[project @ 1999-02-22 10:22:34 by sof]

[ghc-hetmet.git] / ghc / docs / users_guide / glasgow_exts.vsgml

% 
% $Id: glasgow_exts.vsgml,v 1.5 1999/02/22 10:22:35 sof Exp $
%
% GHC Language Extensions.
%

As with all known Haskell systems, GHC implements some extensions to
the language.  To use them, you'll need to give a @-fglasgow-exts@%
<nidx>-fglasgow-exts option</nidx> option.

Virtually all of the Glasgow extensions serve to give you access to
the underlying facilities with which we implement Haskell.  Thus, you
can get at the Raw Iron, if you are willing to write some non-standard
code at a more primitive level.  You need not be ``stuck'' on
performance because of the implementation costs of Haskell's
``high-level'' features---you can always code ``under'' them.  In an
extreme case, you can write all your time-critical code in C, and then
just glue it together with Haskell!

Executive summary of our extensions:

<descrip>

<tag>Unboxed types and primitive operations:</tag> 

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 Section <ref name="Unboxed types"
id="glasgow-unboxed"> and following.

<tag>Multi-parameter type classes:</tag>

GHC's type system supports extended type classes with multiple
parameters.  Please see Section <ref name="Mult-parameter type
classes" id="multi-param-type-classes">.

<tag>Local universal quantification:</tag>

GHC's type system supports explicit unversal quantification in
constructor fields and function arguments.  This is useful for things
like defining @runST@ from the state-thread world.  See Section <ref
name="Local universal quantification" id="universal-quantification">.

<tag>Extistentially quantification in data types:</tag>

Some or all of the type variables in a datatype declaration may be
<em>existentially quantified</em>.  More details in Section <ref
name="Existential Quantification" id="existential-quantification">.

<tag>Scoped type variables:</tag>

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 Section <ref name="Scoped Type Variables"
id="scoped-type-variables">.

<tag>Calling out to C:</tag> 

Just what it sounds like.  We provide <em>lots</em> of rope that you
can dangle around your neck.  Please see Section <ref name="Calling~C
directly from Haskell" id="glasgow-ccalls">.

</descrip>

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 system libraries that provide a ``Haskellised
veneer'' over the features you want.  See Section <ref name="GHC
Prelude and libraries" id="ghc-prelude">.

%************************************************************************
%*                                                                      *
<sect1>Unboxed types
<label id="glasgow-unboxed">
<p>
<nidx>Unboxed types (Glasgow extension)</nidx>
%*                                                                      *
%************************************************************************

These types correspond to the ``raw machine'' types you would use in
C: @Int#@ (long int), @Double#@ (double), @Addr#@ (void *), etc.  The
<em>primitive operations</em> (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.

There are some restrictions on the use of unboxed types, the main one
being that you can't pass an unboxed value to a polymorphic function
or store one in a polymorphic data type.  This rules out things like
@[Int#]@ (ie. lists of unboxed 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 <em>lot</em> faster than its ``standard'' counterpart---we saw a
threefold speedup on one example.

Please see Section <ref name="The module PrelGHC: really primitive
stuff" id="ghc-libs-ghc"> for the details of unboxed types and the
operations on them.

%************************************************************************
%*                                                                      *
<sect1>Primitive state-transformer monad
<label id="glasgow-ST-monad">
<p>
<nidx>state transformers (Glasgow extensions)</nidx>
<nidx>ST monad (Glasgow extension)</nidx>
%*                                                                      *
%************************************************************************

This monad underlies our implementation of arrays, mutable and
immutable, and our implementation of I/O, including ``C calls''.

The @ST@ library, which provides access to the @ST@ monad, is a
GHC/Hugs extension library and is described in the separate <htmlurl
name="GHC/Hugs Extension Libraries" url="libs.html"> document.

%************************************************************************
%*                                                                      *
<sect1>Primitive arrays, mutable and otherwise
<label id="glasgow-prim-arrays">
<p>
<nidx>primitive arrays (Glasgow extension)</nidx>
<nidx>arrays, primitive (Glasgow extension)</nidx>
%*                                                                      *
%************************************************************************

GHC knows about quite a few flavours of Large Swathes of Bytes.

First, GHC distinguishes between primitive arrays of (boxed) Haskell
objects (type @Array# obj@) and primitive arrays of bytes (type
@ByteArray#@).

Second, it distinguishes between...
<descrip>
<tag>Immutable:</tag>
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.

<tag>Mutable:</tag>
Arrays that may be changed or ``mutated.''  All the operations on them
live within the state-transformer monad and the updates happen
<em>in-place</em>.

<tag>``Static'' (in C land):</tag>
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.

<tag>``Stable'' pointers:</tag>
If, for some reason, you wish to hand a Haskell pointer (i.e.,
<em>not</em> 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 Section <ref name="Subverting automatic unboxing with
``stable pointers''" id="glasgow-stablePtrs"> for more details.

<tag>``Foreign objects'':</tag>
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 Section <ref name="Pointing outside the Haskell heap"
id="glasgow-foreignObjs"> for more details.

