A Haskell retrospective

Posted on Sat 18 August 2018 in Programming • Tagged with Haskell, functional programming, type systems, FacebookLeave a comment

Approximately a year ago, I had the opportunity to work on Sigma — a large, distributed system that protects Facebook users from spam and other kinds of abuse.

One reason it was a pretty unique experience is that Sigma is almost entirely a Haskell codebase. It was the first time I got to work with the language in a professional setting, so I was eager to see how it performs in a real-world, production-grade application.

In this (rather long) post, I’ll draw on this experience and highlight Haskell’s notable features from a practical, engineering standpoint. In other words, I’ll be interested in how much does it help with solving actual problems that arise in the field of software development & maintenance.

Haskell Who?

Before we start, however, it seems necessary to clarify what “Haskell” are we actually talking about.

Granted, this may be a little surprising. From a far-away vantage point, Haskell is typically discussed as a rather uniform language, and it is often treated as synonymous with functional programming in general.

But if you look closer, that turns out to be a bit of a misrepresentation. In reality, Haskell is a complex manifold of different components, some of which can be thought as their own sublanguages. Roughly speaking, Haskell — as it’s used in the industry and in the OSS world today — should be thought of as a cake with at least the following layers:

  • The base Haskell language, as defined by the Haskell ‘98 and 2010 reports. At least in theory, this is the portable version of the language that any conforming compiler is supposed to accept. In practice, given the absolute monopoly of GHC, it is merely a theoretical base that needs to be significantly augmented in order to reach some level of practical usability.

  • A bunch of GHC extensions that are widely considered mandatory for any real-world project. Some, like TupleSections or MultiParamTypeClasses, are mostly there to fix some surprising feature gaps that would be more confusing if you had worked around them instead. Others, like GADTs or DataKinds, open up completely new avenues for type-level abstractions.

  • A repertoire of common third-party libraries with unique DSLs, like conduit, pipes, or lens. Unlike many “regular” packages that merely bring in some domain-specific API, these fundamental libraries shape both the deeper architecture and the surface-level look & feel of any Haskell codebase that uses them.

  • A selection of less common extensions which are nevertheless encountered in Haskell code with some regularity.

  • Template Haskell, the language for compile-time metaprogramming whose main application is probably generics.
    To be clear, neither “template” nor “generics” have anything to do with the usual meanings of those terms in C++ and Java/C#/Go1. Rather, it refers to a kind of AST-based “preprocessing” that allows Haskell code to operate on the generic structure of user-defined types: their constructors, parameters, and record fields2.
    Direct use of TH in application code is extremely rare, but many projects rely on libraries which utilize it behind the scenes. A great example would be Persistent, a database interface library where the ORM uses Template Haskell to construct record types from a DB schema at compile time.

There is a language in my type system

What’s striking about this ensemble of features and ideas is that most of them don’t seem to follow from the ostensible premise of the language: that it is functional, pure / referentially transparent, and non-strict / lazily evaluated. Instead, they are mostly a collection of progressively more sophisticated refinements and applications of Haskell’s type system.

This singular focus on type theory — especially in the recent years3 — is probably why many people in the wider programming world think it is necessary to grok advanced type system concepts if you even want to dabble in functional programming

That is, of course, patently untrue4. Some features of a strong static type system are definitely useful to have in a functional language. You can look at Elm to see how awkward things become when you deprive an FP language of its typeclasses and composition sugar.

But when the focus on type systems becomes too heavy, the concepts keep piling up and the language becomes increasingly impenetrable. Eventually, you may end up with an ecosystem where the recommended way to implement an HTTP API is to call upon half a dozen compiler extensions in order to specify it as one humongous type.

But hey, isn’t it desirable to have this kind of increased type safety?

In principle, the answer would of course be yes. However, the price we pay here is in the precious currency of complexity, and it often turns out to be way too high. When libraries, frameworks, and languages get complicated and abstract, it’s not just safety and/or productivity that can (hopefully) increase — it is also the burden on developers’ thought processes. While the exact threshold of diminishing or even negative returns is hard to pinpoint, it can definitely be reached even by the smartest and most talented teams. Add in the usual obstacles of software engineering — shifting requirements, deadlines, turnover — and you may encounter it much sooner than you think.

For some, this is a sufficient justification to basically give up on type systems altogether. And while I’d say such a knee-jerk reaction is rather excessive and unwarranted, it is at least equally harmful to letting your typing regime grow in boundless complexity. Both approaches are just too extreme to stand the test of practicality.

The legacy of bleeding edge

In other words, Haskell is hard and this does count as one of its serious problems. This conclusion isn’t exactly novel or surprising, even if some people would still argue with it.

Suppose, however, that we have somehow caused this issue to disappear completely. Let’s say that through some kind of divine intervention, it was made so that the learning curve of Haskell is no longer a problem for the majority of programmers. Maybe we found a magic lamp and — for the lack of better ideas — we wished that everyone be as proficient in applicative parsers as they are in inheritance hierarchies.

Even in this hypothetical scenario, I posit that the value proposition of Haskell would still be a tough sell.

There is this old quote from Bjarne Stroustrup (creator of C++) where he says that programming languages divide into those everyone complains about, and those that no one uses.
The first group consists of old, established technologies that managed to accrue significant complexity debt through years and decades of evolution. All the while, they’ve been adapting to the constantly shifting perspectives on what are the best industry practices. Traces of those adaptations can still be found today, sticking out like a leftover appendix or residual tail bone — or like the built-in support for XML in Java.

Languages that “no one uses”, on the other hand, haven’t yet passed the industry threshold of sufficient maturity and stability. Their ecosystems are still cutting edge, and their future is uncertain, but they sometimes champion some really compelling paradigm shifts. As long as you can bear with things that are rough around the edges, you can take advantage of their novel ideas.

Unfortunately for Haskell, it manages to combine the worst parts of both of these worlds.

On one hand, it is a surprisingly old language, clocking more than two decades of fruitful research around many innovative concepts. Yet on the other hand, it bears the signs of a fresh new technology, with relatively few production-grade libraries, scarce coverage of some domains (e.g. GUI programming), and not too many stories of commercial successes.

There are many ways to do it

Nothing shows better the problems of Haskell’s evolution over the years than the various approaches to handling strings and errors that it now has.5

String theory

Historically, String has been defined as a list of Characters, which is normally denoted as the [Char] type. The good thing about this representation is that many string-based algorithms can simply be written using just the list functions.

