X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=ghc%2Fdocs%2Fusers_guide%2Fglasgow_exts.sgml;h=4602650e46b62c4077d89bdfa5ab1e0a8e9f2071;hb=ce136f8bc3bfffc60a0c29f42466c309c8cdac63;hp=1893765a319ff11ec1f4655792ef950f8a7dcaf0;hpb=f74c3a0e15b6c5e650fc9ae6760276f564605fbc;p=ghc-hetmet.git
diff --git a/ghc/docs/users_guide/glasgow_exts.sgml b/ghc/docs/users_guide/glasgow_exts.sgml
index 1893765..4602650 100644
--- a/ghc/docs/users_guide/glasgow_exts.sgml
+++ b/ghc/docs/users_guide/glasgow_exts.sgml
@@ -16,160 +16,15 @@ performance because of the implementation costs of Haskell's
-Executive summary of our extensions:
-
-
-
-
-
- Unboxed types and primitive operations:
-
- You can get right down to the raw machine types and
- operations; included in this are “primitive
- arrays” (direct access to Big Wads of Bytes). Please
- see and following.
-
-
-
-
- Type system extensions:
-
- GHC supports a large number of extensions to Haskell's
- type system. Specifically:
-
-
-
- Multi-parameter type classes:
-
-
-
-
-
-
- Functional dependencies:
-
-
-
-
-
-
- Implicit parameters:
-
-
-
-
-
-
- Linear implicit parameters:
-
-
-
-
-
-
- Local universal quantification:
-
-
-
-
-
-
- Extistentially quantification in data types:
-
-
-
-
-
-
- Scoped type variables:
-
- Scoped type variables enable the programmer to
- supply type signatures for some nested declarations,
- where this would not be legal in Haskell 98. Details in
- .
-
-
-
-
-
-
-
- Pattern guards
-
- Instead of being a boolean expression, a guard is a list
- of qualifiers, exactly as in a list comprehension. See .
-
-
-
-
- Data types with no constructors
-
- See .
-
-
-
-
- Parallel list comprehensions
-
- An extension to the list comprehension syntax to support
- zipWith-like functionality. See .
-
-
-
-
- Foreign calling:
-
- Just what it sounds like. We provide
- lots of rope that you can dangle around
- your neck. Please see .
-
-
-
-
- Pragmas
-
- Pragmas are special instructions to the compiler placed
- in the source file. The pragmas GHC supports are described in
- .
-
-
-
-
- Rewrite rules:
-
- The programmer can specify rewrite rules as part of the
- source program (in a pragma). GHC applies these rewrite rules
- wherever it can. Details in .
-
-
-
-
- Generic classes:
-
- (Note: support for generic classes is currently broken
- in GHC 5.02).
-
- Generic class declarations allow you to define a class
- whose methods say how to work over an arbitrary data type.
- Then it's really easy to make any new type into an instance of
- the class. This generalises the rather ad-hoc "deriving"
- feature of Haskell 98. Details in .
-
-
-
-
-
Before you get too carried away working at the lowest level (e.g.,
sloshing MutableByteArray#s around your
program), you may wish to check if there are libraries that provide a
-“Haskellised veneer” over the features you want. See
-.
+“Haskellised veneer” over the features you want. The
+separate libraries documentation describes all the libraries that come
+with GHC.
+
Language options
@@ -198,6 +53,30 @@ program), you may wish to check if there are libraries that provide a
+ and :
+
+
+
+ This option enables the language extension defined in the
+ Haskell 98 Foreign Function Interface Addendum plus deprecated
+ syntax of previous versions of the FFI for backwards
+ compatibility.
+
+
+
+
+ :
+
+
+ This option enables the deprecated with
+ keyword for implicit parameters; it is merely provided for backwards
+ compatibility.
+ It is independent of the
+ flag.
+
+
+
+ :
@@ -231,6 +110,15 @@ program), you may wish to check if there are libraries that provide a
+
+
+
+ See . Independent of
+ .
+
+
+
+
@@ -252,7 +140,7 @@ program), you may wish to check if there are libraries that provide a
module namespace is flat, and you must not conflict with
any Prelude module.)
- Even though you have not imported the Prelude, all
+ Even though you have not imported the Prelude, most of
the built-in syntax still refers to the built-in Haskell
Prelude types and values, as specified by the Haskell
Report. For example, the type [Int]
@@ -261,51 +149,9 @@ program), you may wish to check if there are libraries that provide a
translation for list comprehensions continues to use
Prelude.map etc.
- With one group of exceptions! 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.
-
-
-
- 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.(-)").
-
-
-
- Note: Negative literals, such as -3, are
- specified by (a careful reading of) the Haskell Report as
- meaning Prelude.negate (Prelude.fromInteger 3).
- However, GHC deviates from this slightly, and treats them as meaning
- fromInteger (-3). One particular effect of this
- slightly-non-standard reading is that there is no difficulty with
- the literal -2147483648 at type Int;
- it means fromInteger (-2147483648). The strict interpretation
- would be negate (fromInteger 2147483648),
- and the call to fromInteger would overflow
- (at type Int, remember).
-
+ However, does
+ change the handling of certain built-in syntax: see
+ .
@@ -314,144 +160,279 @@ program), you may wish to check if there are libraries that provide a
-&primitives;
+
+
+
+ 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
+
+
+
+Unboxed types (Glasgow extension)
+
-
-Primitive state-transformer monad
+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.
+
-state transformers (Glasgow extensions)
-ST monad (Glasgow extension)
+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.
-This monad underlies our implementation of arrays, mutable and
-immutable, and our implementation of I/O, including “C calls”.
+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.
-The ST library, which provides access to the
-ST monad, is described in .
+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.
-
+
+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).
+
+
+
+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.
+
+
+
-
-Primitive arrays, mutable and otherwise
+
+Unboxed Tuples
-primitive arrays (Glasgow extension)
-arrays, primitive (Glasgow extension)
+Unboxed tuples aren't really exported by GHC.Exts,
+they're available by default with . An
+unboxed tuple looks like this:
-GHC knows about quite a few flavours of Large Swathes of Bytes.
+
+
+(# e_1, ..., e_n #)
+
+
-First, GHC distinguishes between primitive arrays of (boxed) Haskell
-objects (type Array# obj) and primitive arrays of bytes (type
-ByteArray#).
+where e_1..e_n are expressions of any
+type (primitive or non-primitive). The type of an unboxed tuple looks
+the same.
-Second, it distinguishes between…
-
+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.
+
-
-Immutable:
-
-Arrays that do not change (as with “standard” Haskell arrays); you
-can only read from them. Obviously, they do not need the care and
-attention of the state-transformer monad.
+There are some pretty stringent restrictions on the use of unboxed tuples:
-
-
-
-Mutable:
+
+
+
+
+
-Arrays that may be changed or “mutated.” All the operations on them
-live within the state-transformer monad and the updates happen
-in-place.
+ 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.
+
-
-
-“Static” (in C land):
+
-A C routine may pass an Addr# pointer back into Haskell land. There
-are then primitive operations with which you may merrily grab values
-over in C land, by indexing off the “static” pointer.
+ 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:
+
+
+
+f x y = (# x+1, y-1 #)
+g x = case f x x of { (# a, b #) -> a + b }
+
+
+
+but the following are invalid:
+
+
+
+f x y = g (# x, y #)
+g (# x, y #) = x + y
+
+
+
-
-
-“Stable” pointers:
-
-If, for some reason, you wish to hand a Haskell pointer (i.e.,
-not an unboxed value) to a C routine, you first make the
-pointer “stable,” so that the garbage collector won't forget that it
-exists. That is, GHC provides a safe way to pass Haskell pointers to
-C.
-
-Please see for more details.
+ No variable can have an unboxed tuple type. This is illegal:
+
+
+
+f :: (# Int, Int #) -> (# Int, Int #)
+f x = x
+
+
+
+because x has an unboxed tuple type.
+
-
-
-“Foreign objects”:
-
-
-A “foreign object” is a safe way to pass an external object (a
-C-allocated pointer, say) to Haskell and have Haskell do the Right
-Thing when it no longer references the object. So, for example, C
-could pass a large bitmap over to Haskell and say “please free this
-memory when you're done with it.”
+
+
+
-Please see for more details.
-
-
-
-
+Note: we may relax some of these restrictions in the future.
-The libraries documentatation gives more details on all these
-“primitive array” types and the operations on them.
+The IO and ST monads use unboxed
+tuples to avoid unnecessary allocation during sequences of operations.
+
-
-Data types with no constructors
+
+
+
+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
+
+module A.B.C
+
+
+ It is a common strategy to use the as
+ keyword to save some typing when using qualified names with
+ hierarchical modules. For example:
-With the flag, GHC lets you declare
-a data type with no constructors. For example:
- data S -- S :: *
- data T a -- T :: * -> *
+import qualified Control.Monad.ST.Strict as ST
-Syntactically, the declaration lacks the "= constrs" part. The
-type can be parameterised, but only over ordinary types, of kind *; since
-Haskell does not have kind signatures, you cannot parameterise over higher-kinded
-types.
-Such data types have only one value, namely bottom.
-Nevertheless, they can be useful when defining "phantom types".
-
+ For details on how GHC searches for source and interface
+ files in the presence of hierarchical modules, 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.