</descrip>

The libraries section gives more details on all these ``primitive
array'' types and the operations on them, Section <ref name="The GHC
Prelude and Libraries" id="ghc-prelude">.  Some of these extensions
are also supported by Hugs, and the supporting libraries are described
in the <htmlurl name="GHC/Hugs Extension Libraries" url="libs.html">
document.

%************************************************************************
%*                                                                      *
<sect1>Calling~C directly from Haskell
<label id="glasgow-ccalls">
<p>
<nidx>C calls (Glasgow extension)</nidx>
<nidx>_ccall_ (Glasgow extension)</nidx>
<nidx>_casm_ (Glasgow extension)</nidx>
%*                                                                      *
%************************************************************************

GOOD ADVICE: Because this stuff is not Entirely Stable as far as names
and things go, you would be well-advised to keep your C-callery
corraled in a few modules, rather than sprinkled all over your code.
It will then be quite easy to update later on.

%************************************************************************
%*                                                                      *
<sect2>@_ccall_@ and @_casm_@: an introduction
<label id="ccall-intro">
<p>
%*                                                                      *
%************************************************************************

The simplest way to use a simple C function

<tscreen><verb>
double fooC( FILE *in, char c, int i, double d, unsigned int u )
</verb></tscreen>

is to provide a Haskell wrapper:

<tscreen><verb>
fooH :: Char -> Int -> Double -> Word -> IO Double
fooH c i d w = _ccall_ fooC (``stdin''::Addr) c i d w
</verb></tscreen>

The function @fooH@ will unbox all of its arguments, call the C
function @fooC@ and box the corresponding arguments.

One of the annoyances about @_ccall_@s is when the C types don't quite
match the Haskell compiler's ideas.  For this, the @_casm_@ variant
may be just the ticket (NB: <em>no chance</em> of such code going
through a native-code generator):

<tscreen><verb>
oldGetEnv name
  = _casm_ ``%r = getenv((char *) %0);'' name >>= \ litstring@(A# str#) ->
    return (
        if (litstring == ``NULL'') then
            Left ("Fail:oldGetEnv:"++name)
        else
            Right (unpackCString# str#)
    )
</verb></tscreen>

The first literal-literal argument to a @_casm_@ is like a @printf@
format: @%r@ is replaced with the ``result,'' @%0@--@%n-1@ are
replaced with the 1st--nth arguments.  As you can see above, it is an
easy way to do simple C~casting.  Everything said about @_ccall_@ goes
for @_casm_@ as well.

The use of @_casm_@ in your code does pose a problem to the compiler
when it comes to generating an interface file for a freshly compiled
module. Included in an interface file is the unfolding (if any) of a
declaration. However, if a declaration's unfolding happens to contain
a @_casm_@, its unfolding will <em/not/ be emitted into the interface
file even if it qualifies by all the other criteria. The reason why
the compiler prevents this from happening is that unfolding @_casm_@s
into an interface file unduly constrains how code that import your
module have to be compiled. If an imported declaration is unfolded and
it contains a @_casm_@, you now have to be using a compiler backend
capable of dealing with it (i.e., the C compiler backend). If you are
using the C compiler backend, the unfolded @_casm_@ may still cause you
problems since the C code snippet it contains may mention CPP symbols
that were in scope when compiling the original module are not when
compiling the importing module.

If you're willing to put up with the drawbacks of doing cross-module
inlining of C code (GHC - A Better C Compiler :-), the option
@-funfold-casms-in-hi-file@ will turn off the default behaviour.
<nidx>-funfold-casms-in-hi-file option</nidx>

%************************************************************************
%*                                                                      *
<sect2>Using function headers
<label id="glasgow-foreign-headers">
<p>
<nidx>C calls, function headers</nidx>
%*                                                                      *
%************************************************************************

When generating C (using the @-fvia-C@ directive), one can assist the
C compiler in detecting type errors by using the @-#include@ directive
to provide @.h@ files containing function headers.

For example,

<tscreen><verb>
typedef unsigned long *StgForeignObj;
typedef long StgInt;

void          initialiseEFS (StgInt size);
StgInt        terminateEFS (void);
StgForeignObj emptyEFS(void);
StgForeignObj updateEFS (StgForeignObj a, StgInt i, StgInt x);
StgInt        lookupEFS (StgForeignObj a, StgInt i);
</verb></tscreen>

You can find appropriate definitions for @StgInt@, @StgForeignObj@,
etc using @gcc@ on your architecture by consulting
@ghc/includes/StgTypes.h@.  The following table summarises the
relationship between Haskell types and C types.

<tabular ca="ll">
<bf>C type name</bf>      | <bf>Haskell Type</bf> @@
@@
@StgChar@          | @Char#@ @@               
@StgInt@           | @Int#@ @@                
@StgWord@          | @Word#@ @@               
@StgAddr@          | @Addr#@ @@               
@StgFloat@         | @Float#@ @@              
@StgDouble@        | @Double#@ @@             

@StgArray@         | @Array#@ @@              
@StgByteArray@     | @ByteArray#@ @@          
@StgArray@         | @MutableArray#@ @@       
@StgByteArray@     | @MutableByteArray#@ @@   

@StgStablePtr@     | @StablePtr#@ @@
@StgForeignObj@    | @ForeignObj#@
</tabular>

Note that this approach is only <em>essential</em> for returning
@float@s (or if @sizeof(int) != sizeof(int *)@ on your
architecture) but is a Good Thing for anyone who cares about writing
solid code.  You're crazy not to do it.

