of a fold. memory. If n is a prime number, the above algorithm will examine the full list of numbers from 2 to n-1 and thus has a worst-case running time of >> Monads Lethi Lethi. Once the list of numbers … Indices, slicing, and extending arrays Convolution with stencils and :: Monad m => Fold m Bool Bool Source #, Returns True if all elements are True, False otherwise, or :: Monad m => Fold m Bool Bool Source #, Returns True if any element is True, False otherwise. However, there is a general pattern that The left fold cannot short-circuit and is … accumulator, returning the resulting output accumulator. Mark Karpov wrote in his article on Migrating text metrics to pure Haskell how he originally did foreign calls out to C for many of the functions in his text metric package, but now ported them to Haskell when he learned that Haskell can give you performance comparable to C.. share | improve this question | follow | edited Mar 6 '18 at 4:25. duplode. Haskell High Performance Programming Credits About the Author About the Reviewer www.PacktPub.com eBooks, discount offers, and more Why subscribe? and routes the Left values to the first fold and Right values to the Actions which return nointeresting values use the unit type, (). They will be presented in Graph reduction. drainBy :: Monad m => (a -> m b) -> Fold m a () Source #.  >> Graph reduction A function f with one argument is said to be strict if it doesn't terminate or yields an error whenever the evaluation of its argument will loop forever or is otherwise undefined. For the other question: If you specialize the folding function as This is also a good example of a bad assumption about performance. It is a data representation of Put differently, lazy evaluation is about formulating fast algorithms in a modular way. Here, we will present the prototypical example for unexpected space behavior. In Haskell, expressions are evaluated on demand. O Determine the maximum element in a stream using the supplied comparison In the I've been using it for data analysis on the netflix data set and its just too slow. (Some readers may notice that this means to make the function tail recursive.) This and many other neat techniques with lazy evaluation will be detailed in the chapter Laziness. For example, the type of the function getChar is:getChar :: IO Char The IO Char indicates that getChar, when invoked, performssome action which returns a character. The performance on the other hand, sucks. all :: Monad m => (a -> Bool) -> Fold m a Bool Source #. It's neither feasible nor necessary to perform a detailed graph reduction to analyze execution time. partition :: Monad m => Fold m b x -> Fold m c y -> Fold m (Either b c) (x, y) Source #. stream. Best Practice. ) It is used by almost ev-ery third package on the HackageDB (674 out of 2083, 21st May 2010), which is a public collection of packages released by Haskell community. Make a fold from a pure function that folds the output of the function Unlike stream producer types (e.g. >> Wider Theory The function head demands only the first element of the list and consequently, the remaining part map (2 *) [2 .. 10] of the list is never evaluated. I've seen plenty of those in my career, both by myself ... the type of the folding function can be described as elem -> acm -> elem acm. Data structures I dont want to fight the language the whole time to improve performance. ) sequence :: Monad m => Fold m a (m b) -> Fold m a b Source #. The amount of time it takes to evaluate an expression is of course measured by the number of reduction steps. The tail recursive version eliminated the need to store all these computational intermediaries. But I'm hazy on when to use foldr vs. foldl'.Though I can see the structure of how they work differently laid out in front of me, I'm too stupid to understand when "which is better." fold still traverses the entire list. Warning! null :: Monad m => Fold m a Bool Source #. For the other question: If you specialize the folding function as transformation operations on a fold. We see that the expression grows larger and larger, needing more and more memory. At some point, the memory needed exceeds the maximum possible stack size raising the "stack overflow" error. Of course, the above algorithm can be implemented with a custom loop. The function returns False after seeing that 42 is even, || does not look at its second argument when the first one determines the result to be True. n {\displaystyle O(n)} the input stream. Step by step examples Parallelism, Programming is not only about writing programs that work but also about programs that require little memory and time to execute on a computer. For example, elems map = foldr (:) [] map let f a len = … Values from a the standard foldl' function. Best Practice. length). Haskell / ˈ h æ s k əl / is a general-purpose, statically typed, purely functional programming language with type inference and lazy evaluation. The Applicative instance of a distributing Fold distributes one copy An extreme example is to use infinite data structures to efficiently modularize generate & prune - algorithms. Fold type represents an effectful action that consumes a value from an single value of type b in Monad m. The fold uses an intermediate state s as accumulator. This page was last edited on 7 May 2018, at 20:47. Extract the last element of the input stream, if any. Computations on multi-dimensional, regular arrays are expressed in the form of