Why Your Code Has Lots of Spelling Mistakes

Spelling mistakes are cognitive noise. Everyone makes them, but you’d be hard pressed to find any obvious ones in the average word document for a simple reason: Word’s got a spell checker. So, for that matter, has Firefox. In general terms, if you’re writing English text, a spell checker’s got you covered.

So, what’s the state of play for spell checkers on programming language text? Parlous. Forget contextual errors and weird homophones, just basic “Is this word in the dictionary?” stuff doesn’t work in most editors.

I probably wouldn’t have thought that deeply about the problem if it wasn’t for a rather excellent plug-in for Visual Studio with a profoundly boring but search friendly name. This does everything I need and improves my day job immensely.

So, I thought, how about I write something to do the same thing for Visual Studio Code? Well, I’ll save you reading the rest of the article and say that you are basically doomed. And if you use Vim or Emacs and are feeling superior right now, let me tell you right now that you’re basically doomed for the same reason.

Check Yourself

Let’s start with what a spell checker for a programming language should do:

  • It should be able to spell check comments.
  • It should be able to spell check identifiers.
  • It should be able to distinguish between identifiers defined in the file from identifiers that are not, or you’re going to spend your life with errors you can’t correct.

This is pretty minimal. I’d also like to be able to include directives that specify language etcetera.

The comment requirement’s not too bad. There’s only a couple of comment formats out there and you could easily write some code to support them all. Identifiers are a whole different ball game, though. To recognize when something’s an identifier, you need at least a lexer for the language. Even that’s surmountable: there’s CSON files for most languages out there. The final requirement is the one that’s going to break you. Recognizing when and where an identifier is defined requires a parser.

Just as well we’ve got language servers to help us out isn’t it? No, they’re not going to help a bit. Language servers don’t really have any high level protocols. They just say “offer the following actions here”. What our putative spell checker plug-in would need is a protocol that said “this is the definition of a PascalCase identifier”. This is kind of doubly moot since Visual Studio Code only allows one language server at once, so any hope for modularity is gone before we started.

So, what can be done? Well, you could write a spell check library (most of the hard work’s already done for you) and then try to submit PRs to every last language server there is. This sounds like a prohibitively large amount of unpaid work.

Check Please

Unless your editor has spell checking built in and a way for your language plug-ins to interact with it and explain their identifier conventions et al, the chances are you’ll never have a decent spellchecker in your code editor. Meanwhile your code will continue to have spelling errors and your colleagues will curse you for being an illiterate. Of course, you’ll be cursing them at the same time whilst staring at the screen displaying the tool whose fault it really is.


Haskell: More about TypeClasses and QuickCheck

Last time, I was looking into establishing equality on various conditions on Wai.Request, but established that this wasn’t what I was looking for. We did, however, establish how to perform casts and use polymorphic lists in a fashion that’s quite OO. Now I’m planning to drive right off road and try a bit of type-level reasoning.

Let’s start by simplifying the problem we had last time. Let’s stoop worrying about complex record types and just deal with primitive types. We’ll restrict our attention to equality and comparison conditions on those types. Let’s start by setting up some machinery.

data Equality = Eql | NEql deriving (Show, Ord, Eq, Typeable)
equalityAsFunc :: (Eq a) => Equality -> a -> a -> Bool
equalityAsFunc Eql = (==) equalityAsFunc NEql = (/=)
data Comparison = LTh | LThE | GThE | GTh deriving (Show, Eq, Ord, Typeable)
comparisonAsFunc :: (Ord a) => Comparison -> a -> a -> Bool
comparisonAsFunc LTh = (<)
comparisonAsFunc LThE = (<=)
comparisonAsFunc GTh = (>)
comparisonAsFunc GThE = (>=)
class Invertable a where
  invert :: a -> a
instance Invertable Comparison where
  invert LTh = GThE
  invert GTh = LThE
  invert GThE = LTh
  invert LThE = GTh
instance Invertable Equality where
  invert Eql = NEql
  invert NEql = Eql
-- I could make all functors of a invertable invertable, but I'm not sure that would actually be a good idea.
instance (Invertable a) => Invertable (Maybe a) where
  invert = fmap invert
-- Util
infixl 3 <|!> (<|!>) :: Maybe a -> a -> a
(<|!>) = flip fromMaybe

Now, we’re going to have a Condition typeclass, and at the very least we’re going to have instances for “always true/false”, “test for equality/inequality” and “compare against value”. And here’s the important bit: we’re going to want to analyze the relationship between them, even if they’re not the same type.

data ConditionRelationship = Same | Compatible | Incompatible | AImpliesB | BImpliesA deriving (Show, Ord, Eq, Typeable)
instance Invertable ConditionRelationship where
  invert AImpliesB = ImpliesA
  invert BImpliesA = AImpliesB
  invert x = x

Young Rankenstein

Now, how would we achieve this in an OO world? Well, we’d implement something like this:

class Condition0 c where
  analyze = (Condition0 d) => c -> d -> Maybe ConditionRelatioship

Where we’d return Nothing if c didn’t know how to analyze its relationship with d. Using the cast mechanism we’ve already seen, you can definitely implement this. And indeed, I did. (I tried an approach involving a more symmetric approach and some type magic, but ultimately couldn’t get it to fly.)

Let’s revise the definition a little so that we can actually it to test values. But we’re going to have to introduce a second type, v, the value under test.

{-# LANGUAGE RankNTypes #-}
class Condition1 v a where
  analyzeSame :: a -> a -> ConditionRelationship
  analyzeDifferent :: (Condition1 v b) => a -> b -> Maybe ConditionRelationship
  test :: a -> v -> Bool
analyze :: (Condition1 v a, Condition1 v b) => a -> b -> ConditionRelationship
analyze x y = a <|> b <|> c <|!> Compatible
                      -- If we have no idea, say it's compatible
  where a = analyzeSame x <$> (cast y)
        b = analyzeDifferent x y
        c = invert $ analyzeDifferent y x

Now, there’s actually a serious problem with this code: it doesn’t even compile! The problem is with the vs in analyze. It can’t determine that they’re the same. This I actually find weird, given that I’ve specified that a and b share a v, but it’s solvable.

First, I want to talk a bit about what the rank 2 typeclass actually is. It specifies a set of functions that can be called with an a and a v, but doesn’t restrict the a or the v in any way. So, all it’s really giving you is a relationship between the two types. And analyze never uses v, so it can’t deduce anything about it.

Now, there’s an extension called FunctionalDependencies and another called TypeFamilies that’d resolve this, but actually all we need to do is take the test method back out.

class (Eq a, Show a, Typeable a, Invertable a) => Condition2 a where
  analyzeSame2 :: a -> a -> ConditionRelationship
  analyzeDifferent2 :: (Condition2 b) => a -> b -> Maybe ConditionRelationship
class (Condition2 a) => Condition3 v a where
  test :: a -> v -> Bool
analyze2 :: (Condition2 a, Condition2 b) => a -> b -> ConditionRelationship
analyze2 x y = a <|> b <|> c <|!> Compatible -- We have no idea, say it's compatible
    where a = analyzeSame2 x <$> (cast y)
          b = analyzeDifferent2 x y
          c = invert $ analyzeDifferent2 y x

That works, doesn’t use any more extensions, (although Lord knows I’ve been playing extension pokemon recently) and also leaves us with the possibility of using different vs with the same a, even if in this particular case I can’t see why we’d wish to. For that matter, we could remove the interdependency between the two.

class Condition4 v a where
  test :: a -> v -> Bool

I found it really interesting the process I went through here: we actually ended up with a better design and separated our concerns as a consequence of the type system complaining about the functions we actually implemented.