%************************************************************************
%*                                                                      *
<sect2>Subverting automatic unboxing with ``stable pointers''
<label id="glasgow-stablePtrs">
<p>
<nidx>stable pointers (Glasgow extension)</nidx>
%*                                                                      *
%************************************************************************

The arguments of a @_ccall_@ are automatically unboxed before the
call.  There are two reasons why this is usually the Right Thing to
do:

<itemize>
<item>
C is a strict language: it would be excessively tedious to pass
unevaluated arguments and require the C programmer to force their
evaluation before using them.

<item> Boxed values are stored on the Haskell heap and may be moved
within the heap if a garbage collection occurs---that is, pointers
to boxed objects are not <em>stable</em>.
</itemize>

It is possible to subvert the unboxing process by creating a ``stable
pointer'' to a value and passing the stable pointer instead.  For
example, to pass/return an integer lazily to C functions @storeC@ and
@fetchC@, one might write:

<tscreen><verb>
storeH :: Int -> IO ()
storeH x = makeStablePtr x              >>= \ stable_x ->
           _ccall_ storeC stable_x

fetchH :: IO Int
fetchH x = _ccall_ fetchC               >>= \ stable_x ->
           deRefStablePtr stable_x      >>= \ x ->
           freeStablePtr stable_x       >>
           return x
</verb></tscreen>

The garbage collector will refrain from throwing a stable pointer away
until you explicitly call one of the following from C or Haskell.

<tscreen><verb>
void freeStablePointer( StgStablePtr stablePtrToToss )
freeStablePtr :: StablePtr a -> IO ()
</verb></tscreen>

As with the use of @free@ in C programs, GREAT CARE SHOULD BE
EXERCISED to ensure these functions are called at the right time: too
early and you get dangling references (and, if you're lucky, an error
message from the runtime system); too late and you get space leaks.

And to force evaluation of the argument within @fooC@, one would
call one of the following C functions (according to type of argument).

<tscreen><verb>
void     performIO  ( StgStablePtr stableIndex /* StablePtr s (IO ()) */ );
StgInt   enterInt   ( StgStablePtr stableIndex /* StablePtr s Int */ );
StgFloat enterFloat ( StgStablePtr stableIndex /* StablePtr s Float */ );
</verb></tscreen>

<nidx>performIO</nidx>
<nidx>enterInt</nidx>
<nidx>enterFloat</nidx>

Note Bene: @_ccall_GC_@<nidx>_ccall_GC_</nidx> must be used if any of
these functions are used.

%************************************************************************
%*                                                                      *
<sect2>Foreign objects: pointing outside the Haskell heap
<label id="glasgow-foreignObjs">
<p>
<nidx>foreign objects (Glasgow extension)</nidx>
%*                                                                      *
%************************************************************************

There are two types that @ghc@ programs can use to reference
(heap-allocated) objects outside the Haskell world: @Addr@ and
@ForeignObj@.

If you use @Addr@, it is up to you to the programmer to arrange
allocation and deallocation of the objects.

If you use @ForeignObj@, @ghc@'s garbage collector will call upon the
user-supplied <em>finaliser</em> function to free the object when the
Haskell world no longer can access the object.  (An object is
associated with a finaliser function when the abstract
 Haskell type @ForeignObj@ is created). The finaliser function is
expressed in C, and is passed as argument the object:

<tscreen><verb>
void foreignFinaliser ( StgForeignObj fo )
</verb></tscreen>

when the Haskell world can no longer access the object.  Since
@ForeignObj@s only get released when a garbage collection occurs, we
provide ways of triggering a garbage collection from within C and from
within Haskell.

<tscreen><verb>
void GarbageCollect()
performGC :: IO ()
</verb></tscreen>

More information on the programmers' interface to @ForeignObj@ can be
found in the library documentation.

%************************************************************************
%*                                                                      *
<sect2>Avoiding monads
<label id="glasgow-avoiding-monads">
<p>
<nidx>C calls to `pure C'</nidx>
<nidx>unsafePerformIO</nidx>
%*                                                                      *
%************************************************************************

The @_ccall_@ construct is part of the @IO@ monad because 9 out of 10
uses will be to call imperative functions with side effects such as
@printf@.  Use of the monad ensures that these operations happen in a
predictable order in spite of laziness and compiler optimisations.

To avoid having to be in the monad to call a C function, it is
possible to use @unsafePerformIO@, which is available from the
@IOExts@ module.  There are three situations where one might like to
call a C function from outside the IO world:

<itemize>
<item>
Calling a function with no side-effects:
<tscreen><verb>
atan2d :: Double -> Double -> Double
atan2d y x = unsafePerformIO (_ccall_ atan2d y x)

sincosd :: Double -> (Double, Double)
sincosd x = unsafePerformIO $ do
        da <- newDoubleArray (0, 1)
        _casm_ ``sincosd( %0, &((double *)%1[0]), &((double *)%1[1]) );'' x da
        s <- readDoubleArray da 0
        c <- readDoubleArray da 1
        return (s, c)
</verb></tscreen>

<item> Calling a set of functions which have side-effects but which can
be used in a purely functional manner.

