X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=docs%2Fusers_guide%2Fglasgow_exts.xml;h=4fbd08c5c41326775b9ceebde0de78cba6d7a75c;hb=69443f18d24fb9a911f27ad46c298cc21be57c61;hp=c370ce3388308a602a0f020a8745652fed0b5d3e;hpb=ea283aa74e6fd2bec2b88eae19908bba903adea1;p=ghc-hetmet.git diff --git a/docs/users_guide/glasgow_exts.xml b/docs/users_guide/glasgow_exts.xml index c370ce3..4fbd08c 100644 --- a/docs/users_guide/glasgow_exts.xml +++ b/docs/users_guide/glasgow_exts.xml @@ -38,11 +38,28 @@ documentation describes all the libraries that come with GHC. extensionsoptions controlling - These flags control what variation of the language are + The language option flag control what variation of the language are permitted. Leaving out all of them gives you standard Haskell 98. - NB. turning on an option that enables special syntax + Generally speaking, all the language options are introduced by "" or ""; + e.g. . Before anything else is done, the string following + "" is normalised by removing hyphens and converting + to lower case. So , , and + are all equivalent. + + + All the language options can be turned off by using the prefix ""; + e.g. "". + + Language options recognised by Cabal can also be enabled using the LANGUAGE pragma, + thus {-# LANGUAGE TemplateHaskell #-} (see >). + + All the language options can be introduced with "" as well as "", + but this is a deprecated feature for backward compatibility. Use the "" + or LANGUAGE-pragma form. + + Turning on an option that enables special syntax might cause working Haskell 98 code to fail to compile, perhaps because it uses a variable name which has become a reserved word. So, together with each option below, we @@ -81,7 +98,8 @@ documentation describes all the libraries that come with GHC. This simultaneously enables all of the extensions to Haskell 98 described in , except where otherwise - noted. + noted. We are trying to move away from this portmanteau flag, + and towards enabling features individaully. New reserved words: forall (only in types), mdo. @@ -95,14 +113,20 @@ documentation describes all the libraries that come with GHC. float##, (#, #), |), {|. + + Implies these specific language options: + , + , + , + , + . - and : - - + and : + This option enables the language extension defined in the @@ -114,7 +138,7 @@ documentation describes all the libraries that come with GHC. - ,: + ,: These two flags control how generalisation is done. @@ -125,8 +149,8 @@ documentation describes all the libraries that come with GHC. - : - + : + Use GHCi's extended default rules in a regular module (). @@ -137,16 +161,16 @@ documentation describes all the libraries that come with GHC. - - + + - - + + - - + + @@ -171,8 +195,8 @@ documentation describes all the libraries that come with GHC. - - + + See . Independent of @@ -190,8 +214,8 @@ documentation describes all the libraries that come with GHC. - - + + See . Independent of @@ -200,13 +224,13 @@ documentation describes all the libraries that come with GHC. - + - -fno-implicit-prelude + -XnoImplicitPrelude option GHC normally imports Prelude.hi files for you. If you'd rather it didn't, then give it a - option. The idea is + option. The idea is that you can then import a Prelude of your own. (But don't call it Prelude; the Haskell module namespace is flat, and you must not conflict with any @@ -221,14 +245,14 @@ documentation describes all the libraries that come with GHC. translation for list comprehensions continues to use Prelude.map etc. - However, does + However, does change the handling of certain built-in syntax: see . - + Enables implicit parameters (see ). Currently also implied by @@ -241,7 +265,15 @@ documentation describes all the libraries that come with GHC. - + + + Enables overloaded string literals (see ). + + + + + Enables lexically-scoped type variables (see ). Implied by @@ -250,7 +282,7 @@ documentation describes all the libraries that come with GHC. - + , Enables Template Haskell (see ). This flag must @@ -269,8 +301,6 @@ documentation describes all the libraries that come with GHC. - - Unboxed types and primitive operations @@ -375,6 +405,13 @@ worse, the unboxed value might be larger than a pointer (Double# for instance). + You cannot define a newtype whose representation type +(the argument type of the data constructor) is an unboxed type. Thus, +this is illegal: + + newtype A = MkA Int# + + You cannot bind a variable with an unboxed type in a top-level binding. @@ -544,14 +581,11 @@ import qualified Control.Monad.ST.Strict as ST linkend="search-path"/>. GHC comes with a large collection of libraries arranged - hierarchically; see the accompanying library documentation. - There is an ongoing project to create and maintain a stable set - of core libraries used by several Haskell - compilers, and the libraries that GHC comes with represent the - current status of that project. For more details, see Haskell - Libraries. - + hierarchically; see the accompanying library + documentation. More libraries to install are available + from HackageDB. @@ -620,7 +654,7 @@ to write clunky would be to use case expressions: -clunky env var1 var1 = case lookup env var1 of +clunky env var1 var2 = case lookup env var1 of Nothing -> fail Just val1 -> case lookup env var2 of Nothing -> fail @@ -645,7 +679,7 @@ Here is how I would write clunky: -clunky env var1 var1 +clunky env var1 var2 | Just val1 <- lookup env var1 , Just val2 <- lookup env var2 = val1 + val2 @@ -741,13 +775,6 @@ than do). -You should import Control.Monad.Fix. -(Note: Strictly speaking, this import is required only when you need to refer to the name -MonadFix in your program, but the import is always safe, and the programmers -are encouraged to always import this module when using the mdo-notation.) - - - As with other extensions, ghc should be given the flag -fglasgow-exts @@ -832,7 +859,7 @@ This name is not supported by GHC. hierarchy. It completely defeats that purpose if the literal "1" means "Prelude.fromInteger 1", which is what the Haskell Report specifies. - So the flag causes + So the flag causes the following pieces of built-in syntax to refer to whatever is in scope, not the Prelude versions: @@ -935,18 +962,56 @@ definitions; you must define such a function in prefix form. - + +Record field disambiguation + +In record construction and record pattern matching +it is entirely unambiguous which field is referred to, even if there are two different +data types in scope with a common field name. For example: + +module M where + data S = MkS { x :: Int, y :: Bool } +module Foo where + import M - - -Type system extensions + data T = MkT { x :: Int } + + ok1 (MkS { x = n }) = n+1 -- Unambiguous + ok2 n = MkT { x = n+1 } -- Unambiguous - -Data types and type synonyms + bad1 k = k { x = 3 } -- Ambiguous + bad2 k = x k -- Ambiguous + +Even though there are two x's in scope, +it is clear that the x in the pattern in the +definition of ok1 can only mean the field +x from type S. Similarly for +the function ok2. However, in the record update +in bad1 and the record selection in bad2 +it is not clear which of the two types is intended. + + +Haskell 98 regards all four as ambiguous, but with the + flag, GHC will accept +the former two. The rules are precisely the same as those for instance +declarations in Haskell 98, where the method names on the left-hand side +of the method bindings in an instance declaration refer unambiguously +to the method of that class (provided they are in scope at all), even +if there are other variables in scope with the same name. +This reduces the clutter of qualified names when you import two +records from different modules that use the same field name. + + + + + + + +Extensions to data types and type synonyms - + Data types with no constructors With the flag, GHC lets you declare @@ -960,13 +1025,13 @@ a data type with no constructors. For example: Syntactically, the declaration lacks the "= constrs" part. The type can be parameterised over types of any kind, but if the kind is not * then an explicit kind annotation must be used -(see ). +(see ). Such data types have only one value, namely bottom. Nevertheless, they can be useful when defining "phantom types". - + - + Infix type constructors, classes, and type variables @@ -1033,9 +1098,9 @@ to be written infix, very much like expressions. More specifically: - + - + Liberalised type synonyms @@ -1125,10 +1190,10 @@ this will be rejected: because GHC does not allow unboxed tuples on the left of a function arrow. - + - + Existentially quantified data constructors @@ -1222,7 +1287,7 @@ that collection of packages in a uniform manner. You can express quite a bit of object-oriented-like programming this way. - + Why existential? @@ -1245,9 +1310,9 @@ But Haskell programmers can safely think of the ordinary adding a new existential quantification construct. - + - + Type classes @@ -1307,9 +1372,9 @@ Notice the way that the syntax fits smoothly with that used for universal quantification earlier. - + - + Record Constructors @@ -1326,7 +1391,7 @@ data Counter a = forall self. NewCounter Here tag is a public field, with a well-typed selector function tag :: Counter a -> a. The self type is hidden from the outside; any attempt to apply _this, -_inc or _output as functions will raise a +_inc or _display as functions will raise a compile-time error. In other words, GHC defines a record selector function only for fields whose type does not mention the existentially-quantified variables. (This example used an underscore in the fields for which record selectors @@ -1361,20 +1426,6 @@ main = do display (inc (inc counterB)) -- prints "##" -In GADT declarations (see ), the explicit -forall may be omitted. For example, we can express -the same Counter a using GADT: - - -data Counter a where - NewCounter { _this :: self - , _inc :: self -> self - , _display :: self -> IO () - , tag :: a - } - :: Counter a - - At the moment, record update syntax is only supported for Haskell 98 data types, so the following function does not work: @@ -1386,10 +1437,10 @@ setTag obj t = obj{ tag = t } - + - + Restrictions @@ -1515,7 +1566,7 @@ are convincing reasons to change it. You can't use deriving to define instances of a data type with existentially quantified data constructors. -Reason: in most cases it would not make sense. For example:# +Reason: in most cases it would not make sense. For example:; data T = forall a. MkT [a] deriving( Eq ) @@ -1540,195 +1591,765 @@ declarations. Define your own instances! - - + + +Declaring data types with explicit constructor signatures - -Class declarations - - -This section, and the next one, documents GHC's type-class extensions. -There's lots of background in the paper Type -classes: exploring the design space (Simon Peyton Jones, Mark -Jones, Erik Meijer). - - -All the extensions are enabled by the flag. - - - -Multi-parameter type classes - -Multi-parameter type classes are permitted. For example: - - +GHC allows you to declare an algebraic data type by +giving the type signatures of constructors explicitly. For example: - class Collection c a where - union :: c a -> c a -> c a - ...etc. + data Maybe a where + Nothing :: Maybe a + Just :: a -> Maybe a - - - - - -The superclasses of a class declaration - - -There are no restrictions on the context in a class declaration -(which introduces superclasses), except that the class hierarchy must -be acyclic. So these class declarations are OK: - - +The form is called a "GADT-style declaration" +because Generalised Algebraic Data Types, described in , +can only be declared using this form. +Notice that GADT-style syntax generalises existential types (). +For example, these two declarations are equivalent: - class Functor (m k) => FiniteMap m k where - ... - - class (Monad m, Monad (t m)) => Transform t m where - lift :: m a -> (t m) a + data Foo = forall a. MkFoo a (a -> Bool) + data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' } - - - -As in Haskell 98, The class hierarchy must be acyclic. However, the definition -of "acyclic" involves only the superclass relationships. For example, -this is OK: - - +Any data type that can be declared in standard Haskell-98 syntax +can also be declared using GADT-style syntax. +The choice is largely stylistic, but GADT-style declarations differ in one important respect: +they treat class constraints on the data constructors differently. +Specifically, if the constructor is given a type-class context, that +context is made available by pattern matching. For example: - class C a where { - op :: D b => a -> b -> b - } - - class C a => D a where { ... } - + data Set a where + MkSet :: Eq a => [a] -> Set a + makeSet :: Eq a => [a] -> Set a + makeSet xs = MkSet (nub xs) -Here, C is a superclass of D, but it's OK for a -class operation op of C to mention D. (It -would not be OK for D to be a superclass of C.) + insert :: a -> Set a -> Set a + insert a (MkSet as) | a `elem` as = MkSet as + | otherwise = MkSet (a:as) + +A use of MkSet as a constructor (e.g. in the definition of makeSet) +gives rise to a (Eq a) +constraint, as you would expect. The new feature is that pattern-matching on MkSet +(as in the definition of insert) makes available an (Eq a) +context. In implementation terms, the MkSet constructor has a hidden field that stores +the (Eq a) dictionary that is passed to MkSet; so +when pattern-matching that dictionary becomes available for the right-hand side of the match. +In the example, the equality dictionary is used to satisfy the equality constraint +generated by the call to elem, so that the type of +insert itself has no Eq constraint. - - - - - - -Class method types - - -Haskell 98 prohibits class method types to mention constraints on the -class type variable, thus: +This behaviour contrasts with Haskell 98's peculiar treament of +contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report). +In Haskell 98 the defintion - class Seq s a where - fromList :: [a] -> s a - elem :: Eq a => a -> s a -> Bool + data Eq a => Set' a = MkSet' [a] -The type of elem is illegal in Haskell 98, because it -contains the constraint Eq a, constrains only the -class type variable (in this case a). -GHC lifts this restriction. - - - - - - - -Functional dependencies - - - Functional dependencies are implemented as described by Mark Jones -in “Type Classes with Functional Dependencies”, Mark P. Jones, -In Proceedings of the 9th European Symposium on Programming, -ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782, -. - +gives MkSet' the same type as MkSet above. But instead of +making available an (Eq a) constraint, pattern-matching +on MkSet' requires an (Eq a) constraint! +GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations, +GHC's behaviour is much more useful, as well as much more intuitive. -Functional dependencies are introduced by a vertical bar in the syntax of a -class declaration; e.g. +For example, a possible application of GHC's behaviour is to reify dictionaries: - class (Monad m) => MonadState s m | m -> s where ... + data NumInst a where + MkNumInst :: Num a => NumInst a - class Foo a b c | a b -> c where ... + intInst :: NumInst Int + intInst = MkNumInst + + plus :: NumInst a -> a -> a -> a + plus MkNumInst p q = p + q -There should be more documentation, but there isn't (yet). Yell if you need it. +Here, a value of type NumInst a is equivalent +to an explicit (Num a) dictionary. -Rules for functional dependencies -In a class declaration, all of the class type variables must be reachable (in the sense -mentioned in ) -from the free variables of each method type. -For example: +The rest of this section gives further details about GADT-style data +type declarations. + + + +The result type of each data constructor must begin with the type constructor being defined. +If the result type of all constructors +has the form T a1 ... an, where a1 ... an +are distinct type variables, then the data type is ordinary; +otherwise is a generalised data type (). + + +The type signature of +each constructor is independent, and is implicitly universally quantified as usual. +Different constructors may have different universally-quantified type variables +and different type-class constraints. +For example, this is fine: - class Coll s a where - empty :: s - insert :: s -> a -> s + data T a where + T1 :: Eq b => b -> T b + T2 :: (Show c, Ix c) => c -> [c] -> T c + -is not OK, because the type of empty doesn't mention -a. Functional dependencies can make the type variable -reachable: + +Unlike a Haskell-98-style +data type declaration, the type variable(s) in the "data Set a where" header +have no scope. Indeed, one can write a kind signature instead: - class Coll s a | s -> a where - empty :: s - insert :: s -> a -> s + data Set :: * -> * where ... + +or even a mixture of the two: + + data Foo a :: (* -> *) -> * where ... + +The type variables (if given) may be explicitly kinded, so we could also write the header for Foo +like this: + + data Foo a (b :: * -> *) where ... + -Alternatively Coll might be rewritten + +You can use strictness annotations, in the obvious places +in the constructor type: - class Coll s a where - empty :: s a - insert :: s a -> a -> s a + data Term a where + Lit :: !Int -> Term Int + If :: Term Bool -> !