The bad thing is that Haskell lists are the so-called cons lists. They consist of the single element (called head), followed by another list of the remaining elements (called tail). This makes them roughly equivalent to what the data structures theory calls a singly-linked list — a rarely used construct that has a number of undesirable characteristics:

  • linear time (O(n)) for finding a specific element in the list
  • linear time for finding an element with a specific index in the list
  • linear time for insertion in the middle of the list
  • poor cache coherency due to scattered allocations of list nodes6

On top of that, keeping only a single character inside each node results in a significant waste of memory.

Given those downsides, it isn’t very surprising that virtually no serious Haskell program uses Strings for any meaningful text processing. The community-accepted replacement is the text package, whose implementation stores strings inside packed arrays, i.e. just as you would expect. As a result, Haskell has at least two main types of “strings” — or even three, since Text has both lazy and strict variants.

That’s not all, however: there is also the bytestring package. Although technically it implements generic byte buffers, its API has been pretty rich and enticing. As a result, many other packages would rather use ByteStrings directly in their interfaces than to incur the conversions to and from Text.
And just like in case of Text, separate lazy and strict variants of ByteString are also available. But unlike Text, byte strings also have Word8 and Char8 versions, where the latter is designed to handle legacy cases of ASCII-exclusive text support.

Well, I hope you kept count of all these types! I also hope you can memorize the correct way of converting between them, because it’s commonplace to see them used simultaneously. This may sometimes happen even within the same library, but it definitely occurs in application code that utilizes many different dependencies. What it usually results in are numerous occurrences of something like Text.pack . foo . Text.unpack, with conversion functions copiously sprinkled in to help win in the Type Tetris.

Errors and how to handle them

A somewhat similar issue applies to error handling. Over the years, Haskell has tried many approaches to this problem, often mixing techniques that are very rarely found in a single language, like exceptions combined with result types.

Nowadays, there is some consensus about those mistakes of the past, but the best we got is their deprecation: the current version of GHC still supports them all.

What are all those techniques? Here’s an abridged list:

  • the error function, terminating the program with a message (which is obviously discouraged)
  • the fail method of the Monad typeclass (which is now deprecated and moved to MonadFail)
  • the MonadError class with the associated ErrorT transformer, now deprecated in favor of…
  • a different MonadError class, with ExceptT as the new transformer
  • exceptions in the IO monad, normally raised by the standard I/O calls to signal abnormal conditions and error; however, libraries and application code are free to also throw them and use for their own error handling
  • the Either sum type / monad, which is essentially a type-safe version of the venerable return codes

If you really stretched the definition of error handling, I could also imagine counting Maybe/MaybeT as yet another method. But even without it, that’s half a dozen distinct approaches which you are likely to encounter in the wild in one form or another.

Implicit is better than explicit

The other kind of troublesome legacy of Haskell relates to the various design choices in the language itself. They reflect ideas straight from the time they were conceived in, which doesn’t necessarily agree with the best engineering practices as we understand them now.

Leaky modules

Take the module system, for example.

Today, it is rather uncontroversial that the purpose of splitting code into multiple submodules is to isolate it as much as possible and prevent accidental dependencies. The benefit of such isolation is better internal cohesion for each module. This can simplify testing, improve readability, foster simplicity, and reduce cognitive burden on the maintainers.

Contemporary languages help achieving this goal by making inter-module dependencies explicit. If you want to use a symbol (functions, class) from module A inside another module B, you typically have to both:

  • declare it public in module A
  • explicitly import its name in module B

The first step helps to ensure that the API of module A is limited and tractable. The second step does the same to the external dependencies of module B.

Unfortunately, Haskell requires neither of those steps. In fact, it encourages precisely the opposite of well-defined, self-contained modules, all by the virtue of its default behaviors:

  • the default module declaration (module Foo where ...) implicitly declares every symbol defined in the module Foo as public and importable by others
  • the default import statement (import Foo) brings in every public symbol from the module Foo into the global namespace of the current module

In essence, this is like putting public on each and every class or method that you’d define in a Java project, while simultaneously using nothing but wildcard (star) imports. In a very short order, you will end up with project where everything depends on everything else, and nothing can be developed in isolation.

Namespaces are apparently a bad idea

Thankfully, it is possible to avoid this pitfall by explicitly declaring both your exported and imported symbols:

-- Foo.hs --
module Foo ( foo, bar ) where

foo = ...
bar = ...
baz = ...  -- not exported

-- Bar.hs --
import Foo (foo)
-- `bar` is inaccessible here, but `foo` is available

But while this helps fighting the tangle of dependencies, it still results in cluttering the namespace of any non-trivial module with a significant number of imported symbols.

In many other languages, you can instead import the module as a whole and only refer to its members using qualified names. This is possible in Haskell as well, though it requires yet another variant of the import statement:

import qualified Data.Text as Text

duplicateWords :: Text.Text -> Text.Text
duplicateWords = Text.unwords . map (Text.unwords . replicate 2) . Text.words

What if you want both, though? In the above code, for example, the qualified name Text.Text looks a little silly, especially when it’s such a common type. It would be nice to import it directly, so that we can use it simply as Text.

Unfortunately, this is only possible when using two import statements:

import Data.Text (Text)
import qualified Data.Text as Text

duplicateWords :: Text -> Text
duplicateWords = Text.unwords . map (Text.unwords . replicate 2) . Text.words

You will find this duplication pervasive throughout Haskell codebases. Given how it affects the most important third-party packages (like text and bytestring), there have been a few proposals to improve the situation7, but it seems that none can go through the syntax bikeshedding phase.

Contrast this with Rust, for example, where it’s common to see imports such as this:

use std::io::{self, Read};

fn read_first_half(path: &Path) -> io::Result<String> {
    // (omitted)

where self conveniently stands for the module as a whole.

Wild records

Another aspect of the difficulties with keeping your namespaces in check relates to Haskell record types — its rough equivalent of structs from C and others.

When you define a record type:

data User = User { usrFirstName :: String
                 , usrLastName :: String
                 , usrEmail :: String
                 } deriving (Show)

you are declaring not one but multiple different names, and dumping them all straight into the global namespace. These names include:

  • the record type (here, User)
  • its type constructor (also User, second one above)
  • all of its fields (usrFirstName, usrLastName, usrEmail)

Yep, thats right. Because Haskell has no special syntax for accessing record fields, each field declaration creates an unqualified getter function. Combined with the lack of function overloading, this creates many opportunities for name collisions.