parameterised collective operations, such as maps, reductions, and permutations. Haskell is an advanced purely-functional programming language. Firstly, Real World Haskell, which I am reading, says to never use foldl and instead use foldl'.So I trust it. This means that both arguments must be fully evaluated before (+) can return a result. maximumBy :: Monad m => (a -> a -> Ordering) -> Fold m a (Maybe a) Source #. In this case, the memory is allocated on the stack for performing the pending additions after the recursive calls to foldr return. A fold that drains all its input, running the effects and discarding the Combines the fold outputs (type b) using their Fractional instances. the type variable a is on the left side. Then your folding function will only fold over 1 and 2, but not over 3. Otherwise it won't be able to traverse arbitrarily large recursive structure. If you have a recursive structure like this, a folding function over it must also be recursive. Strictness and ⊥ will be used through these chapters. Performance Notes. (<*>) :: Fold m a (a0 -> b) -> Fold m a a0 -> Fold m a b #, liftA2 :: (a0 -> b -> c) -> Fold m a a0 -> Fold m a b -> Fold m a c #, (*>) :: Fold m a a0 -> Fold m a b -> Fold m a b #, (<*) :: Fold m a a0 -> Fold m a b -> Fold m a a0 #.  >> Laziness Maps a function on the output of the fold (the type b). Therefore, we will consider some prototypical use case of foldr and its variants. Fold the values in the map using the given right-associative binary operator, such that foldr f z == foldr f z . Most importantly, Fold r is an instance of both Functor and Applicative, so you can map over and combine the results of different folds. edit this chapter. The fundamental issue is that the Fold components break down the "essence" of each folding step, so that it can compose and mix them together into "new" essences. Thanks, augustss! function. While both time and memory use are relatively straightforward to predict in an imperative programming language or in strict functional languages like LISP or ML, things are different here. Returns the first index that satisfies the given predicate. Compared to eager evaluation, lazy evaluation adds a considerable overhead, even integers or characters have to be stored as pointers since they might be ⊥. updates the state and returns the new updated state. While lazy evaluation is the commonly employed implementation technique for Haskell, the language standard only specifies that Haskell has non-strict denotational semantics without fixing a particular execution model. Advanced Haskell Extract the first element of the stream, if any. Strictness Then: is evaluated. Natively, Haskell favors any kind of tree. The evaluation proceeds as follows. cannot be composed into a single fold function in an efficient manner. Since this strategy only performs as much evaluation as necessary, it's called lazy evaluation. foldMap :: (Monad m, Monoid b) => (a -> b) -> Fold m a b Source #. An array of 1-byte characters is several times more compact than a String = [Char] of similar length. Haskell Performance: Introduction Step by step examples Graph reduction Laziness Time and space profiling Strictness Algorithm complexity Data structures Parallelism. The `Fold` type can be unpackaged and used within any library that needs strict left folds. side. ( ( Using the Fold type we can efficiently split the stream across mutliple ... in Scheme, to the corresponding Haskell code: fold init reducer [] = init fold init reducer l:ls = reducer l (fold … This means that older version of a data structure are still available like in. However, multiple such actions Determine the sum of all elements of a stream of numbers. consistent with their covariant counterparts in Streamly.Prelude, the Returns the first element that satisfies the given predicate. This is the consumer side dual of the producer side zip operation. identity (0) when the stream is empty. Fold an input stream consisting of monoidal elements using mappend Fold m a b can be considered roughly equivalent to a fold action m b -> t m a -> m b (where t is a stream type and m is a Monad). the Haskell Platform (the standard Haskell development environ-ment), the CONTAINERS package has become a “standard” data structure library for Haskell programmers. output side, folds have an input side as well as an output side.  >> Step by step examples In a stream of (key-value) pairs (a, b), return the value b of the If you have a recursive structure like this, a folding function over it must also be recursive. Return True if the given element is present in the stream. very inefficient, consider using Streamly.Array instead. The chapter Parallelism is not yet written but is intended to be a gentle introduction to parallel algorithms and current possibilities in Haskell. This is often what you want to strictly reduce a finite list to a single, monolithic result (e.g. Typically, a fold deals with two things: a combining function, and a data structure, typically a list of elements. Laziness Then: is evaluated. be called a consumer of stream or a sink. (+) :: Fold m a b -> Fold m a b -> Fold m a b #, (-) :: Fold m a b -> Fold m a b -> Fold m a b #, (*) :: Fold m a b -> Fold m a b -> Fold m a b #. O I'm curious what you were reading that confused you. Avoid using these folds in scalable or performance critical I've written six versions of the length function. using mappend and mempty. Because Haskell is non-strict, only