Into The Lens

Let’s rename our concepts:

class (Eq a, Show a, Typeable a, Invertable a) => Analyzable a where
  analyzeSame :: a -> a -> ConditionRelationship
  analyzeDifferent :: (Analyzable b) => a -> b -> Maybe ConditionRelationship
class Testable v a where
  test :: a -> v -> Bool

First some definitions:

data Value c v = Value {
  _value :: v,
  _condition :: c
} deriving (Typeable, Eq, Show)
makeLenses ''Value
instance (Invertable c) => Invertable (Value c v) where
  invert = over condition invert

I’m using the lens package here, although to be honest I’m really only using it to start learning it. The actual practical benefits of it in the code I’ve written are very small, but I’m hoping to slowly pick up more aspects. In fact, of the code I’ve written so far this is the only bit that actually shows an improvement.

Breaking it down, we’re saying that if a condition is invertable, a Value using that condition is invertable by inverting the condition. Even though this is pretty elegant, but it’s going to take me a fair while to get my head around lens in general (There’s been loose talk of a lens NICTA-style course, that would be awesome.).

Scopes Monkey

So, we can declare an equality value to be a condition:

instance (Typeable a, Show a, Eq a) => Condition a (Value Equality a) where

I’m deliberately skipping the instance code because it’s pretty boring and predictable. The interesting case is when we’re implementing comparison:

analyzeEqualOther :: (Invertable b, Testable v b) => b -> Equal v -> ConditionRelationship

(I’ll skip the implementation.) Now for an instance:

instance (Typeable a, Show a, Ord a) => Analyzable (Value Comparison a) where
  analyzeSame = analyzeCompSame -- elided
  analyzeDifferent x y = analyzeEqualOther x <$> y2
    where y2 = cast y

Makes sense. Doesn’t compile. The reason’s a bit weird: it can’t figure out exactly what to cast y to. So let’s try this:

    where y2 = (cast y :: Maybe (Value Equality a))

Still doesn’t work. Here, the error message isn’t particularly helpful (unlike quite a few that just point you directly to the extension that you might need). The problem is actually that the a in the y2 expression isn’t the same as the a in the instance declaration. I don’t really understand why that decision was made (the explanation probably features the word “parametricity”), but you can reverse it by adding in another extension:

{-# LANGUAGE ScopedTypeVariables #-}

QuickCheck Yourself

There’s a plethora of things we could test, but let’s start with this one: What actually is the relationship between the Analyzeable version of condition and the Testable version of condition? Well, the answer is approximately that given two types that are both, we should be able to pick a set of vs such that we can deduce the behaviour of one from the other.

It would be lovely if we could achieve this through the type system, but I think that would be a serious reach, and even if it was possible it’s doubtful it would be readable. So instead let’s try using QuickCheck, the original property testing tool.

Aside: conversely, there should be no value of v where the behaviour of the two contradict one another. However, this latter condition is kind of hard to demonstrate using any example-based system. For that, you really do want Idris.

We need to set up some infrastructure to make cabal run tests.

Test-suite test
  Type:              exitcode-stdio-1.0
  Hs-source-dirs:    test
  Main-is:           Main.hs
  Build-depends:     base >=4.7 && <4.8,

This introduces a new target called test. I’ve not used quickcheck before so this is quite interesting. tasty appears to be the standard test running infrastructure. Note that since the test code is actually a separate executable, you need to put your own code as a dependency.

Stuck In The Middle With You

So, let’s pick five distinct values, a, b, c, d and e. We’ll put conditions at b and d and then test all five values in pairs. We can then read out from the set of pairs what the correct relationships between the two conditions is.

import Test.QuickCheck

data TestValues x = TestValues {
  a :: x,
  b :: x,
  c :: x,
  d :: x,
  e :: x
} deriving (Show, Eq, Ord)

instance (Arbitrary a, Ord a, Num a) => Arbitrary (TestValues a) where
  arbitrary = do
    a <- getPositive <$> arbitrary
    b <- (a +) <$> getPositive <$> arbitrary
    c <- (b +) <$> getPositive <$> arbitrary
    d <- (c +) <$> getPositive <$> arbitrary
    e <- (d +) <$> getPositive <$> arbitrary
    return (TestValues a b c d e)

This is all rather fun: arbitrary returns a value in the Gen monad. getPositive unwraps a Positive and return type polymorphism kicks in.

Normally, though, how to create an Arbitrary instance is obvious given its components, setting them up is going to get boring real fast, which is where the derive package kicks in

{-# LANGUAGE TemplateHaskell #-}
import Data.DeriveTH

derive makeArbitrary ''Equality
derive makeArbitrary ''Comparison
derive makeArbitrary ''Value

This now enables us to write the code we wanted:

propDeduce :: (Analyzable (Value c1 v), R.Testable v (Value c1 v), Analyzable (Value c2 v), R.Testable v (Value c2 v))
  => c1 -> c2 -> TestValues v -> Bool
propDeduce c1 c2 testValues = expected == drawConclusion x y testValues where
  x = Value c1 (b testValues)
  y = Value c2 (d testValues)
  expected = analyze x y

drawResults :: (R.Testable v (Value c1 v), R.Testable v (Value c2 v))
  => (Value c1 v) -> (Value c2 v) -> TestValues v -> [(Bool,Bool)]
drawResults x y testValues = result where
  result = f <$> ([a, b, c, d, e] <*> (pure testValues))
  f v = (test x v, test y v)

drawConclusion :: (R.Testable v (Value c1 v), R.Testable v (Value c2 v))
  => (Value c1 v) -> (Value c2 v) -> TestValues v -> ConditionRelationship
drawConclusion x y testValues = ac (length conclusions) conclusions where
  conclusions = nub $ drawResults x y testValues
  ac 4 _ = Compatible
  ac 3 _ = ac3 missingConclusion
  ac _ x | null $ x \ [(True,True),(False,False)] = Same
  ac _ _ = Incompatible
  missingConclusion = head $ [(True, True),(True, False),(False, True),(False,False)] \ conclusions
  ac3 (False, True) = BImpliesA
  ac3 (True, False) = AImpliesB
  ac3 (True, True) = Incompatible
  ac3 _ = Compatible

You can now write quickcheck properties like

prop_deduceCompEq :: Comparison -> Equality -> TestValues Int -> Bool
prop_deduceCompEq = propDeduce

(There may be a better way of instantiating propDeduce with different types, but this definitely works.)

In practice, what now happens is you spend a large amount of time actually fixing your code and your tests. What you’re seeing above is the output of that process. I learned a few things in the process.

  • Although QuickCheck is good at telling you there’s a problem, it’s got no facilities at all for telling you why.
  • Having relatively complex types makes it quite hard to reproduce a test in the repl. Conceivably the tooling for this could be improved.
  • You need to split your code up into chunks that are testable in the repl. This is a lesson Clojure taught me as well, but having access to an excellent debugger in other languages keeps unteaching it.

This is getting really long: I’ve skipped over the entire tasty code and the entire implementation.