+
+
+
+
-
+Pattern guards
@@ -576,9 +557,96 @@ f x | [y] <- x
Haskell's current guards therefore emerge as a special case, in which the
qualifier list has just one element, a boolean expression.
-
+
+
+
+
+
+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:
+
+
+import Control.Monad.Fix
+
+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
+
+
+
+
+
+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.
+
+
+
+
+
+
+
+ Parallel List Comprehensionslist comprehensionsparallel
@@ -626,1544 +694,1860 @@ qualifier list has just one element, a boolean expression.
where `zipN' is the appropriate zip for the given number of
branches.
-
+
-
-Multi-parameter type classes
-
+
+Rebindable syntax
-
-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).
-
-
-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.)
-
+ 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.
-
-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.
-
+ 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:
-
-Types
+
+
+ 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.
+
-
-There are the following restrictions on the form of a qualified
-type:
-
+
+ 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.(-)").
+
-
- forall tv1..tvn (c1, ...,cn) => type
-
+
+ "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.
-
-(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 ).
-
+
+
-
-
-
+
+
+Type system extensions
-
- 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:
+
+Data types and type synonyms
+
+
+Data types with no constructors
+With the flag, GHC lets you declare
+a data type with no constructors. For example:
- forall a. Eq a => Int
+ 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 ).
-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.
+Such data types have only one value, namely bottom.
+Nevertheless, they can be useful when defining "phantom types".
+
-
-
-
+
+Infix type constructors
- Every constraint ci must mention at least one of the
-universally quantified type variables tvi.
+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.
+
-For example, this type is OK because C a b mentions the
-universally quantified type variable b:
+
+
+
+
+Liberalised type synonyms
+
+Type synonmys are like macros at the type level, and
+GHC does validity checking on types only after expanding type synonyms.
+That means that GHC can be very much more liberal about type synonyms than Haskell 98:
+
+You can write a forall (including overloading)
+in a type synonym, thus:
- forall a. C a b => burble
+ type Discard a = forall b. Show b => a -> b -> (a, String)
+
+ f :: Discard a
+ f x y = (x, show y)
+
+ g :: Discard Int -> (Int,Bool) -- A rank-2 type
+ g f = f Int True
+
+
+
+You can write an unboxed tuple in a type synonym:
+
+ type Pr = (# Int, Int #)
-The next type is illegal because the constraint Eq b does not
-mention a:
+ h :: Int -> Pr
+ h x = (# x, x #)
+
+
+
+You can apply a type synonym to a forall type:
+
+ type Foo a = a -> a -> Bool
+
+ f :: Foo (forall b. b->b)
+
+After expanding the synonym, f has the legal (in GHC) type:
+
+ f :: (forall b. b->b) -> (forall b. b->b) -> Bool
+
+
+
+You can apply a type synonym to a partially applied type synonym:
- forall a. Eq b => burble
+ type Generic i o = forall x. i x -> o x
+ type Id x = x
+
+ foo :: Generic Id []
+
+After epxanding the synonym, foo has the legal (in GHC) type:
+
+ foo :: forall x. x -> [x]
+
+
+
-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.
+
+GHC currently does kind checking before expanding synonyms (though even that
+could be changed.)
+
+
+After expanding type synonyms, GHC does validity checking on types, looking for
+the following mal-formedness which isn't detected simply by kind checking:
+
+
+Type constructor applied to a type involving for-alls.
+
+
+Unboxed tuple on left of an arrow.
+
+
+Partially-applied type synonym.
+
+
+So, for example,
+this will be rejected:
+
+ type Pr = (# Int, Int #)
+ h :: Pr -> Int
+ h x = ...
+
+because GHC does not allow unboxed tuples on the left of a function arrow.
-
+
-
+
+Existentially quantified data constructors
+
+
+
+The idea of using existential quantification in data type declarations
+was suggested by Laufer (I believe, thought doubtless someone will
+correct me), and implemented in Hope+. It's been in Lennart
+Augustsson's hbc Haskell compiler for several years, and
+proved very useful. Here's the idea. Consider the declaration:
-These restrictions apply to all types, whether declared in a type signature
-or inferred.
+
+
+ data Foo = forall a. MkFoo a (a -> Bool)
+ | Nil
+
+
-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
+The data type Foo has two constructors with types:
- f :: Eq (m a) => [m a] -> [m a]
- g :: Eq [a] => ...
+ MkFoo :: forall a. a -> (a -> Bool) -> Foo
+ Nil :: Foo
-This choice recovers principal types, a property that Haskell 1.4 does not have.
+Notice that the type variable a in the type of MkFoo
+does not appear in the data type itself, which is plain Foo.
+For example, the following expression is fine:
-
+
-
-Class declarations
+
+ [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
+
-
+
-
-
+
+Here, (MkFoo 3 even) packages an integer with a function
+even that maps an integer to Bool; and MkFoo 'c'
+isUpper packages a character with a compatible function. These
+two things are each of type Foo and can be put in a list.
+
- Multi-parameter type classes are permitted. For example:
+What can we do with a value of type Foo?. In particular,
+what happens when we pattern-match on MkFoo?
+
+
- class Collection c a where
- union :: c a -> c a -> c a
- ...etc.
+ f (MkFoo val fn) = ???
-
-
-
-
- The class hierarchy must be acyclic. However, the definition
-of "acyclic" involves only the superclass relationships. For example,
-this is OK:
+Since all we know about val and fn is that they
+are compatible, the only (useful) thing we can do with them is to
+apply fn to val to get a boolean. For example:
+
+
- class C a where {
- op :: D b => a -> b -> b
- }
-
- class C a => D a where { ... }
+ f :: Foo -> Bool
+ f (MkFoo val fn) = fn val
+
-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.)
-
+
+What this allows us to do is to package heterogenous values
+together with a bunch of functions that manipulate them, and then treat
+that collection of packages in a uniform manner. You can express
+quite a bit of object-oriented-like programming this way.
-
-
+
+
+Why existential?
+
- 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:
+What has this to do with existential quantification?
+Simply that MkFoo has the (nearly) isomorphic type
+
+
- class Functor (m k) => FiniteMap m k where
- ...
-
- class (Monad m, Monad (t m)) => Transform t m where
- lift :: m a -> (t m) a
+ MkFoo :: (exists a . (a, a -> Bool)) -> Foo
-
-
-
- In the signature of a class operation, every constraint
-must mention at least one type variable that is not a class type
-variable.
+But Haskell programmers can safely think of the ordinary
+universally quantified type given above, thereby avoiding
+adding a new existential quantification construct.
+
+
+
+
+
+Type classes
-Thus:
+
+An easy extension (implemented in hbc) is to allow
+arbitrary contexts before the constructor. For example:
+
+
- class Collection c a where
- mapC :: Collection c b => (a->b) -> c a -> c b
+data Baz = forall a. Eq a => Baz1 a a
+ | forall b. Show b => Baz2 b (b -> b)
+
-is OK because the constraint (Collection a b) mentions
-b, even though it also mentions the class variable
-a. On the other hand:
+
+The two constructors have the types you'd expect:
+
+
- class C a where
- op :: Eq a => (a,b) -> (a,b)
+Baz1 :: forall a. Eq a => a -> a -> Baz
+Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
+
-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:
+
+But when pattern matching on Baz1 the matched values can be compared
+for equality, and when pattern matching on Baz2 the first matched
+value can be converted to a string (as well as applying the function to it).
+So this program is legal:
+
+
- class Eq a => C a where
- op ::(a,b) -> (a,b)
+ f :: Baz -> String
+ f (Baz1 p q) | p == q = "Yes"
+ | otherwise = "No"
+ f (Baz2 v fn) = show (fn v)
+
+
+
+Operationally, in a dictionary-passing implementation, the
+constructors Baz1 and Baz2 must store the
+dictionaries for Eq and Show respectively, and
+extract it on pattern matching.
+
+
+
+Notice the way that the syntax fits smoothly with that used for
+universal quantification earlier.
+
+
+
-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.
+
+Restrictions
+
+There are several restrictions on the ways in which existentially-quantified
+constructors can be use.
-
+
+
+
+
- The type of each class operation must mention all of
-the class type variables. For example:
+ When pattern matching, each pattern match introduces a new,
+distinct, type for each existential type variable. These types cannot
+be unified with any other type, nor can they escape from the scope of
+the pattern match. For example, these fragments are incorrect:
- class Coll s a where
- empty :: s
- insert :: s -> a -> s
+f1 (MkFoo a f) = a
-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
+Here, the type bound by MkFoo "escapes", because a
+is the result of f1. One way to see why this is wrong is to
+ask what type f1 has:
- class Coll s a where
- empty :: s a
- insert :: s a -> a -> s a
+ f1 :: Foo -> a -- Weird!
-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:
+What is this "a" in the result type? Clearly we don't mean
+this:
- class CollE s where
- empty :: s
-
- class CollE s => Coll s a where
- insert :: s -> a -> s
+ f1 :: forall a. Foo -> a -- Wrong!
-
-
+The original program is just plain wrong. Here's another sort of error
-
-
+
+ f2 (Baz1 a b) (Baz1 p q) = a==q
+
-
-
-Instance declarations
+It's ok to say a==b or p==q, but
+a==q is wrong because it equates the two distinct types arising
+from the two Baz1 constructors.