(Term a) -> !(Term a) -> Term a + Pair :: Term a -> Term b -> Term (a,b) + + +You can use a deriving clause on a GADT-style data type +declaration. For example, these two declarations are equivalent + + data Maybe1 a where { + Nothing1 :: Maybe1 a ; + Just1 :: a -> Maybe1 a + } deriving( Eq, Ord ) -which makes the connection between the type of a collection of -a's (namely (s a)) and the element type a. -Occasionally this really doesn't work, in which case you can split the -class like this: + data Maybe2 a = Nothing2 | Just2 a + deriving( Eq, Ord ) + + + +You can use record syntax on a GADT-style data type declaration: - class CollE s where - empty :: s - - class CollE s => Coll s a where - insert :: s -> a -> s + data Person where + Adult { name :: String, children :: [Person] } :: Person + Child { name :: String } :: Person +As usual, for every constructor that has a field f, the type of +field f must be the same (modulo alpha conversion). - - + +At the moment, record updates are not yet possible with GADT-style declarations, +so support is limited to record construction, selection and pattern matching. +For exmaple + + aPerson = Adult { name = "Fred", children = [] } - -Background on functional dependencies + shortName :: Person -> Bool + hasChildren (Adult { children = kids }) = not (null kids) + hasChildren (Child {}) = False + + -The following description of the motivation and use of functional dependencies is taken -from the Hugs user manual, reproduced here (with minor changes) by kind -permission of Mark Jones. - - -Consider the following class, intended as part of a -library for collection types: + +As in the case of existentials declared using the Haskell-98-like record syntax +(), +record-selector functions are generated only for those fields that have well-typed +selectors. +Here is the example of that section, in GADT-style syntax: - class Collects e ce where - empty :: ce - insert :: e -> ce -> ce - member :: e -> ce -> Bool +data Counter a where + NewCounter { _this :: self + , _inc :: self -> self + , _display :: self -> IO () + , tag :: a + } + :: Counter a -The type variable e used here represents the element type, while ce is the type -of the container itself. Within this framework, we might want to define -instances of this class for lists or characteristic functions (both of which -can be used to represent collections of any equality type), bit sets (which can +As before, only one selector function is generated here, that for tag. +Nevertheless, you can still use all the field names in pattern matching and record construction. + + + + + +Generalised Algebraic Data Types (GADTs) + +Generalised Algebraic Data Types generalise ordinary algebraic data types +by allowing constructors to have richer return types. Here is an example: + + data Term a where + Lit :: Int -> Term Int + Succ :: Term Int -> Term Int + IsZero :: Term Int -> Term Bool + If :: Term Bool -> Term a -> Term a -> Term a + Pair :: Term a -> Term b -> Term (a,b) + +Notice that the return type of the constructors is not always Term a, as is the +case with ordinary data types. This generality allows us to +write a well-typed eval function +for these Terms: + + eval :: Term a -> a + eval (Lit i) = i + eval (Succ t) = 1 + eval t + eval (IsZero t) = eval t == 0 + eval (If b e1 e2) = if eval b then eval e1 else eval e2 + eval (Pair e1 e2) = (eval e1, eval e2) + +The key point about GADTs is that pattern matching causes type refinement. +For example, in the right hand side of the equation + + eval :: Term a -> a + eval (Lit i) = ... + +the type a is refined to Int. That's the whole point! +A precise specification of the type rules is beyond what this user manual aspires to, +but the design closely follows that described in +the paper Simple +unification-based type inference for GADTs, +(ICFP 2006). +The general principle is this: type refinement is only carried out +based on user-supplied type annotations. +So if no type signature is supplied for eval, no type refinement happens, +and lots of obscure error messages will +occur. However, the refinement is quite general. For example, if we had: + + eval :: Term a -> a -> a + eval (Lit i) j = i+j + +the pattern match causes the type a to be refined to Int (because of the type +of the constructor Lit), and that refinement also applies to the type of j, and +the result type of the case expression. Hence the addition i+j is legal. + + +These and many other examples are given in papers by Hongwei Xi, and +Tim Sheard. There is a longer introduction +on the wiki, +and Ralf Hinze's +Fun with phantom types also has a number of examples. Note that papers +may use different notation to that implemented in GHC. + + +The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with +. + + +A GADT can only be declared using GADT-style syntax (); +the old Haskell-98 syntax for data declarations always declares an ordinary data type. +The result type of each constructor must begin with the type constructor being defined, +but for a GADT the arguments to the type constructor can be arbitrary monotypes. +For example, in the Term data +type above, the type of each constructor must end with Term ty, but +the ty may not be a type variable (e.g. the Lit +constructor). + + + +You cannot use a deriving clause for a GADT; only for +an ordianary data type. + + + +As mentioned in , record syntax is supported. +For example: + + data Term a where + Lit { val :: Int } :: Term Int + Succ { num :: Term Int } :: Term Int + Pred { num :: Term Int } :: Term Int + IsZero { arg :: Term Int } :: Term Bool + Pair { arg1 :: Term a + , arg2 :: Term b + } :: Term (a,b) + If { cnd :: Term Bool + , tru :: Term a + , fls :: Term a + } :: Term a + +However, for GADTs there is the following additional constraint: +every constructor that has a field f must have +the same result type (modulo alpha conversion) +Hence, in the above example, we cannot merge the num +and arg fields above into a +single name. Although their field types are both Term Int, +their selector functions actually have different types: + + + num :: Term Int -> Term Int + arg :: Term Bool -> Term Int + + + + + + + + + + + + +Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal> + + +Haskell 98 allows the programmer to add "deriving( Eq, Ord )" to a data type +declaration, to generate a standard instance declaration for classes specified in the deriving clause. +In Haskell 98, the only classes that may appear in the deriving clause are the standard +classes Eq, Ord, +Enum, Ix, Bounded, Read, and Show. + + +GHC extends this list with two more classes that may be automatically derived +(provided the flag is specified): +Typeable, and Data. These classes are defined in the library +modules Data.Typeable and Data.Generics respectively, and the +appropriate class must be in scope before it can be mentioned in the deriving clause. + +An instance of Typeable can only be derived if the +data type has seven or fewer type parameters, all of kind *. +The reason for this is that the Typeable class is derived using the scheme +described in + +Scrap More Boilerplate: Reflection, Zips, and Generalised Casts +. +(Section 7.4 of the paper describes the multiple Typeable classes that +are used, and only Typeable1 up to +Typeable7 are provided in the library.) +In other cases, there is nothing to stop the programmer writing a TypableX +class, whose kind suits that of the data type constructor, and +then writing the data type instance by hand. + + + + +Generalised derived instances for newtypes + + +When you define an abstract type using newtype, you may want +the new type to inherit some instances from its representation. In +Haskell 98, you can inherit instances of Eq, Ord, +Enum and Bounded by deriving them, but for any +other classes you have to write an explicit instance declaration. For +example, if you define + + + newtype Dollars = Dollars Int + + +and you want to use arithmetic on Dollars, you have to +explicitly define an instance of Num: + + + instance Num Dollars where + Dollars a + Dollars b = Dollars (a+b) + ... + +All the instance does is apply and remove the newtype +constructor. It is particularly galling that, since the constructor +doesn't appear at run-time, this instance declaration defines a +dictionary which is wholly equivalent to the Int +dictionary, only slower! + + + + Generalising the deriving clause + +GHC now permits such instances to be derived instead, so one can write + + newtype Dollars = Dollars Int deriving (Eq,Show,Num) + + +and the implementation uses the same Num dictionary +for Dollars as for Int. Notionally, the compiler +derives an instance declaration of the form + + + instance Num Int => Num Dollars + + +which just adds or removes the newtype constructor according to the type. + + + +We can also derive instances of constructor classes in a similar +way. For example, suppose we have implemented state and failure monad +transformers, such that + + + instance Monad m => Monad (State s m) + instance Monad m => Monad (Failure m) + +In Haskell 98, we can define a parsing monad by + + type Parser tok m a = State [tok] (Failure m) a + + +which is automatically a monad thanks to the instance declarations +above. With the extension, we can make the parser type abstract, +without needing to write an instance of class Monad, via + + + newtype Parser tok m a = Parser (State [tok] (Failure m) a) + deriving Monad + +In this case the derived instance declaration is of the form + + instance Monad (State [tok] (Failure m)) => Monad (Parser tok m) + + +Notice that, since Monad is a constructor class, the +instance is a partial application of the new type, not the +entire left hand side. We can imagine that the type declaration is +``eta-converted'' to generate the context of the instance +declaration. + + + +We can even derive instances of multi-parameter classes, provided the +newtype is the last class parameter. In this case, a ``partial +application'' of the class appears in the deriving +clause. For example, given the class + + + class StateMonad s m | m -> s where ... + instance Monad m => StateMonad s (State s m) where ... + +then we can derive an instance of StateMonad for Parsers by + + newtype Parser tok m a = Parser (State [tok] (Failure m) a) + deriving (Monad, StateMonad [tok]) + + +The derived instance is obtained by completing the application of the +class to the new type: + + + instance StateMonad [tok] (State [tok] (Failure m)) => + StateMonad [tok] (Parser tok m) + + + + +As a result of this extension, all derived instances in newtype + declarations are treated uniformly (and implemented just by reusing +the dictionary for the representation type), except +Show and Read, which really behave differently for +the newtype and its representation. + + + + A more precise specification + +Derived instance declarations are constructed as follows. Consider the +declaration (after expansion of any type synonyms) + + + newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm) + + +where + + + The ci are partial applications of + classes of the form C t1'...tj', where the arity of C + is exactly j+1. That is, C lacks exactly one type argument. + + + The k is chosen so that ci (T v1...vk) is well-kinded. + + + The type t is an arbitrary type. + + + The type variables vk+1...vn do not occur in t, + nor in the ci, and + + + None of the ci is Read, Show, + Typeable, or Data. These classes + should not "look through" the type or its constructor. You can still + derive these classes for a newtype, but it happens in the usual way, not + via this new mechanism. + + +Then, for each ci, the derived instance +declaration is: + + instance ci t => ci (T v1...vk) + +As an example which does not work, consider + + newtype NonMonad m s = NonMonad (State s m s) deriving Monad + +Here we cannot derive the instance + + instance Monad (State s m) => Monad (NonMonad m) + + +because the type variable s occurs in State s m, +and so cannot be "eta-converted" away. It is a good thing that this +deriving clause is rejected, because NonMonad m is +not, in fact, a monad --- for the same reason. Try defining +>>= with the correct type: you won't be able to. + + + +Notice also that the order of class parameters becomes +important, since we can only derive instances for the last one. If the +StateMonad class above were instead defined as + + + class StateMonad m s | m -> s where ... + + +then we would not have been able to derive an instance for the +Parser type above. We hypothesise that multi-parameter +classes usually have one "main" parameter for which deriving new +instances is most interesting. + +Lastly, all of this applies only for classes other than +Read, Show, Typeable, +and Data, for which the built-in derivation applies (section +4.3.3. of the Haskell Report). +(For the standard classes Eq, Ord, +Ix, and Bounded it is immaterial whether +the standard method is used or the one described here.) + + + + + + +Stand-alone deriving declarations + + +GHC now allows stand-alone deriving declarations, enabled by -fglasgow-exts: + + data Foo a = Bar a | Baz String + + derive instance Eq (Foo a) + +The token "derive" is a keyword only when