X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=ghc%2Fdocs%2Fusers_guide%2Fglasgow_exts.sgml;h=b43f6d4abbcd6e4165bca70aef3ef9d5ccdf7200;hb=5d86a0c4dae6b6c04f03316ffe8a4c10ada38662;hp=a3ff83c2507625172ed20eeb6402025d57ff20e7;hpb=a8cf15f207bb5b3d7173cf8e2f9314ad9a80d40b;p=ghc-hetmet.git diff --git a/ghc/docs/users_guide/glasgow_exts.sgml b/ghc/docs/users_guide/glasgow_exts.sgml index a3ff83c..b43f6d4 100644 --- a/ghc/docs/users_guide/glasgow_exts.sgml +++ b/ghc/docs/users_guide/glasgow_exts.sgml @@ -152,489 +152,1034 @@ with GHC. -&primitives; - - - - -Type system extensions - - -Data types with no constructors - -With the flag, GHC lets you declare -a data type with no constructors. For example: - - - data S -- S :: * - data T a -- T :: * -> * - - -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 ). - -Such data types have only one value, namely bottom. -Nevertheless, they can be useful when defining "phantom types". - - - -Infix type constructors + + + Unboxed types and primitive operations + +GHC is built on a raft of primitive data types and operations. +While you really can use this stuff to write fast code, + we generally find it a lot less painful, and more satisfying in the + long run, to use higher-level language features and libraries. With + any luck, the code you write will be optimised to the efficient + unboxed version in any case. And if it isn't, we'd like to know + about it. + +We do not currently have good, up-to-date documentation about the +primitives, perhaps because they are mainly intended for internal use. +There used to be a long section about them here in the User Guide, but it +became out of date, and wrong information is worse than none. + +The Real Truth about what primitive types there are, and what operations +work over those types, is held in the file +fptools/ghc/compiler/prelude/primops.txt. +This file is used directly to generate GHC's primitive-operation definitions, so +it is always correct! It is also intended for processing into text. + + Indeed, +the result of such processing is part of the description of the + External + Core language. +So that document is a good place to look for a type-set version. +We would be very happy if someone wanted to volunteer to produce an SGML +back end to the program that processes primops.txt so that +we could include the results here in the User Guide. + +What follows here is a brief summary of some main points. + + +Unboxed types + -GHC allows type constructors to be operators, and to be written infix, very much -like expressions. More specifically: - - - A type constructor can be an operator, beginning with a colon; e.g. :*:. - The lexical syntax is the same as that for data constructors. - - - Types can be written infix. For example Int :*: Bool. - - - Back-quotes work - as for expressions, both for type constructors and type variables; e.g. Int `Either` Bool, or - Int `a` Bool. Similarly, parentheses work the same; e.g. (:*:) Int Bool. - - - Fixities may be declared for type constructors just as for data constructors. However, - one cannot distinguish between the two in a fixity declaration; a fixity declaration - sets the fixity for a data constructor and the corresponding type constructor. For example: - - infixl 7 T, :*: - - sets the fixity for both type constructor T and data constructor T, - and similarly for :*:. - Int `a` Bool. - - - Function arrow is infixr with fixity 0. (This might change; I'm not sure what it should be.) - - - Data type and type-synonym declarations can be written infix. E.g. - - data a :*: b = Foo a b - type a :+: b = Either a b - - - - The only thing that differs between operators in types and operators in expressions is that - ordinary non-constructor operators, such as + and * - are not allowed in types. Reason: the uniform thing to do would be to make them type - variables, but that's not very useful. A less uniform but more useful thing would be to - allow them to be type constructors. But that gives trouble in export - lists. So for now we just exclude them. - - - +Unboxed types (Glasgow extension) - - - -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. +Most types in GHC are boxed, which means +that values of that type are represented by a pointer to a heap +object. The representation of a Haskell Int, for +example, is a two-word heap object. An unboxed +type, however, is represented by the value itself, no pointers or heap +allocation are involved. + -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 - - +Unboxed types correspond to the “raw machine” types you +would use in C: Int# (long int), +Double# (double), Addr# +(void *), etc. The primitive operations +(PrimOps) on these types are what you might expect; e.g., +(+#) is addition on +Int#s, and is the machine-addition that we all +know and love—usually one instruction. -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. +Primitive (unboxed) types cannot be defined in Haskell, and are +therefore built into the language and compiler. Primitive types are +always unlifted; that is, a value of a primitive type cannot be +bottom. We use the convention that primitive types, values, and +operations have a # suffix. -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. +Primitive values are often represented by a simple bit-pattern, such +as Int#, Float#, +Double#. But this is not necessarily the case: +a primitive value might be represented by a pointer to a +heap-allocated object. Examples include +Array#, the type of primitive arrays. A +primitive array is heap-allocated because it is too big a value to fit +in a register, and would be too expensive to copy around; in a sense, +it is accidental that it is represented by a pointer. If a pointer +represents a primitive value, then it really does point to that value: +no unevaluated thunks, no indirections…nothing can be at the +other end of the pointer than the primitive value. - - - -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). +There are some restrictions on the use of primitive types, the main +one being that you can't pass a primitive value to a polymorphic +function or store one in a polymorphic data type. This rules out +things like [Int#] (i.e. lists of primitive +integers). The reason for this restriction is that polymorphic +arguments and constructor fields are assumed to be pointers: if an +unboxed integer is stored in one of these, the garbage collector would +attempt to follow it, leading to unpredictable space leaks. Or a +seq operation on the polymorphic component may +attempt to dereference the pointer, with disastrous results. Even +worse, the unboxed value might be larger than a pointer +(Double# for instance). + -With the GHC lifts this restriction. +Nevertheless, A numerically-intensive program using unboxed types can +go a lot faster than its “standard” +counterpart—we saw a threefold speedup on one example. - -Multi-parameter type classes +<sect2 id="unboxed-tuples"> +<title>Unboxed Tuples -This section documents GHC's implementation of multi-parameter type -classes. There's lots of background in the paper Type -classes: exploring the design space (Simon Peyton Jones, Mark -Jones, Erik Meijer). +Unboxed tuples aren't really exported by GHC.Exts, +they're available by default with . An +unboxed tuple looks like this: -I'd like to thank people who reported shorcomings in the GHC 3.02 -implementation. Our default decisions were all conservative ones, and -the experience of these heroic pioneers has given useful concrete -examples to support several generalisations. (These appear below as -design choices not implemented in 3.02.) - - -I've discussed these notes with Mark Jones, and I believe that Hugs -will migrate towards the same design choices as I outline here. -Thanks to him, and to many others who have offered very useful -feedback. - + +(# e_1, ..., e_n #) + - -Types + -There are the following restrictions on the form of a qualified -type: +where e_1..e_n are expressions of any +type (primitive or non-primitive). The type of an unboxed tuple looks +the same. - - - forall tv1..tvn (c1, ...,cn) => type - - +Unboxed tuples are used for functions that need to return multiple +values, but they avoid the heap allocation normally associated with +using fully-fledged tuples. When an unboxed tuple