-
-
+
+
- Instance declarations may not overlap. The two instance
-declarations
+You can't pattern-match on an existentially quantified
+constructor in a let or where group of
+bindings. So this is illegal:
- instance context1 => C type1 where ...
- instance context2 => C type2 where ...
+ f3 x = a==b where { Baz1 a b = x }
+Instead, use a case expression:
-"overlap" if type1 and type2 unify
-
-However, if you give the command line option
--fallow-overlapping-instances
-option then overlapping instance declarations are permitted.
-However, GHC arranges never to commit to using an instance declaration
-if another instance declaration also applies, either now or later.
+
+ f3 x = case x of Baz1 a b -> a==b
+
-
-
+In general, you can only pattern-match
+on an existentially-quantified constructor in a case expression or
+in the patterns of a function definition.
-
- EITHER type1 and type2 do not unify
-
-
-
+The reason for this restriction is really an implementation one.
+Type-checking binding groups is already a nightmare without
+existentials complicating the picture. Also an existential pattern
+binding at the top level of a module doesn't make sense, because it's
+not clear how to prevent the existentially-quantified type "escaping".
+So for now, there's a simple-to-state restriction. We'll see how
+annoying it is.
-
- OR type2 is a substitution instance of type1
-(but not identical to type1), or vice versa.
-
-Notice that these rules
-
- make it clear which instance decl to use
-(pick the most specific one that matches)
-
-
-
-
+You can't use existential quantification for newtype
+declarations. So this is illegal:
-
- do not mention the contexts context1, context2
-Reason: you can pick which instance decl
-"matches" based on the type.
-
-
-
-However the rules are over-conservative. Two instance declarations can overlap,
-but it can still be clear in particular situations which to use. For example:
-
- instance C (Int,a) where ...
- instance C (a,Bool) where ...
-
-These are rejected by GHC's rules, but it is clear what to do when trying
-to solve the constraint C (Int,Int) because the second instance
-cannot apply. Yell if this restriction bites you.
-
-
-GHC is also conservative about committing to an overlapping instance. For example:
- class C a where { op :: a -> a }
- instance C [Int] where ...
- instance C a => C [a] where ...
-
- f :: C b => [b] -> [b]
- f x = op x
+ newtype T = forall a. Ord a => MkT a
-From the RHS of f we get the constraint C [b]. But
-GHC does not commit to the second instance declaration, because in a paricular
-call of f, b might be instantiate to Int, so the first instance declaration
-would be appropriate. So GHC rejects the program. If you add
-GHC will instead silently pick the second instance, without complaining about
-the problem of subsequent instantiations.
-
-
-Regrettably, GHC doesn't guarantee to detect overlapping instance
-declarations if they appear in different modules. GHC can "see" the
-instance declarations in the transitive closure of all the modules
-imported by the one being compiled, so it can "see" all instance decls
-when it is compiling Main. However, it currently chooses not
-to look at ones that can't possibly be of use in the module currently
-being compiled, in the interests of efficiency. (Perhaps we should
-change that decision, at least for Main.)
+
+
+Reason: a value of type T must be represented as a pair
+of a dictionary for Ord t and a value of type t.
+That contradicts the idea that newtype should have no
+concrete representation. You can get just the same efficiency and effect
+by using data instead of newtype. If there is no
+overloading involved, then there is more of a case for allowing
+an existentially-quantified newtype, because the data
+because the data version does carry an implementation cost,
+but single-field existentially quantified constructors aren't much
+use. So the simple restriction (no existential stuff on newtype)
+stands, unless there are convincing reasons to change it.
+
- There are no restrictions on the type in an instance
-head, except that at least one must not be a type variable.
-The instance "head" is the bit after the "=>" in an instance decl. For
-example, these are OK:
+ 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:#
- instance C Int a where ...
+data T = forall a. MkT [a] deriving( Eq )
+
- instance D (Int, Int) where ...
+To derive Eq in the standard way we would need to have equality
+between the single component of two MkT constructors:
- instance E [[a]] where ...
+
+instance Eq T where
+ (MkT a) == (MkT b) = ???
+But a and b have distinct types, and so can't be compared.
+It's just about possible to imagine examples in which the derived instance
+would make sense, but it seems altogether simpler simply to prohibit such
+declarations. Define your own instances!
+
+
-Note that instance heads may contain repeated type variables.
-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 ...
-
+
+Class declarations
+
+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).
+
+
+There are the following constraints on class declarations:
+
+
-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:
+
+ Multi-parameter type classes are permitted. For example:
- instance C a where
- op = ... -- Default
+ class Collection c a where
+ union :: c a -> c a -> c a
+ ...etc.
-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 { }
+
+ The class hierarchy must be acyclic. However, the definition
+of "acyclic" involves only the superclass relationships. For example,
+this is OK:
- instance (C1 a, C2 a, C3 a) => C a where { }
-
+
+ class C a where {
+ op :: D b => a -> b -> b
+ }
-This allows you to write shorter signatures:
+ class C a => D a where { ... }
+
-
- f :: C a => ...
-
+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.)
+
+
+
-instead of
+
+ 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:
- f :: (C1 a, C2 a, C3 a) => ...
-
+ class Functor (m k) => FiniteMap m k where
+ ...
+ class (Monad m, Monad (t m)) => Transform t m where
+ lift :: m a -> (t m) 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.
+
- Unlike Haskell 1.4, instance heads may use type
-synonyms. As always, using a type synonym is just shorthand for
-writing the RHS of the type synonym definition. For example:
+ All of the class type variables must be reachable (in the sense
+mentioned in )
+from the free varibles of each method type
+. For example:
- type Point = (Int,Int)
- instance C Point where ...
- instance C [Point] where ...
+ class Coll s a where
+ empty :: s
+ insert :: s -> a -> s
-is legal. However, if you added
+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
- instance C (Int,Int) where ...
+ class Coll s a where
+ empty :: s a
+ insert :: s a -> a -> s a
-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:
+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:
- type P a = [[a]]
- instance Monad P where ...
-
+ class CollE s where
+ empty :: s
+ class CollE s => Coll s a where
+ insert :: s -> a -> s
+
-This design decision is independent of all the others, and easily
-reversed, but it makes sense to me.
-
-
-
-The types in an instance-declaration context must all
-be type variables. Thus
+
+
+
+Class method types
+
+Haskell 98 prohibits class method types to mention constraints on the
+class type variable, thus:
-instance C a b => Eq (a,b) where ...
+ 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.
+
+
-is OK, but
+
+
+Type signatures
+The context of a type signature
+
+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
-instance C Int b => Foo b where ...
+ 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.
+
+
+GHC imposes the following restrictions on the constraints in a type signature.
+Consider the type:
+
+ forall tv1..tvn (c1, ...,cn) => type
+
-is not OK. Again, the intent here is to make sure that context
-reduction terminates.
-
-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.
-
+(Here, we 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:
-
-Implicit parameters
-
- Implicit paramters 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.)
-
-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]
+ forall a. Eq a => Int
-The dynamic binding constraints are just a new form of predicate in the type class system.
+
+
+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.
+
+
+
+
-An implicit parameter is introduced by 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
-shows how we can define an implicitly parameterized sort function in
-terms of an explicitly parameterized sortBy function:
-
- sortBy :: (a -> a -> Bool) -> [a] -> [a]
+ 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:
+
- sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
- sort = sortBy ?cmp
-
-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:
- least :: (?cmp :: a -> a -> Bool) => [a] -> a
- least xs = fst (sort xs)
+ forall a. C a b => burble
-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 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.
-
-
-An implicit parameter is bound using an expression of the form
-exprwithbinds,
-where with is a new keyword. 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.
+
+
+The next type is illegal because the constraint Eq b does not
+mention a:
+
+
- min :: [a] -> a
- min = least with ?cmp = (<=)
+ forall a. Eq b => burble
-Syntactically, the binds part of a with construct must be a
-collection of simple bindings to variables (no function-style
-bindings, and no type signatures); these bindings are neither
-polymorphic or recursive.
+
+
+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.
+
-
-Note the following additional 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.
-
-
-
+
-
-Linear implicit parameters
-
-
-Linear implicit parameters are an idea developed by Koen Claessen,
-Mark Shields, and Simon PJ. They address the long-standing
-problem that monads seem over-kill for certain sorts of problem, notably:
-
- distributing a supply of unique names
- distributing a suppply of random numbers
- distributing an oracle (as in QuickCheck)
-
+
+
+For-all hoisting
-Linear implicit parameters are just like ordinary implicit parameters,
-except that they are "linear" -- that is, they cannot be copied, and
-must be explicitly "split" instead. Linear implicit parameters are
-written '%x' instead of '?x'.
-(The '/' in the '%' suggests the split!)
-
-
-For example:
+It is often convenient to use generalised type synonyms (see ) at the right hand
+end of an arrow, thus:
- data NameSupply = ...
-
- splitNS :: NameSupply -> (NameSupply, NameSupply)
- newName :: NameSupply -> Name
-
- instance PrelSplit.Splittable NameSupply where
- split = splitNS
-
+ type Discard a = forall b. a -> b -> a
- f :: (%ns :: NameSupply) => Env -> Expr -> Expr
- f env (Lam x e) = Lam x' (f env e)
- where
- x' = newName %ns
- env' = extend env x x'
- ...more equations for f...