followed by "instance"; +you can use it as a variable name elsewhere. +The stand-alone syntax is generalised for newtypes in exactly the same +way that ordinary deriving clauses are generalised (). +For example: + + newtype Foo a = MkFoo (State Int a) + + derive instance MonadState Int Foo + +GHC always treats the last parameter of the instance +(Foo in this exmample) as the type whose instance is being derived. + + + + + + + + + +Other type system extensions + + +Class declarations + + +This section, and the next one, documents GHC's type-class extensions. +There's lots of background in the paper Type +classes: exploring the design space (Simon Peyton Jones, Mark +Jones, Erik Meijer). + + +All the extensions are enabled by the flag. + + + +Multi-parameter type classes + +Multi-parameter type classes are permitted. For example: + + + + class Collection c a where + union :: c a -> c a -> c a + ...etc. + + + + + + +The superclasses of a class declaration + + +There are no restrictions on the context in a class declaration +(which introduces superclasses), except that the class hierarchy must +be acyclic. So these class declarations are OK: + + + + class Functor (m k) => FiniteMap m k where + ... + + class (Monad m, Monad (t m)) => Transform t m where + lift :: m a -> (t m) a + + + + + +As in Haskell 98, The class hierarchy must be acyclic. However, the definition +of "acyclic" involves only the superclass relationships. For example, +this is OK: + + + + class C a where { + op :: D b => a -> b -> b + } + + class C a => D a where { ... } + + + +Here, C is a superclass of D, but it's OK for a +class operation op of C to mention D. (It +would not be OK for D to be a superclass of C.) + + + + + + + +Class method types + + +Haskell 98 prohibits class method types to mention constraints on the +class type variable, thus: + + class Seq s a where + fromList :: [a] -> s a + elem :: Eq a => a -> s a -> Bool + +The type of elem is illegal in Haskell 98, because it +contains the constraint Eq a, constrains only the +class type variable (in this case a). +GHC lifts this restriction. + + + + + + + +Functional dependencies + + + Functional dependencies are implemented as described by Mark Jones +in “Type Classes with Functional Dependencies”, Mark P. Jones, +In Proceedings of the 9th European Symposium on Programming, +ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782, +. + + +Functional dependencies are introduced by a vertical bar in the syntax of a +class declaration; e.g. + + class (Monad m) => MonadState s m | m -> s where ... + + class Foo a b c | a b -> c where ... + +There should be more documentation, but there isn't (yet). Yell if you need it. + + +Rules for functional dependencies + +In a class declaration, all of the class type variables must be reachable (in the sense +mentioned in ) +from the free variables of each method type. +For example: + + + class Coll s a where + empty :: s + insert :: s -> a -> s + + +is not OK, because the type of empty doesn't mention +a. Functional dependencies can make the type variable +reachable: + + class Coll s a | s -> a where + empty :: s + insert :: s -> a -> s + + +Alternatively Coll might be rewritten + + + class Coll s a where + empty :: s a + insert :: s a -> a -> s a + + + +which makes the connection between the type of a collection of +a's (namely (s a)) and the element type a. +Occasionally this really doesn't work, in which case you can split the +class like this: + + + + class CollE s where + empty :: s + + class CollE s => Coll s a where + insert :: s -> a -> s + + + + + + +Background on functional dependencies + +The following description of the motivation and use of functional dependencies is taken +from the Hugs user manual, reproduced here (with minor changes) by kind +permission of Mark Jones. + + +Consider the following class, intended as part of a +library for collection types: + + class Collects e ce where + empty :: ce + insert :: e -> ce -> ce + member :: e -> ce -> Bool + +The type variable e used here represents the element type, while ce is the type +of the container itself. Within this framework, we might want to define +instances of this class for lists or characteristic functions (both of which +can be used to represent collections of any equality type), bit sets (which can be used to represent collections of characters), or hash tables (which can be used to represent any collection whose elements have a hash function). Omitting standard implementation details, this would lead to the following declarations: @@ -1877,1881 +2498,1569 @@ declarations cannot appear together in the same scope because they violate the dependency for D, even though either one on its own would be acceptable: instance D Bool Int where ... - instance D Bool Char where ... - -Note also that the following declaration is not allowed, even by itself: - - instance D [a] b where ... - -The problem here is that this instance would allow one particular choice of [a] -to be associated with more than one choice for b, which contradicts the -dependency specified in the definition of D. More generally, this means that, -in any instance of the form: - - instance D t s where ... - -for some particular types t and s, the only variables that can appear in s are -the ones that appear in t, and hence, if the type t is known, then s will be -uniquely determined. - - -The benefit of including dependency information is that it allows us to define -more general multiple parameter classes, without ambiguity problems, and with -the benefit of more accurate types. To illustrate this, we return to the -collection class example, and annotate the original definition of Collects -with a simple dependency: - - class Collects e ce | ce -> e where - empty :: ce - insert :: e -> ce -> ce - member :: e -> ce -> Bool - -The dependency ce -> e here specifies that the type e of elements is uniquely -determined by the type of the collection ce. Note that both parameters of -Collects are of kind *; there are no constructor classes here. Note too that -all of the instances of Collects that we gave earlier can be used -together with this new definition. - - -What about the ambiguity problems that we encountered with the original -definition? The empty function still has type Collects e ce => ce, but it is no -longer necessary to regard that as an ambiguous type: Although the variable e -does not appear on the right of the => symbol, the dependency for class -Collects tells us that it is uniquely determined by ce, which does appear on -the right of the => symbol. Hence the context in which empty is used can still -give enough information to determine types for both ce and e, without -ambiguity. More generally, we need only regard a type as ambiguous if it -contains a variable on the left of the => that is not uniquely determined -(either directly or indirectly) by the variables on the right. - - -Dependencies also help to produce more accurate types for user defined -functions, and hence to provide earlier detection of errors, and less cluttered -types for programmers to work with. Recall the previous definition for a -function f: - - f x y = insert x y = insert x . insert y - -for which we originally obtained a type: - - f :: (Collects a c, Collects b c) => a -> b -> c -> c - -Given the dependency information that we have for Collects, however, we can -deduce that a and b must be equal because they both appear as the second -parameter in a Collects constraint with the same first parameter c. Hence we -can infer a shorter and more accurate type for f: - - f :: (Collects a c) => a -> a -> c -> c - -In a similar way, the earlier definition of g will now be flagged as a type error. - - -Although we have given only a few examples here, it should be clear that the -addition of dependency information can help to make multiple parameter classes -more useful in practice, avoiding ambiguity problems, and allowing more general -sets of instance declarations. - - - - - - -Instance declarations - - -Relaxed rules for instance declarations - -An instance declaration has the form - - instance ( assertion1, ..., assertionn) => class type1 ... typem where ... - -The part before the "=>" is the -context, while the part after the -"=>" is the head of the instance declaration. - - - -In Haskell 98 the head of an instance declaration -must be of the form C (T a1 ... an), where -C is the class, T is a type constructor, -and the a1 ... an are distinct type variables. -Furthermore, the assertions in the context of the instance declaration -must be of the form C a where a -is a type variable that occurs in the head. - - -The flag loosens these restrictions -considerably. Firstly, multi-parameter type classes are permitted. Secondly, -the context and head of the instance declaration can each consist of arbitrary -(well-kinded) assertions (C t1 ... tn) subject only to the -following rules: - - -For each assertion in the context: - -No type variable has more occurrences in the assertion than in the head -The assertion has fewer constructors and variables (taken together - and counting repetitions) than the head - - - -The coverage condition. For each functional dependency, -tvsleft -> -tvsright, of the class, -every type variable in -S(tvsright) must appear in -S(tvsleft), where S is the -substitution mapping each type variable in the class declaration to the -corresponding type in the instance declaration. - - -These restrictions ensure that context reduction terminates: each reduction -step makes the problem smaller by at least one -constructor. For example, the following would make the type checker -loop if it wasn't excluded: - - instance C a => C a where ... - -For example, these are OK: - - instance C Int [a] -- Multiple parameters - instance Eq (S [a]) -- Structured type in head - - -- Repeated type variable in head - instance C4 a a => C4 [a] [a] - instance Stateful (ST s) (MutVar s) - - -- Head can consist of type variables only - instance C a - instance (Eq a, Show b) => C2 a b - - -- Non-type variables in context - instance Show (s a) => Show (Sized s a) - instance C2 Int a => C3 Bool [a] - instance C2 Int a => C3 [a] b - -But these are not: - - -- Context assertion no smaller than head - instance C a => C a where ... - -- (C b b) has more more occurrences of b than the head - instance C b b => Foo [b] where ... - - - - -The same restrictions apply to instances generated by -deriving clauses. Thus the following is accepted: - - data MinHeap h a = H a (h a) - deriving (Show) - -because the derived instance - - instance (Show a, Show (h a)) => Show (MinHeap h a) - -conforms to the above rules. - - - -A useful idiom permitted by the above rules is as follows. -If one allows overlapping instance declarations then it's quite -convenient to have a "default instance" declaration that applies if -something more specific does not: - - instance C a where - op = ... -- Default - - -You can find lots of background material about the reason for these -restrictions in the paper -Understanding functional dependencies via Constraint Handling Rules. - - - - -Undecidable instances - - -Sometimes even the rules of are too onerous. -For example, sometimes you might want to use the following to get the -effect of a "class synonym": - - class (C1 a, C2 a, C3 a) => C a where { } - - instance (C1 a, C2 a, C3 a) => C a where { } - -This allows you to write shorter signatures: - - f :: C a => ... - -instead of - - f :: (C1 a, C2 a, C3 a) => ... - -The restrictions on functional dependencies () are particularly troublesome. -It is tempting to introduce type variables in the context that do not appear in -the head, something that is excluded by the normal rules. For example: - - class HasConverter a b | a -> b where - convert :: a -> b - - data Foo a = MkFoo a - - instance (HasConverter a b,Show b) => Show (Foo a) where - show (MkFoo value) = show (convert value) - -This is dangerous territory, however. Here, for example, is a program that would make the -typechecker loop: - - class D a - class F a b | a->b - instance F [a] [[a]] - instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head - -Similarly, it can be tempting to lift the coverage condition: - - class Mul a b c | a b -> c where - (.*.) :: a -> b -> c - - instance Mul Int Int Int where (.*.) = (*) - instance Mul Int Float Float where x .*. y = fromIntegral x * y - instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v + instance D Bool Char where ... -The third instance declaration does not obey the coverage condition; -and indeed the (somewhat strange) definition: +Note also that the following declaration is not allowed, even by itself: - f = \ b x y -> if b then x .*. [y] else y + instance D [a] b where ... -makes instance inference go into a loop, because it requires the constraint -(Mul a [b] b). - - -Nevertheless, GHC allows you to experiment with more liberal rules. If you use -the experimental flag --fallow-undecidable-instances -option, you can use arbitrary -types in both an instance context and instance head. Termination is ensured by having a -fixed-depth recursion stack. If you exceed the stack depth you get a -sort of backtrace, and the opportunity to increase the stack depth -with N. - - - - - - -Overlapping instances - -In general, GHC requires that that it be unambiguous which instance -declaration -should be used to resolve a type-class constraint. This behaviour -can be modified by two flags: --fallow-overlapping-instances - -and --fallow-incoherent-instances -, as this section discusses. Both these -flags are dynamic flags, and can be set on a per-module basis, using -an OPTIONS_GHC pragma if desired (). - -When GHC tries to resolve, say, the constraint C Int Bool, -it tries to match every instance declaration against the -constraint, -by instantiating the head of the instance declaration. For example, consider -these declarations: +The problem here is that this instance would allow one particular choice of [a] +to be associated with more than one choice for b, which contradicts the +dependency specified in the definition of D. More generally, this means that, +in any instance of the form: - instance context1 => C Int a where ... -- (A) - instance context2 => C a Bool where ... -- (B) - instance context3 => C Int [a] where ... -- (C) - instance context4 => C Int [Int] where ... -- (D) + instance D t s where ... -The instances (A) and (B) match the constraint C Int Bool, -but (C) and (D) do not. When matching, GHC takes -no account of the context of the instance declaration -(context1 etc). -GHC's default behaviour is that exactly one instance must match the -constraint it is trying to resolve. -It is fine for there to be a potential of overlap (by -including both declarations (A) and (B), say); an error is only reported if a -particular constraint matches more than one. - - - -The flag instructs GHC to allow -more than one instance to match, provided there is a most specific one. For -example, the constraint C Int [Int] matches instances (A), -(C) and (D), but the last is more specific, and hence is chosen. If there is no -most-specific match, the program is rejected. +for some particular types t and s, the only variables that