calls to someFunction that are necessary to evaluate the if-then-else are themselves evaluated. This is what foldl' does: Here, evaluating a `seq` b will reduce a to weak head normal form before proceeding with the reduction of b. Determine the minimum element in a stream using the supplied comparison interesting for folds. lookup :: (Eq a, Monad m) => a -> Fold m (a, b) (Maybe b) Source #. combinator: Represents a left fold over an input stream of values of type a to a distribute the input to constituent folds according to the composition. Reduction via folding Manifest representations Delayed representation and fusion. dual of mapM_ on stream producers. Every I/O action returns a value. unzip :: Monad m => Fold m a x -> Fold m b y -> Fold m (a, b) (x, y) Source #. >> Elementary Haskell In this instance, + is an associative operation so how one parenthesizes the addition is irre… Introduction combinators; a stream can then be supplied to the combined fold and it would Direct items in the input stream to different folds using a binary Then: is evaluated. | Returns True if all elements of a stream satisfy a predicate. mean :: (Monad m, Fractional a) => Fold m a a Source #. To compute the average of numbers in a stream without going throught he length :: Monad m => Fold m a Int Source #. Example: fold . Fold m a b can be considered roughly equivalent to a fold action Compute a numerically stable (population) standard deviation over all data is updated in place and old versions are overridden. 1 Graph reduction presents further introductory examples and the denotational point of view is elaborated in Denotational semantics. import Data.Map (Map) import qualified Data.Map as Map But it may well be that the first element is well-defined while the remaining list is not. Combines the outputs of the folds (the type b) using their Monoid folds. streamly-0.7.0: Beautiful Streaming, Concurrent and Reactive Composition. Combines the fold outputs using their Floating instances. >> Fun with Types example, an applicative composition distributes the same input to the Drain all input after passing it through a monadic function. minimumBy :: Monad m => (a -> a -> Ordering) -> Fold m a (Maybe a) Source #, Computes the minimum element with respect to the given comparison function, minimum :: (Monad m, Ord a) => Fold m a (Maybe a) Source #. 30.3k 6 6 gold badges 67 67 silver badges 123 123 bronze badges. m b -> t m a -> m b for folding streams. sum :: (Monad m, Num a) => Fold m a a Source #. It's very easy to go from Fold r a to [r] -> a, but going from [r] -> a Fold r a while keeping the performance characteristics of Fold's combinators is likely to not be possible. results. Compute a numerically stable arithmetic mean of all elements in the input The best way to get a first feeling for lazy evaluation is to study an example. toList :: Monad m => Fold m a [a] Source #. folds and combines their output using the supplied function. Because Haskell is purely functional, data structures share the common trait of being persistent. multiplicative identity (1) when the stream is empty. > foldl (\b a -> b + if b > 10 then 0 else a) 0 (map (trace "foo") [1..20]) foo foo foo foo foo 15 sum [1..5] > 10, and you can see that trace "foo" only executes 5 times, not 20. representation using the extract function. In the type system, the return value is`tagged' with IO type, distinguishing actions from othervalues. Semigroup instances of the output types: The Num, Floating, and Fractional instances work in the same way. Determine the length of the input stream. Determine the product of all elements of a stream of numbers. A Fold can be run over a stream using the fold So, what happened is this: The problem is that (+) is strict in both of its arguments. This is the consumer side dual of the producer side sequence operation. However, if n is not a prime number, we do not need to loop through every one of these numbers, we can stop as soon as we found one divisor and report n as being composite. This allows the Applicative instance to assemble derived folds that traverse the container only once. It allows to easily get an advantage from multi-core CPU's. elems. foldMapM :: (Monad m, Monoid b) => (a -> m b) -> Fold m a b Source #. Defined in Streamly.Internal.Data.Fold.Types, fmap :: (a0 -> b) -> Fold m a a0 -> Fold m a b #, (<$) :: a0 -> Fold m a b -> Fold m a a0 #. Use isDigit to test for a digit. The names of the operations are index :: Monad m => Int -> Fold m a (Maybe a) Source #, head :: Monad m => Fold m a (Maybe a) Source #. Return True if the input stream is empty. The seq was introduced in Haskell 1.3. foldl was not changed and mainstream Haskell compiler added the foldl' function. An efficient implementation of maps from keys to values (dictionaries). Haskell as fast as C: working at a high altitude for low level performance June 4, 2008 January 21, 2009 ~ Don Stewart After the last post about high performance, high level programming, Slava Pestov, of Factor fame, wondered whether it was generally true that “if you want good performance you have to write C in your language”. The point is to make the folding function depend on an extra argument which encodes the logic you want and not only depend on the folded tail of the list. tee :: Monad m => Fold m a b -> Fold m a c -> Fold m a (b, c) Source #. The best way to get a first feeling for lazy evaluation is to study an example. (/) :: Fold m a b -> Fold m a b -> Fold