is returned, the +components are put directly into registers or on the stack; the +unboxed tuple itself does not have a composite representation. Many +of the primitive operations listed in this section return unboxed +tuples. -(Here, I write the "foralls" explicitly, although the Haskell source -language omits them; in Haskell 1.4, 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 ). +There are some pretty stringent restrictions on the use of unboxed tuples: - + - Each universally quantified type variable -tvi must be mentioned (i.e. appear free) in type. - -The reason for this is that a value with a type that does not obey -this restriction could not be used without introducing -ambiguity. Here, for example, is an illegal type: - - - - forall a. Eq a => Int - - - -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. + Unboxed tuple types are subject to the same restrictions as +other unboxed types; i.e. they may not be stored in polymorphic data +structures or passed to polymorphic functions. - 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: + Unboxed tuples may only be constructed as the direct result of +a function, and may only be deconstructed with a case expression. +eg. the following are valid: - forall a. C a b => burble +f x y = (# x+1, y-1 #) +g x = case f x x of { (# a, b #) -> a + b } -The next type is illegal because the constraint Eq b does not -mention a: +but the following are invalid: - forall a. Eq b => burble +f x y = g (# x, y #) +g (# x, y #) = x + y -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. - - - - - - - -These restrictions apply to all types, whether declared in a type signature -or inferred. - + -Unlike Haskell 1.4, constraints in types do not have to be of -the form (class type-variables). Thus, these type signatures -are perfectly OK - + No variable can have an unboxed tuple type. This is illegal: - - f :: Eq (m a) => [m a] -> [m a] - g :: Eq [a] => ... +f :: (# Int, Int #) -> (# Int, Int #) +f x = x - - -This choice recovers principal types, a property that Haskell 1.4 does not have. +because x has an unboxed tuple type. + + - + - -Class declarations + - - - +Note: we may relax some of these restrictions in the future. + - Multi-parameter type classes are permitted. For example: - +The IO and ST monads use unboxed +tuples to avoid unnecessary allocation during sequences of operations. + - - class Collection c a where - union :: c a -> c a -> c a - ...etc. - + + + - - - + +Syntactic extensions + + - - The class hierarchy must be acyclic. However, the definition -of "acyclic" involves only the superclass relationships. For example, -this is OK: + + Hierarchical Modules + GHC supports a small extension to the syntax of module + names: a module name is allowed to contain a dot + ‘.’. This is also known as the + “hierarchical module namespace” extension, because + it extends the normally flat Haskell module namespace into a + more flexible hierarchy of modules. - - class C a where { - op :: D b => a -> b -> b - } + This extension has very little impact on the language + itself; modules names are always fully + qualified, so you can just think of the fully qualified module + name as the module name. In particular, this + means that the full module name must be given after the + module keyword at the beginning of the + module; for example, the module A.B.C must + begin - class C a => D a where { ... } - +module A.B.C -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.) + It is a common strategy to use the as + keyword to save some typing when using qualified names with + hierarchical modules. For example: - - - + +import qualified Control.Monad.ST.Strict as ST + - - 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: + Hierarchical modules have an impact on the way that GHC + searches for files. For a description, see . + 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. - - class Functor (m k) => FiniteMap m k where - ... + - class (Monad m, Monad (t m)) => Transform t m where - lift :: m a -> (t m) a - + + +Pattern guards + +Pattern guards (Glasgow extension) +The discussion that follows is an abbreviated version of Simon Peyton Jones's original proposal. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.) - - - In the signature of a class operation, every constraint -must mention at least one type variable that is not a class type -variable. - -Thus: - +Suppose we have an abstract data type of finite maps, with a +lookup operation: - class Collection c a where - mapC :: Collection c b => (a->b) -> c a -> c b +lookup :: FiniteMap -> Int -> Maybe Int +The lookup returns Nothing if the supplied key is not in the domain of the mapping, and (Just v) otherwise, +where v is the value that the key maps to. Now consider the following definition: + -is OK because the constraint (Collection a b) mentions -b, even though it also mentions the class variable -a. On the other hand: + +clunky env var1 var2 | ok1 && ok2 = val1 + val2 +| otherwise = var1 + var2 +where + m1 = lookup env var1 + m2 = lookup env var2 + ok1 = maybeToBool m1 + ok2 = maybeToBool m2 + val1 = expectJust m1 + val2 = expectJust m2 + + +The auxiliary functions are + - class C a where - op :: Eq a => (a,b) -> (a,b) - +maybeToBool :: Maybe a -> Bool +maybeToBool (Just x) = True +maybeToBool Nothing = False +expectJust :: Maybe a -> a +expectJust (Just x) = x +expectJust Nothing = error "Unexpected Nothing" + -is not OK because the constraint (Eq a) mentions on the class -type variable a, but not b. However, any such -example is easily fixed by moving the offending context up to the -superclass context: + +What is clunky doing? The guard ok1 && +ok2 checks that both lookups succeed, using +maybeToBool to convert the Maybe +types to booleans. The (lazily evaluated) expectJust +calls extract the values from the results of the lookups, and binds the +returned values to val1 and val2 +respectively. If either lookup fails, then clunky takes the +otherwise case and returns the sum of its arguments. + + +This is certainly legal Haskell, but it is a tremendously verbose and +un-obvious way to achieve the desired effect. Arguably, a more direct way +to write clunky would be to use case expressions: + - class Eq a => C a where - op ::(a,b) -> (a,b) +clunky env var1 var1 = case lookup env var1 of + Nothing -> fail + Just val1 -> case lookup env var2 of + Nothing -> fail + Just val2 -> val1 + val2 +where + fail = val1 + val2 - -A yet more relaxed rule would allow the context of a class-op signature -to mention only class type variables. However, that conflicts with -Rule 1(b) for types above. - + +This is a bit shorter, but hardly better. Of course, we can rewrite any set +of pattern-matching, guarded equations as case expressions; that is +precisely what the compiler does when compiling equations! The reason that +Haskell provides guarded equations is because they allow us to write down +the cases we want to consider, one at a time, independently of each other. +This structure is hidden in the case version. Two of the right-hand sides +are really the same (fail), and the whole expression +tends to become more and more indented. - - - The type of each class operation must mention all of -the class type variables. For example: - +Here is how I would write clunky: + - class Coll s a where - empty :: s - insert :: s -> a -> s +clunky env var1 var1 + | Just val1 <- lookup env var1 + , Just val2 <- lookup env var2 + = val1 + val2 +...other equations for clunky... + +The semantics should be clear enough. The qualifers are matched in order. +For a <- qualifier, which I call a pattern guard, the +right hand side is evaluated and matched against the pattern on the left. +If the match fails then the whole guard fails and the next equation is +tried. If it succeeds, then the appropriate binding takes place, and the +next qualifier is matched, in the augmented environment. Unlike list +comprehensions, however, the type of the expression to the right of the +<- is the same as the type of the pattern to its +left. The bindings introduced by pattern guards scope over all the +remaining guard qualifiers, and over the right hand side of the equation. + -is not OK, because the type of empty doesn't mention -a. This rule is a consequence of Rule 1(a), above, for -types, and