For example, an imperative implementation of a purely functional
lookup-table might be accessed using the following functions.

<tscreen><verb>
empty  :: EFS x
update :: EFS x -> Int -> x -> EFS x
lookup :: EFS a -> Int -> a

empty = unsafePerformIO (_ccall_ emptyEFS)

update a i x = unsafePerformIO $
        makeStablePtr x         >>= \ stable_x ->
        _ccall_ updateEFS a i stable_x

lookup a i = unsafePerformIO $
        _ccall_ lookupEFS a i   >>= \ stable_x ->
        deRefStablePtr stable_x
</verb></tscreen>

You will almost always want to use @ForeignObj@s with this.

<item> Calling a side-effecting function even though the results will
be unpredictable.  For example the @trace@ function is defined by:

<tscreen><verb>
trace :: String -> a -> a
trace string expr
  = unsafePerformIO (
        ((_ccall_ PreTraceHook sTDERR{-msg-}):: IO ())  >>
        fputs sTDERR string                             >>
        ((_ccall_ PostTraceHook sTDERR{-msg-}):: IO ()) >>
        return expr )
  where
    sTDERR = (``stderr'' :: Addr)
</verb></tscreen>

(This kind of use is not highly recommended --- it is only really
useful in debugging code.)
</itemize>

%************************************************************************
%*                                                                      *
<sect2>C-calling ``gotchas'' checklist
<label id="ccall-gotchas">
<p>
<nidx>C call dangers</nidx>
%*                                                                      *
%************************************************************************

And some advice, too.

<itemize>
<item> For modules that use @_ccall_@s, etc., compile with
@-fvia-C@.<nidx>-fvia-C option</nidx> You don't have to, but you should.

Also, use the @-#include "prototypes.h"@ flag (hack) to inform the C
compiler of the fully-prototyped types of all the C functions you
call.  (Section <ref name="Using function headers"
id="glasgow-foreign-headers"> says more about this...)

This scheme is the <em>only</em> way that you will get <em>any</em>
typechecking of your @_ccall_@s.  (It shouldn't be that way, but...).
GHC will pass the flag @-Wimplicit@ to gcc so that you'll get warnings
if any @_ccall_@ed functions have no prototypes.

<item>
Try to avoid @_ccall_@s to C~functions that take @float@
arguments or return @float@ results.  Reason: if you do, you will
become entangled in (ANSI?) C's rules for when arguments/results are
promoted to @doubles@.  It's a nightmare and just not worth it.
Use @doubles@ if possible.

If you do use @floats@, check and re-check that the right thing is
happening.  Perhaps compile with @-keep-hc-file-too@ and look at
the intermediate C (@.hc@ file).

<item> The compiler uses two non-standard type-classes when
type-checking the arguments and results of @_ccall_@: the arguments
(respectively result) of @_ccall_@ must be instances of the class
@CCallable@ (respectively @CReturnable@).  Both classes may be
imported from the module @CCall@, but this should only be
necessary if you want to define a new instance.  (Neither class
defines any methods --- their only function is to keep the
type-checker happy.)

The type checker must be able to figure out just which of the
C-callable/returnable types is being used.  If it can't, you have to
add type signatures. For example,

<tscreen><verb>
f x = _ccall_ foo x
</verb></tscreen>

is not good enough, because the compiler can't work out what type @x@
is, nor what type the @_ccall_@ returns.  You have to write, say:

<tscreen><verb>
f :: Int -> IO Double
f x = _ccall_ foo x
</verb></tscreen>

This table summarises the standard instances of these classes.

% ToDo: check this table against implementation!

<tabular ca="llll">
<bf>Type</bf>       |<bf>CCallable</bf>|<bf>CReturnable</bf> | <bf>Which is probably...</bf> @@

@Char@              | Yes  | Yes   | @unsigned char@ @@
@Int@               | Yes  | Yes   | @long int@ @@
@Word@              | Yes  | Yes   | @unsigned long int@ @@
@Addr@              | Yes  | Yes   | @void *@ @@
@Float@             | Yes  | Yes   | @float@ @@
@Double@            | Yes  | Yes   | @double@ @@
@()@                | No   | Yes   | @void@ @@
@[Char]@            | Yes  | No    | @char *@ (null-terminated) @@
                                      
@Array@             | Yes  | No    | @unsigned long *@ @@
@ByteArray@         | Yes  | No    | @unsigned long *@ @@
@MutableArray@      | Yes  | No    | @unsigned long *@ @@
@MutableByteArray@  | Yes  | No    | @unsigned long *@ @@
                                       
@State@             | Yes  | Yes   | nothing!@@
                                       
@StablePtr@         | Yes  | Yes   | @unsigned long *@ @@
@ForeignObjs@       | Yes  | Yes   | see later @@
</tabular>

Actually, the @Word@ type is defined as being the same size as a
pointer on the target architecture, which is <em>probably</em>
@unsigned long int@.  