So the Condition design looks more appropriate to the aim of actually allowing us to optimize our tests, and Haskell’s led us to a typeclass design better than the original item. There are, however, certain problems. For instance, the design I’ve outlined here is incapable of spotting that “> 2” is the same as “>= 3” in the Integer domain. Pretty much the only good solution to this is to require stronger conditions than just Eq and Ord for condition values, which allow you to perform these analyses. I’m not very inclined to do that, but this problem doesn’t ruin my intended use. However, it highlights again just how challenging it is to write something truly polymorphic and correct.

It’s pretty easy to see how you can extend this into projections as well. However, in practice it gets pretty tricky, because you need to do an order 2 cast. Thankfully, I got a good answer on StackOverflow of exactly how to achieve that. Separating out the concept of the condition from the projection also seems like a strong idea. Ultimately, though, I don’t really like the way this is going. Casts work, and Maybe makes them safe, but the design feels like I’m circumventing the type system rather than using it.

Principled Casts in Haskell

TL;DR I continue trying to implement a routing library, but instead end up learning about Typeable, writing about orphan instances, reading and (so far) failing to understand type-magic and sending my first Haskell PR.

I remember when I was starting Clojure, one of the big catchphrases was that everything was opt in. A type system, inheritance, multiple dispatch, &c. On the other hand, there were actually plenty of things that weren’t opt-in: Java itself, polymorphism, reflection and so on.

Haskell is another opt-in language. The basic type system and language is a requisite, but there’s still a phenomenal number of things to opt into. Equality is opt in, Hashable is opt in, as we saw in the previous article, polymorphism through existential types is opt-in. Next, we’re going to see “opt-in” type casts, and hopefully you’ll see how they’re better than what you can achieve in Java or C#.

{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE FlexibleInstances #-}
import qualified Network.Wai as Wai
import qualified Network.HTTP.Types as H

So, the question I asked last time was, how can I tell if two RequestConditionBoxs are equal? To do that, we’re going to want to make RequestConditions themselves implement equality.

(As an aside: the whole of the functionality of the last post might have been better implemented using good old functions or possibly the reader monad. However, I always wanted the conditions to be instances of Eq and Show. That’s not going to be possible with that approach.)

class (Show rc, Eq rc) => RequestCondition rc where
  isMatch :: Wai.Request -> rc -> Bool
data RequestConditionBox where
  RC :: (RequestCondition rc) => rc -> RequestConditionBox
  deriving (Show)

Oops, that isn’t going to work: you can’t derive Show on a GADT. So delete it. We’ll need to implement Eq and Show for RequestConditionBox. (I’m going to skip Show.)

instance Eq RequestConditionBox where
  (==) (RC a) (RC b) = a == b

Small problem: a and b are different types. And Eq only allows you to test that two members of the same type are equal. We need some way of checking that the two types are equal. Now, you can test for type equality in a type precondition but I can’t see how I could make that work. We need something more like

testEqual :: (Eq a, Eq b) => a -> b -> Bool

Only right now we have no idea how to implement it.

He’s My Typeable

George Pollard pointed me to an experimental class called Typeable. As I alluded to earlier, it’s opt-in, although I think the opt-in nature is more to do with the fact that it’s not standardized yet than that there are types that can’t logically have a typeclass instance.

Typeable looks like a pretty unpromising typeclass:

typeRep# :: Proxy# a -> TypeRep

Actually, it’s more than just unpromising, it looks positively hostile. What are those hashes? Well, it turns out that hash is a valid character in an identifier if you enable the MagicHash extension. As a convention, GHC uses it to represent unboxed types. Unboxed means exactly the same thing as it does in C# and Java: something that doesn’t have a garbage collected pointer around it. This is a very deep rabbit-hole that I’m just going to carefully step around right now.

Actually, I’m going to skip pretty much everything except to notice that Data.Typeable exports a rather useful function called cast.

cast :: (Typeable a, Typeable b) => a -> Maybe b

Yep, that’s exactly what as does in C#. I’ll skip over the implementation, because it’s slightly scary and I’d need to get into unsafeCoerce. One thing I can’t tell is if this code is actually run at runtime or whether it’s possible for the compiler to optimize it out. After all, the types of a and b are known at compile time.

With that, we can actually test if two values of different types are equal:

testEqual :: (Typeable a, Eq a, Typeable b, Eq b) => a -> b -> Bool
testEqual x y = fromMaybe False $ (== x) <$> cast y

Reading from right to left:

  • cast y
  • map (<$>) the maybe with (== x)
  • this gives us Nothing if x and y are different types, and Just (x==y) if they’re the same.
  • finally, we use fromMaybe to strip off the Just and replace Nothing with False

Orphan Black

To use testEqual, we need to make our RequestConditions typeable

class (Typeable rc, Show rc, Eq rc) => RequestCondition rc where
  isMatch :: W.Request -> rc -> Bool

How do we implement it? Well, we don’t. Typeable is special. Not only is it derivable, the compiler requires you use the deriving version. And that needs an extension:

-- Put this up at the top
{-# LANGUAGE DeriveDataTypeable #-}
newtype And rc = And [rc] deriving Typeable

Unfortunately, H.HttpVersion doesn’t implement Typeable. Luckily we can implement it ourselves. But, you guessed it, we need another extension:

-- Put this up at the top
{-# LANGUAGE StandaloneDeriving #-}
deriving instance Typeable H.HttpVersion

We’re probably alright here, but what we’ve done is, in general, ridiculously dangerous. We’ve implemented an instance in a library that is neither the library that declares the typeclass, nor the library that declares the type. This is known as an orphan instance and will have seasoned Haskellers gathering with torches and pitchforks around your codebase. The reason for this is that, while typeclasses provide the power of ruby’s mixins, orphan instances provide the problems. (They call it “incoherence”, and they mean it.)

While we’re on the subject, you’ll probably have already noticed that when you add projects into your cabal file, you pull in the world, Maven style. This is pretty horrific, but the reason for this is orphan instances. For instance, the functionality of the semigroups package looks pretty small: it just exposes a couple of typeclasses. But when you take a look at what is an instance just of Semigroup you’ll see a whole list of types that the semigroups package needs just to compile. Semigroups itself has defines to try to ameliorate this situation but the truth is that it’s just too much work (at least given cabal in its current design) to enforce small dependency lists and coherence.

Long story short, it’d probably be best to just expose Typeable from the library, so I’ve sent a pull request. (As everyone knows, open source software collaboration is a variable experience. But even at my beginner level, it is possible to make small contributions.)

The Equalizer

Remember last time I mentioned that we could destructure existential types? Now we can actually use this.

equalRC1 :: RequestConditionBox -> RequestConditionBox -> Bool
equalRC1 (RC a) (RC b) = testEqual a b

That looks pretty promising. But we haven’t handled the case where a or b are themselves a RequestConditionBox

equalRC2 :: RequestConditionBox -> RequestConditionBox -> Bool
equalRC2 a1@(RC a) b1@(RC b) = eq3 (cast a) (cast b)
  where eq3 (Just x) _ = equalRC2 x b1
        eq3 _ (Just y) = equalRC2 a1 y
        eq3 _ _ = testEqual a b

Well, that’s kind of fun, but an alternative formulation is arguably better:

infixl 3 <|!> -- Left associative, use same precedence as <|>
(<|!>) :: Maybe a -> a -> a
(<|!>) = flip fromMaybe
equalRC4 :: (Typeable a, Eq a) => a -> RequestConditionBox -> Bool
equalRC4 x (RC y) = a <|> b <|!> c
  where a = equalRC3 x <$> (cast y)
        b = equalRC3 y <$> (cast x)
        c = testEqual x y

<|> is a fairly general function, but in general it means “take the first valid parameter”. Its type is

(<|>) :: Alternative f => f a -> f a -> f a

Here, just remember that Maybe is an Alternative. I’ve also introduced my own infix operator <|!> to get me out of Maybe land. (Hey, I don’t even need an extension for this!)