+ g :: Int -> Discard Int
+ g x y z = x+y
-Notice that the implicit parameter %ns is consumed
-
- once by the call to newName
- once by the recursive call to f
-
-
-
-So the translation done by the type checker makes
-the parameter explicit:
+Simply expanding the type synonym would give
- f :: NameSupply -> Env -> Expr -> Expr
- f ns env (Lam x e) = Lam x' (f ns1 env e)
- where
- (ns1,ns2) = splitNS ns
- x' = newName ns2
- env = extend env x x'
+ g :: Int -> (forall b. Int -> b -> Int)
-Notice the call to 'split' introduced by the type checker.
-How did it know to use 'splitNS'? Because what it really did
-was to introduce a call to the overloaded function 'split',
-defined by
+but GHC "hoists" the forall to give the isomorphic type
- class Splittable a where
- split :: a -> (a,a)
+ g :: forall b. Int -> Int -> b -> Int
-The instance for Splittable NameSupply tells GHC how to implement
-split for name supplies. But we can simply write
+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:
- g x = (x, %ns, %ns)
+ type1 -> forall a1..an. context2 => type2
+==>
+ forall a1..an. context2 => type1 -> type2
-and GHC will infer
+(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:
- g :: (Splittable a, %ns :: a) => b -> (b,a,a)
+ g :: Int -> Int -> forall b. b -> Int
-The Splittable class is built into GHC. It's defined in PrelSplit,
-and exported by GlaExts.
-Other points:
-
- '?x' and '%x'
-are entirely distinct implicit parameters: you
- can use them together and they won't intefere with each other.
-
+When doing this hoisting operation, GHC eliminates duplicate constraints. For
+example:
+
+ type Foo a = (?x::Int) => Bool -> a
+ g :: Foo (Foo Int)
+
+means
+
+ g :: (?x::Int) => Bool -> Bool -> Int
+
+
+
- You can bind linear implicit parameters in 'with' clauses.
-You cannot have implicit parameters (whether linear or not)
- in the context of a class or instance declaration.
-
-
+
-Warnings
+
+Instance declarations
+
+Overlapping instances
-The monomorphism restriction is even more important than usual.
-Consider the example above:
-
- f :: (%ns :: NameSupply) => Env -> Expr -> Expr
- f env (Lam x e) = Lam x' (f env e)
- where
- x' = newName %ns
- env' = extend env x x'
-
-If we replaced the two occurrences of x' by (newName %ns), which is
-usually a harmless thing to do, we get:
+In general, instance declarations may not overlap. The two instance
+declarations
+
+
- f :: (%ns :: NameSupply) => Env -> Expr -> Expr
- f env (Lam x e) = Lam (newName %ns) (f env e)
- where
- env' = extend env x (newName %ns)
+ instance context1 => C type1 where ...
+ instance context2 => C type2 where ...
-But now the name supply is consumed in three places
-(the two calls to newName,and the recursive call to f), so
-the result is utterly different. Urk! We don't even have
-the beta rule.
-
-
-Well, this is an experimental change. With implicit
-parameters we have already lost beta reduction anyway, and
-(as John Launchbury puts it) we can't sensibly reason about
-Haskell programs without knowing their typing.
-
-
-
+"overlap" if type1 and type2 unify
-
-Functional dependencies
-
+However, if you give the command line option
+-fallow-overlapping-instances
+option then overlapping instance declarations are permitted.
+However, GHC arranges never to commit to using an instance declaration
+if another instance declaration also applies, either now or later.
- 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.
+
+
+
+
+ EITHER type1 and type2 do not unify
+
+
-There should be more documentation, but there isn't (yet). Yell if you need it.
+ OR type2 is a substitution instance of type1
+(but not identical to type1), or vice versa.
-
+
+
+Notice that these rules
+
+
+
+ make it clear which instance decl to use
+(pick the most specific one that matches)
-
-Explicit universal quantification
-
+
+
+
-Haskell type signatures are implicitly quantified. The new keyword forall
-allows us to say exactly what this means. For example:
+ do not mention the contexts context1, context2
+Reason: you can pick which instance decl
+"matches" based on the type.
-
-
- g :: b -> b
-
-means this:
+
+
+
+However the rules are over-conservative. Two instance declarations can overlap,
+but it can still be clear in particular situations which to use. For example:
- g :: forall b. (b -> b)
+ instance C (Int,a) where ...
+ instance C (a,Bool) where ...
-The two are treated identically.
+These are rejected by GHC's rules, but it is clear what to do when trying
+to solve the constraint C (Int,Int) because the second instance
+cannot apply. Yell if this restriction bites you.
-
-However, GHC's type system supports arbitrary-rank
-explicit universal quantification in
-types.
-For example, all the following types are legal:
+GHC is also conservative about committing to an overlapping instance. For example:
- 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
+ class C a where { op :: a -> a }
+ instance C [Int] where ...
+ instance C a => C [a] where ...
+
+ f :: C b => [b] -> [b]
+ f x = op 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 arrrow. As g2
-shows, the polymorphic type on the left of the function arrow can be overloaded.
+From the RHS of f we get the constraint C [b]. But
+GHC does not commit to the second instance declaration, because in a paricular
+call of f, b might be instantiate to Int, so the first instance declaration
+would be appropriate. So GHC rejects the program. If you add
+GHC will instead silently pick the second instance, without complaining about
+the problem of subsequent instantiations.
-The functions f3 and g3 have rank-3 types;
-they have rank-2 types on the left of a function arrow.
+Regrettably, GHC doesn't guarantee to detect overlapping instance
+declarations if they appear in different modules. GHC can "see" the
+instance declarations in the transitive closure of all the modules
+imported by the one being compiled, so it can "see" all instance decls
+when it is compiling Main. However, it currently chooses not
+to look at ones that can't possibly be of use in the module currently
+being compiled, in the interests of efficiency. (Perhaps we should
+change that decision, at least for Main.)
+
+
+
+Type synonyms in the instance head
+
-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,g3 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:
+Unlike Haskell 1.4, 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:
+
+
- x1 :: [forall a. a->a]
- x2 :: (forall a. a->a, Int)
- x3 :: Maybe (forall a. a->a)
+ type Point = (Int,Int)
+ instance C Point where ...
+ instance C [Point] where ...
-Of course forall becomes a keyword; you can't use forall as
-a type variable any more!
-
-
-Examples
-
+is legal. However, if you added
+
+
+
+ instance C (Int,Int) where ...
+
+
-
-In a data or newtype declaration one can quantify
-the types of the constructor arguments. Here are several examples:
-
+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:
-
-data T a = T1 (forall b. b -> b -> b) a
+ type P a = [[a]]
+ instance Monad P where ...
+
-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])
-
+This design decision is independent of all the others, and easily
+reversed, but it makes sense to me.
+
-
-The constructors have rank-2 types:
-
+
+Undecidable instances
-
+An instance declaration must normally obey the following rules:
+
+At least one of the types in the head of
+an instance declaration must not be a type variable.
+For example, these are OK:
-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
-
+ instance C Int a where ...
-
+ instance D (Int, Int) where ...
-
-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.
+ instance E [[a]] where ...
+
+but this is not:
+
+ instance F a where ...
+
+Note that instance heads may contain repeated type variables.
+For example, this is OK:
+
+ instance Stateful (ST s) (MutVar s) where ...
+
+
-
-As for type signatures, implicit quantification happens for non-overloaded
-types too. So if you write this:
+
+All of the types in the context of
+an instance declaration must be type variables.
+Thus
- data T a = MkT (Either a b) (b -> b)
+instance C a b => Eq (a,b) where ...
+
+is OK, but
+
+instance C Int b => Foo b where ...
+
+is not OK.
+
+
+
+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:
-it's just as if you had written this:
- data T a = MkT (forall b. Either a b) (forall b. b -> b)
+ instance C a where
+ op = ... -- Default
-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.)
-
-
-You construct values of types T1, MonadT, Swizzle by applying
-the constructor to suitable values, just as usual. For example,
-
+Second, sometimes you might want to use the following to get the
+effect of a "class synonym":
-
- 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
+ class (C1 a, C2 a, C3 a) => C a where { }
- mkTs :: (forall b. b -> b -> b) -> a -> [T a]
- mkTs f x y = [T1 f x, T1 f y]
+ instance (C1 a, C2 a, C3 a) => C a where { }
-
-
-
-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.)
-
-
-When you use pattern matching, the bound variables may now have
-polymorphic types. For example:
-
+This allows you to write shorter signatures:
-
- f :: T a -> a -> (a, Char)
- f (T1 w k) x = (w k x, w 'c' 'd')
+ f :: C a => ...
+
- 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)
+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.
+
-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.
+I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
+allowing these idioms interesting idioms.
+
+
+
-
-Type inference
+
+Implicit parameters
-
-In general, type inference for arbitrary-rank types is undecideable.
-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:
+ Implicit paramters 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.)
-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.
+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.
-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:
+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.
- h :: (forall a. a->a) -> (Bool,Char)
- h f = (f True, f 'c')
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
-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:
+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:
- f :: T a -> a -> (a, Char)
- f (T1 w k) x = (w k x, w 'c' 'd')
+ sortBy :: (a -> a -> Bool) -> [a] -> [a]
+
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
+ sort = sortBy ?cmp
-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.