The brave and careful programmer can add their own instances of these
classes for the following types:

<itemize>
<item>
A <em>boxed-primitive</em> type may be made an instance of both
@CCallable@ and @CReturnable@.  

A boxed primitive type is any data type with a
single unary constructor with a single primitive argument.  For
example, the following are all boxed primitive types:

<tscreen><verb>
Int
Double
data XDisplay = XDisplay Addr#
data EFS a = EFS# ForeignObj#
</verb></tscreen>

<tscreen><verb>
instance CCallable   (EFS a)
instance CReturnable (EFS a)
</verb></tscreen>

<item> Any datatype with a single nullary constructor may be made an
instance of @CReturnable@.  For example:

<tscreen><verb>
data MyVoid = MyVoid
instance CReturnable MyVoid
</verb></tscreen>

<item> As at version 2.09, @String@ (i.e., @[Char]@) is still
not a @CReturnable@ type.

Also, the now-builtin type @PackedString@ is neither
@CCallable@ nor @CReturnable@.  (But there are functions in
the PackedString interface to let you get at the necessary bits...)
</itemize>

<item> The code-generator will complain if you attempt to use @%r@ in
a @_casm_@ whose result type is @IO ()@; or if you don't use @%r@
<em>precisely</em> once for any other result type.  These messages are
supposed to be helpful and catch bugs---please tell us if they wreck
your life.

<item> If you call out to C code which may trigger the Haskell garbage
collector or create new threads (examples of this later...), then you
must use the @_ccall_GC_@<nidx>_ccall_GC_ primitive</nidx> or
@_casm_GC_@<nidx>_casm_GC_ primitive</nidx> variant of C-calls.  (This
does not work with the native code generator - use @\fvia-C@.) This
stuff is hairy with a capital H!  </itemize>

<sect1> Multi-parameter type classes
<label id="multi-param-type-classes">
<p>

This section documents GHC's implementation of multi-paramter type
classes.  There's lots of background in the paper <url name="Type
classes: exploring the design space"
url="http://www.dcs.gla.ac.uk/~simonpj/multi.ps.gz"> (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.)

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.

<sect2>Types
<p>

There are the following restrictions on the form of a qualified 
type:

<tscreen><verb>
  forall tv1..tvn (c1, ...,cn) => type
</verb></tscreen>

(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 Section <ref
name="Explicit universal quantification"
id="universal-quantification">).

<enum>

<item> <bf>Each universally quantified type variable 
@tvi@ must be mentioned (i.e. appear free) in @type@</bf>.

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:

<tscreen><verb>
  forall a. Eq a => Int
</verb></tscreen>

When a value with this type was used, the constraint <tt>Eq tv</tt>
would be introduced where <tt>tv</tt> is a fresh type variable, and
(in the dictionary-translation implementation) the value would be
applied to a dictionary for <tt>Eq tv</tt>.  The difficulty is that we
can never know which instance of <tt>Eq</tt> to use because we never
get any more information about <tt>tv</tt>.

<item> <bf>Every constraint @ci@ must mention at least one of the
universally quantified type variables @tvi@</bf>.

For example, this type is OK because <tt>C a b</tt> mentions the
universally quantified type variable <tt>b</tt>:

<tscreen><verb>
  forall a. C a b => burble
</verb></tscreen>

The next type is illegal because the constraint <tt>Eq b</tt> does not
mention <tt>a</tt>:

<tscreen><verb>
  forall a. Eq b => burble
</verb></tscreen>

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.

</enum>

These restrictions apply to all types, whether declared in a type signature
or inferred.

Unlike Haskell 1.4, constraints in types do <bf>not</bf> have to be of
the form <em>(class type-variables)</em>.  Thus, these type signatures
are perfectly OK

<tscreen><verb>
  f :: Eq (m a) => [m a] -> [m a]
  g :: Eq [a] => ...
</verb></tscreen>

This choice recovers principal types, a property that Haskell 1.4 does not have.

<sect2>Class declarations
<p>

<enum>

<item> <bf>Multi-parameter type classes are permitted</bf>. For example:

<tscreen><verb>
  class Collection c a where
    union :: c a -> c a -> c a
    ...etc..
</verb></tscreen>


<item> <bf>The class hierarchy must be acyclic</bf>.  However, the definition
of "acyclic" involves only the superclass relationships.  For example,
this is OK:

<tscreen><verb>
  class C a where { 
    op :: D b => a -> b -> b
  }

  class C a => D a where { ... }
</verb></tscreen>

Here, <tt>C</tt> is a superclass of <tt>D</tt>, but it's OK for a
class operation <tt>op</tt> of <tt>C</tt> to mention <tt>D</tt>.  (It
would not be OK for <tt>D</tt> to be a superclass of <tt>C</tt>.)

<item> <bf>There are no restrictions on the context in a class declaration
(which introduces superclasses), except that the class hierarchy must
be acyclic</bf>.  So these class declarations are OK:

<tscreen><verb>
  class Functor (m k) => FiniteMap m k where
    ...

  class (Monad m, Monad (t m)) => Transform t m where
    lift :: m a -> (t m) a
</verb></tscreen>

<item> <bf>In the signature of a class operation, every constraint
must mention at least one type variable that is not a class type
variable</bf>.

