Haskell retrospective

Wearing the hair shirt A retrospective on Haskell Simon Peyton Jones Microsoft Research, Cambridge

Haskell is 15 years old (born FPCA 87)

Haskell is 15 years old (born FPCA’87) Simon is 45 years old (born 18 Jan: POPL’58)

The primoridal soup FPCA, Sept 1987: initial meeting. A dozen lazy functional programmers, wanting to agree on a common language. Suitable for teaching, research, and application Formally-described syntax and semantics Freely available Embody the apparent consensus of ideas Reduce unnecessary diversity Led to...a succession of face-to-face meetings April 1990: Haskell 1.0 report released (editors: Hudak, Wadler)

Timeline Sept 87: kick off Apr 90: Haskell 1.0 May 92: Haskell 1.2 (SIGPLAN Notices) (164pp) Aug 91: Haskell 1.1 (153pp) May 96: Haskell 1.3. Monadic I/O, separate library report Apr 97: Haskell 1.4 (213pp) Feb 99: Haskell 98 (240pp) Dec 02: Haskell 98 revised (260pp) The Book!

Haskell 98 Haskell development Haskell 98 Stable Documented Consistent across implementations Useful for teaching, books Haskell + extensions Dynamic, exciting Unstable, undocumented, implementations vary...

Reflections on the process The idea of having a fixed standard (Haskell 98) in parallel with an evolving language, has worked really well Formal semantics only for fragments (but see [Faxen2002]) A smallish, rather pointy-headed user-base makes Haskell nimble. Haskell has evolved rapidly and continues to do so. Motto: avoid success at all costs

The price of usefulness Libraries increasingly important: 1996: Separate libraries Report 2001: Hierarchical library naming structure, increasingly populated Foreign-function interface increasingly important 1993 onwards: a variety of experiments 2001: successful effort to standardise a FFI across implementations Any language large enough to be useful is dauntingly complex

Reflections on process Self-appointed committee initially, but increasingly open process: there is now no Haskell committee Language development by user suggestion + implementers Gives too much power to implementers?

Good ideas from other languages List comprehensions head :: [a] -> a head (x:xs) = x head [] = error “head of nil” [(x,y) | x <- xs, y <- ys, x+y < 10] Separate type signatures DIY infix operators f `map` xs Optional layout let x = 3 y = 4 in x+y let { x = 3; y = 4} in x+y

Syntactic redundancy Seductive idea: provide just one way of doing any particular thing Haskell’s choice: provide multiple ways, and let the programmer decide Main example: “declaration style” vs “expression style”

“ Declaration style” Define a function as a series of independent equations map f [] = [] map f (x:xs) = f x : map f xs sign x | x>0 = 1 | x==0 = 0 | x<0 = -1

“ Expression style” Define a function as an expression map = \f xs -> case xs of [] -> [] (x:xs) -> map f xs sign = \x -> if x>0 then 1 else if x==0 then 0 else -1

Fat vs thin Expression style Let Lambda Case If Declaration style Where Function arguments on lhs Pattern-matching Guards SLPJ’s conclusion syntactic redundancy is a big win Tony Hoare’s comment “I fear that Haskell is doomed to succeed”

Example (ICFP02 prog comp) sp_help item@(Item cur_loc cur_link _) wq vis | cur_length > limit -- Beyond limit = sp wq vis | Just vis_link <- lookupVisited vis cur_loc = -- Already visited; update the visited -- map if cur_link is better if cur_length >= linkLength vis_link then -- Current link is no better sp wq vis else -- Current link is better emit vis item ++ sp wq vis' | otherwise -- Not visited yet = emit vis item ++ sp wq' vis' where vis’ = ... wq = ... Guard Pattern guard Pattern match Conditional Where clause

So much for syntax... What is important or interesting about Haskell?

What really matters? Laziness Type classes Sexy types

Laziness John Hughes’s famous paper “Why functional programming matters” Modular programming needs powerful glue Lazy evaluation enables new forms of modularity; in particular, separating generation from selection . Non-strict semantics means that unrestricted beta substitution is OK.

But... Laziness makes it much, much harder to reason about performance, especially space. Tricky uses of seq for effect seq :: a -> b -> b Laziness has a real implementation cost Laziness can be added to a strict language (although not as easily as you might think) And it’s not so bad only having  V instead of  So why wear the hair shirt of laziness?