has the same motivation. - -Sometimes, offending class declarations exhibit misunderstandings. For -example, Coll might be rewritten - + +Just as with list comprehensions, boolean expressions can be freely mixed +with among the pattern guards. For example: + - class Coll s a where - empty :: s a - insert :: s a -> a -> s a +f x | [y] <- x + , y > 3 + , Just z <- h y + = ... + +Haskell's current guards therefore emerge as a special case, in which the +qualifier list has just one element, a boolean expression. + + -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: + + +The recursive do-notation + + The recursive do-notation (also known as mdo-notation) is implemented as described in +"A recursive do for Haskell", +Levent Erkok, John Launchbury", +Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania. + + +The do-notation of Haskell does not allow recursive bindings, +that is, the variables bound in a do-expression are visible only in the textually following +code block. Compare this to a let-expression, where bound variables are visible in the entire binding +group. It turns out that several applications can benefit from recursive bindings in +the do-notation, and this extension provides the necessary syntactic support. + + +Here is a simple (yet contrived) example: + - class CollE s where - empty :: s +import Control.Monad.Fix - class CollE s => Coll s a where - insert :: s -> a -> s +justOnes = mdo xs <- Just (1:xs) + return xs + +As you can guess justOnes will evaluate to Just [1,1,1,.... + - + +The Control.Monad.Fix library introduces the MonadFix class. It's definition is: - + +class Monad m => MonadFix m where + mfix :: (a -> m a) -> m a + + +The function mfix +dictates how the required recursion operation should be performed. If recursive bindings are required for a monad, +then that monad must be declared an instance of the MonadFix class. +For details, see the above mentioned reference. + + +The following instances of MonadFix are automatically provided: List, Maybe, IO. +Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class +for Haskell's internal state monad (strict and lazy, respectively). + + +There are three important points in using the recursive-do notation: + + +The recursive version of the do-notation uses the keyword mdo (rather +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 + + - - - -Instance declarations + +The web page: http://www.cse.ogi.edu/PacSoft/projects/rmb +contains up to date information on recursive monadic bindings. + +Historical note: The old implementation of the mdo-notation (and most +of the existing documents) used the name +MonadRec for the class and the corresponding library. +This name is not supported by GHC. + - - + - - Instance declarations may not overlap. The two instance -declarations + - - instance context1 => C type1 where ... + + Parallel List Comprehensions + list comprehensionsparallel + + parallel list comprehensions + + + Parallel list comprehensions are a natural extension to list + comprehensions. List comprehensions can be thought of as a nice + syntax for writing maps and filters. Parallel comprehensions + extend this to include the zipWith family. + + A parallel list comprehension has multiple independent + branches of qualifier lists, each separated by a `|' symbol. For + example, the following zips together two lists: + + + [ (x, y) | x <- xs | y <- ys ] + + + The behavior of parallel list comprehensions follows that of + zip, in that the resulting list will have the same length as the + shortest branch. + + We can define parallel list comprehensions by translation to + regular comprehensions. Here's the basic idea: + + Given a parallel comprehension of the form: + + + [ e | p1 <- e11, p2 <- e12, ... + | q1 <- e21, q2 <- e22, ... + ... + ] + + + This will be translated to: + + + [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...] + [(q1,q2) | q1 <- e21, q2 <- e22, ...] + ... + ] + + + where `zipN' is the appropriate zip for the given number of + branches. + + + + +Rebindable syntax + + + GHC allows most kinds of built-in syntax to be rebound by + the user, to facilitate replacing the Prelude + with a home-grown version, for example. + + You may want to define your own numeric class + 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 + the following pieces of built-in syntax to refer to + whatever is in scope, not the Prelude + versions: + + + + Integer and fractional literals mean + "fromInteger 1" and + "fromRational 3.2", not the + Prelude-qualified versions; both in expressions and in + patterns. + However, the standard Prelude Eq class + is still used for the equality test necessary for literal patterns. + + + + Negation (e.g. "- (f x)") + means "negate (f x)" (not + Prelude.negate). + + + + In an n+k pattern, the standard Prelude + Ord class is still used for comparison, + but the necessary subtraction uses whatever + "(-)" is in scope (not + "Prelude.(-)"). + + + + "Do" notation is translated using whatever + functions (>>=), + (>>), fail, and + return, are in scope (not the Prelude + versions). List comprehensions, and parallel array + comprehensions, are unaffected. + + + Be warned: this is an experimental facility, with fewer checks than + usual. In particular, it is essential that the functions GHC finds in scope + must have the appropriate types, namely: + + fromInteger :: forall a. (...) => Integer -> a + fromRational :: forall a. (...) => Rational -> a + negate :: forall a. (...) => a -> a + (-) :: forall a. (...) => a -> a -> a + (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b + (>>) :: forall m a. (...) => m a -> m b -> m b + return :: forall m a. (...) => a -> m a + fail :: forall m a. (...) => String -> m a + + (The (...) part can be any context including the empty context; that part + is up to you.) + If the functions don't have the right type, very peculiar things may + happen. Use -dcore-lint to + typecheck the desugared program. If Core Lint is happy you should be all right. + + + + + + + +Type system extensions + + +Data types with no constructors + +With the flag, GHC lets you declare +a data type with no constructors. For example: + + + data S -- S :: * + data T a -- T :: * -> * + + +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 ). + +Such data types have only one value, namely bottom. +Nevertheless, they can be useful when defining "phantom types". + + + +Infix type constructors + + +GHC allows type constructors to be operators, and to be written infix, very much +like expressions. More specifically: + + + A type constructor can be an operator, beginning with a colon; e.g. :*:. + The lexical syntax is the same as that for data constructors. + + + Types can be written infix. For example Int :*: Bool. + + + Back-quotes work + as for expressions, both for type constructors and type variables; e.g. Int `Either` Bool, or + Int `a` Bool. Similarly, parentheses work the same; e.g. (:*:) Int Bool. + + + Fixities may be declared for type constructors just as for data constructors. However, + one cannot distinguish between the two in a fixity declaration; a fixity declaration + sets the fixity for a data constructor and the corresponding type constructor. For example: + + infixl 7 T, :*: + + sets the fixity for both type constructor T and data constructor T, + and similarly for :*:. + Int `a` Bool. + + + Function arrow is infixr with fixity 0. (This might change; I'm not sure what it should be.) + + + Data type and type-synonym declarations can be written infix. E.g. + + data a :*: b = Foo a b + type a :+: b = Either a b + + + + The only thing that differs between operators in types and operators in expressions is that + ordinary non-constructor operators, such as + and * + are not allowed in types. Reason: the uniform thing to do would be to make them type + variables, but that's not very useful. A less uniform but more useful thing would be to + allow them to be type constructors. But that gives trouble in export + lists. So for now we just exclude them. + + + + + + + +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 + + + + + +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. + + + + + +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). + + +With the GHC lifts this restriction. + + + + + +Multi-parameter type classes + + + +This section documents GHC's implementation of multi-parameter type +classes. There's lots of background in the paper Type +classes: exploring the design space (Simon Peyton Jones, Mark +Jones, Erik Meijer). + + + + +Types + + +GHC imposes the following restrictions on the form of a qualified +type, whether declared in a type signature +or inferred. Consider the type: + + + forall tv1..tvn (c1, ...,cn) => type + + +(Here, I write the "foralls" explicitly, although the Haskell source +language omits them; in Haskell 1.4, 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 ). + + + + + + + + + Each universally quantified type variable +tvi must be reachable from type. + +A type variable is "reachable" if it it is functionally dependent +(see ) +on the type variables free in type. +The reason for this is that a value with a type that does not obey +this restriction could not be used without introducing +ambiguity. +Here, for example, is an illegal type: + + + + forall a. Eq a => Int + + + +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. + + + + + + + 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: + + + + forall a. C a b => burble + + + +The next type is illegal because the constraint Eq b does not +mention a: + + + + 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. + + + + + + + + + + +Unlike Haskell 1.4, constraints in types do not have to be of +the form (class type-variables). Thus, these type signatures +are perfectly OK + + + + + + f :: Eq (m a) => [m a] -> [m a] + g :: Eq [a] => ... + + + + + +This choice recovers principal types, a property that Haskell 1.4 does not have. + + + + + +Class declarations + + + + + + + + Multi-parameter type classes are permitted. For example: + + + + class Collection c a where + union :: c a -> c a -> c a + ...etc. + + + + + + + + + + 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.) + + + + + + + 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 + + + + + + + + + + All of the class type variables must be reachable (in the sense +mentioned in ) +from the free varibles 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. This rule is a consequence of Rule 1(a), above, for +types, and has the same motivation. + +Sometimes, offending class declarations exhibit misunderstandings. For +example, 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 + + + + + + + + + + + + + +Instance declarations + + + + + + + + Instance declarations may not overlap. The two instance +declarations + + + + instance context1 => C type1 where ... instance context2 => C type2 where ... @@ -747,63 +1292,8 @@ For example, this is OK: instance Stateful (ST s) (MutVar s) where ... - -The "at least one not a type variable" restriction is to ensure that -context reduction terminates: each reduction step removes one type -constructor. For example, the following would make the type checker -loop if it wasn't excluded: - - - - instance C a => C a where ... - - - -There are two situations in which the rule is a bit of a pain. First, -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 - - - -Second, 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) => ... - - - -I'm on the lookout for a simple rule that preserves decidability while -allowing these idioms. The experimental flag --fallow-undecidable-instances -option lifts this restriction, allowing all the types in an -instance head to be type variables. - +See for an experimental +extension to lift this restriction. @@ -865,16 +1355,10 @@ instance C Int b => Foo b where ... -is not OK. Again, the intent here is to make sure that context -reduction terminates. +is not OK. See for an experimental +extension to lift this restriction. + -Voluminous correspondence on the Haskell mailing list has convinced me -that it's worth experimenting with a more liberal rule. If you use -the flag can use arbitrary -types in an instance context. 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. @@ -882,9 +1366,83 @@ with N. - - - + + + + + + +Undecidable instances + +The rules for instance declarations state that: + +At least one of the types in the head of +an instance declaration must not be a type variable. + +All of the types in the context of +an instance declaration must be type variables. + + +These restrictions ensure that +context reduction terminates: each reduction step removes one type +constructor. For example, the following would make the type checker +loop if it wasn't excluded: + + instance C a => C a where ... + +There are two situations in which the rule is a bit of a pain. First, +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 + + + +Second, 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) => ... + + + +Voluminous correspondence on the Haskell mailing list has convinced me +that it's worth experimenting 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. + + +I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while +allowing these idioms interesting idioms. + @@ -923,10 +1481,12 @@ implicitly parameterized by a comparison function named cmp. The dynamic binding constraints are just a new form of predicate in the type class system. -An implicit parameter is introduced by the special form ?x, +An implicit parameter occurs in an expression using the special form ?x, where x is -any valid identifier. Use if this construct also introduces new -dynamic binding constraints. For example, the following definition +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: @@ -935,6 +1495,11 @@ terms of an explicitly parameterized sortBy function: sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] sort = sortBy ?cmp + + + +Implicit-parameter type constraints + 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 @@ -951,68 +1516,93 @@ propagated. With implicit parameters, the default is to always propagate them. -An implicit parameter differs from other type class constraints in the +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: + + 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. + + + + +Implicit-parameter bindings + -An implicit parameter is bound using the standard -let binding form, where the bindings 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. This form binds the implicit -parameters arising in the body, not the free variables as a -let or where would do. For -example, we define the min function by binding -cmp. +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 let expression; they are not treated +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, each scoping over the bindings that -follow. For example, consider: +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 y = let { ?x = y; ?x = ?x+1 } in ?x + f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y -This function adds one to its argument. - - - -You may not have an implicit-parameter binding in a where clause, -only in a let binding. - - - - You can't have an implicit parameter in the context of a class or instance -declaration. For example, both these declarations are illegal: +The use of ?x in the binding for ?y does not "see" +the binding for ?x, so the type of f is - class (?x::Int) => C a where ... - instance (?x::a) => Foo [a] where ... + f :: (?x::Int) => Int -> Int -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. - + + @@ -1196,8 +1786,14 @@ 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. @@ -2206,49 +2802,6 @@ scope over the methods defined in the where part. For exampl -Result type signatures - - - - - - - - The result type of a function can be given a signature, -thus: - - - - f (x::a) :: [a] = [x,x,x] - - - -The final :: [a] after all the patterns gives a signature to the -result type. Sometimes this is the only way of naming the type variable -you want: - - - - f :: Int -> [a] -> [a] - f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x) - in \xs -> map g (reverse xs `zip` xs) - - - - - - - - - - - -Result type signatures are not yet implemented in Hugs. - - - - - Where a pattern type signature can occur @@ -2361,488 +2914,515 @@ in f4's scope. - - - - - - - - - -Assertions -<indexterm><primary>Assertions</primary></indexterm> - + +Result type signatures -If you want to make use of assertions in your standard Haskell code, you -could define a function like the following: - +The result type of a function can be given