-
-
-
-
-Implicit quantification
-
+
+Implicit-parameter type constraints
-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:
+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:
- f :: a -> a
- f :: forall a. a -> a
+ least :: (?cmp :: a -> a -> Bool) => [a] -> a
+ least xs = fst (sort xs)
+
+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.
+
- 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 ...
+ 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.
-Notice that GHC does not find the innermost possible quantification
-point. For example:
+Implicit-parameter constraints do not cause ambiguity. For example, consider:
- f :: (a -> a) -> Int
- -- MEANS
- f :: forall a. (a -> a) -> Int
- -- NOT
- f :: (forall a. a -> a) -> Int
-
+ f :: (?x :: [a]) => Int -> Int
+ f n = n + length ?x
- 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
+ g :: (Read a, Show a) => String -> String
+ g s = show (read s)
-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.
+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.
-
-
+
-
-Type synonyms and hoisting
-
+
+Implicit-parameter bindings
-Type synonmys are like macros at the type level, and GHC is much more liberal
-about them than Haskell 98. In particular:
-
-You can write a forall (including overloading)
-in a type synonym, thus:
+An implicit parameter is bound using the standard
+let or where binding forms.
+For example, we define the min function by binding
+cmp.
- type Discard a = forall b. Show b => a -> b -> (a, String)
-
- f :: Discard a
- f x y = (x, show y)
-
- g :: Discard Int -> (Int,Bool) -- A rank-2 type
- g f = f Int True
+ 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 can write an unboxed tuple in a type synonym:
+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:
- type Pr = (# Int, Int #)
-
- h :: Int -> Pr
- h x = (# x, x #)
+ 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
-
-GHC does validity checking on types after expanding type synonyms
-so, for example,
-this will be rejected:
-
- type Pr = (# Int, Int #)
- h :: Pr -> Int
- h x = ...
-
-because GHC does not allow unboxed tuples on the left of a function arrow.
+
+
+
+
+Linear implicit parameters
+
+Linear implicit parameters are an idea developed by Koen Claessen,
+Mark Shields, and Simon PJ. They address the long-standing
+problem that monads seem over-kill for certain sorts of problem, notably:
+
+ distributing a supply of unique names
+ distributing a suppply of random numbers
+ distributing an oracle (as in QuickCheck)
+
-However, it is often convenient to use these sort of generalised synonyms at the right hand
-end of an arrow, thus:
+Linear implicit parameters are just like ordinary implicit parameters,
+except that they are "linear" -- that is, they cannot be copied, and
+must be explicitly "split" instead. Linear implicit parameters are
+written '%x' instead of '?x'.
+(The '/' in the '%' suggests the split!)
+
+
+For example:
- type Discard a = forall b. a -> b -> a
+ import GHC.Exts( Splittable )
- g :: Int -> Discard Int
- g x y z = x+y
+ data NameSupply = ...
+
+ splitNS :: NameSupply -> (NameSupply, NameSupply)
+ newName :: NameSupply -> Name
+
+ instance Splittable NameSupply where
+ split = splitNS
+
+
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+ ...more equations for f...
-Simply expanding the type synonym would give
+Notice that the implicit parameter %ns is consumed
+
+ once by the call to newName
+ once by the recursive call to f
+
+
+
+So the translation done by the type checker makes
+the parameter explicit:
- g :: Int -> (forall b. Int -> b -> Int)
+ f :: NameSupply -> Env -> Expr -> Expr
+ f ns env (Lam x e) = Lam x' (f ns1 env e)
+ where
+ (ns1,ns2) = splitNS ns
+ x' = newName ns2
+ env = extend env x x'
-but GHC "hoists" the forall to give the isomorphic type
+Notice the call to 'split' introduced by the type checker.
+How did it know to use 'splitNS'? Because what it really did
+was to introduce a call to the overloaded function 'split',
+defined by the class Splittable:
- g :: forall b. Int -> Int -> b -> Int
+ class Splittable a where
+ split :: a -> (a,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 instance for Splittable NameSupply tells GHC how to implement
+split for name supplies. But we can simply write
- type1 -> forall a1..an. context2 => type2
-==>
- forall a1..an. context2 => type1 -> type2
+ g x = (x, %ns, %ns)
-(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:
+and GHC will infer
- g :: Int -> Int -> forall b. b -> Int
+ g :: (Splittable a, %ns :: a) => b -> (b,a,a)
+The Splittable class is built into GHC. It's exported by module
+GHC.Exts.
-
-
+
+Other points:
+
+ '?x' and '%x'
+are entirely distinct implicit parameters: you
+ can use them together and they won't intefere with each other.
+
-
-Existentially quantified data constructors
-
+ You can bind linear implicit parameters in 'with' clauses.
-
-The idea of using existential quantification in data type declarations
-was suggested by Laufer (I believe, thought doubtless someone will
-correct me), and implemented in Hope+. It's been in Lennart
-Augustsson's hbc Haskell compiler for several years, and
-proved very useful. Here's the idea. Consider the declaration:
+You cannot have implicit parameters (whether linear or not)
+ in the context of a class or instance declaration.
+
-
+Warnings
+
+The monomorphism restriction is even more important than usual.
+Consider the example above:
- data Foo = forall a. MkFoo a (a -> Bool)
- | Nil
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
-
+If we replaced the two occurrences of x' by (newName %ns), which is
+usually a harmless thing to do, we get:
+
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam (newName %ns) (f env e)
+ where
+ env' = extend env x (newName %ns)
+
+But now the name supply is consumed in three places
+(the two calls to newName,and the recursive call to f), so
+the result is utterly different. Urk! We don't even have
+the beta rule.
-
-The data type Foo has two constructors with types:
+Well, this is an experimental change. With implicit
+parameters we have already lost beta reduction anyway, and
+(as John Launchbury puts it) we can't sensibly reason about
+Haskell programs without knowing their typing.
-
+
+Recursive functions
+Linear implicit parameters can be particularly tricky when you have a recursive function
+Consider
- MkFoo :: forall a. a -> (a -> Bool) -> Foo
- Nil :: Foo
+ foo :: %x::T => Int -> [Int]
+ foo 0 = []
+ foo n = %x : foo (n-1)
-
-
-
+where T is some type in class Splittable.
-Notice that the type variable a in the type of MkFoo
-does not appear in the data type itself, which is plain Foo.
-For example, the following expression is fine:
+Do you get a list of all the same T's or all different T's
+(assuming that split gives two distinct T's back)?
+
+If you supply the type signature, taking advantage of polymorphic
+recursion, you get what you'd probably expect. Here's the
+translated term, where the implicit param is made explicit:
+
+ foo x 0 = []
+ foo x n = let (x1,x2) = split x
+ in x1 : foo x2 (n-1)
+
+But if you don't supply a type signature, GHC uses the Hindley
+Milner trick of using a single monomorphic instance of the function
+for the recursive calls. That is what makes Hindley Milner type inference
+work. So the translation becomes
+
+ foo x = let
+ foom 0 = []
+ foom n = x : foom (n-1)
+ in
+ foom
+
+Result: 'x' is not split, and you get a list of identical T's. So the
+semantics of the program depends on whether or not foo has a type signature.
+Yikes!
+
+You may say that this is a good reason to dislike linear implicit parameters
+and you'd be right. That is why they are an experimental feature.
+
-
+
+
+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.
- [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
+ 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.
+
+
+
+
+
+
+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
+
+
-Here, (MkFoo 3 even) packages an integer with a function
-even that maps an integer to Bool; and MkFoo 'c'
-isUpper packages a character with a compatible function. These
-two things are each of type Foo and can be put in a list.
+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.
-What can we do with a value of type Foo?. In particular,
-what happens when we pattern-match on MkFoo?
+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.
+
-
-
-
- f (MkFoo val fn) = ???
-
-
+
+Arbitrary-rank polymorphism
+
-Since all we know about val and fn is that they
-are compatible, the only (useful) thing we can do with them is to
-apply fn to val to get a boolean. For example:
+Haskell type signatures are implicitly quantified. The new keyword forall
+allows us to say exactly what this means. For example:
-
-
- f :: Foo -> Bool
- f (MkFoo val fn) = fn val
+ g :: b -> b
-
-
-
-
-What this allows us to do is to package heterogenous values
-together with a bunch of functions that manipulate them, and then treat
-that collection of packages in a uniform manner. You can express
-quite a bit of object-oriented-like programming this way.
+means this:
+
+ g :: forall b. (b -> b)
+
+The two are treated identically.
-
-Why existential?
-
-
-What has this to do with existential quantification?
-Simply that MkFoo has the (nearly) isomorphic type
-
+However, GHC's type system supports arbitrary-rank
+explicit universal quantification in
+types.
+For example, all the following types are legal:
+
+ 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
-
- MkFoo :: (exists a . (a, a -> Bool)) -> Foo
+ f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
-
+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.
-
-But Haskell programmers can safely think of the ordinary
-universally quantified type given above, thereby avoiding
-adding a new existential quantification construct.
+The functions f2 and g2 have rank-2 types;
+the forall is on the left of a function arrrow. As g2
+shows, the polymorphic type on the left of the function arrow can be overloaded.