can appear in s are +the ones that appear in t, and hence, if the type t is known, then s will be +uniquely determined. -However, GHC is conservative about committing to an overlapping instance. For example: +The benefit of including dependency information is that it allows us to define +more general multiple parameter classes, without ambiguity problems, and with +the benefit of more accurate types. To illustrate this, we return to the +collection class example, and annotate the original definition of Collects +with a simple dependency: - f :: [b] -> [b] - f x = ... + class Collects e ce | ce -> e where + empty :: ce + insert :: e -> ce -> ce + member :: e -> ce -> Bool -Suppose that from the RHS of f we get the constraint -C Int [b]. But -GHC does not commit to instance (C), because in a particular -call of f, b might be instantiate -to Int, in which case instance (D) would be more specific still. -So GHC rejects the program. If you add the flag , -GHC will instead pick (C), without complaining about -the problem of subsequent instantiations. - - -The willingness to be overlapped or incoherent is a property of -the instance declaration itself, controlled by the -presence or otherwise of the -and flags when that mdodule is -being defined. Neither flag is required in a module that imports and uses the -instance declaration. Specifically, during the lookup process: - - -An instance declaration is ignored during the lookup process if (a) a more specific -match is found, and (b) the instance declaration was compiled with -. The flag setting for the -more-specific instance does not matter. - - -Suppose an instance declaration does not matche the constraint being looked up, but -does unify with it, so that it might match when the constraint is further -instantiated. Usually GHC will regard this as a reason for not committing to -some other constraint. But if the instance declaration was compiled with -, GHC will skip the "does-it-unify?" -check for that declaration. - - -These rules make it possible for a library author to design a library that relies on -overlapping instances without the library client having to know. +The dependency ce -> e here specifies that the type e of elements is uniquely +determined by the type of the collection ce. Note that both parameters of +Collects are of kind *; there are no constructor classes here. Note too that +all of the instances of Collects that we gave earlier can be used +together with this new definition. -If an instance declaration is compiled without -, -then that instance can never be overlapped. This could perhaps be -inconvenient. Perhaps the rule should instead say that the -overlapping instance declaration should be compiled in -this way, rather than the overlapped one. Perhaps overlap -at a usage site should be permitted regardless of how the instance declarations -are compiled, if the flag is -used at the usage site. (Mind you, the exact usage site can occasionally be -hard to pin down.) We are interested to receive feedback on these points. - -The flag implies the - flag, but not vice versa. +What about the ambiguity problems that we encountered with the original +definition? The empty function still has type Collects e ce => ce, but it is no +longer necessary to regard that as an ambiguous type: Although the variable e +does not appear on the right of the => symbol, the dependency for class +Collects tells us that it is uniquely determined by ce, which does appear on +the right of the => symbol. Hence the context in which empty is used can still +give enough information to determine types for both ce and e, without +ambiguity. More generally, we need only regard a type as ambiguous if it +contains a variable on the left of the => that is not uniquely determined +(either directly or indirectly) by the variables on the right. - - - -Type synonyms in the instance head - -Unlike Haskell 98, instance heads may use type -synonyms. (The instance "head" is the bit after the "=>" in an instance decl.) -As always, using a type synonym is just shorthand for -writing the RHS of the type synonym definition. For example: - - +Dependencies also help to produce more accurate types for user defined +functions, and hence to provide earlier detection of errors, and less cluttered +types for programmers to work with. Recall the previous definition for a +function f: - type Point = (Int,Int) - instance C Point where ... - instance C [Point] where ... + f x y = insert x y = insert x . insert y - - -is legal. However, if you added - - +for which we originally obtained a type: - instance C (Int,Int) where ... + f :: (Collects a c, Collects b c) => a -> b -> c -> c - - -as well, then the compiler will complain about the overlapping -(actually, identical) instance declarations. As always, type synonyms -must be fully applied. You cannot, for example, write: - - +Given the dependency information that we have for Collects, however, we can +deduce that a and b must be equal because they both appear as the second +parameter in a Collects constraint with the same first parameter c. Hence we +can infer a shorter and more accurate type for f: - type P a = [[a]] - instance Monad P where ... + f :: (Collects a c) => a -> a -> c -> c - - -This design decision is independent of all the others, and easily -reversed, but it makes sense to me. - +In a similar way, the earlier definition of g will now be flagged as a type error. + + +Although we have given only a few examples here, it should be clear that the +addition of dependency information can help to make multiple parameter classes +more useful in practice, avoiding ambiguity problems, and allowing more general +sets of instance declarations. + - - - -Type signatures - -The context of a type signature - -Unlike Haskell 98, constraints in types do not have to be of -the form (class type-variable) or -(class (type-variable type-variable ...)). Thus, -these type signatures are perfectly OK - - g :: Eq [a] => ... - g :: Ord (T a ()) => ... - - - -GHC imposes the following restrictions on the constraints in a type signature. -Consider the type: + +Instance declarations - - forall tv1..tvn (c1, ...,cn) => type - + +Relaxed rules for instance declarations -(Here, we write the "foralls" explicitly, although the Haskell source -language omits them; in Haskell 98, all the free type variables of an -explicit source-language type signature are universally quantified, -except for the class type variables in a class declaration. However, -in GHC, you can give the foralls if you want. See ). +An instance declaration has the form + + instance ( assertion1, ..., assertionn) => class type1 ... typem where ... + +The part before the "=>" is the +context, while the part after the +"=>" is the head of the instance declaration. - +In Haskell 98 the head of an instance declaration +must be of the form C (T a1 ... an), where +C is the class, T is a type constructor, +and the a1 ... an are distinct type variables. +Furthermore, the assertions in the context of the instance declaration +must be of the form C a where a +is a type variable that occurs in the head. + + +The flag loosens these restrictions +considerably. Firstly, multi-parameter type classes are permitted. Secondly, +the context and head of the instance declaration can each consist of arbitrary +(well-kinded) assertions (C t1 ... tn) subject only to the +following rules: - + +The Paterson Conditions: for each assertion in the context + +No type variable has more occurrences in the assertion than in the head +The assertion has fewer constructors and variables (taken together + and counting repetitions) than the head + + +The Coverage Condition. For each functional dependency, +tvsleft -> +tvsright, of the class, +every type variable in +S(tvsright) must appear in +S(tvsleft), where S is the +substitution mapping each type variable in the class declaration to the +corresponding type in the instance declaration. + + +These restrictions ensure that context reduction terminates: each reduction +step makes the problem smaller by at least one +constructor. Both the Paterson Conditions and the Coverage Condition are lifted +if you give the +flag (). +You can find lots of background material about the reason for these +restrictions in the paper +Understanding functional dependencies via Constraint Handling Rules. + - Each universally quantified type variable -tvi must be reachable from type. +For example, these are OK: + + instance C Int [a] -- Multiple parameters + instance Eq (S [a]) -- Structured type in head -A type variable a is "reachable" if it it appears -in the same constraint as either a type variable free in in -type, or another reachable type variable. -A value with a type that does not obey -this reachability restriction cannot be used without introducing -ambiguity; that is why the type is rejected. -Here, for example, is an illegal type: + -- Repeated type variable in head + instance C4 a a => C4 [a] [a] + instance Stateful (ST s) (MutVar s) + -- Head can consist of type variables only + instance C a + instance (Eq a, Show b) => C2 a b - - forall a. Eq a => Int + -- Non-type variables in context + instance Show (s a) => Show (Sized s a) + instance C2 Int a => C3 Bool [a] + instance C2 Int a => C3 [a] b - - -When a value with this type was used, the constraint Eq tv -would be introduced where tv is a fresh type variable, and -(in the dictionary-translation implementation) the value would be -applied to a dictionary for Eq tv. The difficulty is that we -can never know which instance of Eq to use because we never -get any more information about tv. - - -Note -that the reachability condition is weaker than saying that a is -functionally dependent on a type variable free in -type (see ). The reason for this is there -might be a "hidden" dependency, in a superclass perhaps. So -"reachable" is a conservative approximation to "functionally dependent". -For example, consider: +But these are not: - class C a b | a -> b where ... - class C a b => D a b where ... - f :: forall a b. D a b => a -> a + -- Context assertion no smaller than head + instance C a => C a where ... + -- (C b b) has more more occurrences of b than the head + instance C b b => Foo [b] where ... -This is fine, because in fact a does functionally determine b -but that is not immediately apparent from f's type. - - - Every constraint ci must mention at least one of the -universally quantified type variables tvi. - -For example, this type is OK because C a b mentions the -universally quantified type variable b: - - +The same restrictions apply to instances generated by +deriving clauses. Thus the following is accepted: - forall a. C a b => burble + data MinHeap h a = H a (h a) + deriving (Show) - - -The next type is illegal because the constraint Eq b does not -mention a: - - +because the derived instance - forall a. Eq b => burble + instance (Show a, Show (h a)) => Show (MinHeap h a) - - -The reason for this restriction is milder than the other one. The -excluded types are never useful or necessary (because the offending -context doesn't need to be witnessed at this point; it can be floated -out). Furthermore, floating them out increases sharing. Lastly, -excluding them is a conservative choice; it leaves a patch of -territory free in case we need it later. - +conforms to the above rules. - - - + +A useful idiom permitted by the above rules is as follows. +If one allows overlapping instance declarations then it's quite +convenient to have a "default instance" declaration that applies if +something more specific does not: + + instance C a where + op = ... -- Default + - -For-all hoisting + +Undecidable instances + -It is often convenient to use generalised type synonyms (see ) at the right hand -end of an arrow, thus: +Sometimes even the rules of are too onerous. +For example, sometimes you might want to use the following to get the +effect of a "class synonym": - type Discard a = forall b. a -> b -> a + class (C1 a, C2 a, C3 a) => C a where { } - g :: Int -> Discard Int - g x y z = x+y + instance (C1 a, C2 a, C3 a) => C a where { } -Simply expanding the type synonym would give +This allows you to write shorter signatures: - g :: Int -> (forall b. Int -> b -> Int) + f :: C a => ... -but GHC "hoists" the forall to give the isomorphic type +instead of - g :: forall b. Int -> Int -> b -> Int + f :: (C1 a, C2 a, C3 a) => ... -In general, the rule is this: to determine the type specified by any explicit -user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly -performs the transformation: +The restrictions on functional dependencies () are particularly troublesome. +It is tempting to introduce type variables in the context that do not appear in +the head, something that is excluded by the normal rules. For example: - type1 -> forall a1..an. context2 => type2 -==> - forall a1..an. context2 => type1 -> type2 + class HasConverter a b | a -> b where + convert :: a -> b + + data Foo a = MkFoo a + + instance (HasConverter a b,Show b) => Show (Foo a) where + show (MkFoo value) = show (convert value) -(In fact, GHC tries to retain as much synonym information as possible for use in -error messages, but that is a usability issue.) This rule applies, of course, whether -or not the forall comes from a synonym. For example, here is another -valid way to write g's type signature: +This is dangerous territory, however. Here, for example, is a program that would make the +typechecker loop: - g :: Int -> Int -> forall b. b -> Int - - - -When doing this hoisting operation, GHC eliminates duplicate constraints. For -example: + class D a + class F a b | a->b + instance F [a] [[a]] + instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head + +Similarly, it can be tempting to lift the coverage condition: - type Foo a = (?x::Int) => Bool -> a - g :: Foo (Foo Int) + class Mul a b c | a b -> c where + (.*.) :: a -> b -> c + + instance Mul Int Int Int where (.*.) = (*) + instance Mul Int Float Float where x .*. y = fromIntegral x * y + instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v -means +The third instance declaration does not obey the coverage condition; +and indeed the (somewhat strange) definition: - g :: (?x::Int) => Bool -> Bool -> Int + f = \ b x y -> if b then x .