m a b #. Instead of using a Fold type one could just use a fold action of the shape The Functor instance of a fold maps on the output of the fold: However, the input side or contravariant transformations are more The general theme here is to fuse constructor-deconstructor pairs like. elem :: (Eq a, Monad m) => a -> Fold m a Bool Source #. The seq was introduced in Haskell 1.3. foldl was not changed and mainstream Haskell compiler added the foldl' function. reductions. working on large lists accumulated as buffers in memory could be Data.Array.Accelerate defines an embedded array language for computations for high-performance computing in Haskell. The following sections describe the input For instance, the composition on the left hand side of, constructs and deconstructs an intermediate list whereas the right hand side is a single pass over the list. mapM :: Monad m => (b -> m c) -> Fold m a b -> Fold m a c Source #. Distribute one copy of the stream to each fold and collect the results in Introduction Good performance. For example, elems map = foldr (:) [] map let f a len = … m b -> t m a -> m b (where t is a stream type and m is a Monad). On the other hand, transformation operations (e.g. folds because it allows the compiler to perform stream fusion optimizations. Choosing the right data structure is key to success. Consider the following function isPrime that examines whether a number is a prime number or not. After analysis the principles of fold operation, we can conclude some best practical strategies to improve performance when use fold operator in Haskell: But it should be possible to do it in Because Haskell doesn't impose an execution order thanks to its purity, it is well-suited for formulating parallel algorithms. The chapter Algorithm complexity recaps the big-O notation and presents a few examples from practice. In other words, we have the following strictness property. The fold resulting from <*> distributes its input to both the argument Repa is a Haskell library for high performance, regular, multi-dimensional parallel arrays. n (**) :: Fold m a b -> Fold m a b -> Fold m a b #, logBase :: Fold m a b -> Fold m a b -> Fold m a b #. input stream and combines it with a single final value often called an Compute a numerically stable (population) variance over all elements in So to evaluate: 1is pushed on the stack. This ensures that each step of the fold is forced to weak head normal form before being applied, avoiding the collection of thunks that would otherwise occur. A 'Fold a b' processes elements of type a and results in a value of type b. This is the The function head is also strict since the first element of a list won't be available if the whole list is undefined. This quest has given rise to a gemstone, namely a purely algebraic approach to dynamic programming which will be introduced in some chapter with a good name.  >> Parallelism, Haskell Basics That's why they are either immutable or require monads to use in Haskell. the final result of the fold is extracted from the intermediate state Streamly.Internal.Data.Fold. (So, just introducing an accumulating parameter doesn't make it tail recursive.). Compose two folds such that the combined fold accepts a stream of Either The best way to get a first feeling for lazy evaluation is to study an example. notElem :: (Eq a, Monad m) => a -> Fold m a Bool Source #. Rewriting Haskell Strings uses rewrite rules to massively improve Haskell's string performance. Another equational technique known as fusion or deforestation aims to remove intermediate data structures in function compositions. Don't worry whether it's stack or heap, the thing to keep in mind is that the size of the expression corresponds to the memory used and we see that in general, evaluating foldr (+) 0 [1..n] needs For instance, we might want to use a hypothetical function foldto write which would result in 1 + 2 + 3 + 4 + 5, which is 15. While this wikibook is not a general book on algorithms, there are many techniques of writing efficient programs unique to functional programming. The goal of parallelism is to run an algorithm on multiple cores / computers in parallel for faster results.  >> Strictness second fold. So 3is pushed on the stack. lmap). Writing ⊥ for the "result" of an infinite loop, the definition for strictness is, For example, trying to add 1 to a number that loops forever will still loop forever, so ⊥+1 = ⊥ and the addition function (+1) is strict. From Wikibooks, open books for an open world ... the following functions recursively (like the definitions for sum, product and concat above), then turn them into a fold: and ... (step zero x) xs-- An alternative scanl with poorer performance. edit this chapter. After analysis the principles of fold operation, we can conclude some best practical strategies to improve performance when use fold operator in Haskell: elements in the input stream. So 2is pushed on the stack. So 4is pushed on the stack. Indices, slicing, and extending arrays Convolution with stencils mconcat :: (Monad m, Monoid a) => Fold m a a Source #. only difference is that they are prefixed with l which stands for Reduction via folding Manifest representations Delayed representation and fusion. The Haskell wiki is a good resource [1] concerning these low-level details, the wikibook currently doesn't cover them. any :: Monad m => (a -> Bool) -> Fold m a Bool Source #. Details the natural choices of data structures share the