Laziness Laziness is jolly convenient sp_help item@(Item cur_loc cur_link _) wq vis | cur_length > limit -- Beyond limit = sp wq vis | Just vis_link <- lookupVisited vis cur_loc = if cur_length >= linkLength vis_link then sp wq vis else emit vis item ++ sp wq vis' | otherwise = emit vis item ++ sp wq' vis' where vis’ = ... wq’ = ... Used in two cases Used in one case

Combinator libraries Recursive values are jolly useful type Parser a = String -> (a, String) exp :: Parser Expr exp = lit “let” <+> decls <+> lit “in” <+> exp ||| exp <+> aexp ||| ...etc... This is illegal in ML, because of the value restriction Can only be made legal by eta expansion. But that breaks the Parser abstraction, and is extremely gruesome: exp x = ( lit “let” <+> decls <+> lit “in” <+> exp ||| exp <+> aexp ||| ...etc... ) x

Laziness keeps you honest Every call-by-value language has given into the siren call of side effects But in Haskell (print “yes”) + (print “no”) just does not make sense. Even worse is [print “yes”, print “no”] So effects (I/O, references, exceptions) are just not an option. Result: prolonged embarrassment . Stream-based I/O, continuation I/O... but NO DEALS WIH THE DEVIL

Monadic I/O A value of type ( IO t ) is an “ action ” that, when performed, may do some input/output before delivering a result of type t. eg. getChar :: IO Char putChar :: Char -> IO ()

Performing I/O A program is a single I/O action Running the program performs the action Can’t do I/O from pure code. Result: clean separation of pure code from imperative code main :: IO a

Connecting I/O operations (>>=) :: IO a -> (a -> IO b) -> IO b return :: a -> IO a eg. getChar >>= ( \a -> getChar >>= ( \b -> putChar b >>= ( \() -> return (a,b) )))

The do-notation Syntactic sugar only Easy translation into (>>=), return Deliberately imperative “look and feel” getChar >>= \a -> getChar >>= \b -> putchar b >>= \()-> return (a,b) do { a <- getChar; b <- getChar; putchar b; return (a,b) } ==

Control structures Values of type (IO t) are first class So we can define our own “control structures” forever :: IO () -> IO () forever a = do { a; forever a } repeatN :: Int -> IO () -> IO () repeatN 0 a = return () repeatN n a = do { a; repeatN (n-1) a } e.g. repeatN 10 (putChar ‘x’)

Monads generally A monad consists of: A type constructor M bind :: M a -> (a -> M b) -> M b unit :: a -> M a PLUS some per-monad operations (e.g. getChar :: IO Char) There are lots of useful monads, not only I/O

Monads Exceptions type Exn a = Either String a fail :: String -> Exn a Unique supply type Uniq a = Int -> (a, Int) new :: Uniq Int Parsers type Parser a = String -> [(a,String)] alt :: Parser a -> Parser a -> Parser a Monad combinators (e.g. sequence, fold, etc), and do-notation, work over all monads

Example: a type checker tcExpr :: Expr -> Tc Type tcExpr (App fun arg) = do { fun_ty <- tcExpr fun ; arg_ty <- tcExpr arg ; res_ty <- newTyVar ; unify fun_ty (arg_ty --> res_ty) ; return res_ty } Tc monad hides all the plumbing: Exceptions and failure Current substitution (unification) Type environment Current source location Manufacturing fresh type variables Robust to changes in plumbing

The IO monad The IO monad allows controlled introduction of other effect-ful language features (not just I/O) State newRef :: IO (IORef a) read :: IORef s a -> IO a write :: IORef s a -> a -> IO () Concurrency fork :: IO a -> IO ThreadId newMVar :: IO (MVar a) takeMVar :: MVar a -> IO a putMVar :: MVar a -> a -> IO ()

What have we achieved? The ability to mix imperative and purely-functional programming Purely-functional core Imperative “skin”

What have we achieved? ...without ruining either All laws of pure functional programming remain unconditionally true, even of actions e.g. let x=e in ...x....x... = ....e....e.....