-
-
-
-
-Type classes
-
-An easy extension (implemented in hbc) is to allow
-arbitrary contexts before the constructor. For example:
+The functions f3 and g3 have rank-3 types;
+they have 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 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,g3 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:
-data Baz = forall a. Eq a => Baz1 a a
- | forall b. Show b => Baz2 b (b -> b)
+ x1 :: [forall a. a->a]
+ x2 :: (forall a. a->a, Int)
+ x3 :: Maybe (forall a. a->a)
-
+Of course forall becomes a keyword; you can't use forall as
+a type variable any more!
+
+
+Examples
+
+
-The two constructors have the types you'd expect:
+In a data or newtype declaration one can quantify
+the types of the constructor arguments. Here are several examples:
-Baz1 :: forall a. Eq a => a -> a -> Baz
-Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
+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
+ }
+
+newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
-But when pattern matching on Baz1 the matched values can be compared
-for equality, and when pattern matching on Baz2 the first matched
-value can be converted to a string (as well as applying the function to it).
-So this program is legal:
+The constructors have rank-2 types:
- f :: Baz -> String
- f (Baz1 p q) | p == q = "Yes"
- | otherwise = "No"
- f (Baz2 v fn) = show (fn v)
+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
-Operationally, in a dictionary-passing implementation, the
-constructors Baz1 and Baz2 must store the
-dictionaries for Eq and Show respectively, and
-extract it on pattern matching.
-
-
-
-Notice the way that the syntax fits smoothly with that used for
-universal quantification earlier.
-
-
-
-
-
-Restrictions
-
-
-There are several restrictions on the ways in which existentially-quantified
-constructors can be use.
+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.
-
-
-
-
-
- When pattern matching, each pattern match introduces a new,
-distinct, type for each existential type variable. These types cannot
-be unified with any other type, nor can they escape from the scope of
-the pattern match. For example, these fragments are incorrect:
-
-
-
-f1 (MkFoo a f) = a
-
-
-
-Here, the type bound by MkFoo "escapes", because a
-is the result of f1. One way to see why this is wrong is to
-ask what type f1 has:
-
-
-
- f1 :: Foo -> a -- Weird!
-
-
-
-What is this "a" in the result type? Clearly we don't mean
-this:
-
+As for type signatures, implicit quantification happens for non-overloaded
+types too. So if you write this:
- f1 :: forall a. Foo -> a -- Wrong!
+ data T a = MkT (Either a b) (b -> b)
-
-The original program is just plain wrong. Here's another sort of error
-
+it's just as if you had written this:
- f2 (Baz1 a b) (Baz1 p q) = a==q
+ data T a = MkT (forall b. Either a b) (forall b. b -> b)
-
-It's ok to say a==b or p==q, but
-a==q is wrong because it equates the two distinct types arising
-from the two Baz1 constructors.
-
-
+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.)
-
-
-You can't pattern-match on an existentially quantified
-constructor in a let or where group of
-bindings. So this is illegal:
+You construct values of types T1, MonadT, Swizzle by applying
+the constructor to suitable values, just as usual. For example,
+
+
- f3 x = a==b where { Baz1 a b = x }
-
-
+ 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
-You can only pattern-match
-on an existentially-quantified constructor in a case expression or
-in the patterns of a function definition.
+ mkTs :: (forall b. b -> b -> b) -> a -> [T a]
+ mkTs f x y = [T1 f x, T1 f y]
+
-The reason for this restriction is really an implementation one.
-Type-checking binding groups is already a nightmare without
-existentials complicating the picture. Also an existential pattern
-binding at the top level of a module doesn't make sense, because it's
-not clear how to prevent the existentially-quantified type "escaping".
-So for now, there's a simple-to-state restriction. We'll see how
-annoying it is.
+
+
+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.)
-
-
-You can't use existential quantification for newtype
-declarations. So this is illegal:
+When you use pattern matching, the bound variables may now have
+polymorphic types. For example:
+
+
- newtype T = forall a. Ord a => MkT a
-
-
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
-Reason: a value of type T must be represented as a pair
-of a dictionary for Ord t and a value of type t.
-That contradicts the idea that newtype should have no
-concrete representation. You can get just the same efficiency and effect
-by using data instead of newtype. If there is no
-overloading involved, then there is more of a case for allowing
-an existentially-quantified newtype, because the data
-because the data version does carry an implementation cost,
-but single-field existentially quantified constructors aren't much
-use. So the simple restriction (no existential stuff on newtype)
-stands, unless there are convincing reasons to change it.
+ 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)
+
-
-
- You can't use deriving to define instances of a
-data type with existentially quantified data constructors.
+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.
+
+
-Reason: in most cases it would not make sense. For example:#
+
+Type inference
+
+In general, type inference for arbitrary-rank types is undecideable.
+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:
+
+
+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.
+
+
+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:
-data T = forall a. MkT [a] deriving( Eq )
+ \ 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.
+
-To derive Eq in the standard way we would need to have equality
-between the single component of two MkT constructors:
+
+
+
+
+Implicit quantification
+
+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:
-instance Eq T where
- (MkT a) == (MkT b) = ???
-
+ f :: a -> a
+ f :: forall a. a -> a
-But a and b have distinct types, and so can't be compared.
-It's just about possible to imagine examples in which the derived instance
-would make sense, but it seems altogether simpler simply to prohibit such
-declarations. Define your own instances!
+ 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
-
+ 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.
-
+
-
-
-Scoped Type Variables
+
+
+
+Scoped type variables
@@ -2213,7 +2597,7 @@ are noted.
So much for the basic idea. Here are the details.
-
+What a pattern type signature means
A type variable brought into scope by a pattern type signature is simply
@@ -2251,9 +2635,9 @@ For example, all of these are legal:
w (x::a) = x -- a unifies with [b]
-
+
-
+Scope and implicit quantification
@@ -2377,27 +2761,135 @@ scope over the methods defined in the where part. For exampl
-(Not implemented in Hugs yet, Dec 98).
+(Not implemented in Hugs yet, Dec 98).
+
+
+
+
+
+
+
+
+
+
+Where a pattern type signature can occur
+
+
+A pattern type signature can occur in any pattern. For example:
+
+
+
+
+A pattern type signature can be on an arbitrary sub-pattern, not
+ust on a variable:
+
+
+
+ f ((x,y)::(a,b)) = (y,x) :: (b,a)
+
+
+
+
+
+
+
+
+ Pattern type signatures, including the result part, can be used
+in lambda abstractions:
+
+
+ (\ (x::a, y) :: a -> x)
+
+
+
+
+
+
+ Pattern type signatures, including the result part, can be used
+in case expressions:
+
+
+
+ case e of { (x::a, y) :: a -> x }
+
+
+
+
+
+
+
+To avoid ambiguity, the type after the “::” in a result
+pattern signature on a lambda or case must be atomic (i.e. a single
+token or a parenthesised type of some sort). To see why,
+consider how one would parse this:
+
+
+
+ \ x :: a -> b -> x
+
+
+
+
+
+
+
+
+
+ Pattern type signatures can bind existential type variables.
+For example:
+
+
+
+ data T = forall a. MkT [a]
+
+ f :: T -> T
+ f (MkT [t::a]) = MkT t3
+ where
+ t3::[a] = [t,t,t]
+
+
+
+
+
+
+
+
+
+
+Pattern type signatures
+can be used in pattern bindings:
+
+
+ f x = let (y, z::a) = x in ...
+ f1 x = let (y, z::Int) = x in ...
+ f2 (x::(Int,a)) = let (y, z::a) = x in ...
+ f3 :: (b->b) = \x -> x
+
+
+In all such cases, the binding is not generalised over the pattern-bound
+type variables. Thus f3 is monomorphic; f3
+has type b -> b for some type b,
+and notforall b. b -> b.
+In contrast, the binding
+
+ f4 :: b->b
+ f4 = \x -> x
+
+makes a polymorphic function, but b is not in scope anywhere
+in f4's scope.
+
-
-
-
+
-
+Result type signatures
-
-
-
-
-
- The result type of a function can be given a signature,
-thus:
+The result type of a function can be given a signature, thus:
@@ -2416,196 +2908,901 @@ you want:
in \xs -> map g (reverse xs `zip` xs)
-
-
-
-
+
+The type variables bound in a result type signature scope over the right hand side
+of the definition. However, consider this corner-case:
+
+ rev1 :: [a] -> [a] = \xs -> reverse xs
+ 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).
+
+
+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
+
Result type signatures are not yet implemented in Hugs.
+
+
-
-Where a pattern type signature can occur
+
+Deriving clause for classes Typeable and Data
-A pattern type signature can occur in any pattern. For example:
-
+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.Dynamic and Data.Generics respectively, and the
+appropriate class must be in scope before it can be mentioned in the deriving clause.
+
+
+
+
+Generalised derived instances for newtypes
-
-A pattern type signature can be on an arbitrary sub-pattern, not
-ust on a variable:
+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
+
-
- f ((x,y)::(a,b)) = (y,x) :: (b,a)
+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 sameNum 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.
+
- Pattern type signatures, including the result part, can be used
-in lambda abstractions:
-
- (\ (x::a, y) :: a -> x)
+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', 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.
+
- Pattern type signatures, including the result part, can be used
-in case expressions:
+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)
+
-
- case e of { (x::a, y) :: a -> x }
+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.
+
+
+
+
+
+
+
+
+
+
+
+
+Template Haskell
+
+Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
+Template Haskell at
+http://www.haskell.org/th/, while
+the background to
+the main technical innovations is discussed in "
+Template Meta-programming for Haskell" (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
-To avoid ambiguity, the type after the “::” in a result
-pattern signature on a lambda or case must be atomic (i.e. a single
-token or a parenthesised type of some sort). To see why,
-consider how one would parse this:
+
+
+ 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.