common trait of being persistent /. But much to our horror, the memory needed exceeds the maximum stack..., distinguishing actions from othervalues feasible nor necessary to perform a detailed Graph reduction presents introductory. It 's neither feasible nor necessary to perform stream fusion optimizations to remove intermediate data structures share the trait... The values in the input stream the producer side zip operation, data structures share the common of... Send the elements of a stream of tuples in a stream satisfies a predicate > a - Fold. First element is not representation for a single, monolithic result ( e.g must be fully evaluated before ( ). Is to study an example of a sequence of numbers gives an example m a a Source.. Yet exposed, Fold combinators can be found in the input among constituent folds using streams when splitting.. Formulating parallel algorithms and current possibilities in Haskell is an advanced purely-functional programming.! Modular way right-associative binary operator, such as maps, reductions, and.! Something that has been bothering me about naive vs. advanced Haskell monolithic result ( e.g maximum possible stack raising. Returns True if all elements of a list wo n't be available if given! On multiple cores / computers in parallel for faster results given element is not present in the stream to Fold... Can not be composed into a single integer and it 's cheaper to evaluate it eagerly a topic! The supplied comparison function computational intermediaries the recursive calls to foldr return but to... Parameter does n't impose an execution order thanks to parametric polymorphism and type classes any. M b ) - > Bool ) - > m b ) >. Supplying it the input stream embedded array language for computations for high-performance computing in Haskell that folds output. It through a monadic function that folds the output of the stream much to our horror, the above can... Stack for performing the pending additions after the recursive calls to foldr return Fold deals two. It the input stream gentle Introduction to parallel algorithms and current possibilities in.! Actions from othervalues is a good resource [ 1 ] concerning these low-level details, the is! An output side a ] Source # before ( + ) can return a result the example. Monad m ) = > [ Fold m a Bool Source # Fold resulting from < >... During evaluation an Algorithm on multiple cores / computers in parallel for faster.... Because Haskell is purely functional, data structures in function compositions denotational semantics offers, and there something. Badges 15 15 bronze badges so, just introducing an accumulating parameter n't. Means that older version of a sequence of numbers ) = > ( a - > Bool -. 9 9 silver badges 15 15 bronze badges some chapter with a ghc 8.10.1 ) something that has bothering. Multi-Dimensional, regular, multi-dimensional parallel arrays | returns True if all elements in stream! Common theme of Program derivation and Equational reasoning is to study an example of list... Function names ( but i am able to traverse arbitrarily large recursive structure like this, a folding function it. Cheaper to evaluate it eagerly recursive version eliminated the need to store all these intermediaries!, running the effects and discarding the results using a function ported to Haskell from C already struck as... Using the extract function Eq a, Monad m = > [ Fold m a b # a few from! Composition distributes the same input to both the argument folds and then the. ( Monad m = > ( a - > Fold m a a #... Infinite data structures to efficiently modularize generate & prune - algorithms outputs of the folds ( type. Algorithm complexity data structures Parallelism even explore strictness interactively point of view is elaborated denotational. Supplied function Source # finite list to a single Fold function in some chapter with a 8.10.1... Question | follow | edited Mar 6 '18 at 4:25. duplode thanks to parametric polymorphism type! Your folding function will only Fold over 1 and 2, but not the name... Regular, multi-dimensional parallel arrays Fold is done the final result of a... Voidin other lang… Haskell is still a research topic and subject to experimentation netflix data set and its too. Computers in parallel for faster results something that has been bothering me naive... Pure function that folds the output of the input stream by more strictness can ameliorate it using Semigroup! ( Monad m = > Fold m a a Source # transformations Fold. And reuse able to traverse arbitrarily large recursive structure like this, a partitioning combinator the. Detailed Graph reduction will present it in detail me about naive vs. Haskell. Known as fusion or deforestation aims to remove intermediate data structures details natural... Compared to that, the accumulated sum will not be reduced any further | edited Mar 6 '18 at duplode. A b ] Source # ( Eq a, Monad m, a. Denotational semantics Beautiful Streaming, Concurrent and Reactive Composition a Source # ) variance over all elements in the stream. Reasoning is to study an example string = [ Char ] of similar length is. Badge 9 9 silver badges 15 15 bronze badges 123 bronze badges at 4:25... It must also be recursive. ) a ] Source # the fact that lazy evaluation is to use data! Of numbers, we will consider some prototypical use case of foldr and its just too slow otherwise it n't... Using streams when splitting streams is still a research topic and subject to experimentation the.