We now have a vastly better implementation of Eq:

instance Eq RequestConditionBox where
  (==) == equalRC4

(Aside: there’s a very interesting looking function in Data.Typeable called gcast that I thought could be useful here, but I couldn’t figure it out, so everything here stays at the cast level.)

Designed By An Idiot In London

Let’s load what we’re got into a REPL.

> :m + Main
> :m + Data.List
> :m + Network.HTTP.Types
> let td = [RC methodGet, RC methodGet, RC (RC methodGet), RC http10, RC http11]
> nub td

gives us

[RC "GET",RC HTTP/1.0,RC HTTP/1.1]

Well, that’s demonstrated that Eq works. But it also demonstrates something else: Eq isn’t actually what we wanted in the first place. Really we want to be unifying to [RC "GET",RC HTTP/1.1]. To do that, we’re going to have to rip up everything we’ve done so far and start again.

FOOTNOTE: Elise Huard pointed me to the AdvancedOverlap page on the wiki, which details techniques for branching your code by typeclass rather than type. In practice, I decided to just make everything an instance of Eq, which isn’t so much of a problem given the problem domain I’m working within.

A Route To Learning The Haskell Type System

TL;DR I start trying to write a library and get sidetracked into learning about Haskell’s type system.

So last time, I talked about Wai and how you could use it directly. However, if you’re going to do that, you’ll need a routing library. So, let’s talk about how we could build one up. One of the first things you’d need to do is to provide simple boolean conditions on the request object.

It turns out that this raises enough questions for someone at my level to fill more than one blog post.

{-# LANGUAGE TypeSynonymInstances #-}
{-# LANGUAGE FlexibleInstances #-}
import qualified Network.Wai as Wai
import qualified Network.HTTP.Types as H

So, how should we define conditions? Well, the Clojure model of keyword and string isn’t going to work here, because the Wai.Request object is heavily strongly typed. So how about instead we just use the expected values and deduce the key from the type?

So, we’re going to want to implement the same method for several different types. There’s several different ways of doing that: * Create a union/enum class. This is a good approach, but not extensible. * Create a typeclass, which is extensible. * Create a type family, which is also extensible, but I don’t really understand.

You Can’t Buy Class

With that in mind, let’s create our first typeclass!

class RequestCondition rc where
  isMatch :: Wai.Request -> rc -> Bool

So, in English this says “If the type rc is a RequestCondition then there is a method isMatch which takes a Wai.Request and an rc and returns a Bool.” This is pretty interesting from an OO standpoint. The OO representation would look like rc.isMatch(request). A Clojure protocol would change this to (isMatch rc request). In practice, it doesn’t matter: what’s happening is that there’s dynamic dispatch going on on the first parameter.

In the Haskell case, there’s no dynamic dispatch in sight and the first parameter isn’t special. isMatch on HTTPVersion and isMatch on Method are different functions.

We can now implement the RequestCondition for some obvious data types.

instance RequestCondition H.HttpVersion where
  isMatch = (>=) . W.httpVersion

So, here we’ve said “calling isMatch with a HttpVersion as a parameter calls (>=) . W.httpVersion i.e. checks the request is using the version specified. We’d probably need a more sophisticated way of dealing with this if we were writing a real system.

instance RequestCondition H.Method where
  isMatch = (==) . W.requestMethod

This is much the same, with one wrinkle: H.Method isn’t actually a type. It’s a type synonym. In C++ you’d introduce one with typedef, in C# with using. Haskell, because it likes to confuse you, introduces something that is not a type with the keyword type. If you look up method on Hackage you see:

type Method = ByteString

You might wonder why this matters. The answer is that the Haskell standard doesn’t allow you to declare instances of synonyms. You can understand why when you realize that you might have multiple synonyms for ByteString and shoot yourself in the foot. However, for now I’m going to assume we know what we’re doing and just switch on TypeSynonyms in the header.

Let’s do one more, because three’s a charm.

instance RequestCondition H.Header where
  isMatch = flip elem . W.requestHeaders

We’d need (a lot) more functionality regarding headers, but let’s not worry about that now. However, again this will fail to compile. This time H.Header is a type synonym, but a type synonym for a very specific tuple.

type Header = (CIByteString, ByteString)

Problem is, Haskell doesn’t like you declaring instances of specific tuples either. This time, you need FlexibleInstances to make the compiler error go away. To the best of my knowledge, FlexibleInstances is much less of a hefalump trap than TypeSynonyms could be.

For fun, let’s throw in a newtype

newtype IsSecure = IsSecure Bool
isSecure :: IsSecure
isSecure = IsSecure True
instance RequestCondition IsSecure where
  isMatch r (IsSecure isSecure) = W.isSecure r == isSecure

Under Construction

How about when we’ve got multiple conditions to apply? Well, if we were writing Java, we’d be calling for a composite pattern right now. Let’s declare some types for these.

newtype And rc = MkAnd [rc]
newtype Or rc = MkOr [rc]

I described newtypes back in Fox Goose Corn Haskell. Note that there’s no reference to RequestCondition in the declaration. By default, type variables in declarations are completely unbound.

Before we go any futher, let’s fire up a REPL (if you’re in a Haskell project right now you can type cabal repl) and take a look at what that does:

data And rc = MkAnd [rc]
:t MkAnd
MkAnd :: [rc] -> And rc

Yes, MkAnd is just a function. (Not exactly, it can also be used in destructuring, but there isn’t a type for that.) Let’s try expressing it a different way while we’re here:

:set -XGADTs
data And2 rc where MkAnd2 :: [rc] -> And2 rc

(You’ll need to hit return twice) Now we’re saying “And2 has one constructor, MkAnd2, which takes a list of m. The GADTs extension does way more than this, some of which I’ll cover later on, but even then I’m only really scratching the surface of what this does. For now I’ll just observe how the GADTs extension provides a syntax that is actually more regular than the standard syntax.

Incidentally, I could have called MkAnd just And, but I’ve avoided doing so for clarity.

Composing Ourselves

With the data types, we can easily write quick functions that implement the RequestCondition typeclass.

instance (RequestCondition rc) => RequestCondition (And rc) where
  isMatch r (MkAnd l) = all (isMatch r) l
instance (RequestCondition rc) => RequestCondition (Or rc) where
  isMatch r (MkOr l) = any (isMatch r) l

The most interesting thing here is that we haven’t said that And is an instance of RequestCondition, we’re say that it is if its type parameter is an instance of RequestCondition. Since data types normally don’t have type restrictions themselves, this is the standard mode of operation in Haskell.

So, now I can write

Or [H.methodGet, H.methodPost]

and it’ll behave. So we’re finished. Right? Not even close.

What if we wanted to write

And [H.methodGet, H.http10]

It’s going to throw a type error at you because HTTP methods aren’t HTTP versions. If you take a look at the declaration, it says “list of rcs that are instances of RequestCondition” not “list of arbitrary types that are instances of RequestCondition“. If you’re used to OO, (and I have some bad news for you if you’re a Clojure programmer, that means you) this makes no sense at all. If you’re a C++ programmer, this is going to make a lot more sense. You see, when you do that in Java you’re telling Java to call through a vtable to the correct method. Haskell doesn’t have pervasive vtables in the same way. If you want one, you’re going to have to ask nicely.