This is why in the above example, Hungarian notation is used to prevent those clashes. Despite its age and almost complete disuse in basically every other language, it is still a widely accepted practice in Haskell8.

Purity beats practicality

We have previously discussed the multiple ways of working with strings and handling errors in Haskell. While somewhat confusing at times, there at least appears to be an agreement in the community as to which one should generally be preferred.

This is not the case for some subtler and more abstract topics.

Haskell is, famously, a purely functional programming language. Evaluating functions, in a mathematical sense, is all a Haskell program is supposed to be doing. But the obvious problem is that such a program wouldn’t be able to do anything actually useful; there needs to be some way for it to effect the environment it runs in, if only to print the results it computed.

How to reconcile the functional purity with real-world applications is probably the most important problem that the Haskell language designers have to contend with. After a couple of decades of research and industrial use it still doesn’t have a satisfactory answer.

Yes, there is the IO monad, but it is a very blunt instrument. It offers a distinction between pure code and “effectful” code, but allows for no granularity or structure for the latter. An IO-returning function can do literally anything, while a pure function can only compute some value based on its arguments. Most code, however, is best placed somewhere between those two extremes.

How to represent different varieties of effects (filesystem, logging, network, etc.)?
How to express them as function constraints that can be verified by the compiler?
How to compose them? How to extend them?

These (and others) are still very much open questions in the Haskell community. The traditional way of dealing with them are monad transformers, but they suffer from many shortcomings9. More recent solutions like effects or free monads are promising, but exhibit performance issues that likely won’t be solvable without full compiler support. And even so, you can convincingly argue against those new approaches, which suggests that we may ultimately need something else entirely.

Of course, this state of affairs doesn’t really prevent anyone from writing useful applications in Haskell. “Regular” monads are still a fine choice. Indeed, even if you end up stuffing most of your code inside plain IO, it will already be a step up compared to most other languages.

Good Enoughâ„¢

Incidentally, something similar could probably be said about the language as a whole.

Yes, it has numerous glaring flaws and some not-so-obvious shortcomings.
Yes, it requires disciplined coding style and attention to readability.
Yes, it will force you to courageously tackle problems that are completely unknown to programmers using other languages.
In the end, however, you will probably find it better than most alternatives.

Basically, Haskell is like pizza: even when it’s bad, it is still pretty good.

But what’s possibly the best thing about it is that you don’t even really need to adopt Haskell in order to benefit from its innovations (and avoid the legacy warts).

There is already a breed of mainstream languages that can aptly be characterized as “Haskell-lite”: heavily influenced by FP paradigms but without subscribing to them completely. The closest example in this category is of course Scala, while the newest one would be Rust.
In many aspects, they offer a great compromise that provides some important functional features while sparing you most of the teething issues that Haskell still has after almost 30 years. Functional purists may not be completely satisfied, but at least they’ll get to keep their typeclasses and monoids.

And what if you don’t want to hear about this FP nonsense at all?… Well, I’m afraid it will get harder and harder to avoid. These days, it’s evidently fine for a language to omit generics but it seems inconceivable to ditch first-class functions. Even the traditional OOP powerhouse like Java cannot do without support for anonymous (“lambda”) functions anymore. And let’s not forget all the numerous examples of monadic constructs that pervade many of the mature APIs, libraries, and languages.

So even if you, understandably, don’t really want to come to Haskell, it’s looking more and more likely that Haskell will soon come to you :)

  1. In case of Go, I’m of course referring to a feature that’s notoriously missing from the language. 

  2. For a close analogue in languages other than Haskell, you can look at the current state of procedural macros in Rust (commonly known as “custom derives”). 

  3. What seems to excite the Haskell community in 2018, for example, are things like linear types and dependent types

  4. The obvious counterexample is Clojure and its cousins in the Lisp family of languages. 

  5. Although the abundance of pretty-printing libraries is high up there, too :) 

  6. This can be mitigated somewhat by using a contiguous chunk of memory through a dedicated arena allocator, or implementing the list as an array. 

  7. See for example this project

  8. Some GHC extensions like DisambiguateRecordFields allow for correct type inference even in case of “overloaded” field names, though. 

  9. To name a few: they don’t compose well (e.g. can only have one instance of a particular monad in the stack); they can cause some extremely tricky bugs; they don’t really cooperate with the standard library which uses IO everywhere (often requiring tricks like this). 

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Currying and API design

Posted on Sun 12 November 2017 in Programming • Tagged with functional programming, currying, partial application, Haskell, API, abstractionLeave a comment

In functional programming, currying is one of the concepts that contribute greatly to its expressive power. Its importance could be compared to something as ubiquitous as chaining method calls (foo.bar().baz()) in imperative, object-oriented languages.

Although a simple idea on the surface, it has significant consequences for the way functional APIs are designed. This post is an overview of various techniques that help utilize currying effectively when writing your functions. While the examples are written in Haskell syntax, I believe it should be useful for developers working in other functional languages, too.

The basics

Let’s start with a short recap.

Intuitively, we say that an N-argument function is curried if you can invoke it with a single argument and get back an (N-1)-argument function. Repeat this N times, and it’ll be equivalent to supplying all N arguments at once.

Here’s an example: the Data.Text module in Haskell contains the following function called splitOn:

splitOn :: Text -> Text -> [Text]
splitOn sep text = ...

It’s a fairly standard string splitting function, taking a separator as its first argument, with the second one being a string to perform the splitting on:

splitOn "," "1,2,3"  -- produces ["1", "2", "3"]

Both arguments are of type Text (Haskell strings), while the return type is [Text] — a list of strings. This add up to the signature (type) of splitOn, written above as Text -> Text -> [Text].

Like all functions in Haskell, however, splitOn is curried. We don’t have to provide it with both arguments at once; instead, we can stop at one in order to obtain another function:

splitOnComma :: Text -> [Text]
splitOnComma = splitOn ","

This new function is a partially applied version of splitOn, with its first argument (the separator) already filled in. To complete the call, all you need to do now is provide the text to split:

splitOnComma "1,2,3"  -- also produces ["1", "2", "3"]

and, unsurprisingly, you’ll get the exact same result.

Compare now the type signatures of both splitOn and splitOnComma:

splitOn :: Text -> Text -> [Text]
splitOnComma :: Text -> [Text]

It may be puzzling at first why the same arrow symbol (->) is used for what seems like two distinct meanings: the “argument separator”, and the return type indicator.

