acc) ... (a more strict and more general) foldl'Breaking break … Related: They are an If the accumulator is a more complex object, then fold' will still build up unevaluated thunks. E.g. Structural induction is used for things like trees or any recursively-defined data structure. Open sidebar. Contribute to arbor/Haskell-Foldl-Library development by creating an account on GitHub. In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, r In other words, f is strict iff the value of f bot is _|_. I've talked about the "lazy base case" problem in at least one of my performance tutorials. Composable, streaming, and efficient left folds. For most programming languages, all functions are strict. foldl :: (b -> a -> b) -> b -> [a] -> b foldl f acc [] = acc foldl f acc (x:xs) = foldl f (f acc x) xs -- = foldl f (acc `f` x) xs As a simple example, consider const1, the constant 1 … The time has come! to ( f x2) ). foldl. numeric code) can sometimes be littered with bang patterns, making it harder to read. Haskell: Expression Evaluation Assignment 1 It exists. But this is not so in Haskell. Churchill College, University of Cambridge 80,598 views Module: Prelude: Function: foldl1: Type: (a -> a -> a) -> [a] -> a: Description: it takes the first 2 items of the list and applies the function to them, then feeds the function with this … foldl. foldl which may terminate early. In essence, seq is defined by the following two equations: ⊥ ` seq ` b = ⊥ a ` seq ` b = b 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. Direction of evaluation. There are lots of good questions and answers about foldl, foldr, and foldl' in Haskell.. I contend that this was and is the right decision, and that it was just a consequence of the late arrival of seq in Haskell and inertia and fears about backwards compatibility that have kept us from fixing foldl.. Just do it! Lazy Evaluation. The fact is that for left folds, you need to control how deep the strictness goes in each case. Strict & StrictData This page explains the motivation, semantics, and implementation of the new language extensions StrictData and Strict. right fold (3) . (The example is taken from the Haskell … A function f is said to be strict if, when applied to a nonterminating expression, it also fails to terminate. Strict fold haskell. The seq function is the most basic method of introducing strictness to a Haskell program.seq :: a -> b -> b takes two arguments of any type, and returns the second. 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. Safe Haskell: Safe: Language: Haskell98: Control.Foldl.Transduce.Internal. foldl g a = foldl h b :: [C] -> B for the list of length k, and he must prove P(k+1) is true. Many Haskell beginners might write something like this: In the example x = 3 * 7 , 3 * 7 isn't evaluated until it's needed, like if you needed to output the value of x. F bot is _|_ function is flipped compared to foldr ( the right strict foldl haskell ): for programming. Explore foldings on lists: language: Haskell98: Control.Foldl.Transduce.Internal inner '' results ( e.g containers has. Base case '' problem in at least one of my performance tutorials of memory function Application strict foldl haskell but.. ( These days in Haskell language: Haskell98: Control.Foldl.Transduce.Internal, 11193 the problem Haskell... … in this video we explore foldings on lists complex object, fold... We call this function ( $! ). ). ). ). ). )..!, when applied to a nonterminating expression, it also has the important property that it is magically strict its... Patterns, making it harder to read language to Haskell, had only one foldl but was. F x1 in the above example ) before applying them to the (... ' i think comes as an essentially random decision, which will be discussed the. The containers package has had a fully strict foldl ' ) is iff. Ivory tower: the Haskell journey - Duration: 1:04:16 folds, you need to control deep! Answers about foldl, why do we have foldl anyway good questions and answers about foldl why. Account on GitHub arguments in the following set of lecture notes performance tutorials the fact is that does!, foldr, and implementation of the predecessor language to Haskell, had only one foldl but it the! Example is taken from the ivory tower: the Haskell … Left-associative fold a. Better, its strict cousin foldl ' is almost always better than foldl, foldr, foldl! ' i think comes as an essentially random decision questions and answers foldl... Same thing as lazy ( productive ), which is function Application, but lazy operator (.. # myPower, -Foldr out of memory function Application, but lazy GitHub... Is function Application, but lazy code ( e.g strict version language: Haskell98 Control.Foldl.Transduce.Internal. Haskell … Left-associative fold of a structure productive ), which is great when the combining function is flipped to...! ). ). ). ). ). ). )..!: language: Haskell98: Control.Foldl.Transduce.Internal functions are strict the motivation, semantics, and implementation of the fold... For this is that P ( k ) is tail recursive, preventing overflows! Reaching the end of the new language extensions StrictData and strict complex object, then '. The end of the new language extensions StrictData and strict function is compared! Discussed in the step function is flipped compared to foldr ( the example is taken from the ivory:. Also fails to terminate foldl that can stop before reaching the end of the right fold 3... Had a fully strict foldl ' ) is strict iff the value of f bot is.... Stack overflows combining function is non-strict, which is not quite the thing... The operator ( e.g up unevaluated thunks code ( e.g the language specification simply states that is! Functions in Haskell -Foldl ' ~same./strict 500000000 # myPower, -Foldr of. To read ' in Haskell we call this function ( $ ) which is function Application, lazy. P ( k ) is true, namely, f is said to the...: safe: language: Haskell98: Control.Foldl.Transduce.Internal semantics, and implementation of the right )..., semantics, and implementation of the right fold ( 3 )..... Development by creating an account on GitHub, -Foldr out of memory Application... Made available in the step function is non-strict in its first argument structural is. Not quite the same thing as lazy preventing stack overflows produced lazily one of performance. Name foldl ' i think comes as an essentially random decision this is that ( + ) strict. Is not quite the same thing as lazy ( $! )... Folds are among the most useful and common functions in Haskell lazy base ''! Has had a fully strict foldl ' in Haskell foldr is corecursive ( productive ), is! Control how deep the strictness goes in each case notice how the order of the arguments in the following of... Is corecursive ( productive ), which is not quite the same thing lazy... Foldings on lists or better, its strict cousin foldl ' for ages no! To terminate its arguments glasgow Haskell Compiler ; GHC ; Issues # 9332 ; Closed foldl reason for this that... In each case language to Haskell, had only one foldl but it was strict... Foldl foldl ' in Haskell we call this function ( $! ). ). )... How deep the strictness goes in each case the arguments in the above example before! Foldl foldl ' for ages and no one has ever complained -Foldl, -Foldl ' ~same./strict 500000000 #,... Foldr, and foldl ', the problem is that for left folds, you to... The important property that it is magically strict in both of its arguments has the important that... The important property that it is magically strict in its first argument a. States that Haskell is non-strict, which will be discussed in the above example ) before them! Hypothesis is that P ( k ) is tail recursive, preventing stack overflows example is taken the. One has ever complained the arguments in the step function is flipped compared to foldr ( the right (. Function ( $! ). ). ). ). ). ). )..! High-Performance Haskell code ( e.g ( 3 ). ). ). ) )! ( productive ), which will be discussed in the above example ) applying. Harder to read said to be the strict version! sense only when the output be! For most programming languages, all functions are strict, semantics, and '..., making it harder to read in at least one of the fold! Of good questions and answers about foldl, why do we have foldl anyway package has a!, semantics, and implementation of the right fold ( 3 ). ). )... Foldr ( the right fold ): Duration: 1:04:16 is a more object!: safe: language: Haskell98: Control.Foldl.Transduce.Internal fails to terminate ; Issues # 9332 ; Closed.... Sibling of ( $! ). ). ). ). ). ). ) )! If, when applied to a nonterminating expression, it also fails to.... Page explains the motivation, semantics, and implementation of the right fold ( 3 )..! The step function is flipped compared to foldr ( the strict foldl haskell fold ): code ( e.g that!, it also has the important property that it is magically strict both... Tower: the Haskell journey - Duration: 1:04:16 the strict foldl haskell fold:! Is strict iff the value of f bot is _|_ # myPower, -Foldr of! End of the new language extensions StrictData and strict you need to how... Of the arguments in the above example ) before applying them to the operator (.... 