Thus:

<tscreen><verb>
  class Collection c a where
    mapC :: Collection c b => (a->b) -> c a -> c b
</verb></tscreen>

is OK because the constraint <tt>(Collection a b)</tt> mentions
<tt>b</tt>, even though it also mentions the class variable
<tt>a</tt>.  On the other hand:

<tscreen><verb>
  class C a where
    op :: Eq a => (a,b) -> (a,b)
</verb></tscreen>

is not OK because the constraint <tt>(Eq a)</tt> mentions on the class
type variable <tt>a</tt>, but not <tt>b</tt>.  However, any such
example is easily fixed by moving the offending context up to the
superclass context:

<tscreen><verb>
  class Eq a => C a where
    op ::(a,b) -> (a,b)
</verb></tscreen>

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.

<item> <bf>The type of each class operation must mention <em/all/ of
the class type variables</bf>.  For example:

<tscreen><verb>
  class Coll s a where
    empty  :: s
    insert :: s -> a -> s
</verb></tscreen>

is not OK, because the type of <tt>empty</tt> doesn't mention
<tt>a</tt>.  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, <tt>Coll</tt> might be rewritten

<tscreen><verb>
  class Coll s a where
    empty  :: s a
    insert :: s a -> a -> s a
</verb></tscreen>

which makes the connection between the type of a collection of
<tt>a</tt>'s (namely <tt>(s a)</tt>) and the element type <tt>a</tt>.
Occasionally this really doesn't work, in which case you can split the
class like this:

<tscreen><verb>
  class CollE s where
    empty  :: s

  class CollE s => Coll s a where
    insert :: s -> a -> s
</verb></tscreen>

</enum>

<sect2>Instance declarations
<p>

<enum>

<item> <bf>Instance declarations may not overlap</bf>.  The two instance
declarations

<tscreen><verb>
  instance context1 => C type1 where ...
  instance context2 => C type2 where ...
</verb></tscreen>

"overlap" if @type1@ and @type2@ unify

However, if you give the command line option
@-fallow-overlapping-instances@<nidx>-fallow-overlapping-instances
option</nidx> then two overlapping instance declarations are permitted
iff

<itemize>
<item> EITHER @type1@ and @type2@ do not unify
<item> OR @type2@ is a substitution instance of @type1@
                (but not identical to @type1@)
<item> OR vice versa
</itemize>

Notice that these rules

<itemize>
<item> make it clear which instance decl to use
           (pick the most specific one that matches)

<item> do not mention the contexts @context1@, @context2@
            Reason: you can pick which instance decl
            "matches" based on the type.
</itemize>

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 <tt>Main</tt>.  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 <tt>Main</tt>.)

<item> <bf>There are no restrictions on the type in an instance
<em/head/, except that at least one must not be a type variable</bf>.
The instance "head" is the bit after the "=>" in an instance decl. For
example, these are OK:

<tscreen><verb>
  instance C Int a where ...

  instance D (Int, Int) where ...

  instance E [[a]] where ...
</verb></tscreen>

Note that instance heads <bf>may</bf> contain repeated type variables.
For example, this is OK:

<tscreen><verb>
  instance Stateful (ST s) (MutVar s) where ...
</verb></tscreen>

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:

<tscreen><verb>
  instance C a => C a where ...
</verb></tscreen>

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:

<tscreen><verb>
  instance C a where
    op = ... -- Default
</verb></tscreen>

Second, sometimes you might want to use the following to get the
effect of a "class synonym":

<tscreen><verb>
  class (C1 a, C2 a, C3 a) => C a where { }

  instance (C1 a, C2 a, C3 a) => C a where { }
</verb></tscreen>

This allows you to write shorter signatures:

<tscreen><verb>
  f :: C a => ...
</verb></tscreen>

instead of

<tscreen><verb>
  f :: (C1 a, C2 a, C3 a) => ...
</verb></tscreen>

I'm on the lookout for a simple rule that preserves decidability while
allowing these idioms.  The experimental flag
@-fallow-undecidable-instances@<nidx>-fallow-undecidable-instances
option</nidx> lifts this restriction, allowing all the types in an
instance head to be type variables.

<item> <bf>Unlike Haskell 1.4, instance heads may use type
synonyms</bf>.  As always, using a type synonym is just shorthand for
writing the RHS of the type synonym definition.  For example:

<tscreen><verb>
  type Point = (Int,Int) 
  instance C Point   where ...
  instance C [Point] where ...
</verb></tscreen>

is legal.  However, if you added

<tscreen><verb>
  instance C (Int,Int) where ...
</verb></tscreen>

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:

<tscreen><verb>
  type P a = [[a]]
  instance Monad P where ...
</verb></tscreen>

This design decision is independent of all the others, and easily
reversed, but it makes sense to me.

<item><bf>The types in an instance-declaration <em/context/ must all
be type variables</bf>. Thus

<tscreen><verb>
  instance C a b => Eq (a,b) where ...
</verb></tscreen>

is OK, but

<tscreen><verb>
  instance C Int b => Foo b where ...
</verb></tscreen>

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 <tt>-fallow-undecidable-instances</tt> you 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 <tt>-fcontext-stack</tt><em/N/.