Pretty Please and Other Existential Questions

What we want, then, is a function that boxes up a RequestCondition and returns a type that isn’t parameterized by the original type of the RequestCondition. What would that function look like?

boxItUp :: (RequestCondition rc) => rc -> RequestConditionBox

Hang on, that looks like the type of a constructor! Except for one really annoying little detail: as I said before, you can’t put type restrictions in data declarations.

Except you can, if you enable GADTs.

data RequestConditionBox where
  RC :: (RequestCondition rc) => rc -> RequestConditionBox

RequestConditionBox is what’s known as an “existential type”. As I understand it that should be interpreted as “RequestConditionBox declares that it boxes a RequestCondition, but declares nothing else”. So its quite like declaring a variable to be an interface.

Since I wrote this, I’ve learned that existential types are indeed very like interfaces in C#/Java: they are bags of vtables for the relevant type classes. They don’t expose their parameterization externally, but destructuring them still gets the original type out. This is bonkers.

It just remains to actually implement the typeclass:

instance RequestCondition RequestConditionBox where
  isMatch r (RC m) = isMatch r m

And now we can finally write

And [RC H.methodPost, RC isSecure]

And the compiler will finally accept it. Not quite as pretty as in an OO language where polymorphism is baked into everything, but keeping the character count low isn’t everything. We’ve traded implicit polymorphism for explicit polymorphism.

So we’re done, right? Well, we could be, but I want to go further.

The Power of Equality

If you take a look, what we’ve built looks very much like a toy interpreter (because it is one). What if we wanted a toy compiler instead? In particular, imagine that we really were building a routing library and we had thousands of routes. We might want to only check any given condition once by grouping, for example, all of the GET routes togther.

Now, you could leave that to the user of the library, but let’s pose the question: given two RequestConditions, both of which may be composite, how do you determine what conditions are common between the two?

One route is to backtrack, and look at HLists. I think that’s probably an extremely strong approach, but I really haven’t got my head around the type equality proofs-as-types stuff. Another approach is add some stuff to RequestCondition to track the types in some way. It turns out there’s a way to get the compiler to do most of the work here, so I’ll talk about that next time.

FOOTNOTE: On the Reddit discussion it was pointed out that RequestConditionBox is an example of the existential type anti-pattern. To summarize: if all you’ve got is a bunch of methods, why not just have a record with those methods as properties? If all you’ve got is one method, why not just use a function.

This is a completely valid criticism of the code in this post as a practical approach. However, we wouldn’t have learned about existential types in the first place, and we couldn’t make functions implement Eq and Show. Implementing Eq is the subject of the next post.

The commenter also added an elegant implementation of the functionality given above in terms of pure functions.

EDIT: Lennart Augustsson clarified that existential types do indeed construct vtables. So “boxing” something in an existential type is very like casting a struct to an interface it implements in C#. I should also clarify that the word bonkers used in the above text was meant as a good thing. 🙂

Hello World Web Application in Haskell

So, I’m learning Haskell. I’ve done the Yorgey course and want to write a web app. How do I start? Should I learn Snap or Yesod? Well, the short answer is no.

Here I’m going to outline the creation of the simplest possible Haskell “Hello World” web application.

Wai Wai Pom Pom Pom

Snap and Yesod are both “big” web frameworks. Of the two, Snap aims to be the smaller. Both have their own web server, templating system and so on. Both are sufficiently complex to need a program to set up a starter project. Both have fairly sophisticated monad stacks to understand. They’re also both phenomenal high-performance pieces of engineering.

What this means for a beginner is that you’re going to spend as much time trying to get to grips with the framework as you are learning how to use Haskell. If like me, you’re coming from Clojure, they both feel a bit more like Rails than Compojure.

So, are there simpler to understand models out there? Well, the equivalent of Compojure/Sinatra is Scotty. But I found the next level down again more interesting: Wai.

Wai corresponds most closely to Ring or Rack. It was intended to be a common API that Haskell web servers could expose. In practice, it’s only Warp that really supports it. However, Warp is a damn fine web server so that shouldn’t hold us back too much. Nearly every Ring app runs Jetty and hardly anyone really worries that the “standard” isn’t as portable in practice as it is in theory.

Setting up Hello World

To start, create a new directory. For our purposes we’ll call it “example”. Then we set up a completely blank project.

mkdir example
cd example
cabal sandbox init
wget http://www.stackage.org/lts/1.8/cabal.config
cabal init

The “sandbox” and “wget” lines I’ll gloss over, but they basically constitute the best way I know to avoid what’s known as “cabal hell”. And believe me, you don’t want cabal hell.

When you run the init command, you’ll be asked a whole bunch of questions. The defaults are fine, just make sure you specify you’re creating an executable. It’ll create a file “example.cabal”. You then need to go in and make it look like this:

-- Initial semele.cabal generated by cabal init.  For further
-- documentation, see http://haskell.org/cabal/users-guide/

name:                example
-- synopsis:
-- description:
license:             AGPL-3
license-file:        LICENSE
author:              Rainbow Dash
maintainer:          rainbow.dash@gmail.com
-- copyright:
category:            Web
build-type:          Simple
-- extra-source-files:
cabal-version:       >=1.10

executable semele
  hs-source-dirs:      src
  main-is:             Main.hs
  -- other-modules:
  -- other-extensions:
  build-depends:       base >=4.7 && <4.8,
  default-language:    Haskell2010

There’s two import edits here. The first is that we specify hs-source-dirs. The default is that the Haskell files are dumped in the project’s root directory, which is a lousy default. The other is that we set up our dependencies: wai, warp and http-types. Wai and http-types from our API, Warp our implementation. Note that dependencies are case-sensitive.

You may also be wondering why I haven’t specified any version constraints. That’s because we’ve set them up in the cabal.config instead. Welcome to the new world of LTS Haskell.

Writing Hello World

mkdir src
cd src

Now create Main.hs.

{-# LANGUAGE OverloadedStrings #-}

We need this because Wai uses ByteStrings rather than Strings, and overloaded strings makes using them lower friction.

import qualified Network.Wai as W
import qualified Network.HTTP.Types.Status as HS
import qualified Network.Wai.Handler.Warp as Warp

I’m qualifying everything for clarity. In practice, I do this a fair bit even when I’m not writing a blog post.

main :: IO ()
main = main = do
  putStrLn "Starting Web Server..."
  Warp.runSettings Warp.defaultSettings app

So, all we’re saying here is “Run the app with the default settings for a Warp server.” The default port is 3000.

Finally, we need the app itself:

app :: W.Application

Let’s take a huge detour and examine what that actually means.

Understanding W.Application

Now, the type of app is W.Application, but that tells us nothing. So let’s look it up (LTS has a hoogle, search for Wai.Application). You’ll find

type Application = Request -> (Response -> IO ResponseReceived) -> IO ResponseReceived

So, it’s a alias for a type of function. However, the type’s way more complex that we were expecting. What were we expecting? Well, in Ring the type’s more like

type ApplicationRing = Request -> Response

Take a request, return a response. However, in order to allow for correct resource management, it uses a continuation passing style instead. (I’m hoping to expand on that in another post.) So instead, you need a callback. As you see, we called that respond.