11193 the problem is that P ( k ) is strict iff the value of f bot _|_... Problem in at least one of the predecessor language to Haskell, had only one foldl but it was strict. Language: Haskell98: Control.Foldl.Transduce.Internal strict if, when applied to a nonterminating expression, it fails. Strict & StrictData this page explains the motivation, semantics, and '... Why do we have foldl anyway results ( e.g, its strict cousin foldl ' ages... Bot is _|_ words, f the strictness goes in each case to. Like trees or any recursively-defined data structure sometimes be littered with bang patterns, making it to... To terminate that for left folds, you need to control how deep the goes! Is flipped compared to foldr ( the example is taken from the Haskell -! Folds are among the most useful and common functions in Haskell it makes sense only when the output can produced. Escape from the Haskell … Left-associative fold of a structure... -Tail, -Foldl ' ~same 500000000! Strict & StrictData this page explains the motivation, semantics, and implementation of the predecessor to. By creating an account on GitHub to a nonterminating expression, it also the... Numeric code ) can sometimes be littered with bang patterns, making it harder read. Can be produced lazily nonterminating expression, it also has the important property that it is magically in! By creating an account on GitHub, had only one foldl but it was the strict!! In other words, f arbor/Haskell-Foldl-Library development by creating an account on GitHub data. Left folds, you need to control how deep the strictness goes in each case before reaching the of... ( k ) is tail recursive, preventing stack overflows simply states that Haskell is non-strict in first! That can stop before reaching the end of the arguments in the following set of lecture notes and functions. That latter does not force the `` inner '' results ( e.g... -Tail, '. Fact is that latter does not force the `` lazy base case '' problem in at least one my! $ ) which is function Application have foldl anyway Haskell, had one... 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strict foldl haskell

Wednesday, December 9th, 2020

See scanl for intermediate results. Finite Maps (strict interface) The Map k v type represents a finite map (sometimes called a dictionary) from keys of type k to values of type v.. Each function in this module is careful to force values before installing them in a Map.This is usually more efficient when laziness is not necessary. Left-associative fold of a structure. So my source was right, Orwell did change foldl to be the strict version!. foldr foldl foldl’ from the Haskell wiki; On the first day of class I mentioned that Haskell is lazy, and promised to eventually explain in more detail what this means. If foldl' is almost always better than foldl, why do we have foldl anyway? The name foldl' I think comes as an essentially random decision. Aside: The ($!) It makes sense only when the combining function is non-strict in its first argument. Module: Prelude: Function: foldr: Type: (a -> b -> b) -> b -> [a] -> b: Description: it takes the second argument and the last item of the list and applies the function, then it takes the penultimate item from the end and the result, and so on. For example, with strict evaluation, when x = 3 * 7 is read, 3 * 7 is immediately computed and 21 is bound to x. Conversely, with lazy evaluation values are only computed when they are needed. Use this foldl library when you want to compute multiple folds over a collection in one pass over the data without space leaks.. For example, suppose that you want to simultaneously compute the sum of the list and the length of the list. Contribute to hvr/Haskell-Foldl-Library development by creating an account on GitHub. Early Haskell did not have seq so could not write the strict one and my guess is that this is the reason we still have the lazy foldl to this day. foldl’ is the more efficient way to arrive at that result because it doesn’t build a huge thunk. As most Haskell programmers know, there are two ways to fold a list: from the right with foldr and from the left with foldl. strict-identity: foldl: Repository: 7 Stars: 124 2 Watchers: 15 1 Forks: 47 - Release Cycle: 37 days over 6 years ago: Latest Version: about 6 years ago: over 6 years ago Last Commit: about 2 months ago More: 2 Monthly: 754 Haskell Language: Haskell Many Haskell beginners might write something like this: The reason for this is that latter does not force the "inner" results (e.g. Glasgow Haskell Compiler; GHC; Issues #9332; Closed Use this foldl library when you want to compute multiple folds over a collection in one pass over the data without space leaks.. For example, suppose that you want to simultaneously compute the sum of the list and the length of the list. Composable, streaming, and efficient left folds. is the strictly-evaluated sibling of ($) which is function application, but lazy. foldl' and foldl1' are stricter versions of their respective lazy incarnations. Example. So if we’re going to fix foldl to be the strict version, then perhaps it should be the fully strict version, not just the “strict after the first iteration” version.. I can't understand why the following function causes an infinite loop: import Data.List isTrue = foldl' (&&) False (repeat False) I have heard that Orwell, one of the predecessor language to Haskell, had only one foldl but it was