</enum>

% -----------------------------------------------------------------------------
<sect1>Explicit universal quantification
<label id="universal-quantification">
<p>

GHC now allows you to write explicitly quantified types.  GHC's
syntax for this now agrees with Hugs's, namely:

<tscreen><verb>
        forall a b. (Ord a, Eq  b) => a -> b -> a
</verb></tscreen>

The context is, of course, optional.  You can't use <tt>forall</tt> as
a type variable any more!

Haskell type signatures are implicitly quantified.  The <tt>forall</tt>
allows us to say exactly what this means.  For example:

<tscreen><verb>
        g :: b -> b
</verb></tscreen>

means this:

<tscreen><verb>
        g :: forall b. (b -> b)
</verb></tscreen>

The two are treated identically.

<sect2>Universally-quantified data type fields
<label id="univ">
<p>

In a <tt>data</tt> or <tt>newtype</tt> declaration one can quantify
the types of the constructor arguments.  Here are several examples:

<tscreen><verb>
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])
</verb></tscreen>

The constructors now have so-called <em/rank 2/ polymorphic
types, in which there is a for-all in the argument types.:

<tscreen><verb>
T1 :: forall a. (forall b. b -> b -> b) -> a -> T1 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
</verb></tscreen>

Notice that you don't need to use a <tt>forall</tt> if there's an
explicit context.  For example in the first argument of the
constructor <tt>MkSwizzle</tt>, an implicit "<tt>forall a.</tt>" is
prefixed to the argument type.  The implicit <tt>forall</tt>
quantifies all type variables that are not already in scope, and are
mentioned in the type quantified over.

As for type signatures, implicit quantification happens for non-overloaded
types too.  So if you write this:
<tscreen><verb>
  data T a = MkT (Either a b) (b -> b)
</verb></tscreen>
it's just as if you had written this:
<tscreen><verb>
  data T a = MkT (forall b. Either a b) (forall b. b -> b)
</verb></tscreen>
That is, since the type variable <tt>b</tt> isn't in scope, it's
implicitly universally quantified.  (Arguably, it would be better
to <em>require</em> explicit quantification on constructor arguments
where that is what is wanted.  Feedback welcomed.)

<sect2> Construction 
<p>

You construct values of types <tt>T1, MonadT, Swizzle</tt> by applying
the constructor to suitable values, just as usual.  For example,

<tscreen><verb>
(T1 (\xy->x) 3) :: T Int

(MkSwizzle sort)    :: Swizzle
(MkSwizzle reverse) :: Swizzle

(let r x = Just x
     b m k = case m of
                Just y -> k y
                Nothing -> Nothing
  in
  MkMonad r b) :: MonadT Maybe
</verb></tscreen>

The type of the argument can, as usual, be more general than the type
required, as <tt>(MkSwizzle reverse)</tt> shows.  (<tt>reverse</tt>
does not need the <tt>Ord</tt> constraint.)

<sect2>Pattern matching
<p>

When you use pattern matching, the bound variables may now have
polymorphic types.  For example:

<tscreen><verb>
        f :: T a -> a -> (a, Char)
        f (T1 f k) x = (f k x, f 'c' 'd')

        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)
</verb></tscreen>

In the function <tt>h</tt> we use the record selectors <tt>return</tt>
and <tt>bind</tt> to extract the polymorphic bind and return functions
from the <tt>MonadT</tt> data structure, rather than using pattern
matching.

<sect2>The partial-application restriction
<p>

There is really only one way in which data structures with polymorphic
components might surprise you: you must not partially apply them.
For example, this is illegal:

<tscreen><verb>
        map MkSwizzle [sort, reverse]
</verb></tscreen>

The restriction is this: <em>every subexpression of the program must
have a type that has no for-alls, except that in a function
application (f e1 ... en) the partial applications are not subject to
this rule</em>.  The restriction makes type inference feasible.

In the illegal example, the sub-expression <tt>MkSwizzle</tt> has the
polymorphic type <tt>(Ord b => [b] -> [b]) -> Swizzle</tt> and is not
a sub-expression of an enclosing application.  On the other hand, this
expression is OK:

<tscreen><verb>
        map (T1 (\a b -> a)) [1,2,3]
</verb></tscreen>

even though it involves a partial application of <tt>T1</tt>, because
the sub-expression <tt>T1 (\a b -> a)</tt> has type <tt>Int -> T
Int</tt>.

<sect2>Type signatures
<label id="sigs">
<p>

Once you have data constructors with universally-quantified fields, or
constants such as <tt>runST</tt> that have rank-2 types, it isn't long
before you discover that you need more!  Consider:

<tscreen><verb>
  mkTs f x y = [T1 f x, T1 f y]
</verb></tscreen>

<tt>mkTs</tt> is a fuction that constructs some values of type
<tt>T</tt>, using some pieces passed to it.  The trouble is that since
<tt>f</tt> is a function argument, Haskell assumes that it is
monomorphic, so we'll get a type error when applying <tt>T1</tt> to
it.  This is a rather silly example, but the problem really bites in
practice.  Lots of people trip over the fact that you can't make
"wrappers functions" for <tt>runST</tt> for exactly the same reason.
In short, it is impossible to build abstractions around functions with
rank-2 types.