But for curried functions, both of those meanings are in fact identical!

Indeed, we can make it more explicit by defining splitOn as:

splitOn :: Text -> (Text -> [Text])

or even:

splitOn :: Text -> TypeOf splitOnComma -- (not a real Haskell syntax)

From this perspective, what splitOn actually returns is not [Text] but a function from Text to [Text] (Text -> [Text]). And conversely, a call with two arguments:

splitOn "," "1,2,3"

is instead two function calls, each taking just one argument:

(splitOn ",") "1,2,3"

This is why the -> arrow isn’t actually ambiguous: it always signifies the mapping of an argument type to a result type. And it’s always just one argument, too, because:

Currying makes all functions take only one argument.

It’s just that sometimes, what those single-argument functions return will be yet another function.

Least used arguments go first

Now that we have a firmer grasp on the idea of currying, we can see how it influences API design.

There is one thing in particular you will notice almost immediately, especially if you are coming from imperative languages that support default argument values and/or function overloading. It’s the particular order of arguments that a well designed, functional API will almost certainly follow.

See the splitOn function again:

splitOn :: Text -> Text -> [Text]
splitOn sep text = ...

It is no accident that it puts the separator as its first argument. This choice — as opposed to the alternative where text goes first — produces much more useful results when the function is applied partially through currying.

Say, for instance, that you want to splice a list of strings where the individual pieces can be comma-separated:

spliceOnComma :: [Text] -> [Text]
spliceOnComma ["1", "2,3", "4,5,6", "7"]
-- ^ This should produce ["1", "2", "3", "4", "5", "6", "7"]

Because the separator appears first in a splitOn call, you can do it easily through a direct use of currying:

spliceOnComma xs = concat $ map (splitOn ",") xs

-- or equivalently, in a terser point-free style:
-- spliceOnComma = concatMap $ splitOn ","

What we do here is apply the split to every string in the list xs (with map), followed by flattening the result — a list of lists, [[Text]] — back to a regular [Text] with concat.

If we had the alternative version of splitOn, one where the order of arguments is reversed:

splitOn' text sep = ...

we’d have no choice but to “fix it”, with either a lambda function or the flip combinator:

spliceOnComma' xs = concat $ map (\x -> splitOn' x ",") xs
spliceOnComma' xs = concat $ map (flip splitOn' ",") xs

Putting the delimiter first is simply more convenient. It is much more likely you’ll be splitting multiple strings on the same separator, as opposed to a single string and multiple separators. The argument order of splitOn is making the common use case slightly easier by moving the more “stable” parameter to the front.

This practice generalizes to all curried functions, forming a simple rule:

The more likely it is for an argument to remain constant between calls, the sooner it should appear in the function signature.

Note how this is different compared to any language where functions may take variable number of arguments. In Python, for example, the equivalent of splitOn is defined as:

str.split(text, sep)

and the implicit default value for sep is essentially “any whitespace character”. In many cases, this is exactly what we want, making the following calls possible1:

>>> str.split("Alice has a cat")
["Alice", "has", "a", "cat"]

So, as a less-used argument, sep actually goes last in str.split, as it is often desirable to omit it altogether. Under the currying regime, however, we put it first, so that we can fix it to a chosen value and obtain a more specialized version of the function.

The fewer arguments, the better

Another thing you’d encounter in languages with flexible function definitions is the proliferation of optional arguments:

response = requests.get("http://example.com/foo",
                        params={'arg': 42},
                        data={'field': 'value'},
                        auth=('user', 'pass'),
                        headers={'User-Agent': "My Amazing App"},
                        cookies={'c_is': 'for_cookie'},
                        files={'attachment.txt': open('file.txt', 'rb')},

Trying to translate this directly to a functional paradigm would result in extremely unreadable function calls — doubly so when you don’t actually need all those arguments and have to provide some canned defaults:

response <- Requests.get
    "http://example.com/foo" [('arg', 42)]
    [] Nothing [] [] [] True Nothing

What does that True mean, for example? Or what exactly does each empty list signify? It’s impossible to know just by looking at the function call alone.

Long argument lists are thus detrimental to the quality of functional APIs. It’s much harder to correctly apply the previous rule (least used arguments first) when there are so many possible permutations.

What should we do then?… In some cases, including the above example of an HTTP library, we cannot simply cut out features in the name of elegance. The necessary information needs to go somewhere, meaning we need to find at least somewhat acceptable place for it.

Fortunately, we have a couple of options that should help us with solving this problem.

Combinators / builders

Looking back at the last example in Python, we can see why the function call remains readable even if it sprouts a dozen or so additional arguments.

The obvious reason is that each one has been uniquely identified by a name.

In order to emulate some form of what’s called keyword arguments, we can split the single function call into multiple stages. Each one would then supply one piece of data, with a matching function name serving as a readability cue:

response <- sendRequest $
            withHeaders [("User-Agent", "My Amazing App")] $
            withBasicAuth "user" "pass" $
            withData [("field", "value")] $
                get "http://example.com/foo"

If we follow this approach, the caller would only invoke those intermediate functions that fit his particular use case. The API above could still offer withCookies, withFiles, or any of the other combinators, but their usage shall be completely optional.

Pretty neat, right?

Thing is, the implementation would be a little involved here. We would clearly need to carry some data between the various withFoo calls, which requires some additional data types in addition to plain functions. At minimum, we need something to represent the Request, as it is created by the get function:

get :: Text -> Request

and then “piped” through withFoo transformers like this one:

withBasicAuth :: Text -> Text -> (Request -> Request)

so that it can we can finally send it:

sendRequest :: Request -> IO Response

Such Request type needs to keep track of all the additional parameters that may have been tacked onto it:

type Request = (Text, [Param])  -- Text is the URL

data Param = Header Text Text
           | BasicAuth Text Text
           | Data [(Text, Text)]
           -- and so on

-- example
withBasicAuth user pass (url, params) =
    (url, params ++ [BasicAuth user pass])

All of a sudden, what would be a single function explodes into a collection of data types and associated combinators.

In Haskell at least, we can forgo some of the boilerplate by automatically deriving an instance of Monoid (or perhaps a Semigroup). Rather than invoking a series of combinators, clients would then build their requests through repeated mappends2:

response <- sendRequest $ get "http://example.com/foo"
                          <> header "User-Agent" "My Awesome App"
                          <> basicAuth "user" "pass"
                          <> body [("field", "value")]

This mini-DSL looks very similar to keyword arguments in Python, as well as the equivalent Builder pattern from Java, Rust, and others. What’s disappointing, however, is that it doesn’t easily beat those solutions in terms of compile-time safety. Unless you invest into some tricky type-level hacks, there is nothing to prevent the users from building invalid requests at runtime:

let reqParams = get "http://example.com/foo"
-- ... lots of code in between ...
response <- sendRequest $
            reqParams <> get "http://example.com/bar" -- woops!