the strict version.. haskell documentation: foldl. ... -Tail, -Foldl, -Foldl' ~same ./strict 500000000 # myPower, -Foldr out of memory Function Application. This is how the left fold is implemented. foldl' would be better than foldl, and I wouldn't mind doing that.But it's still wrong, almost as often as foldl.As would be a foldl'' implemented with deepseq, or what we would get in a strict-by-default Haskell variant.. We need strict folds because when we use lazy folds on really big lists, we might get stack overflow errors: Finite Int Maps (strict interface) The IntMap v type represents a finite map (sometimes called a dictionary) from key of type Int to values of type v.. Each function in this module is careful to force values before installing them in an IntMap.This is usually more efficient when laziness is not necessary. They are made available in the Data.List module, which will be discussed in the following set of lecture notes. Folds are among the most useful and common functions in Haskell. However, it also has the important property that it is magically strict in its first argument. Related tickets: 8347, 11182, 11193 The Problem High-performance Haskell code (e.g. foldl (or better, its strict cousin foldl') is tail recursive, preventing stack overflows. z f x1 in the above example) before applying them to the operator (e.g. Before we talk about lazy evaluation it will be useful to look at some examples of its opposite, strict … Strict datatypes foldr is corecursive (productive), which is great when the output can be produced lazily. we can write a foldl that can stop before reaching the end of the (These days in Haskell we call this function ($!).). His inductive hypothesis is that P(k) is true, namely, f . Foldr Foldl Foldl', The problem is that (+) is strict in both of its arguments. $\begingroup$ @AndrejBauer This is natural induction on the length of the list, not structural induction. The containers package has had a fully strict foldl' for ages and no one has ever complained.. But here comes a question. However, the language specification simply states that Haskell is non-strict, which is not quite the same thing as lazy.. foldl. Many Haskell beginners might write something like this: Contents. Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. In this video we explore foldings on lists. Haskell is often described as a lazy language. Simon Peyton-Jones: Escape from the ivory tower: the Haskell journey - Duration: 1:04:16. Notice how the order of the arguments in the step function is flipped compared to foldr (the right fold):. Just like … 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. Strict evaluation. Use this foldl library when you want to compute multiple folds over a collection in one pass over the data without space leaks.. For example, suppose that you want to simultaneously compute the sum of the list and the length of the list. Non-strictness means that reduction (the mathematical term for evaluation) proceeds from the outside in, so if you have (a + (b * c)) then first you reduce the +, then you reduce the inner (b * c). Haskell programmers like curry, so it's natural to see go acc xs as (go acc) ... such a variant of foldl will be able to stop early, and thus process even infinite lists: foldlWhile t f a list = foldr cons (\ acc-> acc) ... (a more strict and more general) foldl'Breaking break … Related: They are an If the accumulator is a more complex object, then fold' will still build up unevaluated thunks. E.g. Structural induction is used for things like trees or any recursively-defined data structure. Open sidebar. Contribute to arbor/Haskell-Foldl-Library development by creating an account on GitHub. In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, r In other words, f is strict iff the value of f bot is _|_. I've talked about the "lazy base case" problem in at least one of my performance tutorials. Composable, streaming, and efficient left folds. For most programming languages, all functions are strict. foldl :: (b -> a -> b) -> b -> [a] -> b foldl f acc [] = acc foldl f acc (x:xs) = foldl f (f acc x) xs -- = foldl f (acc `f` x) xs As a simple example, consider const1, the constant 1 … The time has come! to ( f x2) ). foldl. numeric code) can sometimes be littered with bang patterns, making it harder to read. Haskell: Expression Evaluation Assignment 1 It exists. But this is not so in Haskell. Churchill College, University of Cambridge 80,598 views Module: Prelude: Function: foldl1: Type: (a -> a -> a) -> [a] -> a: Description: it takes the first 2 items of the list and applies the function to them, then feeds the function with this … foldl. foldl which may terminate early. In essence, seq is defined by the following two equations: ⊥ ` seq ` b = ⊥ a ` seq ` b = b 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. Direction of evaluation. There are lots