*. [y] else y +makes instance inference go into a loop, because it requires the constraint +(Mul a [b] b). - - - - - - -Implicit parameters - - Implicit parameters are implemented as described in -"Implicit parameters: dynamic scoping with static types", -J Lewis, MB Shields, E Meijer, J Launchbury, -27th ACM Symposium on Principles of Programming Languages (POPL'00), -Boston, Jan 2000. + +Nevertheless, GHC allows you to experiment with more liberal rules. If you use +the experimental flag +-X=AllowUndecidableInstances, +both the Paterson Conditions and the Coverage Condition +(described in ) are lifted. Termination is ensured by having a +fixed-depth recursion stack. If you exceed the stack depth you get a +sort of backtrace, and the opportunity to increase the stack depth +with N. -(Most of the following, stil rather incomplete, documentation is -due to Jeff Lewis.) + -Implicit parameter support is enabled with the option -. + +Overlapping instances -A variable is called dynamically bound when it is bound by the calling -context of a function and statically bound when bound by the callee's -context. In Haskell, all variables are statically bound. Dynamic -binding of variables is a notion that goes back to Lisp, but was later -discarded in more modern incarnations, such as Scheme. Dynamic binding -can be very confusing in an untyped language, and unfortunately, typed -languages, in particular Hindley-Milner typed languages like Haskell, -only support static scoping of variables. - - -However, by a simple extension to the type class system of Haskell, we -can support dynamic binding. Basically, we express the use of a -dynamically bound variable as a constraint on the type. These -constraints lead to types of the form (?x::t') => t, which says "this -function uses a dynamically-bound variable ?x -of type t'". For -example, the following expresses the type of a sort function, -implicitly parameterized by a comparison function named cmp. - - sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] - -The dynamic binding constraints are just a new form of predicate in the type class system. - - -An implicit parameter occurs in an expression using the special form ?x, -where x is -any valid identifier (e.g. ord ?x is a valid expression). -Use of this construct also introduces a new -dynamic-binding constraint in the type of the expression. -For example, the following definition -shows how we can define an implicitly parameterized sort function in -terms of an explicitly parameterized sortBy function: - - sortBy :: (a -> a -> Bool) -> [a] -> [a] - - sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] - sort = sortBy ?cmp - - - - -Implicit-parameter type constraints +In general, GHC requires that that it be unambiguous which instance +declaration +should be used to resolve a type-class constraint. This behaviour +can be modified by two flags: +-X=AllowOverlappingInstances + +and +-X=AllowIncoherentInstances +, as this section discusses. Both these +flags are dynamic flags, and can be set on a per-module basis, using +an OPTIONS_GHC pragma if desired (). -Dynamic binding constraints behave just like other type class -constraints in that they are automatically propagated. Thus, when a -function is used, its implicit parameters are inherited by the -function that called it. For example, our sort function might be used -to pick out the least value in a list: +When GHC tries to resolve, say, the constraint C Int Bool, +it tries to match every instance declaration against the +constraint, +by instantiating the head of the instance declaration. For example, consider +these declarations: - least :: (?cmp :: a -> a -> Bool) => [a] -> a - least xs = head (sort xs) + instance context1 => C Int a where ... -- (A) + instance context2 => C a Bool where ... -- (B) + instance context3 => C Int [a] where ... -- (C) + instance context4 => C Int [Int] where ... -- (D) -Without lifting a finger, the ?cmp parameter is -propagated to become a parameter of least as well. With explicit -parameters, the default is that parameters must always be explicit -propagated. With implicit parameters, the default is to always -propagate them. - - -An implicit-parameter type constraint differs from other type class constraints in the -following way: All uses of a particular implicit parameter must have -the same type. This means that the type of (?x, ?x) -is (?x::a) => (a,a), and not -(?x::a, ?x::b) => (a, b), as would be the case for type -class constraints. +The instances (A) and (B) match the constraint C Int Bool, +but (C) and (D) do not. When matching, GHC takes +no account of the context of the instance declaration +(context1 etc). +GHC's default behaviour is that exactly one instance must match the +constraint it is trying to resolve. +It is fine for there to be a potential of overlap (by +including both declarations (A) and (B), say); an error is only reported if a +particular constraint matches more than one. - You can't have an implicit parameter in the context of a class or instance -declaration. For example, both these declarations are illegal: - - class (?x::Int) => C a where ... - instance (?x::a) => Foo [a] where ... - -Reason: exactly which implicit parameter you pick up depends on exactly where -you invoke a function. But the ``invocation'' of instance declarations is done -behind the scenes by the compiler, so it's hard to figure out exactly where it is done. -Easiest thing is to outlaw the offending types. -Implicit-parameter constraints do not cause ambiguity. For example, consider: - - f :: (?x :: [a]) => Int -> Int - f n = n + length ?x - - g :: (Read a, Show a) => String -> String - g s = show (read s) - -Here, g has an ambiguous type, and is rejected, but f -is fine. The binding for ?x at f's call site is -quite unambiguous, and fixes the type a. +The flag instructs GHC to allow +more than one instance to match, provided there is a most specific one. For +example, the constraint C Int [Int] matches instances (A), +(C) and (D), but the last is more specific, and hence is chosen. If there is no +most-specific match, the program is rejected. - - - -Implicit-parameter bindings - -An implicit parameter is bound using the standard -let or where binding forms. -For example, we define the min function by binding -cmp. +However, GHC is conservative about committing to an overlapping instance. For example: - min :: [a] -> a - min = let ?cmp = (<=) in least + f :: [b] -> [b] + f x = ... +Suppose that from the RHS of f we get the constraint +C Int [b]. But +GHC does not commit to instance (C), because in a particular +call of f, b might be instantiate +to Int, in which case instance (D) would be more specific still. +So GHC rejects the program. If you add the flag , +GHC will instead pick (C), without complaining about +the problem of subsequent instantiations. -A group of implicit-parameter bindings may occur anywhere a normal group of Haskell -bindings can occur, except at top level. That is, they can occur in a let -(including in a list comprehension, or do-notation, or pattern guards), -or a where clause. -Note the following points: +The willingness to be overlapped or incoherent is a property of +the instance declaration itself, controlled by the +presence or otherwise of the +and flags when that mdodule is +being defined. Neither flag is required in a module that imports and uses the +instance declaration. Specifically, during the lookup process: -An implicit-parameter binding group must be a -collection of simple bindings to implicit-style variables (no -function-style bindings, and no type signatures); these bindings are -neither polymorphic or recursive. - - -You may not mix implicit-parameter bindings with ordinary bindings in a -single let -expression; use two nested lets instead. -(In the case of where you are stuck, since you can't nest where clauses.) +An instance declaration is ignored during the lookup process if (a) a more specific +match is found, and (b) the instance declaration was compiled with +. The flag setting for the +more-specific instance does not matter. - -You may put multiple implicit-parameter bindings in a -single binding group; but they are not treated -as a mutually recursive group (as ordinary let bindings are). -Instead they are treated as a non-recursive group, simultaneously binding all the implicit -parameter. The bindings are not nested, and may be re-ordered without changing -the meaning of the program. -For example, consider: - - f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y - -The use of ?x in the binding for ?y does not "see" -the binding for ?x, so the type of f is - - f :: (?x::Int) => Int -> Int - +Suppose an instance declaration does not matche the constraint being looked up, but +does unify with it, so that it might match when the constraint is further +instantiated. Usually GHC will regard this as a reason for not committing to +some other constraint. But if the instance declaration was compiled with +, GHC will skip the "does-it-unify?" +check for that declaration. +These rules make it possible for a library author to design a library that relies on +overlapping instances without the library client having to know. + + +If an instance declaration is compiled without +, +then that instance can never be overlapped. This could perhaps be +inconvenient. Perhaps the rule should instead say that the +overlapping instance declaration should be compiled in +this way, rather than the overlapped one. Perhaps overlap +at a usage site should be permitted regardless of how the instance declarations +are compiled, if the flag is +used at the usage site. (Mind you, the exact usage site can occasionally be +hard to pin down.) We are interested to receive feedback on these points. + +The flag implies the + flag, but not vice versa. - -Implicit parameters and polymorphic recursion + +Type synonyms in the instance head -Consider these two definitions: - - len1 :: [a] -> Int - len1 xs = let ?acc = 0 in len_acc1 xs - - len_acc1 [] = ?acc - len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs - - ------------ - - len2 :: [a] -> Int - len2 xs = let ?acc = 0 in len_acc2 xs - - len_acc2 :: (?acc :: Int) => [a] -> Int - len_acc2 [] = ?acc - len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs - -The only difference between the two groups is that in the second group -len_acc is given a type signature. -In the former case, len_acc1 is monomorphic in its own -right-hand side, so the implicit parameter ?acc is not -passed to the recursive call. In the latter case, because len_acc2 -has a type signature, the recursive call is made to the -polymoprhic version, which takes ?acc -as an implicit parameter. So we get the following results in GHCi: - - Prog> len1 "hello" - 0 - Prog> len2 "hello" - 5 - -Adding a type signature dramatically changes the result! This is a rather -counter-intuitive phenomenon, worth watching out for. - - +Unlike Haskell 98, instance heads may use type +synonyms. (The instance "head" is the bit after the "=>" in an instance decl.) +As always, using a type synonym is just shorthand for +writing the RHS of the type synonym definition. For example: -Implicit parameters and monomorphism -GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the -Haskell Report) to implicit parameters. For example, consider: - f :: Int -> Int - f v = let ?x = 0 in - let y = ?x + v in - let ?x = 5 in - y + type Point = (Int,Int) + instance C Point where ... + instance C [Point] where ... -Since the binding for y falls under the Monomorphism -Restriction it is not generalised, so the type of y is -simply Int, not (?x::Int) => Int. -Hence, (f 9) returns result 9. -If you add a type signature for y, then y -will get type (?x::Int) => Int, so the occurrence of -y in the body of the let will see the -inner binding of ?x, so (f 9) will return -14. - - - - +The next type is illegal because the constraint Eq b does not +mention a: - -Explicitly-kinded quantification - -Haskell infers the kind of each type variable. Sometimes it is nice to be able -to give the kind explicitly as (machine-checked) documentation, -just as it is nice to give a type signature for a function. On some occasions, -it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999) -John Hughes had to define the data type: - - data Set cxt a = Set [a] - | Unused (cxt a -> ()) - -The only use for the Unused constructor was to force the correct -kind for the type variable cxt. - - -GHC now instead allows you to specify the kind of a type variable directly, wherever -a type variable is explicitly bound. Namely: - -data declarations: - - data Set (cxt :: * -> *) a = Set [a] - -type declarations: - - type T (f :: * -> *) = f Int - -class declarations: - - class (Eq a) => C (f :: * -> *) a where ... - -forall's in type signatures: - - f :: forall (cxt :: * -> *). Set cxt Int - - - + + forall a. Eq b => burble + + + +The reason for this restriction is milder than the other one. The +excluded types are never useful or necessary (because the offending +context doesn't need to be witnessed at this point; it can be floated +out). Furthermore, floating them out increases sharing. Lastly, +excluding them is a conservative choice; it leaves a patch of +territory free in case we need it later. - -The parentheses are required. Some of the spaces are required too, to -separate the lexemes. If you write (f::*->*) you -will get a parse error, because "::*->*" is a -single lexeme in Haskell. + + + - -As part of the same extension, you can put kind annotations in types -as well. Thus: - - f :: (Int :: *) -> Int - g :: forall a. a -> (a :: *) - -The syntax is - - atype ::= '(' ctype '::' kind ') - -The parentheses are required. + + + + + +Implicit parameters - -Arbitrary-rank polymorphism - + Implicit parameters are implemented as described in +"Implicit parameters: dynamic scoping with static types", +J Lewis, MB Shields, E Meijer, J Launchbury, +27th ACM Symposium on Principles of Programming Languages (POPL'00), +Boston, Jan 2000. + + +(Most of the following, stil rather incomplete, documentation is +due to Jeff Lewis.) + +Implicit parameter support is enabled with the option +. -Haskell type signatures are implicitly quantified. The new keyword forall -allows us to say exactly what this means. For example: +A variable is called dynamically bound when it is bound by the calling +context of a function and statically bound when bound by the callee's +context. In Haskell, all variables are statically bound. Dynamic +binding of variables is a notion that goes back to Lisp, but was later +discarded in more modern incarnations, such as Scheme. Dynamic binding +can be very confusing in an untyped language, and unfortunately, typed +languages, in particular Hindley-Milner typed languages like Haskell, +only support static scoping of variables. +However, by a simple extension to the type class system of Haskell, we +can support dynamic binding. Basically, we express the use of a +dynamically bound variable as a constraint on the type. These +constraints lead to types of the form (?x::t') => t, which says "this +function uses a dynamically-bound variable ?x +of type t'". For +example, the following expresses the type of a sort function, +implicitly parameterized by a comparison function named cmp. - g :: b -> b - -means this: - - g :: forall b. (b -> b) + sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] -The two are treated identically. +The dynamic binding constraints are just a new form of predicate in the type class system. - -However, GHC's type system supports arbitrary-rank -explicit universal quantification in -types. -For example, all the following types are legal: +An implicit parameter occurs in an expression using the special form ?x, +where x is +any valid identifier (e.g. ord ?x is a valid expression). +Use of this construct also introduces a new +dynamic-binding constraint in the type of the expression. +For example, the following definition +shows how we can define an implicitly parameterized sort function in +terms of an explicitly parameterized sortBy function: - f1 :: forall a b. a -> b -> a - g1 :: forall a b. (Ord a, Eq b) => a -> b -> a - - f2 :: (forall a. a->a) -> Int -> Int - g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int + sortBy :: (a -> a -> Bool) -> [a] -> [a] - f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool + sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] + sort = sortBy ?cmp -Here, f1 and g1 are rank-1 types, and -can be written in standard Haskell (e.g. f1 :: a->b->a). -The forall makes explicit the universal quantification that -is implicitly added by Haskell. - - -The functions f2 and g2 have rank-2 types; -the forall is on the left of a function arrow. As g2 -shows, the polymorphic type on the left of the function arrow can be overloaded. - - -The function f3 has a rank-3 type; -it has rank-2 types on the left of a function arrow. + + +Implicit-parameter type constraints -GHC allows types of arbitrary rank; you can nest foralls -arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but -that restriction has now been lifted.) -In particular, a forall-type (also called a "type scheme"), -including an operational type class context, is legal: - - On the left of a function arrow - On the right of a function arrow (see ) - As the argument of a constructor, or type of a field, in a data type declaration. For -example, any of the f1,f2,f3,g1,g2 above would be valid -field type signatures. - As the type of an implicit parameter - In a pattern type signature (see ) - -There is one place you cannot put a forall: -you cannot instantiate a type variable with a forall-type. So you cannot -make a forall-type the argument of a type constructor. So these types are illegal: +Dynamic binding constraints behave just like other type class +constraints in that they are automatically propagated. Thus, when a +function is used, its implicit parameters are inherited by the +function that called it. For example, our sort function might be used +to pick out the least value in a list: - x1 :: [forall a. a->a] - x2 :: (forall a. a->a, Int) - x3 :: Maybe (forall a. a->a) + least :: (?cmp :: a -> a -> Bool) => [a] -> a + least xs = head (sort xs) -Of course forall becomes a keyword; you can't use forall as -a type variable any more! +Without lifting a finger, the ?cmp parameter is +propagated to become a parameter of least as well. With explicit +parameters, the default is that parameters must always be explicit +propagated. With implicit parameters, the default is to always +propagate them. - - - -Examples - - -In a data or newtype declaration one can quantify -the types of the constructor arguments. Here are several examples: +An implicit-parameter type constraint differs from other type class constraints in the +following way: All uses of a particular implicit parameter must have +the same type. This means that the type of (?x, ?x) +is (?x::a) => (a,a), and not +(?x::a, ?x::b) => (a, b), as would be the case for type +class constraints. + You can't have an implicit parameter in the context of a class or instance +declaration. For example, both these declarations are illegal: + + class (?x::Int) => C a where ... + instance (?x::a) => Foo [a] where ... + +Reason: exactly which implicit parameter you pick up depends on exactly where +you invoke a function. But the ``invocation'' of instance declarations is done +behind the scenes by the compiler, so it's hard to figure out exactly where it is done. +Easiest thing is to outlaw the offending types. - +Implicit-parameter constraints do not cause ambiguity. For example, consider: -data T a = T1 (forall b. b -> b -> b) a - -data MonadT m = MkMonad { return :: forall a. a -> m a, - bind :: forall a b. m a -> (a -> m b) -> m b - } + f :: (?x :: [a]) => Int -> Int + f n = n + length ?x -newtype Swizzle = MkSwizzle (Ord a => [a] -> [a]) + g :: (Read a, Show a) => String -> String + g s = show (read s) - +Here, g has an ambiguous type, and is rejected, but f +is fine. The binding for ?x at f's call site is +quite unambiguous, and fixes the type a. + + + +Implicit-parameter bindings -The constructors have rank-2 types: +An implicit parameter is bound using the standard +let or where binding forms. +For example, we define the min function by binding +cmp. + + min :: [a] -> a + min = let ?cmp = (<=) in least + - +A group of implicit-parameter bindings may occur anywhere a normal group of Haskell +bindings can occur, except at top level. That is, they can occur in a let +(including in a list comprehension, or do-notation, or pattern guards), +or a where clause. +Note the following points: + + +An implicit-parameter binding group must be a +collection of simple bindings to implicit-style variables (no +function-style bindings, and no type signatures); these bindings are +neither polymorphic or recursive. + + +You may not mix implicit-parameter bindings with ordinary bindings in a +single let +expression; use two nested lets instead. +(In the case of where you are stuck, since you can't nest where clauses.) + + +You may put multiple implicit-parameter bindings in a +single binding group; but they are not treated +as a mutually recursive group (as ordinary let bindings are). +Instead they are treated as a non-recursive group, simultaneously binding all the implicit +parameter. The bindings are not nested, and may be re-ordered without changing +the meaning of the program. +For example, consider: -T1 :: forall a. (forall b. b -> b -> b) -> a -> T a -MkMonad :: forall m. (forall a. a -> m a) - -> (forall a b. m a -> (a -> m b) -> m b) - -> MonadT m -MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle + f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y - +The use of ?x in the binding for ?y does not "see" +the binding for ?x, so the type of f is + + f :: (?x::Int) => Int -> Int + + + - -Notice that you don't need to use a forall if there's an -explicit context. For example in the first argument of the -constructor MkSwizzle, an implicit "forall a." is -prefixed to the argument type. The implicit forall -quantifies all type variables that are not already in scope, and are -mentioned in the type quantified over. - + - -As for type signatures, implicit quantification happens for non-overloaded -types too. So if you write this: +Implicit parameters and polymorphic recursion + +Consider these two definitions: - data T a = MkT (Either a b) (b -> b) - + len1 :: [a] -> Int + len1 xs = let ?acc = 0 in len_acc1 xs -it's just as if you had written this: + len_acc1 [] = ?acc + len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs - - data T a = MkT (forall b. Either a b) (forall b. b -> b) - + ------------ -That is, since the type variable b isn't in scope, it's -implicitly universally quantified. (Arguably, it would be better -to require explicit quantification on constructor arguments -where that is what is wanted. Feedback welcomed.) - + len2 :: [a] -> Int + len2 xs = let ?acc = 0 in len_acc2 xs - -You construct values of types T1, MonadT, Swizzle by applying -the constructor to suitable values, just as usual. For example, + len_acc2 :: (?acc :: Int) => [a] -> Int + len_acc2 [] = ?acc + len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs + +The only difference between the two groups is that in the second group +len_acc is given a type signature. +In the former case, len_acc1 is monomorphic in its own +right-hand side, so the implicit parameter ?acc is not +passed to the recursive call. In the latter case, because len_acc2 +has a type signature, the recursive call is made to the +polymoprhic version, which takes ?acc +as an implicit parameter. So we get the following results in GHCi: + + Prog> len1 "hello" + 0 + Prog> len2 "hello" + 5 + +Adding a type signature dramatically changes the result! This is a rather +counter-intuitive phenomenon, worth watching out for. + - +Implicit parameters and monomorphism +GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the +Haskell Report) to implicit parameters. For example, consider: - a1 :: T Int - a1 = T1 (\xy->x) 3 - - a2, a3 :: Swizzle - a2 = MkSwizzle sort - a3 = MkSwizzle reverse - - a4 :: MonadT Maybe - a4 = let r x = Just x - b m k = case m of - Just y -> k y - Nothing -> Nothing - in - MkMonad r b - - mkTs :: (forall b. b -> b -> b) -> a -> [T a] - mkTs f x y = [T1 f x, T1 f y] + f :: Int -> Int + f v = let ?x = 0 in + let y = ?x + v in + let ?x = 5 in + y +Since the binding for y falls under the Monomorphism +Restriction it is not generalised, so the type of y is +simply Int, not (?x::Int) => Int. +Hence, (f 9) returns result 9. +If you add a type signature for y, then y +will get type (?x::Int) => Int, so the occurrence of +y in the body of the let will see the +inner binding of ?x, so (f 9) will return +14. + + + + + + + +Explicitly-kinded quantification + + +Haskell infers the kind of each type variable. Sometimes it is nice to be able +to give the kind explicitly as (machine-checked) documentation, +just as it is nice to give a type signature for a function. On some occasions, +it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999) +John Hughes had to define the data type: + + data Set cxt a = Set [a] + | Unused (cxt a -> ()) + +The only use for the Unused constructor was to force the correct +kind for the type variable cxt. -A lexically scoped type variable can be bound by: +GHC now instead allows you to specify the kind of a type variable directly, wherever +a type variable is explicitly bound. Namely: -A declaration type signature () -An expression type signature () -A pattern type signature () -Class and instance declarations () +data declarations: + + data Set (cxt :: * -> *) a = Set [a] + +type declarations: + + type T (f :: * -> *) = f Int + +class declarations: + + class (Eq a) => C (f :: * -> *) a where ... + +forall's in type signatures: + + f :: forall (cxt :: * -> *). Set cxt Int + + -In Haskell, a programmer-written type signature is implicitly quantifed over -its free type variables (Section -4.1.2 -of the Haskel Report). -Lexically scoped type variables affect this implicit quantification rules -as follows: any type variable that is in scope is not universally -quantified. For example, if type variable a is in scope, -then - - (e :: a -> a) means (e :: a -> a) - (e :: b -> b) means (e :: forall b. b->b) - (e :: a -> b) means (e :: forall b. a->b) - +The parentheses are required. Some of the spaces are required too, to +separate the lexemes. If you write (f::*->*) you +will get a parse error, because "::*->*" is a +single lexeme in Haskell. + +As part of the same extension, you can put kind annotations in types +as well. Thus: + + f :: (Int :: *) -> Int + g :: forall a. a -> (a :: *) + +The syntax is + + atype ::= '(' ctype '::' kind ') + +The parentheses are required. + + - + +Arbitrary-rank polymorphism + - -Declaration type signatures -A declaration type signature that has explicit -quantification (using forall) brings into scope the -explicitly-quantified -type variables, in the definition of the named function(s). For example: + +Haskell type signatures are implicitly quantified. The new keyword forall +allows us to say exactly what this means. For example: + + - f :: forall a. [a] -> [a] - f (x:xs) = xs ++ [ x :: a ] + g :: b -> b -The "forall a" brings "a" into scope in -the definition of "f". - -This only happens if the quantification in f's type -signature is explicit. For example: +means this: - g :: [a] -> [a] - g (x:xs) = xs ++ [ x :: a ] + g :: forall b. (b -> b) -This program will be rejected, because "a" does not scope -over the definition of "f", so "x::a" -means "x::forall a. a" by Haskell's usual implicit -quantification rules. +The two are treated identically. - - - -Expression type signatures -An expression type signature that has explicit -quantification (using forall) brings into scope the -explicitly-quantified -type variables, in the annotated expression. For example: + +However, GHC's type system supports arbitrary-rank +explicit universal quantification in +types. +For example, all the following types are legal: - f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool ) + f1 :: forall a b. a -> b -> a + g1 :: forall a b. (Ord a, Eq b) => a -> b -> a + + f2 :: (forall a. a->a) -> Int -> Int + g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int + + f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool + + f4 :: Int -> (forall a. a -> a) -Here, the type signature forall a. ST s Bool brings the -type variable s into scope, in the annotated expression -(op >>= \(x :: STRef s Int) -> g x). +Here, f1 and g1 are rank-1 types, and +can be written in standard Haskell (e.g. f1 :: a->b->a). +The forall makes explicit the universal quantification that +is implicitly added by Haskell. + + +The functions f2 and g2 have rank-2 types; +the forall is on the left of a function arrow. As g2 +shows, the polymorphic type on the left of the function arrow can be overloaded. + + +The function f3 has a rank-3 type; +it has rank-2 types on the left of a function arrow. + + +GHC allows types of arbitrary rank; you can nest foralls +arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but +that restriction has now been lifted.) +In particular, a forall-type (also called a "type scheme"), +including an operational type class context, is legal: + + On the left or right (see f4, for example) +of a function arrow + As the argument of a constructor, or type of a field, in a data type declaration. For +example, any of the f1,f2,f3,g1,g2 above would be valid +field type signatures. + As the type of an implicit parameter + In a pattern type signature (see ) + +Of course forall becomes a keyword; you can't use forall as +a type variable any more! - - -Pattern type signatures + +Examples + + -A type signature may occur in any pattern; this is a pattern type -signature. -For example: - - -- f and g assume that 'a' is already in scope - f = \(x::Int, y::a) -> x - g (x::a) = x - h ((x,y) :: (Int,Bool)) = (y,x) - -In the case where all the type variables in the pattern type sigature are -already in scope (i.e. bound by the enclosing context), matters are simple: the -signature simply constrains the type of the pattern in the obvious way. +In a data or newtype declaration one can quantify +the types of the constructor arguments. Here are several examples: + -There is only one situation in which you can write a pattern type signature that -mentions a type variable that is not already in scope, namely in pattern match -of an existential data constructor. For example: + - data T = forall a. MkT [a] +data T a = T1 (forall b. b -> b -> b) a - k :: T -> T - k (MkT [t::a]) = MkT t3 - where - t3::[a] = [t,t,t] +data MonadT m = MkMonad { return :: forall a. a -> m a, + bind :: forall a b. m a -> (a -> m b) -> m b + } + +newtype Swizzle = MkSwizzle (Ord a => [a] -> [a]) -Here, the pattern type signature (t::a) mentions a lexical type -variable that is not already in scope. Indeed, it cannot already be in scope, -because it is bound by the pattern match. GHC's rule is that in this situation -(and only then), a pattern type signature can mention a type variable that is -not already in scope; the effect is to bring it into scope, standing for the -existentially-bound type variable. - - -If this seems a little odd, we think so too. But we must have -some way to bring such type