+
+
+
+ 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":
+
+
+{- 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 ( $(pr "Hello") )
+
- \ x :: a -> b -> x
+{- Printf.hs -}
+module Printf where
+
+-- Skeletal printf from the paper.
+-- It needs to be in a separate module to the one where
+-- you intend to use it.
+
+-- Import some Template Haskell syntax
+import Language.Haskell.THSyntax
+
+-- Describe a format string
+data Format = D | S | L String
+
+-- Parse a format string. This is left largely to you
+-- as we are here interested in building our first ever
+-- Template Haskell program and not in building printf.
+parse :: String -> [Format]
+parse s = [ L s ]
+
+-- Generate Haskell source code from a parsed representation
+-- of the format string. This code will be spliced into
+-- the module which calls "pr", at compile time.
+gen :: [Format] -> Expr
+gen [D] = [| \n -> show n |]
+gen [S] = [| \s -> s |]
+gen [L s] = string s
+
+-- Here we generate the Haskell code for the splice
+-- from an input format string.
+pr :: String -> Expr
+pr s = gen (parse s)
+
+
+Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows):
+
+
+ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe
+
+
+Run "main.exe" and here is your output:
+
+
+
+$ ./main
+Hello
+
+
+
+
+
+
+
+Arrow notation
+
+
+Arrows are a generalization of monads introduced by John Hughes.
+For more details, see
+
+
+
+“Generalising Monads to Arrows”,
+John Hughes, in Science of Computer Programming 37,
+pp67–111, May 2000.
-
- Pattern type signatures can bind existential type variables.
-For example:
+“A New Notation for Arrows”,
+Ross Paterson, in ICFP, Sep 2001.
+
+
+
+
+“Arrows and Computation”,
+Ross Paterson, in The Fun of Programming,
+Palgrave, 2003.
+
+
-
- data T = forall a. MkT [a]
+
+and the arrows web page at
+http://www.haskell.org/arrows/.
+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.
+This notation is translated to ordinary Haskell,
+using combinators from the
+Control.Arrow
+module.
+
+
+The extension adds a new kind of expression for defining arrows,
+of the form proc pat -> cmd,
+where proc is a new keyword.
+The variables of the pattern are bound in the body of the
+proc-expression,
+which is a new sort of thing called a command.
+The syntax of commands is as follows:
+
+cmd ::= exp1 -< exp2
+ | exp1 -<< exp2
+ | do { cstmt1 .. cstmtn ; cmd }
+ | let decls in cmd
+ | if exp then cmd1 else cmd2
+ | case exp of { calts }
+ | cmd1 qop cmd2
+ | (| aexp cmd1 .. cmdn |)
+ | \ pat1 .. patn -> cmd
+ | cmd aexp
+ | ( cmd )
+
+cstmt ::= let decls
+ | pat <- cmd
+ | rec { cstmt1 .. cstmtn }
+ | cmd
+
+Commands produce values, but (like monadic computations)
+may yield more than one value,
+or none, and may do other things as well.
+For the most part, familiarity with monadic notation is a good guide to
+using commands.
+However the values of expressions, even monadic ones,
+are determined by the values of the variables they contain;
+this is not necessarily the case for commands.
+
+
+
+A simple example of the new notation is the expression
+
+proc x -> f -< x+1
+
+We call this a procedure or
+arrow abstraction.
+As with a lambda expression, the variable x
+is a new variable bound within the proc-expression.
+It refers to the input to the arrow.
+In the above example, -< is not an identifier but an
+new reserved symbol used for building commands from an expression of arrow
+type and an expression to be fed as input to that arrow.
+(The weird look will make more sense later.)
+It may be read as analogue of application for arrows.
+The above example is equivalent to the Haskell expression
+
+arr (\ x -> x+1) >>> f
+
+That would make no sense if the expression to the left of
+-< involves the bound variable x.
+More generally, the expression to the left of -<
+may not involve any local variable,
+i.e. a variable bound in the current arrow abstraction.
+For such a situation there is a variant -<<, as in
+
+proc x -> f x -<< x+1
+
+which is equivalent to
+
+arr (\ x -> (f, x+1)) >>> app
+
+so in this case the arrow must belong to the ArrowApply
+class.
+Such an arrow is equivalent to a monad, so if you're using this form
+you may find a monadic formulation more convenient.
+
- f :: T -> T
- f (MkT [t::a]) = MkT t3
- where
- t3::[a] = [t,t,t]
-
+
+do-notation for commands
+
+
+Another form of command is a form of do-notation.
+For example, you can write
+
+proc x -> do
+ y <- f -< x+1
+ g -< 2*y
+ let z = x+y
+ t <- h -< x*z
+ returnA -< t+z
+
+You can read this much like ordinary do-notation,
+but with commands in place of monadic expressions.
+The first line sends the value of x+1 as an input to
+the arrow f, and matches its output against
+y.
+In the next line, the output is discarded.
+The arrow returnA is defined in the
+Control.Arrow
+module as arr id.
+The above example is treated as an abbreviation for
+
+arr (\ x -> (x, x)) >>>
+ first (arr (\ x -> x+1) >>> f) >>>
+ arr (\ (y, x) -> (y, (x, y))) >>>
+ first (arr (\ y -> 2*y) >>> g) >>>
+ arr snd >>>
+ arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
+ first (arr (\ (x, z) -> x*z) >>> h) >>>
+ arr (\ (t, z) -> t+z) >>>
+ returnA
+
+Note that variables not used later in the composition are projected out.
+After simplification using rewrite rules (see )
+defined in the
+Control.Arrow
+module, this reduces to
+
+arr (\ x -> (x+1, x)) >>>
+ first f >>>
+ arr (\ (y, x) -> (2*y, (x, y))) >>>
+ first g >>>
+ arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
+ first h >>>
+ arr (\ (t, z) -> t+z)
+
+which is what you might have written by hand.
+With arrow notation, GHC keeps track of all those tuples of variables for you.
+
+
+
+Note that although the above translation suggests that
+let-bound variables like z must be
+monomorphic, the actual translation produces Core,
+so polymorphic variables are allowed.
+
+
+
+It's also possible to have mutually recursive bindings,
+using the new rec keyword, as in the following example:
+
+counter :: ArrowCircuit a => a Bool Int
+counter = proc reset -> do
+ rec output <- returnA -< if reset then 0 else next
+ next <- delay 0 -< output+1
+ returnA -< output
+
+The translation of such forms uses the loop combinator,
+so the arrow concerned must belong to the ArrowLoop class.
+
+
+
+Conditional commands
+
+
+In the previous example, we used a conditional expression to construct the
+input for an arrow.
+Sometimes we want to conditionally execute different commands, as in
+
+proc (x,y) ->
+ if f x y
+ then g -< x+1
+ else h -< y+2
+
+which is translated to
+
+arr (\ (x,y) -> if f x y then Left x else Right y) >>>
+ (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
+
+Since the translation uses |||,
+the arrow concerned must belong to the ArrowChoice class.
+
+
+
+There are also case commands, like
+
+case input of
+ [] -> f -< ()
+ [x] -> g -< x+1
+ x1:x2:xs -> do
+ y <- h -< (x1, x2)
+ ys <- k -< xs
+ returnA -< y:ys
+
+The syntax is the same as for case expressions,
+except that the bodies of the alternatives are commands rather than expressions.
+The translation is similar to that of if commands.
-
+
-
+
+Defining your own control structures
+
+
+As we're seen, arrow notation provides constructs,
+modelled on those for expressions,
+for sequencing, value recursion and conditionals.
+But suitable combinators,
+which you can define in ordinary Haskell,
+may also be used to build new commands out of existing ones.
+The basic idea is that a command defines an arrow from environments to values.
+These environments assign values to the free local variables of the command.
+Thus combinators that produce arrows from arrows
+may also be used to build commands from commands.
+For example, the ArrowChoice class includes a combinator
+
+ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
+
+so we can use it to build commands:
+
+expr' = proc x ->
+ returnA -< x
+ <+> do
+ symbol Plus -< ()
+ y <- term -< ()
+ expr' -< x + y
+ <+> do
+ symbol Minus -< ()
+ y <- term -< ()
+ expr' -< x - y
+
+This is equivalent to
+
+expr' = (proc x -> returnA -< x)
+ <+> (proc x -> do
+ symbol Plus -< ()
+ y <- term -< ()
+ expr' -< x + y)
+ <+> (proc x -> do
+ symbol Minus -< ()
+ y <- term -< ()
+ expr' -< x - y)
+
+It is essential that this operator be polymorphic in e
+(representing the environment input to the command
+and thence to its subcommands)
+and satisfy the corresponding naturality property
+
+arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
+
+at least for strict k.
+(This should be automatic if you're not using seq.)
+This ensures that environments seen by the subcommands are environments
+of the whole command,
+and also allows the translation to safely trim these environments.
+The operator must also not use any variable defined within the current
+arrow abstraction.
+
+
+
+We could define our own operator
+
+untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
+untilA body cond = proc x ->
+ if cond x then returnA -< ()
+ else do
+ body -< x
+ untilA body cond -< x
+
+and use it in the same way.