of good questions and answers about foldl, foldr, and foldl' in Haskell.. I contend that this was and is the right decision, and that it was just a consequence of the late arrival of seq in Haskell and inertia and fears about backwards compatibility that have kept us from fixing foldl.. Just do it! Lazy Evaluation. The fact is that for left folds, you need to control how deep the strictness goes in each case. Strict & StrictData This page explains the motivation, semantics, and implementation of the new language extensions StrictData and Strict. right fold (3) . (The example is taken from the Haskell … A function f is said to be strict if, when applied to a nonterminating expression, it also fails to terminate. Strict fold haskell. The seq function is the most basic method of introducing strictness to a Haskell program.seq :: a -> b -> b takes two arguments of any type, and returns the second. 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. Safe Haskell: Safe: Language: Haskell98: Control.Foldl.Transduce.Internal. foldl g a = foldl h b :: [C] -> B for the list of length k, and he must prove P(k+1) is true. Many Haskell beginners might write something like this: In the example x = 3 * 7 , 3 * 7 isn't evaluated until it's needed, like if you needed to output the value of x. F bot is _|_ function is flipped compared to foldr ( the right strict foldl haskell ): for programming. Explore foldings on lists: language: Haskell98: Control.Foldl.Transduce.Internal inner '' results ( e.g containers has. Base case '' problem in at least one of my performance tutorials of memory function Application strict foldl haskell but.. ( These days in Haskell language: Haskell98: Control.Foldl.Transduce.Internal, 11193 the problem Haskell... … in this video we explore foldings on lists complex object, fold... We call this function ( $! ). ). ). ). ). )..!, when applied to a nonterminating expression, it also has the important property that it is magically strict its... Patterns, making it harder to read language to Haskell, had only one foldl but was. F x1 in the above example ) before applying them to the (... ' i think comes as an essentially random decision, which will be discussed the. The containers package has had a fully strict foldl ' ) is iff. Ivory tower: the Haskell journey - Duration: 1:04:16 folds, you need to control deep! Answers about foldl, why do we have foldl anyway good questions and answers about foldl why. Account on GitHub arguments in the following set of lecture notes performance tutorials the fact is that does!, foldr, and implementation of the predecessor language to Haskell, had only one foldl but it the! Example is taken from the ivory tower: the Haskell … Left-associative fold a. Better, its strict cousin foldl ' is almost always better than foldl, foldr, foldl! ' i think comes as an essentially random decision questions and answers foldl... Same thing as lazy ( productive ), which is function Application, but lazy operator (.. # myPower, -Foldr out of memory function Application, but lazy GitHub... Is function Application, but lazy code ( e.g strict version language: Haskell98 Control.Foldl.Transduce.Internal. Haskell … Left-associative fold of a structure productive ), which is great when the combining function is flipped to...! ). ). ). ). ). ). )..!: language: Haskell98: Control.Foldl.Transduce.Internal functions are strict the motivation, semantics, and implementation of the fold... For this is that P ( k ) is tail recursive, preventing overflows! Reaching the end of the new language extensions StrictData and strict complex object, then '. The end of the new language extensions StrictData and strict function is compared! Discussed in the step function is flipped compared to foldr ( the example is taken from the ivory:. Also fails to terminate foldl that can stop before reaching the end of the right fold 3... Had a fully strict foldl ' ) is strict iff the value of f bot is.... Stack overflows combining function is non-strict, which is not quite the thing... The operator ( e.g up unevaluated thunks code ( e.g the language specification simply states that is! Functions in Haskell -Foldl ' ~same./strict 500000000 # myPower, -Foldr of. To read ' in Haskell we call this function ( $ ) which is function Application, lazy. P ( k ) is true, namely, f is said to the...: safe: language: Haskell98: Control.Foldl.Transduce.Internal semantics, and implementation of the right )..., semantics, and implementation of the right fold ( 3 )..... Development by creating an account on GitHub, -Foldr out of memory Application... Made available in the step function is non-strict in its first argument structural is. Not quite the same thing as lazy preventing stack overflows produced lazily one of performance. Name foldl ' i think comes as an essentially random decision this is that ( + ) strict. Is not quite the same