variables into scope, else we -could not name existentially-bound type variables in subequent type signatures. + + -This is (now) the only situation in which a pattern type -signature is allowed to mention a lexical variable that is not already in -scope. -For example, both f and g would be -illegal if a was not already in scope. +The constructors have rank-2 types: + - + +T1 :: forall a. (forall b. b -> b -> b) -> a -> T a +MkMonad :: forall m. (forall a. a -> m a) + -> (forall a b. m a -> (a -> m b) -> m b) + -> MonadT m +MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle + - + - -Class and instance declarations +The type of the argument can, as usual, be more general than the type +required, as (MkSwizzle reverse) shows. (reverse +does not need the Ord constraint.) + -The type variables in the head of a class or instance declaration -scope over the methods defined in the where part. For example: + +When you use pattern matching, the bound variables may now have +polymorphic types. For example: + + - class C a where - op :: [a] -> a + f :: T a -> a -> (a, Char) + f (T1 w k) x = (w k x, w 'c' 'd') - op xs = let ys::[a] - ys = reverse xs - in - head ys + g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b] + g (MkSwizzle s) xs f = s (map f (s xs)) + + h :: MonadT m -> [m a] -> m [a] + h m [] = return m [] + h m (x:xs) = bind m x $ \y -> + bind m (h m xs) $ \ys -> + return m (y:ys) + - - + +In the function h we use the record selectors return +and bind to extract the polymorphic bind and return functions +from the MonadT data structure, rather than using pattern +matching. + + - -Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal> + +Type inference -Haskell 98 allows the programmer to add "deriving( Eq, Ord )" to a data type -declaration, to generate a standard instance declaration for classes specified in the deriving clause. -In Haskell 98, the only classes that may appear in the deriving clause are the standard -classes Eq, Ord, -Enum, Ix, Bounded, Read, and Show. +In general, type inference for arbitrary-rank types is undecidable. +GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96) +to get a decidable algorithm by requiring some help from the programmer. +We do not yet have a formal specification of "some help" but the rule is this: -GHC extends this list with two more classes that may be automatically derived -(provided the flag is specified): -Typeable, and Data. These classes are defined in the library -modules Data.Typeable and Data.Generics respectively, and the -appropriate class must be in scope before it can be mentioned in the deriving clause. +For a lambda-bound or case-bound variable, x, either the programmer +provides an explicit polymorphic type for x, or GHC's type inference will assume +that x's type has no foralls in it. -An instance of Typeable can only be derived if the -data type has seven or fewer type parameters, all of kind *. -The reason for this is that the Typeable class is derived using the scheme -described in - -Scrap More Boilerplate: Reflection, Zips, and Generalised Casts -. -(Section 7.4 of the paper describes the multiple Typeable classes that -are used, and only Typeable1 up to -Typeable7 are provided in the library.) -In other cases, there is nothing to stop the programmer writing a TypableX -class, whose kind suits that of the data type constructor, and -then writing the data type instance by hand. + +What does it mean to "provide" an explicit type for x? You can do that by +giving a type signature for x directly, using a pattern type signature +(), thus: + + \ f :: (forall a. a->a) -> (f True, f 'c') + +Alternatively, you can give a type signature to the enclosing +context, which GHC can "push down" to find the type for the variable: + + (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char) + +Here the type signature on the expression can be pushed inwards +to give a type signature for f. Similarly, and more commonly, +one can give a type signature for the function itself: + + h :: (forall a. a->a) -> (Bool,Char) + h f = (f True, f 'c') + +You don't need to give a type signature if the lambda bound variable +is a constructor argument. Here is an example we saw earlier: + + f :: T a -> a -> (a, Char) + f (T1 w k) x = (w k x, w 'c' 'd') + +Here we do not need to give a type signature to w, because +it is an argument of constructor T1 and that tells GHC all +it needs to know. - - -Generalised derived instances for newtypes + + + + +Implicit quantification -When you define an abstract type using newtype, you may want -the new type to inherit some instances from its representation. In -Haskell 98, you can inherit instances of Eq, Ord, -Enum and Bounded by deriving them, but for any -other classes you have to write an explicit instance declaration. For -example, if you define +GHC performs implicit quantification as follows. At the top level (only) of +user-written types, if and only if there is no explicit forall, +GHC finds all the type variables mentioned in the type that are not already +in scope, and universally quantifies them. For example, the following pairs are +equivalent: + + f :: a -> a + f :: forall a. a -> a - - newtype Dollars = Dollars Int - + g (x::a) = let + h :: a -> b -> b + h x y = y + in ... + g (x::a) = let + h :: forall b. a -> b -> b + h x y = y + in ... + + + +Notice that GHC does not find the innermost possible quantification +point. For example: + + f :: (a -> a) -> Int + -- MEANS + f :: forall a. (a -> a) -> Int + -- NOT + f :: (forall a. a -> a) -> Int -and you want to use arithmetic on Dollars, you have to -explicitly define an instance of Num: - - instance Num Dollars where - Dollars a + Dollars b = Dollars (a+b) - ... + g :: (Ord a => a -> a) -> Int + -- MEANS the illegal type + g :: forall a. (Ord a => a -> a) -> Int + -- NOT + g :: (forall a. Ord a => a -> a) -> Int + +The latter produces an illegal type, which you might think is silly, +but at least the rule is simple. If you want the latter type, you +can write your for-alls explicitly. Indeed, doing so is strongly advised +for rank-2 types. + + + + + + +Impredicative polymorphism + +GHC supports impredicative polymorphism. This means +that you can call a polymorphic function at a polymorphic type, and +parameterise data structures over polymorphic types. For example: + + f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char]) + f (Just g) = Just (g [3], g "hello") + f Nothing = Nothing -All the instance does is apply and remove the newtype -constructor. It is particularly galling that, since the constructor -doesn't appear at run-time, this instance declaration defines a -dictionary which is wholly equivalent to the Int -dictionary, only slower! +Notice here that the Maybe type is parameterised by the +polymorphic type (forall a. [a] -> +[a]). + +The technical details of this extension are described in the paper +Boxy types: +type inference for higher-rank types and impredicativity, +which appeared at ICFP 2006. + + +Lexically scoped type variables + - Generalising the deriving clause -GHC now permits such instances to be derived instead, so one can write - - newtype Dollars = Dollars Int deriving (Eq,Show,Num) - - -and the implementation uses the same Num dictionary -for Dollars as for Int. Notionally, the compiler -derives an instance declaration of the form +GHC supports lexically scoped type variables, without +which some type signatures are simply impossible to write. For example: + +f :: forall a. [a] -> [a] +f xs = ys ++ ys + where + ys :: [a] + ys = reverse xs + +The type signature for f brings the type variable a into scope; it scopes over +the entire definition of f. +In particular, it is in scope at the type signature for ys. +In Haskell 98 it is not possible to declare +a type for ys; a major benefit of scoped type variables is that +it becomes possible to do so. + +Lexically-scoped type variables are enabled by +. + +Note: GHC 6.6 contains substantial changes to the way that scoped type +variables work, compared to earlier releases. Read this section +carefully! - - instance Num Int => Num Dollars - + +Overview -which just adds or removes the newtype constructor according to the type. +The design follows the following principles + +A scoped type variable stands for a type variable, and not for +a type. (This is a change from GHC's earlier +design.) +Furthermore, distinct lexical type variables stand for distinct +type variables. This means that every programmer-written type signature +(includin one that contains free scoped type variables) denotes a +rigid type; that is, the type is fully known to the type +checker, and no inference is involved. +Lexical type variables may be alpha-renamed freely, without +changing the program. + + + +A lexically scoped type variable can be bound by: + +A declaration type signature () +An expression type signature () +A pattern type signature () +Class and instance declarations () + +In Haskell, a programmer-written type signature is implicitly quantifed over +its free type variables (Section +4.1.2 +of the Haskel Report). +Lexically scoped type variables affect this implicit quantification rules +as follows: any type variable that is in scope is not universally +quantified. For example, if type variable a is in scope, +then + + (e :: a -> a) means (e :: a -> a) + (e :: b -> b) means (e :: forall b. b->b) + (e :: a -> b) means (e :: forall b. a->b) + + -We can also derive instances of constructor classes in a similar -way. For example, suppose we have implemented state and failure monad -transformers, such that - - instance Monad m => Monad (State s m) - instance Monad m => Monad (Failure m) - -In Haskell 98, we can define a parsing monad by - - type Parser tok m a = State [tok] (Failure m) a - + -which is automatically a monad thanks to the instance declarations -above. With the extension, we can make the parser type abstract, -without needing to write an instance of class Monad, via - - newtype Parser tok m a = Parser (State [tok] (Failure m) a) - deriving Monad + +Declaration type signatures +A declaration type signature that has explicit +quantification (using forall) brings into scope the +explicitly-quantified +type variables, in the definition of the named function(s). For example: + + f :: forall a. [a] -> [a] + f (x:xs) = xs ++ [ x :: a ] -In this case the derived instance declaration is of the form - - instance Monad (State [tok] (Failure m)) => Monad (Parser tok m) - - -Notice that, since Monad is a constructor class, the -instance is a partial application of the new type, not the -entire left hand side. We can imagine that the type declaration is -``eta-converted'' to generate the context of the instance -declaration. +The "forall a" brings "a" into scope in +the definition of "f". - - -We can even derive instances of multi-parameter classes, provided the -newtype is the last class parameter. In this case, a ``partial -application'' of the class appears in the deriving -clause. For example, given the class - - - class StateMonad s m | m -> s where ... - instance Monad m => StateMonad s (State s m) where ... - -then we can derive an instance of StateMonad for Parsers by - - newtype Parser tok m a = Parser (State [tok] (Failure m) a) - deriving (Monad, StateMonad [tok]) +This only happens if the quantification in f's type +signature is explicit. For example: + + g :: [a] -> [a] + g (x:xs) = xs ++ [ x :: a ] +This program will be rejected, because "a" does not scope +over the definition of "f", so "x::a" +means "x::forall a. a" by Haskell's usual implicit +quantification rules. + + -The derived instance is obtained by completing the application of the -class to the new type: + +Expression type signatures - - instance StateMonad [tok] (State [tok] (Failure m)) => - StateMonad [tok] (Parser tok m) +An expression type signature that has explicit +quantification (using forall) brings into scope the +explicitly-quantified +type variables, in the annotated expression. For example: + + f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool ) +Here, the type signature forall a. ST s Bool brings the +type variable s into scope, in the annotated expression +(op >>= \(x :: STRef s Int) -> g x). - -As a result of this extension, all derived instances in newtype - declarations are treated uniformly (and implemented just by reusing -the dictionary for the representation type), except -Show and Read, which really behave differently for -the newtype and its representation. - - A more precise specification + +Pattern type signatures -Derived instance declarations are constructed as follows. Consider the -declaration (after expansion of any type synonyms) - - - newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm) - - -where - - - The ci are partial applications of - classes of the form C t1'...tj', where the arity of C - is exactly j+1. That is, C lacks exactly one type argument. - - - The k is chosen so that ci (T v1...vk) is well-kinded. - - - The type t is an arbitrary type. - - - The type variables vk+1...vn do not occur in t, - nor in the ci, and - - - None of the ci is Read, Show, - Typeable, or Data. These classes - should not "look through" the type or its constructor. You can still - derive these classes for a newtype, but it happens in the usual way, not - via this new mechanism. - - -Then, for each ci, the derived instance -declaration is: - - instance ci t => ci (T v1...vk) +A type signature may occur in any pattern; this is a pattern type +signature. +For example: + + -- f and g assume that 'a' is already in scope + f = \(x::Int, y::a) -> x + g (x::a) = x + h ((x,y) :: (Int,Bool)) = (y,x) -As an example which does not work, consider - - newtype NonMonad m s = NonMonad (State s m s) deriving Monad - -Here we cannot derive the instance - - instance Monad (State s m) => Monad (NonMonad m) - +In the case where all the type variables in the pattern type sigature are +already in scope (i.e. bound by the enclosing context), matters are simple: the +signature simply constrains the type of the pattern in the obvious way. + + +There is only one situation in which you can write a pattern type signature that +mentions a type variable that is not already in scope, namely in pattern match +of an existential data constructor. For example: + + data T = forall a. MkT [a] -because the type variable s occurs in State s m, -and so cannot be "eta-converted" away. It is a good thing that this -deriving clause is rejected, because NonMonad m is -not, in fact, a monad --- for the same reason. Try defining ->>= with the correct type: you won't be able to. + k :: T -> T + k (MkT [t::a]) = MkT t3 + where + t3::[a] = [t,t,t] + +Here, the pattern type signature (t::a) mentions a lexical type +variable that is not already in scope. Indeed, it cannot already be in scope, +because it is bound by the pattern match. GHC's rule is that in this situation +(and only then), a pattern type signature can mention a type variable that is +not already in scope; the effect is to bring it into scope, standing for the +existentially-bound type variable. - -Notice also that the order of class parameters becomes -important, since we can only derive instances for the last one. If the -StateMonad class