What’s respond‘s type? Well, it’s got to take a response. At this point I hit the limits of my understanding. I’d have made the function return (), but instead it returns ResponseReceived which appears to be a placeholder type. Finally, obviously respond is going to have to write to a socket, so it’s going to have to incorporate the IO monad. Now, in most of the more complex APIs, what you find here is a monad transformer stack with IO somewhere in the mix. In Wai, you just get a naked IO ResponseReceived and can build your own later.

To summarize, the type of respond is Response -> IO ResponseReceived and that means “when you call it with a response it will do some IO and return that it’s been processed`.

Finally, Application expects IO ResponseReceived to be returned from the function. I believe this to be practically motivated: nearly every handler is going to want to call respond as the last thing it does, and this means that the types work when you do that.

You Had Me At Hello

So, now we’ve understood the type, let’s write the function

app request respond = respond $ W.responseLBS HS.status200 [] "Hello World"

To unpack this: when you receive a request, respond using status 200 (success), no headers ([]) and byte string “Hello World”.

So, that’s about the simplest thing we can possibly do without writing our own web server.

Let’s Be Frank

So, how does this compare to Sinatra’s famously good home page? Well, for a start we have three files instead of one. However, two of those files are devoted to ensuring that our dependencies don’t mess us around, if you want to do the same in Ruby, you’ll be setting up bundler, using a gemfile.lock in addition to your normal gemfile, so three files again.

Haskell actually comes out slightly ahead here if you’re willing to forgo some flexibility, in that the cabal.config is repeatable and upgrading is a matter of trying a new cabal.config/ reverting if it doesn’t work.

In comparison, bundler generates a lock file dependent on your current gemfile. If you need to add another library later, it’s up to you to figure out which versions are compatible with your code.

On the other hand, if you need more flexibility, you’re going to encounter cabal hell pretty quickly. Good luck.

We’ve got three dependencies instead of one. That’s a pity. But it comes from the two sources:

  • We’ve got to import types declaring interfaces as well as just implementation code.
  • We don’t have the web server appearing by magic.

On the other hand, Sinatra’s actually provided a routing library, and we don’t have one yet. But we could have used Scotty instead.

Keep On Running

So, let’s see it in action. Get back to the root project directory and type

cabal install && dist/*/build/example/example

and navigate to http://localhost:3000/. Hey presto, you’ve served a web page. Looking at the headers, all that it’s specified is a Date, the Server and Transfer-Encoding, so we’ll definitely have a bit more work to do to for a full experience.

FOOTNOTE: I’m quite pleased with the response this article had on reddit. This discussion is quite interesting and I recommend reading it.

FOOTNOTE: Quite a few people have remarked that the comparison section isn’t really fair on Haskell in that I’ve implemented something at the Rack/Wai level, rather than the Sinatra/Scotty level, which is true. However, I wanted to use Wai rather than Scotty to avoid going into monads and monad transformers and ultimately, I think the Haskell one is still quite concise and beautiful in a very precise manner.

EDIT:A number of people have pointed out that modern ruby is indeed capable of precise version locking. I’ve updated and expanded the comparison to reflect that.

EDIT:Originally I believed that Wai’s continuation passing style was due to asynchronous concerns. Instead, it’s driven by resource management concerns. I’ve corrected the line.

Fox Goose Corn in Haskell for Clojure Programmers

span.kw { color: #007020; font-weight: bold; }
code > span.dt { color: #902000; }
code > span.dv { color: #40a070; }
code > span.bn { color: #40a070; }
code > span.fl { color: #40a070; }
code > span.ch { color: #4070a0; }
code > span.st { color: #4070a0; }
code > span.co { color: #60a0b0; font-style: italic; }
code > span.ot { color: #007020; }
code > span.al { color: #ff0000; font-weight: bold; }
code > span.fu { color: #06287e; }
code > span.er { color: #ff0000; font-weight: bold; }

This is my attempt at a solution to the fox/goose/corn problem in Haskell. It was inspired by Carin Meier’s Clojure Kata for the same problem, although it deviates from the approach. A better Haskell developer might significantly improve on my version. I didn’t find much use for the standard typeclasses in this, sadly. As a consequence, however, the code is relatively understandable from the perspective of a Clojure programmer with no Haskell experience.

I’ll explain each construct as we encounter it.


First, we have the namespace declaration. Unlike Clojure, we need to declare any identifiers we export. Since we’re writing an executable, we export main just as we would in C.

module Main (main) where

Data.Set exports a lot of things with the same names that Data.List exports, so it’s pretty common to import it qualified. It’s not strictly necessary for the code that follows, though.

import qualified Data.Set as S
import Data.List(unfoldr)
import Data.Foldable(Foldable,foldr,find)

The equivalent of clojure.core is the Prelude. We hide Left and Right because we’ll be using our own concept using those identifiers. We hide foldr because the version in Data.Foldable is more general.

import Prelude hiding (Left, Right, foldr)

The Haskell Prelude is actually kind of frustrating, in that it doesn’t show off the language in its full power. It’s heading in that direction, though. In particular, this particular problem is getting addressed soon. Some people opt out of the Prelude altogether and use an alternative.

Basic Data Types

We’re writing Haskell, so we should write some types down.

You’ll recognize the following declarations as being identical to Java enums. Ord means it’s orderable, which in turn means you can put it in a set (hash sets aren’t the default in Haskell), Eq means you can test for equality using it, which comes along for the ride with Ord, Show means you can print it. Haskell magically writes the code in deriving.

data Item = Fox | Goose | Corn | Me deriving (Ord, Eq, Show)
data Side = Left | Right

We’ll represent everything using only the representation of the right hand side. This has the nice property that the initial state is the empty set. So we’re travelling from the Left to the Right. If we’d used a list, some of the code below would be prettier than using a set, but I believe set is the correct representation since it’s fundamentally unordered. It’s worth considering how it would look in Clojure with Set.

This is a newtype. type would indicate a type alias (so State was exactly the same thing as S.Set Item.) A newtype can’t be mixed with a raw set (which is what a Clojure programmer would naturally do) and requires you to explicitly construct and deconstruct it from the set as necessary. This obviously has a cost in verbosity, but has no runtime overhead because it’s all optimised out. It’s especially useful if you’re dealing with two concepts wih the same type representation. In our case, State and History (defined later) could be very easily confused in Clojure.

newtype State = State (S.Set Item) deriving (Ord, Eq, Show)

State of Play

We’ll need some way of mapping booleans to Left/Right. We’re adopting a convention that Left = True here, and we’ve named the function to help keep this straight. Note that we have two definitions. Each definition is a pattern match on the right hand side. Basically, you need this for two things: identifying the side you’re on, and the side you’re not on, so the Bool -> Side mapping makes sense.

toRight :: Bool -> Side
toRight True = Right
toRight False = Left

Now let’s figure out which side we’re on. Here we destructure State for the first time.

onRight :: State -> Bool
onRight (State s) = S.member Me s

We also need a function that tells you what is on which side.

  • \ means “difference”. Since Data.Set is namespace qualified, so is the operator.
  • Sadly there’s no general type that subsumes sets and lists so there’s a List.\ and a Set.\ and they don’t interoperate well

Coming up with a good type system for lists and list like things is regarded as an open problem in the Haskell world and they’re not prepared to take the kinds of compromises Clojure and Scala have made. (Consider, for instance, that mapping a set returns a list.) However, in practice that means that using different types of lists together or writing general list-like code is a pain I could have introduced my own abstraction, but seriously, what’s the point?

Again, we have two definitions. This is the first time we use a where clause. A where clause is similar to a postfix let clause. Note that we don’t need type declarations for non-top-level declarations.