What we have not achieved Imperative programming is no easier than it always was e.g. do { ...; x <- f 1; y <- f 2; ...} ?=? do { ...; y <- f 2; x <- f 1; ...} ...but there’s less of it! ...and actions are first-class values

Open challenge 1 Open problem: the IO monad has become Haskell’s sin-bin. (Whenever we don’t understand something, we toss it in the IO monad.) Festering sore: unsafePerformIO :: IO a -> a Dangerous, indeed type-unsafe, but occasionally indispensable. Wanted: finer-grain effect partitioning e.g. IO {read x, write y} Int

Open challenge 2 Which would you prefer? do { a <- f x; b <- g y; h a b } h (f x) (g y) In a commutative monad, it does not matter whether we do (f x) first or (g y) . Commutative monads are very common. (Environment, unique supply, random number generation.) For these, monads over-sequentialise. Wanted: theory and notation for some cool compromise.

Monad summary Monads are a beautiful example of a theory-into-practice (more the thought pattern than actual theorems) Hidden effects are like hire-purchase : pay nothing now, but it catches up with you in the end Enforced purity is like paying up front : painful on Day 1, but usually worth it But we made one big mistake...

Our biggest mistake Using the scary term “monad” rather than “ warm fuzzy thing”

What really matters? Laziness Purity and monads Type classes Sexy types

SLPJ conclusions Purity is more important than, and quite independent of, laziness The next ML will be pure, with effects only via monads Still unclear exactly how to add laziness to a strict language. For example, do we want a type distinction between (say) a lazy Int and a strict Int?

Type classes Initially, just a neat way to get systematic overloading of (==), read, show. class Eq a where (==) :: a -> a -> Bool instance Eq Int where i1 == i2 = eqInt i1 i2 instance (Eq a) => Eq [a] where [] == [] = True (x:xs) == (y:ys) = (x == y) && (xs == ys) member :: Eq a => a -> [a] -> Bool member x [] = False member x (y:ys) | x==y = True | otherwise = member x ys

Implementing type classes data Eq a = MkEq (a->a->Bool) eq (MkEq e) = e dEqInt :: Eq Int dEqInt = MkEq eqInt dEqList :: Eq a -> Eq [a] dEqList (MkEq e) = MkEq el where el [] [] = True el (x:xs) (y:ys) = x `e` y && xs `el` ys member :: Eq a -> a -> [a] -> Bool member d x [] = False member d x (y:ys) | eq d x y = True | otherwise = member deq x ys Class witnessed by a “dictionary” of methods Instance declarations create dictionaries Overloaded functions take extra dictionary parameter(s)

Type classes over time Type classes are the most unusual feature of Haskell’s type system Incomprehension Wild enthusiasm 1987 1989 1993 1997 Implementation begins Despair Hack, hack, hack Hey, what’s the big deal?

Type classes are useful Type classes have proved extraordinarily convenient in practice Equality, ordering, serialisation, numerical operations, and not just the built-in ones (e.g. pretty-printing, time-varying values) Monadic operations class Monad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b fail :: String -> m a Note the higher-kinded type variable, m

Quickcheck ghci> quickCheck propRev OK: passed 100 tests ghci> quickCheck propRevApp OK: passed 100 tests Quickcheck (which is just a Haskell 98 library) Works out how many arguments Generates suitable test data Runs tests propRev :: [Int] -> Bool propRev xs = reverse (reverse xs) == xs propRevApp :: [Int] -> [Int] -> Bool propRevApp xs ys = reverse (xs++ys) == reverse ys ++ reverse xs

Quickcheck quickCheck :: Test a => a -> IO () class Test a where prop :: a -> Rand -> Bool class Arby a where arby :: Rand -> a instance (Arby a, Test b) => Test (a->b) where prop f r = prop (f (arby r1)) r2 where (r1,r2) = split r instance Test Bool where prop b r = b

Extensiblity Like OOP, one can add new data types “later”. E.g. QuickCheck works for your new data types (provided you make them instances of Arby ) ...but also not like OOP

Type-based dispatch A bit like OOP, except that method suite passed separately? double :: Num a => a -> a double x = x+x No: type classes implement type-based dispatch, not value-based dispatch class Num a where (+) :: a -> a -> a negate :: a -> a fromInteger :: Integer -> a ...

Type-based dispatch double :: Num a => a -> a double x = 2*x means double :: Num a -> a -> a double d x = mul d (fromInteger d 2) x The overloaded value is returned by fromInteger , not passed to it. It is the dictionary (and type) that are passed as argument to fromInteger class Num a where (+) :: a -> a -> a negate :: a -> a fromInteger :: Integer -> a ...