above were instead defined as - - - class StateMonad m s | m -> s where ... - - -then we would not have been able to derive an instance for the -Parser type above. We hypothesise that multi-parameter -classes usually have one "main" parameter for which deriving new -instances is most interesting. +If this seems a little odd, we think so too. But we must have +some way to bring such type variables into scope, else we +could not name existentially-bound type variables in subequent type signatures. -Lastly, all of this applies only for classes other than -Read, Show, Typeable, -and Data, for which the built-in derivation applies (section -4.3.3. of the Haskell Report). -(For the standard classes Eq, Ord, -Ix, and Bounded it is immaterial whether -the standard method is used or the one described here.) + +This is (now) the only situation in which a pattern type +signature is allowed to mention a lexical variable that is not already in +scope. +For example, both f and g would be +illegal if a was not already in scope. + + - + + +Class and instance declarations + +The type variables in the head of a class or instance declaration +scope over the methods defined in the where part. For example: + + + + class C a where + op :: [a] -> a + + op xs = let ys::[a] + ys = reverse xs + in + head ys + + + Generalised typing of mutually recursive bindings @@ -3772,7 +4081,7 @@ and all others are monomorphic until the group is generalised Following a suggestion of Mark Jones, in his paper Typing Haskell in Haskell, -GHC implements a more general scheme. If is +GHC implements a more general scheme. If is specified: the dependency analysis ignores references to variables that have an explicit type signature. @@ -3801,7 +4110,7 @@ Now, the defintion for f is typechecked, with this type for The same refined dependency analysis also allows the type signatures of mutually-recursive functions to have different contexts, something that is illegal in Haskell 98 (Section 4.5.2, last sentence). With - + GHC only insists that the type signatures of a refined group have identical type signatures; in practice this means that only variables bound by the same pattern binding must have the same context. For example, this is fine: @@ -3815,186 +4124,111 @@ pattern binding must have the same context. For example, this is fine: - - - - - - -Generalised Algebraic Data Types (GADTs) + +Overloaded string literals + -Generalised Algebraic Data Types generalise ordinary algebraic data types by allowing you -to give the type signatures of constructors explicitly. For example: + +GHC supports overloaded string literals. Normally a +string literal has type String, but with overloaded string +literals enabled (with -X=OverloadedStrings) + a string literal has type (IsString a) => a. + + +This means that the usual string syntax can be used, e.g., for packed strings +and other variations of string like types. String literals behave very much +like integer literals, i.e., they can be used in both expressions and patterns. +If used in a pattern the literal with be replaced by an equality test, in the same +way as an integer literal is. + + +The class IsString is defined as: - data Term a where - Lit :: Int -> Term Int - Succ :: Term Int -> Term Int - IsZero :: Term Int -> Term Bool - If :: Term Bool -> Term a -> Term a -> Term a - Pair :: Term a -> Term b -> Term (a,b) +class IsString a where + fromString :: String -> a -Notice that the return type of the constructors is not always Term a, as is the -case with ordinary vanilla data types. Now we can write a well-typed eval function -for these Terms: +The only predefined instance is the obvious one to make strings work as usual: - eval :: Term a -> a - eval (Lit i) = i - eval (Succ t) = 1 + eval t - eval (IsZero t) = eval t == 0 - eval (If b e1 e2) = if eval b then eval e1 else eval e2 - eval (Pair e1 e2) = (eval e1, eval e2) +instance IsString [Char] where + fromString cs = cs -These and many other examples are given in papers by Hongwei Xi, and -Tim Sheard. There is a longer introduction -on the wiki, -and Ralf Hinze's -Fun with phantom types also has a number of examples. Note that papers -may use different notation to that implemented in GHC. +The class IsString is not in scope by default. If you want to mention +it explicitly (for exmaple, to give an instance declaration for it), you can import it +from module GHC.Exts. -The rest of this section outlines the extensions to GHC that support GADTs. -It is far from comprehensive, but the design closely follows that described in -the paper Simple -unification-based type inference for GADTs, -which appeared in ICFP 2006. +Haskell's defaulting mechanism is extended to cover string literals, when is specified. +Specifically: - Data type declarations have a 'where' form, as exemplified above. The type signature of -each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal -Haskell data type declaration, the type variable(s) in the "data Term a where" header -have no scope. Indeed, one can write a kind signature instead: - - data Term :: * -> * where ... - -or even a mixture of the two: - - data Foo a :: (* -> *) -> * where ... - -The type variables (if given) may be explicitly kinded, so we could also write the header for Foo -like this: - - data Foo a (b :: * -> *) where ... - +Each type in a default declaration must be an +instance of Num or of IsString. -There are no restrictions on the type of the data constructor, except that the result -type must begin with the type constructor being defined. For example, in the Term data -type above, the type of each constructor must end with ... -> Term .... +The standard defaulting rule (Haskell Report, Section 4.3.4) +is extended thus: defaulting applies when all the unresolved constraints involve standard classes +or IsString; and at least one is a numeric class +or IsString. - - -You can use record syntax on a GADT-style data type declaration: - - - data Term a where - Lit { val :: Int } :: Term Int - Succ { num :: Term Int } :: Term Int - Pred { num :: Term Int } :: Term Int - IsZero { arg :: Term Int } :: Term Bool - Pair { arg1 :: Term a - , arg2 :: Term b - } :: Term (a,b) - If { cnd :: Term Bool - , tru :: Term a - , fls :: Term a - } :: Term a - -For every constructor that has a field f, (a) the type of -field f must be the same; and (b) the -result type of the constructor must be the same; both modulo alpha conversion. -Hence, in our example, we cannot merge the num and arg -fields above into a -single name. Although their field types are both Term Int, -their selector functions actually have different types: - - - num :: Term Int -> Term Int - arg :: Term Bool -> Term Int - - -At the moment, record updates are not yet possible with GADT, so support is -limited to record construction, selection and pattern matching: - + + + +A small example: - someTerm :: Term Bool - someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } } - - eval :: Term a -> a - eval Lit { val = i } = i - eval Succ { num = t } = eval t + 1 - eval Pred { num = t } = eval t - 1 - eval IsZero { arg = t } = eval t == 0 - eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2) - eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t) - +module Main where - +import GHC.Exts( IsString(..) ) - -You can use strictness annotations, in the obvious places -in the constructor type: - - data Term a where - Lit :: !Int -> Term Int - If :: Term Bool -> !(Term a) -> !(Term a) -> Term a - Pair :: Term a -> Term b -> Term (a,b) - - +newtype MyString = MyString String deriving (Eq, Show) +instance IsString MyString where + fromString = MyString - -You can use a deriving clause on a GADT-style data type -declaration, but only if the data type could also have been declared in -Haskell-98 syntax. For example, these two declarations are equivalent - - data Maybe1 a where { - Nothing1 :: Maybe1 a ; - Just1 :: a -> Maybe1 a - } deriving( Eq, Ord ) +greet :: MyString -> MyString +greet "hello" = "world" +greet other = other - data Maybe2 a = Nothing2 | Just2 a - deriving( Eq, Ord ) +main = do + print $ greet "hello" + print $ greet "fool" -This simply allows you to declare a vanilla Haskell-98 data type using the -where form without losing the deriving clause. - + + +Note that deriving Eq is necessary for the pattern matching +to work since it gets translated into an equality comparison. + + - -Pattern matching causes type refinement. For example, in the right hand side of the equation - - eval :: Term a -> a - eval (Lit i) = ... - -the type a is refined to Int. (That's the whole point!) -A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper -about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page. + +Type families + - The general principle is this: type refinement is only carried out based on user-supplied type annotations. -So if no type signature is supplied for eval, no type refinement happens, and lots of obscure error messages will -occur. However, the refinement is quite general. For example, if we had: - - eval :: Term a -> a -> a - eval (Lit i) j = i+j - -the pattern match causes the type a to be refined to Int (because of the type -of the constructor Lit, and that refinement also applies to the type of j, and -the result type of the case expression. Hence the addition i+j is legal. + +GHC supports the definition of type families indexed by types. They may be +seen as an extension of Haskell 98's class-based overloading of values to +types. When type families are declared in classes, they are also known as +associated types. - - + +There are two forms of type families: data families and type synonym families. +Currently, only the former are fully implemented, while we are still working +on the latter. As a result, the specification of the language extension is +also still to some degree in flux. Hence, a more detailed description of +the language extension and its use is currently available +from the Haskell +wiki page on type families. The material will be moved to this user's +guide when it has stabilised. - -Notice that GADTs generalise existential types. For example, these two declarations are equivalent: - - data T a = forall b. MkT b (b->a) - data T' a where { MKT :: b -> (b->a) -> T' a } - + +Type families are enabled by the flag . - - + + + + + @@ -4035,9 +4269,10 @@ Tim Sheard is going to expand it.) Template Haskell has the following new syntactic constructions. You need to use the flag - + or + to switch these syntactic extensions on - ( is no longer implied by + ( is no longer implied by ). @@ -4069,7 +4304,7 @@ Tim Sheard is going to expand it.) the quotation has type Expr. [d| ... |], where the "..." is a list of top-level declarations; the quotation has type Q [Dec]. - [Planned, but not implemented yet.] [t| ... |], where the "..." is a type; + [t| ... |], where the "..." is a type; the quotation has type Type. @@ -4103,6 +4338,14 @@ Tim Sheard is going to expand it.) (It would make sense to do so, but it's hard to implement.) + + Furthermore, you can only run a function at compile time if it is imported + from another module that is not part of a mutually-recursive group of modules + that includes the module currently being compiled. For example, when compiling module A, + you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly). + The reason should be clear: to run B we must compile and run A, but we are currently type-checking A. + + The flag -ddump-splices shows the expansion of all top-level splices as they happen. @@ -4175,7 +4418,7 @@ pr s = gen (parse s) Now run the compiler (here we are a Cygwin prompt on Windows): -$ ghc --make -fth main.hs -o main.exe +$ ghc --make -X=TemplateHaskell main.hs -o main.exe Run "main.exe" and here is your output: @@ -4264,7 +4507,7 @@ Palgrave, 2003. and the arrows web page at http://www.haskell.org/arrows/. -With the flag, GHC supports the arrow +With the flag, GHC supports the arrow notation described in the second of these papers. What follows is a brief introduction to the notation; it won't make much sense unless you've read Hughes's paper. @@ -4722,7 +4965,7 @@ Because the preprocessor targets Haskell (rather than Core), - + Bang patterns <indexterm><primary>Bang patterns</primary></indexterm> @@ -4734,10 +4977,10 @@ prime feature description contains more discussion and examples than the material below. -Bang patterns are enabled by the flag . +Bang patterns are enabled by the flag . - + Informal description of bang patterns @@ -4792,7 +5035,7 @@ is part of the syntax of let bindings. - + Syntax and semantics @@ -4807,7 +5050,7 @@ f !x = 3 Is this a definition of the infix function "(!)", or of the "f" with a bang pattern? GHC resolves this -ambiguity inf favour of the latter. If you want to define +ambiguity in favour of the latter. If you want to define (!) with bang-patterns enabled, you have to do so using prefix notation: @@ -4866,7 +5109,7 @@ a module. - + Assertions <indexterm><primary>Assertions</primary></indexterm> @@ -5835,12 +6078,6 @@ The following are good consumers: - length - - - - - ++ (on its first argument) @@ -6130,6 +6367,22 @@ r) -> described in this section. All are exported by GHC.Exts. + The <literal>seq</literal> function + +The function seq is as described in the Haskell98 Report. + + seq :: a -> b -> b + +It evaluates its first argument to head normal form, and then returns its +second argument as the result. The reason that it is documented here is +that, despite seq's polymorphism, its +second argument can have an unboxed type, or +can be an unboxed tuple; for example (seq x 4#) +or (seq x (# p,q #)). This requires b +to be instantiated to an unboxed type, which is not usually allowed. + + + The <literal>inline</literal> function The inline function is somewhat experimental. @@ -6188,6 +6441,11 @@ If lazy were not lazy, par would look strict in y which would defeat the whole purpose of par. + +Like seq, the argument of lazy can have +an unboxed type. + + The <literal>unsafeCoerce#</literal> function @@ -6203,7 +6461,14 @@ It is generally used when you want to write a program that you know is well-typed, but where Haskell's type system is not expressive enough to prove that it is well typed. + +The argument to unsafeCoerce# can have unboxed types, +although extremely bad things will happen if you coerce a boxed type +to an unboxed type. + + + @@ -6260,7 +6525,7 @@ where clause and over-ride whichever methods you please. Use the flags (to enable the extra syntax), - (to generate extra per-data-type code), + (to generate extra per-data-type code), and (to make the Generics library available. @@ -6469,21 +6734,21 @@ carried out at let and where bindings. Switching off the dreaded Monomorphism Restriction - + Haskell's monomorphism restriction (see Section 4.5.5 of the Haskell Report) can be completely switched off by -. +. Monomorphic pattern bindings - - + + As an experimental change, we are exploring the possibility of making pattern bindings monomorphic; that is, not generalised at all. @@ -6499,7 +6764,7 @@ can be completely switched off by [x] = e -- A pattern binding Experimentally, GHC now makes pattern bindings monomorphic by -default. Use to recover the +default. Use to recover the standard behaviour.