Compared to a plain function (with however many arguments), we have actually lost some measure of correctness here.

Record types

In many cases, fortunately, there is another way to keep our calls both flexible and safe against runtime errors. We just need to change the representation of the input type (here, Request) into a record.

Record is simply a user-defined type that’s a collection of named fields.

Most languages (especially imperative ones: C, C++, Go, Rust, …) call those structures, and use the struct keyword to signify a record definition. In functional programming parlance, they are also referred to as product types; this is because the joint record type is a Cartesian product of its individual field types3.

Going back to our example, it shouldn’t be difficult to define a record representing an HTTP Request:

data Request = Request { reqURL :: URL
                       , reqMethod :: Method
                       , reqHeaders [(Header, Text)]
                       , reqPostData [(Text, Text)]

In fact, I suspect most programmers would naturally reach for this notation first.

Having this definition, calls to sendRequest can be rewritten to take a record instance that we construct on the spot4:

response <- sendRequest $
    Request { reqURL = "http://example.com/bar"
            , reqMethod = GET
            , reqHeaders = [("User-Agent", "My Awesome App")]
            , reqPostData = []

Compare this snippet to the Python example from the beginning of this section. It comes remarkably close, right? The Request record and its fields can indeed work quite nicely as substitutes for keyword arguments.

But besides the readability boon of having “argument” names at the call site. we’ve also gained stronger correctness checks. For example, there is no way anymore to accidentally supply the URL field twice.

Different functions for different things

Astute readers may have noticed at least two things about the previous solutions.

First, they are not mutually incompatible. Quite the opposite, actually: they compose very neatly, allowing us to combine builder functions with the record update syntax in the final API:

response <- sendRequest $
    (get "http://example.com/baz")
    { reqHeaders = [("User-Agent", "My Awesome App")] }

This cuts out basically all the boilerplate of record-based calls, leaving only the parts that actually differ from the defaults5.

But on the second and more important note: we don’t seem to be talking about currying anymore. Does it mean it loses its usefulness once we go beyond certain threshold of complexity?…

Thankfully, the answer is no. While some APIs may require more advanced techniques to access the full breadth of their functionality, it is always possible to expose some carefully constructed facade that is conducive to partial application.

Consider, for example, the functionality exposed by this set of HTTP wrappers:

head :: URL -> Request
headWith :: [(Header, Text)] -> URL -> Request
get :: URL -> Request
getWith :: [(Header, Text)] -> URL -> Request
postForm :: [(Text, Text)] -> URL -> Request
postFormWith :: [(Header, Text)] -> [(Text, Text)] -> URL -> Request
toURL :: Method -> URL -> Request

Each one is obviously curry-friendly6. Combined, they also offer a pretty comprehensive API surface. And should they prove insufficient, you’d still have the builder pattern and/or record updates to fall back on — either for specialized one-off cases, or for writing your own wrappers.

Naturally, this technique of layered API design — with simple wrappers hiding a progressively more advanced core — isn’t limited to just functional programming. In some way, it is what good API design looks like in general. But in FP languages, it becomes especially important, because the expressive benefits of partial application are so paramount there

Fortunately, these principles seem to be followed pretty consistently, at least within the Haskell ecosystem. You can see it in the design of the http-client package, which is the real world extension of the HTTP interface outlined here. More evidently, it can be observed in any of the numerous packages the expose both a basic foo and a more customizable fooWith functions; popular examples include the async package, the zlib library, and the Text.Regex module.

  1. It’d be more common in Python to write this as "Alice has a cat".split(), but this form would make it less obvious how the arguments are passed. 

  2. A great example of this pattern can be found in the optparse-applicative package

  3. Tuples (like (Int, String)) are also product types. They can be thought of as ad-hoc records where field indices serve as rudimentary “names”. In fact, some languages even use the dotted notation to access fields of both records/structs (x.foo) and tuples (y.0). 

  4. For simplicity, I’m gonna assume the URL and Header types can be “magically” constructed from string literals through the GHC’s OverloadedStrings extension. 

  5. In many languages, we can specify more formally what the “default” means for a compound-type like Request, and sometimes even derive it automatically. Examples include the Default typeclass in Haskell, the Default trait in Rust, and the default/argumentless/trivial constructors in C++ et al

  6. Haskell programmers may especially notice how the last function is designed specifically for infix application: response <- sendRequest $ POST `toUrl` url

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The Printer Monad in Haskell

Posted on Fri 04 August 2017 in Code • Tagged with Haskell, Writer, monads, monad transformers, WriterTLeave a comment

Quite recently, I have encountered an interesting case of monad-based refactoring in Haskell.

Suppose you have a ComplicatedRecord that holds the results of some lengthy and important process in your program. You want to present that data to the user in a nicely formatted way, so you write a function which begins somewhat like this:

{-# LANGUAGE RecordWildcards #-}

-- | Pretty-print the content of the record.
ppRecord :: ComplicatedRecord -> IO ()
ppRecord ComplicatedRecord{..} = do
    -- ...

Inside, there is plenty of putStrLn calls, likely hidden inside more specific subfunctions that format all the numerous parts of ComplicatedRecord. But the IO monad isn’t there just for printing: because the code went through multiple iterations, some of this logic actually takes advantage of it by making additional system & network calls.

So yeah, it’s not particularly pretty.

Now, however, we find out that the output we’re printing here shouldn’t always go directly to stdout. In some cases, unsurprisingly, we actually want it back as a single string, without having it sent to the standard output at all.

Just $ return . it

Your first instinct here may be to simply give back the final string (well, Text) as the function result1:

ppRecord :: ComplicatedRecord -> IO Text

However, this turns out to be rather awkward. While in most other languages we would simply accumulate output by progressively adding more data to a mutable result, this would be much more inconvenient (and somewhat weird) to do in Haskell.