+Of course this infix syntax only makes sense for binary operators;
+there is also a more general syntax involving special brackets:
+
+proc x -> do
+ y <- f -< x+1
+ (|untilA (increment -< x+y) (within 0.5 -< x)|)
+
+
-
-Pattern type signatures
-can be used in pattern bindings:
+
-
- f x = let (y, z::a) = x in ...
- f1 x = let (y, z::Int) = x in ...
- f2 (x::(Int,a)) = let (y, z::a) = x in ...
- f3 :: (b->b) = \x -> x
+
+Primitive constructs
+
+
+Some operators will need to pass additional inputs to their subcommands.
+For example, in an arrow type supporting exceptions,
+the operator that attaches an exception handler will wish to pass the
+exception that occurred to the handler.
+Such an operator might have a type
+
+handleA :: ... => a e c -> a (e,Ex) c -> a e c
+
+where Ex is the type of exceptions handled.
+You could then use this with arrow notation by writing a command
+
+body `handleA` \ ex -> handler
+
+so that if an exception is raised in the command body,
+the variable ex is bound to the value of the exception
+and the command handler,
+which typically refers to ex, is entered.
+Though the syntax here looks like a functional lambda,
+we are talking about commands, and something different is going on.
+The input to the arrow represented by a command consists of values for
+the free local variables in the command, plus a stack of anonymous values.
+In all the prior examples, this stack was empty.
+In the second argument to handleA,
+this stack consists of one value, the value of the exception.
+The command form of lambda merely gives this value a name.
+
+
+
+More concretely,
+the values on the stack are paired to the right of the environment.
+So when designing operators like handleA that pass
+extra inputs to their subcommands,
+More precisely, the type of each argument of the operator (and its result)
+should have the form
+
+a (...(e,t1), ... tn) t
+
+where e is a polymorphic variable
+(representing the environment)
+and ti are the types of the values on the stack,
+with t1 being the top.
+The polymorphic variable e must not occur in
+a, ti or
+t.
+However the arrows involved need not be the same.
+Here are some more examples of suitable operators:
+
+bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
+runReader :: ... => a e c -> a' (e,State) c
+runState :: ... => a e c -> a' (e,State) (c,State)
+
+We can supply the extra input required by commands built with the last two
+by applying them to ordinary expressions, as in
+
+proc x -> do
+ s <- ...
+ (|runReader (do { ... })|) s
+
+which adds s to the stack of inputs to the command
+built using runReader.
+
+
+
+The command versions of lambda abstraction and application are analogous to
+the expression versions.
+In particular, the beta and eta rules describe equivalences of commands.
+These three features (operators, lambda abstraction and application)
+are the core of the notation; everything else can be built using them,
+though the results would be somewhat clumsy.
+For example, we could simulate do-notation by defining
+
+bind :: Arrow a => a e b -> a (e,b) c -> a e c
+u `bind` f = returnA &&& u >>> f
+
+bind_ :: Arrow a => a e b -> a e c -> a e c
+u `bind_` f = u `bind` (arr fst >>> f)
+
+We could simulate do by defining
+
+cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
+cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
+
-In all such cases, the binding is not generalised over the pattern-bound
-type variables. Thus f3 is monomorphic; f3
-has type b -> b for some type b,
-and notforall b. b -> b.
-In contrast, the binding
-
- f4 :: b->b
- f4 = \x -> x
-
-makes a polymorphic function, but b is not in scope anywhere
-in f4's scope.
+
+
+
+Differences with the paper
+
+
+
+Instead of a single form of arrow application (arrow tail) with two
+translations, the implementation provides two forms
+-< (first-order)
+and -<< (higher-order).
-
+
+
+User-defined operators are flagged with banana brackets instead of
+a new form keyword.
+
+
+
-
-
-Explicitly-kinded quantification
+
+Portability
+
+
+Although only GHC implements arrow notation directly,
+there is also a preprocessor
+(available from the
+arrows web page>)
+that translates arrow notation into Haskell 98
+for use with other Haskell systems.
+You would still want to check arrow programs with GHC;
+tracing type errors in the preprocessor output is not easy.
+Modules intended for both GHC and the preprocessor must observe some
+additional restrictions:
+
+
-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.
+The module must import
+Control.Arrow.
+
+
+
-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 preprocessor cannot cope with other Haskell extensions.
+These would have to go in separate modules.
+
+
-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.
+Because the preprocessor targets Haskell (rather than Core),
+let-bound variables are monomorphic.
+
-
-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.
+
+
+
+
-
+
+
+
Assertions
Assertions
@@ -2667,25 +3864,31 @@ assert pred val ==> assertError "Main.hs|15" pred val
The rewrite is only performed by the compiler when it spots
-applications of Exception.assert, so you can still define and
-use your own versions of assert, should you so wish. If not,
-import Exception to make use assert in your code.
+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.
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.
+. -fignore-asserts
+option That is, expressions of the form
+assert pred e will be rewritten to
+e.
Assertion failures can be caught, see the documentation for the
-Exception library ()
-for the details.
+Control.Exception library for the details.
+
+
+
Pragmas
@@ -2709,32 +3912,64 @@ for the details.
unrecognised word is (silently)
ignored.
-
-INLINE pragma
+
+ 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)
@@ -2744,25 +3979,25 @@ 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__
@@ -2771,32 +4006,140 @@ 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
@@ -2822,152 +4165,77 @@ hammeredLookup :: Ord key => [(key, value)] -> key -> value
{-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
- To get very fancy, you can also specify a named function
- to use for the specialised value, as in:
-
-
-{-# RULES hammeredLookup = blah #-}
-
-
- where blah is an implementation of
- hammerdLookup written specialy for
- Widget lookups. It's Your
- Responsibility to make sure that
- blah really behaves as a specialised
- version of hammeredLookup!!!
-
- Note we use the RULE pragma here to
- indicate that hammeredLookup applied at a
- certain type should be replaced by blah. See
- for more information on
- RULES.
-
- An example in which using RULES for
- specialisation will Win Big:
-
-
-toDouble :: Real a => a -> Double
-toDouble = fromRational . toRational
-
-{-# SPECIALIZE toDouble :: Int -> Double = 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.
-
-
-
-SPECIALIZE instance pragma
-
-
-
-SPECIALIZE pragma
-overloading, death to
-Same idea, except for instance declarations. For example:
-
+A SPECIALIZE has the effect of generating (a) a specialised
+version of the function and (b) a rewrite rule (see ) that
+rewrites a call to the un-specialised function into a call to the specialised
+one. You can, instead, provide your own specialised function and your own rewrite rule.
+For example, suppose that:
-instance (Eq a) => Eq (Foo a) where {
- {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
- ... usual stuff ...
- }
+ genericLookup :: Ord a => Table a b -> a -> b
+ intLookup :: Table Int b -> Int -> b
-The pragma must occur inside the where part
-of the instance declaration.
-
-
-Compatible with HBC, by the way, except perhaps in the placement
-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
-
+where intLookup is an implementation of genericLookup
+that works very fast for keys of type Int. Then you can write the rule
+
+ {-# RULES "intLookup" genericLookup = intLookup #-}
+
+(see ). It is Your
+ Responsibility to make sure that
+ intLookup really behaves as a specialised
+ version of genericLookup!!!
-
+ An example in which using RULES for
+ specialisation will Win Big:
-{-# LINE 42 "Foo.vhs" #-}
-
+ toDouble :: Real a => a -> Double
+ toDouble = fromRational . toRational
-
+ {-# RULES "toDouble/Int" toDouble = i2d #-}
+ i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
+
-
-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.
-
+ The i2d function is virtually one machine
+ instruction; the default conversion—via an intermediate
+ Rational—is obscenely expensive by
+ comparison.
-
+
-
-RULES pragma
+
+SPECIALIZE instance pragma
+
-The RULES pragma lets you specify rewrite rules. It is described in
-.
-
-
-
-
-
-DEPRECATED pragma
+SPECIALIZE pragma
+overloading, death to
+Same idea, except for instance declarations. For example:
-
-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
- ...
+instance (Eq a) => Eq (Foo a) where {
+ {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
+ ... usual stuff ...
+ }
-
-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:
+The pragma must occur inside the where part
+of the instance 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.
+Compatible with HBC, by the way, except perhaps in the placement
+of the pragma.
-
-
-You can suppress the warnings with the flag .
+
+
+
+
Rewrite rules
@@ -2977,7 +4245,10 @@ GHC will print the specified message.
The programmer can specify rewrite rules as part of the source program
-(in a pragma). GHC applies these rewrite rules wherever it can.
+(in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
+the flag () is on,
+and (b) the flag
+() is not specified.
@@ -3001,16 +4272,34 @@ 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.
+
+
@@ -3019,6 +4308,7 @@ is set, so you must lay out your rules starting in the same column as the
enclosing definitions.
+
@@ -3406,7 +4696,7 @@ will fuse with one but not the other)
-
+
So, for example, the following should generate no intermediate lists:
@@ -3494,7 +4784,7 @@ 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]
@@ -3512,9 +4802,9 @@ 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.
@@ -3524,6 +4814,69 @@ 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).
+
+
+
+
@@ -3572,7 +4925,7 @@ 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.
@@ -3782,179 +5135,6 @@ 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 sameNum 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.
-
-
-
-
+