Type-based dispatch So the links to intensional polymorphism are much closer than the links to OOP. The dictionary is like a proxy for the (interesting aspects of) the type argument of a polymorphic function. f :: forall a. a -> Int f t (x::t) = ...typecase t... f :: forall a. C a => a -> Int f x = ...(call method of C)... Intensional polymorphism Haskell C.f. Crary et al  R (ICFP98), Baars et al (ICFP02)

Cool generalisations Multi-parameter type classes Higher-kinded type variables (a.k.a. constructor classes) Overlapping instances Functional dependencies (Jones ESOP’00) Type classes as logic programs (Neubauer et al POPL’02)

Qualified types Type classes are an example of qualified types [Jones thesis]. Main features types of form  .Q =>  qualifiers Q are witnessed by run-time evidence Known examples type classes (evidence = tuple of methods) implicit parameters (evidence = value of implicit param) extensible records (evidence = offset of field in record) Another unifying idea: Constraint Handling Rules (Stucky/Sulzmann ICFP’02)

Type classes summary A much more far-reaching idea than we first realised Variants adopted in Isabel, Clean, Mercury, Hal, Escher Open questions: tension between desire for overlap and the open-world goal danger of death by complexity

Sexy types Haskell has become a laboratory and playground for advanced type hackery Polymorphic recursion Higher kinded type variables data T k a = T a ( k (T k a)) Polymorphic functions as constructor arguments data T = MkT ( forall a . [a] -> [a]) Polymorphic functions as arbitrary function arguments (higher ranked types) f :: ( forall a . [a]->[a]) -> ... Existential types data T = exists a . Show a => MkT a

Is sexy good? Yes! Well typed programs don’t go wrong Less mundanely (but more allusively) sexy types let you think higher thoughts and still stay [almost] sane: deeply higher-order functions functors folds and unfolds monads and monad transformers arrows (now finding application in real-time reactive programming) short-cut deforestation bootstrapped data structures

How sexy? Damas-Milner is on a cusp: Can infer most-general types without any type annotations at all But virtually any extension destroys this property Adding type quite modest type annotations lets us go a LOT further (as we have already seen) without losing inference for most of the program. Still missing from the sexiest Haskell impls  at the type level Subtyping Impredicativity

Destination = F w <: Open question What is a good design for user-level type annotation that exposes the power of F w or F w <: , but co-exists with type inference? C.f. Didier & Didier’s MLF work

Modules Power Difficulty Haskell 98 ML functors Haskell + sexy types

Modules Power Haskell 98 ML functors Haskell + sexy types Porsche High power, but poor power/cost ratio Separate module language First class modules problematic Big step in compiler complexity Full power seldom needed Ford Cortina with alloy wheels Medium power, with good power/cost Module parameterisation too weak No language support for module signatures

Modules Haskell has many features that overlap with what ML-style modules offer: type classes first class universals and existentials Does Haskell need functors anyway? No: one seldom needs to instantiate the same functor at different arguments But Haskell lacks a way to distribute “open” libraries, where the client provides some base modules; need module signatures and type-safe linking (e.g. PLT,Knit?).  not  ! Wanted: a design with better power, but good power/weight.

Encapsulating it all runST :: (forall s. ST s a) -> a Stateful computation Pure result data ST s a -- Abstract newRef :: a -> ST s (STRef s a) read :: STRef s a -> ST s a write :: STRef s a -> a -> ST s () sort :: Ord a => [a] -> [a] sort xs = runST (do { ..in-place sort.. })

Encapsulating it all runST :: (forall s. ST s a) -> a Higher rank type Monads Security of encapsulation depends on parametricity Parametricity depends on there being few polymorphic functions (e.g.. f:: a->a means f is the identity function or bottom) And that depends on type classes to make non-parametric operations explicit (e.g. f :: Ord a => a -> a) And it also depends on purity (no side effects)

Shirts off to Wadler Type classes “Making ad hoc polymorphism less ad hoc” [POPL89] Monads “The essence of functional programming” [POPL92] Sexy types “Theorems for free” [FPCA89]

The Haskell committee Arvind Lennart Augustsson Dave Barton Brian Boutel Warren Burton Jon Fairbairn Joseph Fasel Andy Gordon Maria Guzman Kevin Hammond Ralf Hinze Paul Hudak [editor] John Hughes [editor] Thomas Johnsson Mark Jones Dick Kieburtz John Launchbury Erik Meijer Rishiyur Nikhil John Peterson Simon Peyton Jones [editor] Mike Reeve Alastair Reid Colin Runciman Philip Wadler [editor] David Wise Jonathan Young

Haskell retrospective

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Haskell retrospective