Also, this is an arity-2 function. Only there’s no such thing in Haskell. Haskell, like most FP languages (and unlike Clojure) only ever has functions that take one parameter and return one. So what you’re really looking at here is a function that takes a Side and returns another function which takes a State that then returns a set of items. If you just don’t apply enough parameters, you get the partial application of the function. I’ve long since been an advocate of programming Clojure like this ever since I spent a couple of hours in F#’s company.

side :: Side -> State -> S.Set Item
side Left (State s) = everyone S.\ s
  where everyone = S.fromList [Fox,Goose,Corn,Me]
side Right (State s) = s

The whole reason we’ve defined the operations above is this: after this point we’ll never destructure State again, just interact with the State functions we’ve already defined. The hope is that this enables us to think at a higher level about what we’re doing. (I’m not going to argue this point, but there’s plenty of people on the internet prepared to do so.)

Haskell! So We Can Be Safe!

Let’s figure out if a State is safe. Turns out the rules for whether or not you’re safe are pretty easy

  • The attended side is always safe
  • The unattended side is safe if only the Goose is there
  • No other unattended Goose is safe
  • Every other unattended side is safe

We’re using more Haskell features here.

  • . performs functional composition, so (toRight . not . onRight) is equivalent to (comp toRight not onRight).
  • We can have multiple definitions in a where clause.
  • We can call a variable _ if we don’t care about its value.
  • You can put a “guard” on a pattern match. I prefer to use guards and pattern matching over explicit branching primitives.
  • a $ b c d means the same as a (b c d). This prevents ridiculous paren buildup. Clojure has different ways of avoiding this, most obviously ->.
safe :: State -> Bool
safe s = safeSide $ side unattendedSide s
  where unattendedSide = (toRight . not . onRight) s
        safeSide l | S.member Goose l = S.size l == 1
        safeSide _ = True

In practice, the side function is only used within safe so we could have just stuck it into the where clause and saved some newtype book-keeping.

Moving the Boat

I’m not 100% happy with the readability of this next function, mostly because it’s quite long. Suggestions are welcome.

We need to find the next possible states. We’re mapping to set, because there’s no inherent ordering of the future states. You can do the same in Clojure. Unlike clojure, we need a separate map function, S.map rather than map. The good news is that it returns a set rather than a lazy list.

There is a general map function, fmap that will map anything to its correct container type (and more!) but we can’t use fmap here for technical reasons (for the curious, lookup: “Set is not a Functor in Haskell”).

Also, note that this is where we finally actually create a new State, and that we can just use State, the constructor, as a straight function that we can map over.

transitions :: State -> S.Set State
transitions state = S.map State $ S.insert moveBoat carry
  where onRight = S.member Me $ side Right state
        mySide = side (toRight onRight) state

The move command is either a delete or an insert, depending on the direction of travel. In Clojure this would be (if onRight dissoc assoc)

       move = if onRight
         then S.delete
         else S.insert

The list of items is the things that are on your side that aren’t you.

       items = S.delete Me mySide

Effectively, this next line just destructures State.

       right = side Right state

Whatever else happens, you’re definitely moving youself Note that moveBoat is the State represented by just moving yourself.

       moveBoat = move Me right

If you choose to move an item, it’s a motion on top of moveBoat, not on top of s, since you’re also moving.

We’re using flip, which swaps the parameters of move. We could also have said moveItem x = move x moveBoat or something with lambdas (IMO, lambdas are rarely the most clear option, and in this code they’re never used.) Although you could write flip in Clojure, it really isn’t Clojure “style”, but definitely is Haskell style

       moveItem = flip move moveBoat

carry is the set of states if you carry an item with you

       carry = S.map moveItem items

There’s a huge number of different types in the preceding function, and no type declarations other than the top level. You can put more type declarations in that I have, but you can’t put in fewer and compile with -Wall (If you’re OK with warnings, you can throw away the top level type declarations some of the time, but there’s a lot of reasons that’s a bad idea.)

Desperately Seeking Solution

We’ll ignore the State type completely for a while and just talk in general about how you solve this kind of problem.

We need to think about how to represent a sequence of moves. Here we newtype List (List here is a good choice of type, since history is fundamentally ordered). History is stored backwards for convenience.

newtype History a = History [a] deriving (Eq, Ord)

Let’s make history print the right way around though. To do this, we need to implement the Show typeclass by hand. (Typeclasses are a bit like interfaces, but behave very differently.)

=> is the first example in the code of a type restriction. Here we’re saying “If a is showable, then History of a is showable.” Then the implementation says “The way you show it is by taking the list, reversing it and then showing that.”

instance (Show a) => Show (History a) where
  show (History l) = show $ reverse l

How are we’re going to find the solution? You want to use your transition function to construct a set of possible histories and then search that list for a solution. You could basically do this as a breadth-first or a depth-first search. A breadth-first search will have the advantage of finding the minimal solution. To avoid wasting time on cycles such as the boat just going backwards and forwards, we’ll keep track of what positions we’ve already generated.

So, how to we go from all combinations of 2 moves to all combinations of 3 moves? We define a data structure, Generation.

data Generation a = Generation {
  previous :: S.Set a,
  states :: S.Set (History a)

In practice, we know that a will be State, but it’s generally good Haskell style to use the most general type possible. When you get the hang of it, this aids clarity, rather than impeding it. (See also: parametricity and theorems for free).

Generation is a record data type. Like Clojure, you can use previous and states as accessor functions. Unlike Clojure, these functions are strongly typed. That means you can’t have fields with the same name in different records (within the same file/namespace).

Working with Generations would be better if we used lenses, but lets stick to things in the base libraries.

We need to map the function that generates new states to a function that creates new Generations. In Clojure, we’d probably use reduce. In Haskell, we use foldr, which is pretty similar, modulo some laziness and argument order differences.

  • (a -> S.Set a) is a parameter that is a function.
  • We’re specifying that a implements Ord, which we need to be able to put it into a Set.
  • Due to the wonders of partial application, (a -> S.Set a) -> Generation a -> Generation a is exactly the same as (a -> S.Set a) -> (Generation a -> Generation a)
liftG :: (Ord a) => (a -> S.Set a) -> Generation a -> Generation a
liftG f t = foldr (stepG f) initial (states t)
  where initial = Generation {
          previous = (previous t),
          states = S.empty

Actually, I’ve skipped the most important bit of this: the step function. I could have inlined it, but it’s pretty complex I prefer to give it its own top level declaration, along with a semi-scary type signature.

stepG :: (Ord a) => (a -> S.Set a) -> History a -> Generation a -> Generation a
stepG f (History h@(s : _)) t = result

The destructuring of History is a bit more complicated. Here we’re assigning h to the whole history, and s to the latest state in the history. Note that if History is empty, the pattern match won’t work. Clojure would just match it and put nil in s. Type safety is pretty cool here but it means we need a new pattern match for empty histories. Strictly speaking, they aren’t valid, but the way we defined the type they can happen. (If you’re seriously thinking you want a type system that can express “non-empty list” I have two answers for you: core.typed and Idris.) This is the point at which Haskell goes “Well, I’m trying to be a practical FP language, you know.”

  where result = Generation {

Add the new states into the list of known states.

          previous = S.union (previous t) nextStates,

Add the new histories into the current generation.

          states = S.union (states t) (S.map newHistory nextStates)

The next states are the states of the transition function minus the known states.

        nextStates = f s S.\ (previous t)

The newHistory function is interesting. Observe (: h). Now (x : xs) is the same as (cons x xs) in Clojure. (x :) would be (partial cons x) and (: xs) would be #(cons % xs). So (: h) is a function that takes a t and puts it in front of the existing list. This is operator section and works for all operators (you can define your own) except (- x) (which is special cased to unary minus).