This is where the stdout-based approach seems cleaner; instead of straightforward, sequential code like this:

{-# LANGUAGE OverloadedStrings #-}

import Control.Monad.Extra (whenJust)
import Data.Text.IO
import TextShow

ppOrder Order{..} = do
    putStrLn $ "Order #" <> ordNumber
    ppAddress ordDeliveryAddress
    forM_ (zip [1..] ordItems) $ \(i, Item{..}) -> do
        putStrLn $ showt (i::Int) <> ". " <> itName <> " x" <> showt itQuantity
    whenJust ordBillingAddress ppAddress

ppAddress Address{..} = do
    putStrLn $ addrFirstName <> " " <> addrLastName
    putStrLn addrLine1
    whenJust addrLine2 putStrLn
    putStrLn $ addrCity <> ", " <> addrPostalCode

we have to overhaul each function and turn it into a much less pleasant “mappendage”:

ppOrder Order{..} = unlines $ mconcat
    [ "Order #" <> ordNumber
    , ppAddress ordDeliveryAddress
    , ppItems ordItems
    ] + maybe [] (\addr -> [ppAddress addr]) ordBillingAddress
    ppItems = mconcat . map (uncurry ppItem) . zip [1..]
    ppItem i Item{..} = showt i <> ". " <> itName <> " x" <> itQuantity

One may argue that this is, in fact, the more idiomatic approach, but I’m not very fond of all those commas. Plus, it shows rather clearly that any conditional logic (like with ordBillingAddress here) is going to get pretty cumbersome.

Along comes the Writer

What I’m saying here is that even in pure code, it is sometimes very desirable to have a do notation. For that, however, we need a suitable Monad2 to provide the meaning of “invisible semicolon” in a do block.

And Text, obviously, isn’t one. Neither is [Text] (lines of text), nor any other type we’d use to represent the final output of formatting & printing. They are unsuitable, because they cannot encode the computation that eventually produces said output — either the top-level one (ppRecord) or any of its building blocks (like the ppOrder or ppAddress), down to a most elementary putStrLn. The only thing they can stand for is the result itself.

Fortunately, the pattern of executing code and occassionally producing some “additional” output has been abstracted over in the Haskell standard library. This is exactly the use case for the Writer monad!

The definition of Writer is roughly equivalent to the following:

newtype Writer w a = ... -- omitted

Of the two type parameters it takes, the w one signifies what output it can produce “on the side”. This is contrasted with a which is the regular result of a monadic expression or function. In our case, a will basically always be () (unit/”empty” type), but it is nonetheless necessary for the Writer to behave as a monad.

To complement the above definition, Writer comes with several useful functions. Among those, the most interesting one is tell:

tell :: w -> Writer w ()

write would’ve probably been a better name for it, as it’s definitely the main and defining operation of Writer.

Looking at its signature, we can see it takes a bit of the Writers output (w) and results in a Writer action. Internally, it will simply add the argument to the already accumulated output of the writer3.

To make everything more concrete, here’s a literal “Hello world” example coded very verbosly as a Writer action:

import Control.Monad.Writer

hello :: Writer Text ()
hello = do
    tell "Hello"
    tell " "
    tell "world"

main :: IO ()
main = do
    let (_, greeting) = runWriter hello
    Text.putStrLn greeting

It also contains the last element of the Writer puzzle:

runWriter :: Writer w a -> (a, w)

Like its name suggests, this function will “run” any Writer action that we give it, returning both the “regular” result (a) plus any output passed in tells (w).4

My little monad: transformers are magic

The last example may be very simple, but it contains all the building blocks for many of the printing functions we need. If we define a convenience wrapper for tell:

putLn :: Text -> Writer Text ()
putLn line = tell $ line <> "\n"

then both ppAddress and ppOrder can be translated through a mere mechanical substitution of putStrLn with putLn:

ppAddress Address{..} = do
    putLn $ addrFirstName <> " " <> addrLastName
    putLn addrLine1
    whenJust addrLine2 putLn
    putLn $ addrCity <> ", " <> addrPostalCode

-- ppOrder omitted

Unfortunately, a bare Writer like this can only work for pure code, which isn’t a luxury we can expect in every situtation. In my case, some of the printing logic was tied pretty strongly to IO, and it would be difficult and time consuming to decouple it.

Thankfully, the reliance on IO isn’t a complete deal breaker. While we cannot ensure that nothing calls putStrLn anymore, we can provide the tell/putLn capabilities alongside whatever other IO calls our code has to make (for now).

To achieve that, we need to create a monad stack with WriterT:

newtype WriterT w m a = ... -- omitted

WriterT is a monad transformer, one of those scary Haskell concepts that are actually simpler than they appear on the surface. This is because transfomers like WriterT are mere wrappers. The only difference between it and a regular Writer is the additional m parameter, which is the inner monad we’re packaging inside a new Writer.

Here (and in many other cases), m will be substituted with IO:

type Printer a = WriterT Text IO a  -- w == Text, m == IO

thus creating the titular Printer monad. This hybrid beast can both output Text through the Writer API, as well as perform any additional IO operations that the code may (still) require.

Below is an example; the User record requires an I/O call to get the size of its $HOME directory:

import Control.Monad.IO.Class (liftIO)
import System.Directory (getFileSize)

-- To print this data type nicely, we sadly require I/O :(
data User = User { usrName :: Text
                 , usrHomeDir :: FilePath

ppUser :: User -> IO Text
ppUser User{..} = snd <$> runWriterT $ do
    putLn $ "Name: " <> usrName
    homeSize <- liftIO $ getFileSize usrHomeDir
    putLn $ "$HOME: " <> showt usrHomeDir <> "(" <> showt homeSize <> " bytes)"

As a bit of necessary cruft, we have to use liftIO to “lift” (wrap) IO actions such as getFileSize in a full Printer monad before executing them. Besides everything else you can think of, this is yet another argument for eventually getting rid of the IO :)

Making the monads coexist

But our job isn’t done yet. Despite looking very reasonable, this version of ppUser doesn’t actually compile! The actual type error may vary a little, but it all boils down to a difference between WriterT Text IO () (i.e. Printer ()) and Writer Text () at each call site of putLn.

GHC is obviously correct. However, the problem lies not in how we’re calling putLn, but rather the way it’s been defined:

putLn :: Text -> Writer Text ()

This type can only produce a specific, pure Writer action. But to fit inside the do block of our compound monad, we need the Writer + IO combo from WriterT Text IO (i.e. Printer).

We can try to address the mismatch by changing the signature to:

putLn :: Text -> WriterT Text IO ()  -- or just: Printer ()

but this will only result in the opposite problem. Now, all the pure printers like ppAddress are facing the fact that putLn is a (wrapped) IO action, despite not actually doing any I/O whatsoever.