a signature, thus: - -assert :: Bool -> a -> a -assert False x = error "assertion failed!" -assert _ x = x + f (x::a) :: [a] = [x,x,x] - - - -which works, but gives you back a less than useful error message -- -an assertion failed, but which and where? - - - -One way out is to define an extended assert function which also -takes a descriptive string to include in the error message and -perhaps combine this with the use of a pre-processor which inserts -the source location where assert was used. - - -Ghc offers a helping hand here, doing all of this for you. For every -use of assert in the user's source: - +The final :: [a] after all the patterns gives a signature to the +result type. Sometimes this is the only way of naming the type variable +you want: - -kelvinToC :: Double -> Double -kelvinToC k = assert (k >= 0.0) (k+273.15) + f :: Int -> [a] -> [a] + f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x) + in \xs -> map g (reverse xs `zip` xs) - - -Ghc will rewrite this to also include the source location where the -assertion was made, - - - +The type variables bound in a result type signature scope over the right hand side +of the definition. However, consider this corner-case: -assert pred val ==> assertError "Main.hs|15" pred val - - - + rev1 :: [a] -> [a] = \xs -> reverse xs - -The rewrite is only performed by the compiler when it spots -applications of Control.Exception.assert, so you -can still define and use your own versions of -assert, should you so wish. If not, import -Control.Exception to make use -assert in your code. + foo ys = rev (ys::[a]) + +The signature on rev1 is considered a pattern type signature, not a result +type signature, and the type variables it binds have the same scope as rev1 +itself (i.e. the right-hand side of rev1 and the rest of the module too). +In particular, the expression (ys::[a]) is OK, because the type variable a +is in scope (otherwise it would mean (ys::forall a.[a]), which would be rejected). - -To have the compiler ignore uses of assert, use the compiler option -. -fignore-asserts -option That is, expressions of the form -assert pred e will be rewritten to -e. +As mentioned above, rev1 is made monomorphic by this scoping rule. +For example, the following program would be rejected, because it claims that rev1 +is polymorphic: + + rev1 :: [b] -> [b] + rev1 :: [a] -> [a] = \xs -> reverse xs + -Assertion failures can be caught, see the documentation for the -Control.Exception library for the details. +Result type signatures are not yet implemented in Hugs. - - - - -Syntactic extensions - - - - - Hierarchical Modules + - GHC supports a small extension to the syntax of module - names: a module name is allowed to contain a dot - ‘.’. This is also known as the - “hierarchical module namespace” extension, because - it extends the normally flat Haskell module namespace into a - more flexible hierarchy of modules. + - This extension has very little impact on the language - itself; modules names are always fully - qualified, so you can just think of the fully qualified module - name as the module name. In particular, this - means that the full module name must be given after the - module keyword at the beginning of the - module; for example, the module A.B.C must - begin + +Generalised derived instances for newtypes -module A.B.C + +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 + - It is a common strategy to use the as - keyword to save some typing when using qualified names with - hierarchical modules. For example: +and you want to use arithmetic on Dollars, you have to +explicitly define an instance of Num: - -import qualified Control.Monad.ST.Strict as ST + + 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! + - Hierarchical modules have an impact on the way that GHC - searches for files. For a description, see . - - 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. - + 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 - -Pattern guards + + instance Num Int => Num Dollars + - -Pattern guards (Glasgow extension) -The discussion that follows is an abbreviated version of Simon Peyton Jones's original proposal. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.) +which just adds or removes the newtype constructor according to the type. - -Suppose we have an abstract data type of finite maps, with a -lookup operation: - -lookup :: FiniteMap -> Int -> Maybe Int - +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 -The lookup returns Nothing if the supplied key is not in the domain of the mapping, and (Just v) otherwise, -where v is the value that the key maps to. Now consider the following definition: - + + 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 + - -clunky env var1 var2 | ok1 && ok2 = val1 + val2 -| otherwise = var1 + var2 -where - m1 = lookup env var1 - m2 = lookup env var2 - ok1 = maybeToBool m1 - ok2 = maybeToBool m2 - val1 = expectJust m1 - val2 = expectJust m2 +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) + - -The auxiliary functions are +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. + - -maybeToBool :: Maybe a -> Bool -maybeToBool (Just x) = True -maybeToBool Nothing = False +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 -expectJust :: Maybe a -> a -expectJust (Just x) = x -expectJust Nothing = error "Unexpected Nothing" + + 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) + + -What is clunky doing? The guard ok1 && -ok2 checks that both lookups succeed, using -maybeToBool to convert the Maybe -types to booleans. The (lazily evaluated) expectJust -calls extract the values from the results of the lookups, and binds the -returned values to val1 and val2 -respectively. If either lookup fails, then clunky takes the -otherwise case and returns the sum of its arguments. + +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 -This is certainly legal Haskell, but it is a tremendously verbose and -un-obvious way to achieve the desired effect. Arguably, a more direct way -to write clunky would be to use case expressions: - +Derived instance declarations are constructed as follows. Consider the +declaration (after expansion of any type synonyms) - -clunky env var1 var1 = case lookup env var1 of - Nothing -> fail - Just val1 -> case lookup env var2 of - Nothing -> fail - Just val2 -> val1 + val2 -where - fail = val1 + val2 - + + newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm) + - -This is a bit shorter, but hardly better. Of course, we can rewrite any set -of pattern-matching, guarded equations as case expressions; that is -precisely what the compiler does when compiling equations! The reason that -Haskell provides guarded equations is because they allow us to write down -the cases we want to consider, one at a time, independently of each other. -This structure is hidden in the case version. Two of the right-hand sides -are really the same (fail), and the whole expression -tends to become more and more indented. +where + + + S is a type constructor, + + + t1...tk are types, + + + vk+1...vn are type variables which do not occur in any of + the ti, and + + + 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. + + +Then, for each ci, the derived instance +declaration is: + + instance ci (S t1...tk vk+1...v) => ci (T v1...vp) + +where p is chosen so that T v1...vp is of the +right kind for the last parameter of class Ci. - -Here is how I would write clunky: - - -clunky env var1 var1 - | Just val1 <- lookup env var1 - , Just val2 <- lookup env var2 - = val1 + val2 -...other equations for clunky... - +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) + - -The semantics should be clear enough. The qualifers are matched in order. -For a <- qualifier, which I call a pattern guard, the -right hand side is evaluated and matched against the pattern on the left. -If the match fails then the whole guard fails and the next equation is -tried. If it succeeds, then the appropriate binding takes place, and the -next qualifier is matched, in the augmented environment. Unlike list -comprehensions, however, the type of the expression to the right of the -<- is the same as the type of the pattern to its -left. The bindings introduced by pattern guards scope over all the -remaining guard qualifiers, and over the right hand side of the