Again, History is just an ordinary function, that wouldn’t have been needed if we’d done types instead of newtypes.

        newHistory = History . (: h)

Finally, to avoid compiler warnings, tell it what happens when History is empty. This case should never happen.

stepG _ _ t = Generation { previous = previous t, states = S.empty }

The Under-Appreciated Unfold

So, now we’ve got a Generation to Generation function, how do we get the list of all possible histories? Well, we could always just write some recursive code, but like in Clojure, there’s functions that exemplify common recursion structures. In Clojure, iterate might be good choice here. In Haskell, there’s unfoldr.

The type declaration of iterate in Clojure would be iterate :: (a -> a) -> a -> [a].

In comparison, the type declaration of unfoldr is quite complex: unfoldr :: (b -> Maybe (a, b)) -> b -> [a].

You might be wondering why they’re so different. The short answer is that unfoldr is awesome. The key is the step function itself b -> Maybe (a,b). This says that it takes a b and returns either Nothing (nil) or Just a pair of a and b. (Did I mention one of the coolest things about Haskell? null/nil doesn’t exist.) The b gets passed to the next step, the a gets output. So unfoldr supports having an internal state and an external state. What happens if Nothing is returned? The list stops generating. Clojure expects you to then terminate the list in a separate step, an approach that seems simpler but falls down when you start to use things like the state monad.

So, our output a is going to be the set of states of the generation, while b is going to be the Generations themselves. We’ll return Nothing when there’s no states in the Generation.

iterations :: (Ord a) => a -> (a -> S.Set a) -> [S.Set (History a)]
iterations start f = unfoldr (forUnfoldr . (liftG f)) initial
  where forUnfoldr t | S.null (states t) = Nothing
        forUnfoldr t = Just ((states t),t)
        initial = Generation {
          previous = S.empty,
          states = S.singleton $ History [start]

So we just call unfoldr with a generation producing function using forUnfoldr to adapt it to fit.

We’ve done this using unfoldr, which has explicit state. Control.Monad.Loops exposes unfoldM which could be used with a state monad to achieve a similar effect.

Fun with Types

Let’s have some fun. We’ve got a list of sets that contains the solution. There’s a perfectly good function for finding an element in a a list called find (as an aside: there’s no such perfectly reasonable function in Clojure). Small catch: it takes a Foldable (in Clojure, a reducable). List is Foldable, Set is Foldable, but a list of sets of states iterates through the sets, not the states.

We’ll do some type magic and make it iterate through the states. (Thanks to Tony Morris for pointing me to a way to achieve this. Much more brain-bending stuff is available in Control.Compose)

newtype Compose g f a = O (g (f a))
instance (Foldable f1, Foldable f2) => Foldable (Compose f1 f2) where
  foldr f start (O list) = foldr g start list
    where g = flip $ foldr f

So, here we’ve said that a foldable of a foldable of a can be used as a single foldable by using flip $ foldr f as the step function. We could have just written this function out, but hey, why not live a litte.

The Finish Line

Finally, we get to main. Often this is expressed in do notation, but I don’t feel the need here, since it’s literally one line: print solution.

main :: IO ()
main = print solution
  where solution = find success (O allHistories)
        success (History (s : _)) = side Left s == S.empty
        success _ = False
        allHistories = iterations allOnLeft next
        allOnLeft = State S.empty
        next = S.filter safe . transitions

So, you can build it, and run it. time reports that it takes 2ms on my machine. How on earth did it run so fast? Aren’t fully lazy functional languages meant to be slow? Well, there are advantages to running an optimizing compiler, but they’re helped by understanding a bit of what is going on under the hood. An unfold followed by a fold is called a hylomorphism. The thing is, you never need to build the whole structure, you could just run each iteration through the fold as it comes. The Haskell compiler is smart enough that it actually rewrites the code. So a large chunk of our code is actually running imperatively.

How much have types helped me write this code? Well, the early functions, especially safe, I needed to nail in GHCi, the Haskell REPL. On the other hand, the later parts of the code actually worked first time (after I’d managed to fix all of the type errors.). Make of that what you will.

I hope you’ve found this interesting. I’m still very much a beginner Haskell programmer, but I hope the presentation enables you to see how you can express ideas in Haskell. If you’d like to learn more, I can highly recommend starting with Brent Yorgey’s course.

Design Patterns: Happy Birthday and Goodbye

One of the biggest lies we tell starting developers is that design patterns are language independent. Whilst true at a high level, the truth is that a programmer in a modern programming language can junk most of the Gang of Four book. A couple of days ago, it was twenty years old. It’s time to celebrate its lasting positive influences, and then bury it.

Some things are potentially useful as terminology for discussing with people, but others aren’t even useful as that. The really obvious example is the template pattern: if you’re programming in a language that can use functions as values it’s utterly meaningless. Another is iterator: most programming languages have a list/sequence implementation and you just use that.

Prototype, equally is meaningless for two, entirely opposite, reasons: first, the whole concept originates in C++ where you can perform a raw memory copy. In a language such as Java that doesn’t have one it’s so cumbersome you’ll prefer a factory method. In a language such as F# or Clojure, ubiquitous persistence data structures mean that everything’s a prototype.

Command is basically a pattern that replaces functions with objects. In a functional programming language, this is just the normal way you do things. In languages such as Python and Clojure where objects can act as functions the line is further blurred. But that’s nothing compared to what you can do with Clojure’s multimethods.

Multimethods and Protocols

Quite a few patterns are just workarounds for the painfully restricted dispatch patterns in old OO languages. The visitor and adapter patterns are both ways of circumventing the closed nature of classes in C++/Java. When you can just associate new methods with existing data structures, even third party code, you just don’t need them.

Also, if you understand multimethods for more than just class based dispatch, you see that it subsumes the state pattern.

(defmulti state-pattern (fn [tool data] tool))
(defmethod state-pattern pen-tool
  [tool data]

How about a strategy pattern?

(defmulti strategy-pattern (fn determine-strategy [tool data] ...))
(defmethod state-pattern :strategy1
  [tool data]

In practice, you can use multimethods to mix and match dispatch on raw parameter value (state), dispatch on computed value (strategy) and dispatch on class (visitor). Similar effects can be achieved using Haskell’s type features.


Then there’s stuff that’s just a special case of something more general. Chain of responsibilty in Clojure is easily implemented using the some function:

(defn chain-of-responsibility
  ([elements] (partial chain-of-responsibility elements))
  ([elements data] (some #(% data) elements)))

Is chain of responsibility really useful terminology here, or is it just “using the some function”?

Then there’s ones that are just plain outdated: observer and mediator are rarely a better choice than a decent pub/sub mechanism. Heck, even your language’s event system is often a better choice. And I think everyone’s got the message about singleton by now.


I’m concerned this will be seen as down on the whole concept of patterns. Actually, high level patterns, the kind that Martin Fowler talks about are fine and last a long time. But our understanding of patterns constantly evolves (see pub/sub) and the ergonomics of specific patterns varies wildly between languages. GoF was a great book, and made a huge positive impact, but it’s time to take it off our shelves.