The obvious question is, can we have something that fits both?

Earlier on, I’ve said that both vanilla Writer and the IO-spruced Printer support the “Writer API”, most notably the tell function. This notion of a “monadic interface” isn’t just hand-waving, though, and Haskell (obviously!) provides a way to express it programmatically.

Meet the MonadWriter typeclass:

class (Monad m, Monoid w) => MonadWriter w m

Any monad that can work as a Writer will be an instance of it, regardless of whether it wraps over IO or anything else. Functions like tell are defined to be polymorphic over it, enabling us to leverage the same technique they use when we define putLn:

{-# LANGUAGE FlexibleContexts #-}

import Control.Monad.Writer.Class

putLn :: MonadWriter Text m => Text -> m ()
putLn line = tell $ line <> "\n"

If you aren’t very familiar with this syntax, the part before => is a typeclass constraint, or context. It defines the requirements to be satisfied by types which are later used in the function signature.

Here, we request a MonadWriter instance — one where Text is the output but anything can be the inner monad. We refer to that unknown monad only as m, a type variable. The compiler will figure out what to substitute for it at every call site of putLn.

As a result, both a pure Writer and the IO-bound Printer can now use it. In the second case, the relevant instance of MonadWriter will, naturally, have IO fill in the m position.

But curiously, the “pure” Writer also has an inner monad. It just literally does nothing but wrap some other value:

newtype Identity a = Identity { runIdentity :: a }

In most cases, this fact is hidden behind the real definition of Writer, though runIdentity may sometimes come handy for some on-the-spot type hacks5.

The wrap

The many things we’ve talked about here could of course be a starting point for even more advanced stuff, but obviously we have to stop somewhere! But don’t worry: knowing about MonadWriter and other monad typeclasses like this is enough to write quite idiomatic code…

…at least until you learn about free monads, effects, and the like ;-)

In any case, you can check this gist for the complete code from this post.

  1. IO is still necessary due to ad-hoc network fetches and syscalls mentioned earlier. 

  2. Or at least an Applicative, via the ApplicativeDo GHC extension. 

  3. The adding is done via mappend, requiring w to be a Monoid

  4. There is also the execWriter variant which is actually more practical here as it only returns the accumulated output. 

  5. We could, for example, use it alongside mapWriterT to “fix” the calls to putLn if we didn’t have control over its definition. 

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Rust as a gateway drug to Haskell

Posted on Tue 13 June 2017 in Programming • Tagged with Rust, Haskell, traits, typeclasses, monads, ADTs, FPLeave a comment

For work-related reasons, I had to recently get up to speed on programming in Haskell.

Before that, I had very little actual experience with the language, clocking probably at less than a thousand lines of working code over a couple of years. Nothing impressive either: some wrapper script here, some experimental rewrite there…

These days, I heard, there are a few resources for learning Haskell1 that don’t require having a PhD in category theory2. They may be quite helpful when your exposure to the functional programming is limited. In my case, however, the one thing that really enabled me to become (somewhat) productive was not even related to Haskell at all.

It was Rust.

In theory, this shouldn’t really make much of a sense. If you compare both languages by putting checkmarks in a feature chart, you won’t find them to have much in common.

Some of the obvious differences include:

  • predominantly functional vs. mostly imperative
  • garbage collection vs. explicit memory management
  • lazy vs. eager evaluation
  • rich runtime3 vs. almost no runtime
  • global vs. localized type inference
  • indentation vs. braces
  • two decades (!) vs. barely two years since release

Setting aside syntax, most of those differences are pretty significant.

You probably wouldn’t use Haskell for embedded programming, for instance, both for performance (GC) and memory usage reasons (laziness). Similarly, Rust’s ownership system can be too much of a hassle for high level code that isn’t subject to real time requirements.

But if you look a little deeper, beyond just the surface descriptions of both languages, you can find plenty of concepts they share.

Traits: they are typeclasses, essentially

Take Haskell’s typeclasses, for example — the cornerstone of its rich and expressive type system.

A typeclass is, simply speaking, a list of capabilities: it defines what a type can do. There exist analogs of typeclasses in most programming languages, but they are normally called interfaces or protocols, and remain closely tied to the object-oriented paradigm.

Not so in Haskell.

Or in Rust for that matter, where the equivalent concept exists under the name of traits. What typeclasses and traits have in common is that they’re used for all kinds of polymorphism in their respective languages.


For example, let’s consider parametrized types, sometimes also referred to as templates (C++) or generics (C#).

In many cases, a generic function or type requires its type arguments to exhibit certain characteristics. In some languages (like the legacy C++), this is checked only implicitly: as long as the template type-checks after its expansion, everything is okay:

template <typename T> T min(T a, T b) {
    return a > b ? b : a;

struct Foo {};

int main() {
    min(1, 2);  // OK
    min(Foo(), Foo());  // ERROR, no operator `>`

More advanced type systems, however, allow to specify the generic constraints explicitly. This is the case in Rust:

fn min<T: Ord>(a: T, b: T) -> T {
    if a > b { b } else { a }

as well as in Haskell:

min :: (Ord a) => a -> a -> a
min a b = if a > b then b else a

In both languages, the notion of a type supporting certain operations (like comparison/ordering) is represented as its own, first-class concept: a trait (Rust) or a typeclass (Haskell). Since the compiler is aware of those constraints, it can verify that the min function is used correctly even before it tries to generate code for a specific substitution of T.

Dynamic dispatch

On the other hand, let’s look at runtime polymorphism: the one that OO languages implement through abstract base classes and virtual methods. It’s the tool of choice if you need a container of objects of different types, which nevertheless all expose the same interface.

To offer it, Rust has trait objects, and they work pretty much exactly like base class pointers/references from Java, C++, or C#.

// Trait definition
trait Draw {
    fn draw(&self);

// Data type implementing the trait
struct Circle { radius: i32 }
impl Draw for Circle {
    fn draw(&self) { /* omitted */ }

// Usage
fn draw_all(objects: &Vec<Box<Draw>>) {
    for &obj in objects {

The Haskell analogue is, in turn, based on typeclasses, though the specifics can be a little bit trickier:

{-# LANGUAGE ExistentialQuantification #-}

-- Typeclass definition
class Draw a where
    draw :: a -> IO ()

-- Polymorphic wrapper type
data Draw' = forall a. Draw a => Draw' a
instance Draw Draw' where
    draw (Draw' d) = draw d

-- Data types instantiating ("implementing") the typeclass
data Circle = Circle ()
instance Draw Circle where draw = undefined -- omitted
data Square = Square ()
instance Draw Square where draw = undefined -- omitted

-- Usage
drawAll :: (Draw a) => [a] -> IO ()
drawAll ds = mapM_ draw ds

main = do
    let shapes = [Draw' Circle (), Draw' Square ()]
    drawAll shapes

Here, the generic function can use typeclass constraints directly ((Draw a) => ...), but creating a container of different object types requires a polymorphic wrapper4.