equation. +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. - -Just as with list comprehensions, boolean expressions can be freely mixed -with among the pattern guards. For example: - - -f x | [y] <- x - , y > 3 - , Just z <- h y - = ... +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 ... - -Haskell's current guards therefore emerge as a special case, in which the -qualifier list has just one element, a boolean expression. +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. - + - + - -The recursive do-notation - - The recursive do-notation (also known as mdo-notation) is implemented as described in -"A recursive do for Haskell", -Levent Erkok, John Launchbury", -Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania. + + + + + + +Template Haskell + +Template Haskell allows you to do compile-time meta-programming in Haskell. The background +the main technical innovations are discussed in " +Template Meta-programming for Haskell", in +Proc Haskell Workshop 2002. + + + The first example from that paper is set out below as a worked example to help get you started. + + + +The documentation here describes the realisation in GHC. (It's rather sketchy just now; +Tim Sheard is going to expand it.) + + + Syntax + + Template Haskell has the following new syntactic constructions. You need to use the flag + -fglasgow-exts to switch these syntactic extensions on. + + + + A splice is written $x, where x is an + identifier, or $(...), where the "..." is an arbitrary expression. + There must be no space between the "$" and the identifier or parenthesis. This use + of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning + of "." as an infix operator. If you want the infix operator, put spaces around it. + + A splice can occur in place of + + an expression; the spliced expression must have type Expr + a list of top-level declarations; ; the spliced expression must have type Q [Dec] + a type; the spliced expression must have type Type. + + (Note that the syntax for a declaration splice uses "$" not "splice" as in + the paper. Also the type of the enclosed expression must be Q [Dec], not [Q Dec] + as in the paper.) + + + + + A expression quotation is written in Oxford brackets, thus: + + [| ... |], where the "..." is an expression; + the quotation has type Expr. + [d| ... |], where the "..." is a list of top-level declarations; + the quotation has type Q [Dec]. + [t| ... |], where the "..." is a type; + the quotation has type Type. + + + + Reification is written thus: + + reifyDecl T, where T is a type constructor; this expression + has type Dec. + reifyDecl C, where C is a class; has type Dec. + reifyType f, where f is an identifier; has type Typ. + Still to come: fixities + + + + + + + + + Using Template Haskell -The do-notation of Haskell does not allow recursive bindings, -that is, the variables bound in a do-expression are visible only in the textually following -code block. Compare this to a let-expression, where bound variables are visible in the entire binding -group. It turns out that several applications can benefit from recursive bindings in -the do-notation, and this extension provides the necessary syntactic support. + + + The data types and monadic constructor functions for Template Haskell are in the library + Language.Haskell.THSyntax. + + + + You can only run a function at compile time if it is imported from another module. That is, + you can't define a function in a module, and call it from within a splice in the same module. + (It would make sense to do so, but it's hard to implement.) + + + + The flag -ddump-splices shows the expansion of all top-level splices as they happen. + + + If you are building GHC from source, you need at least a stage-2 bootstrap compiler to + run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH + compiles and runs a program, and then looks at the result. So it's important that + the program it compiles produces results whose representations are identical to + those of the compiler itself. + + - -Here is a simple (yet contrived) example: + Template Haskell works in any mode (--make, --interactive, + or file-at-a-time). There used to be a restriction to the former two, but that restriction + has been lifted. + + + A Template Haskell Worked Example +To help you get over the confidence barrier, try out this skeletal worked example. + First cut and paste the two modules below into "Main.hs" and "Printf.hs": + -justOnes = mdo xs <- Just (1:xs) - return xs +{- Main.hs -} +module Main where + +-- Import our template "pr" +import Printf ( pr ) + +-- The splice operator $ takes the Haskell source code +-- generated at compile time by "pr" and splices it into +-- the argument of "putStrLn". +main = putStrLn ( $(pr "Hello") ) - -As you can guess justOnes will evaluate to Just [1,1,1,.... - - -The Control.Monad.Fix library introduces the MonadFix class. It's definition is: - -class Monad m => MonadFix m where - mfix :: (a -> m a) -> m a - - -The function mfix -dictates how the required recursion operation should be performed. If recursive bindings are required for a monad, -then that monad must be declared an instance of the MonadFix class. -For details, see the above mentioned reference. - - -The following instances of MonadFix are automatically provided: List, Maybe, IO, and -state monads (both lazy and strict). - - -There are three important points in using the recursive-do notation: - - -The recursive version of the do-notation uses the keyword mdo (rather -than do). - +{- Printf.hs -} +module Printf where - -If you want to declare an instance of the MonadFix class for one of -your own monads, or you need to refer to the class name MonadFix in any other way (for -instance when writing a type constraint), then your program should -import Control.Monad.MonadFix. -Otherwise, you don't need to import any special libraries to use the mdo-notation. That is, -as long as you only use the predefined instances mentioned above, the mdo-notation will -be automatically available. -To be on the safe side, of course, you can simply import it in all cases. - +-- Skeletal printf from the paper. +-- It needs to be in a separate module to the one where +-- you intend to use it. - -As with other extensions, ghc should be given the flag -fglasgow-exts - - - +-- Import some Template Haskell syntax +import Language.Haskell.THSyntax + +-- Describe a format string +data Format = D | S | L String + +-- Parse a format string. This is left largely to you +-- as we are here interested in building our first ever +-- Template Haskell program and not in building printf. +parse :: String -> [Format] +parse s = [ L s ] - -Historical note: The old implementation of the mdo-notation (and most -of the existing documents) used the name -MonadRec for the class and the corresponding library. -This name is no longer supported. +-- Generate Haskell source code from a parsed representation +-- of the format string. This code will be spliced into +-- the module which calls "pr", at compile time. +gen :: [Format] -> Expr +gen [D] = [| \n -> show n |] +gen [S] = [| \s -> s |] +gen [L s] = string s + +-- Here we generate the Haskell code for the splice +-- from an input format string. +pr :: String -> Expr +pr s = gen (parse s) + + +Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows): + +ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe + - -The web page: http://www.cse.ogi.edu/PacSoft/projects/rmb -contains up to date information on recursive monadic bindings. +Run "main.exe" and here is your output: + +$ ./main +Hello + + + + - + - - Parallel List Comprehensions - list comprehensionsparallel - - parallel list comprehensions - + +Assertions +<indexterm><primary>Assertions</primary></indexterm> + - Parallel list comprehensions are a natural extension to list - comprehensions. List comprehensions can be thought of as a nice - syntax for writing maps and filters. Parallel comprehensions - extend this to include the zipWith family. + +If you want to make use of assertions in your standard Haskell code, you +could define a function like the following: + - A parallel list comprehension has multiple independent - branches of qualifier lists, each separated by a `|' symbol. For - example, the following zips together two lists: + - [ (x, y) | x <- xs | y <- ys ] +assert :: Bool -> a -> a +assert False x = error "assertion failed!" +assert _ x = x - The behavior of parallel list comprehensions follows that of - zip, in that the resulting list will have the same length as the - shortest branch. + - We can define parallel list comprehensions by translation to - regular comprehensions. Here's the basic idea: + +which works, but gives you back a less than useful error message -- +an assertion failed, but which and where? + - Given a parallel comprehension of the form: + +One way out is to define an extended assert function which also +takes a descriptive string to include in the error message and +perhaps combine this with the use of a pre-processor which inserts +the source location where assert was used. + - - [ e | p1 <- e11, p2 <- e12, ... - | q1 <- e21, q2 <- e22, ... - ... - ] - + +Ghc offers a helping hand here, doing all of this for you. For every +use of assert in the user's source: + - This will be translated to: + - [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...] - [(q1,q2) | q1 <- e21, q2 <- e22, ...] - ... - ] +kelvinToC :: Double -> Double +kelvinToC k = assert (k >= 0.0) (k+273.15) - where `zipN' is the appropriate zip for the given number of - branches. - - - - -Rebindable syntax - + - GHC allows most kinds of built-in syntax to be rebound by - the user, to facilitate replacing the Prelude - with a home-grown version, for example. + +Ghc will rewrite this to also include the source location where the +assertion was made, + - You may want to define your own numeric class - 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 - the following pieces of built-in syntax to refer to - whatever is in scope, not the Prelude - versions: + - - - Integer and fractional literals mean - "fromInteger 1" and - "fromRational 3.2", not the - Prelude-qualified versions; both in expressions and in - patterns. - However, the standard Prelude Eq class - is still used for the equality test necessary for literal patterns. - + +assert pred val ==> assertError "Main.hs|15" pred val + - - Negation (e.g. "- (f x)") - means "negate (f x)" (not - Prelude.negate). - + - - In an n+k pattern, the standard Prelude - Ord class is still used for comparison, - but the necessary subtraction uses whatever - "(-)" is in scope (not - "Prelude.(-)"). - + +The rewrite is only performed by the compiler when it spots +applications of Control.Exception.assert, so you +can still define and use your own versions of +assert, should you so wish. If not, import +Control.Exception to make use +assert in your code. + - - "Do" notation is translated using whatever - functions (>>=), - (>>), fail, and - return, are in scope (not the Prelude - versions). List comprehensions, and parallel array - comprehensions, are unaffected. - + +To have the compiler ignore uses of assert, use the compiler option +. -fignore-asserts +option That is, expressions of the form +assert pred e will be rewritten to +e. + - Be warned: this is an experimental facility, with fewer checks than - usual. In particular, it is essential that the functions GHC finds in scope - must have the appropriate types, namely: - - fromInteger :: forall a. (...) => Integer -> a - fromRational :: forall a. (...) => Rational -> a - negate :: forall a. (...) => a -> a - (-) :: forall a. (...) => a -> a -> a - (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b - (>>) :: forall m a. (...) => m a -> m b -> m b - return :: forall m a. (...) => a -> m a - fail :: forall m a. (...) => String -> m a - - (The (...) part can be any context including the empty context; that part - is up to you.) - If the functions don't have the right type, very peculiar things may - happen. Use -dcore-lint to - typecheck the desugared program. If Core Lint is happy you should be all right. + +Assertion failures can be caught, see the documentation for the +Control.Exception library for the details. + - + @@ -2868,32 +3448,64 @@ contains up to date information on recursive monadic bindings. unrecognised word is (silently) ignored. - -INLINE pragma + <sect2 id="deprecated-pragma"> + <title>DEPRECATED pragma + DEPRECATED + -INLINE pragma -pragma, INLINE + The DEPRECATED pragma lets you specify that a particular + function, class, or type, is deprecated. There are two + forms. - -GHC (with , as always) tries to inline (or “unfold”) -functions/values that are “small enough,” thus avoiding the call -overhead and possibly exposing other more-wonderful optimisations. - + + + You can deprecate an entire module thus: + + module Wibble {-# DEPRECATED "Use Wobble instead" #-} where + ... + + When you compile any module that import + Wibble, GHC will print the specified + message. + - -You will probably see these unfoldings (in Core syntax) in your -interface files. - + + You can deprecate a function, class, or type, with the + following top-level declaration: + + {-# DEPRECATED f, C, T "Don't use these" #-} + + When you compile any module that imports and uses any + of the specifed entities, GHC will print the specified + message. + + - -Normally, if GHC decides a function is “too expensive” to inline, it -will not do so, nor will it export that unfolding for other modules to -use. - + You can suppress the warnings with the flag + . + - -The sledgehammer you can bring to bear is the -INLINEINLINE pragma pragma, used thusly: + + INLINE and NOINLINE pragmas + + These pragmas control the inlining of function + definitions. + + + INLINE pragma + INLINE + + GHC (with , as always) tries to + inline (or “unfold”) functions/values that are + “small enough,” thus avoiding the call overhead + and possibly exposing other more-wonderful optimisations. + Normally, if GHC decides a function is “too + expensive” to inline, it will not do so, nor will it + export that unfolding for other modules to use. + + The sledgehammer you can bring to bear is the + INLINEINLINE + pragma pragma, used thusly: key_function :: Int -> String -> (Bool, Double) @@ -2903,25 +3515,25 @@ key_function :: Int -> String -> (Bool, Double) #endif -(You don't need to do the C pre-processor carry-on unless you're going -to stick the code through HBC—it doesn't like INLINE pragmas.) - + (You don't need to do the C pre-processor carry-on + unless you're going to stick the code through HBC—it + doesn't like INLINE pragmas.) - -The major effect of an INLINE pragma is to declare a function's -“cost” to be very low. The normal unfolding machinery will then be -very keen to inline it. - + The major effect of an INLINE pragma + is to declare a function's “cost” to be very low. + The normal unfolding machinery will then be very keen to + inline it. - -An INLINE pragma for a function can be put anywhere its type -signature could be put. - + Syntactially, an INLINE pragma for a + function can be put anywhere its type signature could be + put. - -INLINE pragmas are a particularly good idea for the -then/return (or bind/unit) functions in a monad. -For example, in GHC's own UniqueSupply monad code, we have: + INLINE pragmas are a particularly + good idea for the + then/return (or + bind/unit) functions in + a monad. For example, in GHC's own + UniqueSupply monad code, we have: #ifdef __GLASGOW_HASKELL__ @@ -2930,32 +3542,140 @@ For example, in GHC's own UniqueSupply monad code, we have: #endif - + See also the NOINLINE pragma (). + + + + NOINLINE pragma + + NOINLINE + NOTINLINE + + The NOINLINE pragma does exactly what + you'd expect: it stops the named function from being inlined + by the compiler. You shouldn't ever need to do this, unless + you're very cautious about code size. + + NOTINLINE is a synonym for + NOINLINE (NOTINLINE is + specified by Haskell 98 as the standard way to disable + inlining, so it should be used if you want your code to be + portable). + + + + Phase control + + Sometimes you want to control exactly when in GHC's + pipeline the INLINE pragma is switched on. Inlining happens + only during runs of the simplifier. Each + run of the simplifier has a different phase + number; the phase number decreases towards zero. + If you use you'll see the + sequence of phase numbers for successive runs of the + simpifier. In an INLINE pragma you can optionally specify a + phase number, thus: + + + + You can say "inline f in Phase 2 + and all subsequent phases": + + {-# INLINE [2] f #-} + + + - + + You can say "inline g in all + phases up to, but not including, Phase 3": + + {-# INLINE [~3] g #-} + + + - -NOINLINE pragma - + + If you omit the phase indicator, you mean "inline in + all phases". + + -NOINLINE pragma -pragmaNOINLINE -NOTINLINE pragma -pragmaNOTINLINE + You can use a phase number on a NOINLINE pragma too: - -The NOINLINE pragma does exactly what you'd expect: -it stops the named function from being inlined by the compiler. You -shouldn't ever need to do this, unless you're very cautious about code -size. - + + + You can say "do not inline f + until Phase 2; in Phase 2 and subsequently behave as if + there was no pragma at all": + + {-# NOINLINE [2] f #-} + + + -NOTINLINE is a synonym for -NOINLINE (NOTINLINE is specified -by Haskell 98 as the standard way to disable inlining, so it should be -used if you want your code to be portable). + + You can say "do not inline g in + Phase 3 or any subsequent phase; before that, behave as if + there was no pragma": + + {-# NOINLINE [~3] g #-} + + + - + + If you omit the phase indicator, you mean "never + inline this function". + + + + The same phase-numbering control is available for RULES + (). + + + + + LINE pragma + + LINEpragma + pragmaLINE + This pragma is similar to C's #line + pragma, and is mainly for use in automatically generated Haskell + code. It lets you specify the line number and filename of the + original code; for example + + +{-# LINE 42 "Foo.vhs" #-} + + + if you'd generated the current file from something called + Foo.vhs and this line corresponds to line + 42 in the original. GHC will adjust its error messages to refer + to the line/file named in the LINE + pragma. + + + + OPTIONS pragma + OPTIONS + + pragmaOPTIONS + + + The OPTIONS pragma is used to specify + additional options that are given to the compiler when compiling + this source file. See for + details. + + + + RULES pragma + + The RULES pragma lets you specify rewrite rules. It is + described in . + SPECIALIZE pragma @@ -2981,11 +3701,14 @@ hammeredLookup :: Ord key => [(key, value)] -> key -> value {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-} + A SPECIALIZE pragma for a function can + be put anywhere its type signature could be put. + To get very fancy, you can also specify a named function to use for the specialised value, as in: -{-# RULES hammeredLookup = blah #-} +{-# RULES "hammeredLookup" hammeredLookup = blah #-} where blah is an implementation of @@ -3008,17 +3731,14 @@ hammeredLookup :: Ord key => [(key, value)] -> key -> value toDouble :: Real a => a -> Double toDouble = fromRational . toRational -{-# SPECIALIZE toDouble :: Int -> Double = i2d #-} +{-# RULES "toDouble/Int" toDouble = i2d #-} i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly The i2d function is virtually one machine instruction; the default conversion—via an intermediate Rational—is obscenely expensive by - comparison. - - A SPECIALIZE pragma for a function can - be put anywhere its type signature could be put. + comparison. @@ -3047,83 +3767,7 @@ of the pragma. - -LINE pragma - - - -LINE pragma -pragma, LINE - - - -This pragma is similar to C's #line pragma, and is mainly for use in -automatically generated Haskell code. It lets you specify the line -number and filename of the original code; for example - - - - - -{-# LINE 42 "Foo.vhs" #-} - - - - - -if you'd generated the current file from something called Foo.vhs -and this line corresponds to line 42 in the original. GHC will adjust -its error messages to refer to the line/file named in the LINE -pragma. - - - - - -RULES pragma - - -The RULES pragma lets you specify rewrite rules. It is described in -. - - - - - -DEPRECATED pragma - - -The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated. -There are two forms. - - - -You can deprecate an entire module thus: - - module Wibble {-# DEPRECATED "Use Wobble instead" #-} where - ... - - -When you compile any module that import Wibble, GHC will print -the specified message. - - - - -You can deprecate a function, class, or type, with the following top-level declaration: - - - {-# DEPRECATED f, C, T "Don't use these" #-} - - -When you compile any module that imports and uses any of the specifed entities, -GHC will print the specified message. - - - -You can suppress the warnings with the flag . - @@ -3162,16 +3806,34 @@ From a syntactic point of view: + There may be zero or more rules in a RULES pragma. + + + + + + Each rule has a name, enclosed in double quotes. The name itself has no significance at all. It is only used when reporting how many times the rule fired. - + - There may be zero or more rules in a RULES pragma. +A rule may optionally have a phase-control number (see ), +immediately after the name of the rule. Thus: + + {-# RULES + "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs + #-} + +The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse +notation "[~2]" is also accepted, meaning that the rule is active up to, but not including, +Phase 2. + + @@ -3180,6 +3842,7 @@ is set, so you must lay out your rules starting in the same column as the enclosing definitions. + @@ -3655,7 +4318,7 @@ If you add you get a more detailed listing. - The defintion of (say) build in PrelBase.lhs looks llike this: + The defintion of (say) build in GHC/Base.lhs looks llike this: build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a] @@ -3673,9 +4336,9 @@ in the RHS of the INLINE thing. I regret the delicacy of thi - In ghc/lib/std/PrelBase.lhs look at the rules for map to + In libraries/base/GHC/Base.lhs look at the rules for map to see how to write rules that will do fusion and yet give an efficient -program even if fusion doesn't happen. More rules in PrelList.lhs. +program even if fusion doesn't happen. More rules in GHC/List.lhs. @@ -3685,6 +4348,69 @@ program even if fusion doesn't happen. More rules in PrelList.lhs + + CORE pragma + + CORE pragma + pragma, CORE + core, annotation + + + The external core format supports Note annotations; + the CORE pragma gives a way to specify what these + should be in your Haskell source code. Syntactically, core + annotations are attached to expressions and take a Haskell string + literal as an argument. The following function definition shows an + example: + + +f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x) + + + Sematically, this is equivalent to: + + +g x = show x + + + + + However, when external for is generated (via + ), there will be Notes attached to the + expressions show and x. + The core function declaration for f is: + + + + f :: %forall a . GHCziShow.ZCTShow a -> + a -> GHCziBase.ZMZN GHCziBase.Char = + \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) -> + (%note "foo" + %case zddShow %of (tpl::GHCziShow.ZCTShow a) + {GHCziShow.ZCDShow + (tpl1::GHCziBase.Int -> + a -> + GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha +r) + (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char) + (tpl3::GHCziBase.ZMZN a -> + GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha +r) -> + tpl2}) + (%note "foo" + eta); + + + + Here, we can see that the function show (which + has been expanded out to a case expression over the Show dictionary) + has a %note attached to it, as does the + expression eta (which used to be called + x). + + + + @@ -3733,7 +4459,7 @@ Now you can make a data type into an instance of Bin like this: instance (Bin a, Bin b) => Bin (a,b) instance Bin a => Bin [a] -That is, just leave off the "where" clasuse. Of course, you can put in the +That is, just leave off the "where" clause. Of course, you can put in the where clause and over-ride whichever methods you please. @@ -3943,180 +4669,6 @@ Just to finish with, here's another example I rather like: - -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' (S t1...tk vk+1...vn) deriving (c1...cm) - - -where S is a type constructor, t1...tk are -types, -vk+1...vn are type variables which do not occur in any of -the ti, and the ci are partial applications of -classes of the form C t1'...tj'. The derived instance -declarations are, for each ci, - - - instance ci (S t1...tk vk+1...v) => ci (T v1...vp) - -where p is chosen so that T v1...vp is of the -right kind for the last parameter of class Ci. - - - -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. - - - - -