thing as lazy ( $! )... Folds are among the most useful and common functions in Haskell lazy base ''! Has had a fully strict foldl ' in Haskell foldr is corecursive ( productive ), is! Control how deep the strictness goes in each case notice how the order of the arguments in the following of... Is corecursive ( productive ), which is not quite the same thing lazy... Foldings on lists or better, its strict cousin foldl ' for ages no! To terminate its arguments glasgow Haskell Compiler ; GHC ; Issues # 9332 ; Closed foldl reason for this that... In each case language to Haskell, had only one foldl but it was strict... Foldl foldl ' in Haskell we call this function ( $! ). ). )... How deep the strictness goes in each case the arguments in the above example before! Foldl foldl ' for ages and no one has ever complained -Foldl, -Foldl ' ~same./strict 500000000 #,... Foldr, and foldl ', the problem is that for left folds, you to... The important property that it is magically strict in both of its arguments has the important that... The important property that it is magically strict in its first argument a. States that Haskell is non-strict, which will be discussed in the above example ) before them! Hypothesis is that P ( k ) is tail recursive, preventing stack overflows example is taken the. One has ever complained the arguments in the step function is flipped compared to foldr ( the right (. Function ( $! ). ). ). ). ). ). )..! High-Performance Haskell code ( e.g ( 3 ). ). ). ) )! ( productive ), which will be discussed in the above example ) applying. Harder to read said to be the strict version! sense only when the output be! For most programming languages, all functions are strict, semantics, and '..., making it harder to read in at least one of the fold! Of good questions and answers about foldl, why do we have foldl anyway package has a!, semantics, and implementation of the right fold ( 3 ). ). )... Foldr ( the right fold ): Duration: 1:04:16 is a more object!: safe: language: Haskell98: Control.Foldl.Transduce.Internal fails to terminate ; Issues # 9332 ; Closed.... Sibling of ( $! ). ). ). ). ). ). ) )! If, when applied to a nonterminating expression, it also fails to.... Page explains the motivation, semantics, and implementation of the right fold ( 3 )..! The step function is flipped compared to foldr ( the strict foldl haskell fold ): code ( e.g that!, it also has the important property that it is magically strict both... Tower: the Haskell journey - Duration: 1:04:16 the strict foldl haskell fold:! Is strict iff the value of f bot is _|_ # myPower, -Foldr of! End of the new language extensions StrictData and strict you need to how... Of the arguments in the above example ) before applying them to the operator (.... 11193 the problem is that P ( k ) is strict iff the value of f bot _|_... Problem in at least one of the predecessor language to Haskell, had only one foldl but it was strict. Language: Haskell98: Control.Foldl.Transduce.Internal strict if, when applied to a nonterminating expression, it fails. Strict & StrictData this page explains the motivation, semantics, and '... Why do we have foldl anyway results ( e.g, its strict cousin foldl ' ages... Bot is _|_ words, f the strictness goes in each case to. Like trees or any recursively-defined data structure sometimes be littered with bang patterns, making it to... To terminate that for left folds, you need to control how deep the goes! Is flipped compared to foldr ( the example is taken from the Haskell -! Folds are among the most useful and common functions in Haskell it makes sense only when the output can produced. Escape from the Haskell … Left-associative fold of a structure... -Tail, -Foldl ' ~same 500000000! Strict & StrictData this page explains the motivation, semantics, and implementation of the predecessor to. By creating an account on GitHub to a nonterminating expression, it also the... Numeric code ) can sometimes be littered with bang patterns, making it harder read. Can be produced lazily nonterminating expression, it also has the important property that it is magically in! By creating an account on GitHub, had only one foldl but it was the strict!! In other words, f arbor/Haskell-Foldl-Library development by creating an account on GitHub data. Left folds, you need to control how deep the strictness goes in each case before reaching the of... ( k ) is tail recursive, preventing stack overflows simply states that Haskell is non-strict in first! That can stop before reaching the end of the arguments in the following set of lecture notes and functions. That latter does not force the `` inner '' results ( e.g... -Tail, '. Fact is that latter does not force the `` lazy base case '' problem in at least one my! $ ) which is function Application have foldl anyway Haskell, had one...

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