All those similarities do not mean that Rust traits and Haskell typeclasses are one and the same. There are, in fact, quite a few differences, owing mostly to the fact that Haskell’s type system is more expressive:

  • Rust lacks higher kinded types, making certain abstractions impossible to encode as traits. It is possible, however, to implement a trait for infinitely many types at once if the implementation itself is generic (like here).

  • When defining a trait in Rust, you can ask implementors to provide some auxiliary, associated types in addition to just methods5. A similar mechanism in Haskell is expanded into type families, and requires enabling a GHC extension.

  • While typeclasses in Haskell can be implemented for multiple types simultaneously via a GHC extension, Rust’s take on this feature is to make traits themselves generic (e.g. trait Foo<T>). The end result is roughly similar; however, the “main implementing type” (one after for in impl ... for ...) is still a method receiver (self), just like in OO languages.

  • Rust enforces coherence rules on trait implementations. The topic is actually rather complicated, but the gist is about local (current package) vs. remote (other packages / standard library) traits and types.
    Without too much detail, coherence demands that there be a local type or trait somewhere in the impl ... for ... construct. Haskell doesn’t have this limitation, although it is recommended not to take advantage of this.

The M-word

Another area of overlap between Haskell and Rust exists in the data model utilized by those languages. Both are taking heavy advantage of algebraic data types (ADT), including the ability to define both product types (“regular” structs and records) as well as sum types (tagged unions).

Maybe you’d like Some(T)?

Even more interestingly, code in both languages makes extensive use of the two most basic ADTs:

  • Option (Rust) or Maybe (Haskell) — for denoting a presence or absence of a value
  • Result (Rust) or Either (Haskell) — for representing the alternative of “correct” and “erroneous” value

These aren’t just simple datatypes. They are deeply interwoven into the basic semantics of both languages, not to mention their standard libraries and community-provided packages.

The Option/Maybe type, for example, is the alternative to nullable references: something that’s been heavily criticized for making programs prone to unexpected NullReferenceExceptions. The idea behind both of those types is to make actual values impossible to confuse with nulls by encoding the potential nullability into the type system:

enum Option<T> { Some(T), None }
data Maybe a = Just a | Nothing

Result and Either, on the other hand, can be thought as an extension of this idea. They also represent two possibilities, but the “wrong” one isn’t just None or Nothing — it has some more information associated with it:

enum Result<T, E> { Ok(T), Err(E) }
data Either e a = Left e | Right a

This dichotomy between the Ok (or Right) value and the Error value (or the Left one) makes it a great vehicle for carrying results of functions that can fail.

In Rust, this replaces the traditional error handling mechanisms based on exceptions. In Haskell, the exceptions are present and sometimes necessary, but Either is nevertheless the preferred approach to dealing with errors.

What to do?

One thing that Haskell does better is composing those fallible functions into bigger chunks of logic.

Relatively recently, Rust has added the ? operator as a replacement for the try! macro. This is now the preferred way of error propagation, allowing for a more concise composition of functions that return Results:

/// Read an integer from given file.
fn int_from_file(path: &Path) -> io::Result<i32> {
    let mut file = fs::File::open(path)?;
    let mut s = String::new();
    file.read_to_string(&mut s)?;
    let result = s.parse().map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;

But Haskell had it for much longer, and it’s something of a hallmark of the language and functional programming in general — even though it looks thoroughly imperative:

intFromFile :: FilePath -> IO Int
intFromFile path = do
    s <- readFile path
    i <- readIO s
    return i

If you haven’t seen it before, this is of course a monad — the IO monad, to be precise. While discussing monads in detail is way outside of the scope of this article, we can definitely notice some analogies with Rust. The do notation with <- arrows is evidently similar to how in Rust you’d assign the result of a fallible operation after “unpacking” it with ?.

But of course, there’s plenty of different monads in Haskell: not just IO, but also Either, Maybe, Reader, Writer, Cont, STM, and many others. In Rust (at least as of 1.19), the ? operator only works for Result types, although there is some talk about extending it to Option as well6.

Eventually, we may see the language adopt some variant of the do notation, though the motivation for this will most likely come from asynchronous programming with Futures rather than plain Results. General monads, however, require support for higher kinded types which isn’t coming anytime soon.

A path through Rust?

Now that we’ve discussed those similarities, the obvious question arises.

Is learning Rust worthwhile if your ultimate goal is getting proficient at functional programming in general, or Haskell in particular?

My answer to that is actually pretty straightforward.

If “getting to FP” is your main goal, then Rust will not help you very much. Functional paradigm isn’t the main idea behind the language — its shtick is mostly memory safety, and zero-cost abstractions. While it succeeds somewhat at being “Haskell Lite”, it really strives to be safer C++7.

But if, on the other hand, you regard FP mostly as a curiosity that seems to be seeping into your favorite imperative language at an increasing rate, Rust can be a good way to gain familiarity with this peculiar beast.

At the very least, you will learn the functional way of modeling programs, with lots of smart enums/unions and structs but without inheritance.

And the best part is: you will be so busy fighting the borrow checker you won’t even notice when it happens ;-)

  1. Just ask in #haskell-beginners on Freenode if you’re interested. 

  2. Though ironically, I found the CT lectures by Bartosz Milewski very helpful in developing the right intuitions, even though they’re very abstract. 

  3. For example, Haskell has green threads (created with forkIO) which are somewhat similar to goroutines from Go. To get anything remotely similar in Rust, you need to use external libraries

  4. Note that such containers aren’t very idiomatic Haskell. A more typical solution would be to just curry the draw function, implicitly putting the Draw object inside its closure. 

  5. This mechanisms expands to associated constants in Rust 1.20. 

  6. Those two types also have a form of monadic bind (>>= in Haskell) exposed as the and_then method

  7. If you want another language for easing into the concept of functional programming, I’ve heard that Scala fills that niche quite well. 

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