The solution is fairly clear.  We provide the ability to give a rank-2
type signature for <em>ordinary</em> functions (not only data
constructors), thus:

<tscreen><verb>
  mkTs :: (forall b. b -> b -> b) -> a -> [T a]
  mkTs f x y = [T1 f x, T1 f y]
</verb></tscreen>

This type signature tells the compiler to attribute <tt>f</tt> with
the polymorphic type <tt>(forall b. b -> b -> b)</tt> when type
checking the body of <tt>mkTs</tt>, so now the application of
<tt>T1</tt> is fine.

There are two restrictions:

<itemize>
<item> You can only define a rank 2 type, specified by the following
grammar:

<tscreen><verb>
   rank2type ::= [forall tyvars .] [context =>] funty
   funty     ::= ([forall tyvars .] [context =>] ty) -> funty
               | ty
   ty        ::= ...current Haskell monotype syntax...
</verb></tscreen>

Informally, the universal quantification must all be right at the beginning, 
or at the top level of a function argument.

<item> There is a restriction on the definition of a function whose
type signature is a rank-2 type: the polymorphic arguments must be
matched on the left hand side of the "<tt>=</tt>" sign.  You can't
define <tt>mkTs</tt> like this:

<tscreen><verb>
  mkTs :: (forall b. b -> b -> b) -> a -> [T a]
  mkTs = \ f x y -> [T1 f x, T1 f y]
</verb></tscreen>


The same partial-application rule applies to ordinary functions with
rank-2 types as applied to data constructors.  

</itemize>

% -----------------------------------------------------------------------------
<sect1>Existentially quantified data constructors
<label id="existential-quantification">
<p>

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 <tt>hbc</tt> Haskell compiler for several years, and
proved very useful.  Here's the idea.  Consider the declaration:

<tscreen><verb>
  data Foo = forall a. MkFoo a (a -> Bool)
           | Nil
</verb></tscreen>

The data type <tt>Foo</tt> has two constructors with types:

<tscreen><verb>
  MkFoo :: forall a. a -> (a -> Bool) -> Foo
  Nil   :: Foo
</verb></tscreen>

Notice that the type variable <tt>a</tt> in the type of <tt>MkFoo</tt>
does not appear in the data type itself, which is plain <tt>Foo</tt>.
For example, the following expression is fine:

<tscreen><verb>
  [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
</verb></tscreen>

Here, <tt>(MkFoo 3 even)</tt> packages an integer with a function
<tt>even</tt> that maps an integer to <tt>Bool</tt>; and <tt>MkFoo 'c'
isUpper</tt> packages a character with a compatible function.  These
two things are each of type <tt>Foo</tt> and can be put in a list.

What can we do with a value of type <tt>Foo</tt>?.  In particular,
what happens when we pattern-match on <tt>MkFoo</tt>?

<tscreen><verb>
  f (MkFoo val fn) = ???
</verb></tscreen>

Since all we know about <tt>val</tt> and <tt>fn</tt> is that they
are compatible, the only (useful) thing we can do with them is to
apply <tt>fn</tt> to <tt>val</tt> to get a boolean.  For example:

<tscreen><verb>
  f :: Foo -> Bool
  f (MkFoo val fn) = fn val
</verb></tscreen>

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.

<sect2>Why existential?
<label id="existential">
<p>

What has this to do with <em>existential</em> quantification?
Simply that <tt>MkFoo</tt> has the (nearly) isomorphic type

<tscreen><verb>
  MkFoo :: (exists a . (a, a -> Bool)) -> Foo
</verb></tscreen>

But Haskell programmers can safely think of the ordinary
<em>universally</em> quantified type given above, thereby avoiding
adding a new existential quantification construct.

<sect2>Type classes
<p>

An easy extension (implemented in <tt>hbc</tt>) is to allow 
arbitrary contexts before the constructor.  For example:

<tscreen><verb>
  data Baz = forall a. Eq a => Baz1 a a
           | forall b. Show b => Baz2 b (b -> b)
</verb></tscreen>

The two constructors have the types you'd expect:

<tscreen><verb>
  Baz1 :: forall a. Eq a => a -> a -> Baz
  Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
</verb></tscreen>

But when pattern matching on <tt>Baz1</tt> the matched values can be compared
for equality, and when pattern matching on <tt>Baz2</tt> the first matched
value can be converted to a string (as well as applying the function to it).  
So this program is legal:

<tscreen><verb>
  f :: Baz -> String
  f (Baz1 p q) | p == q    = "Yes"
               | otherwise = "No"
  f (Baz1 v fn)            = show (fn v)
</verb></tscreen>

Operationally, in a dictionary-passing implementation, the
constructors <tt>Baz1</tt> and <tt>Baz2</tt> must store the
dictionaries for <tt>Eq</tt> and <tt>Show</tt> respectively, and
extract it on pattern matching.

Notice the way that the syntax fits smoothly with that used for
universal quantification earlier.

<sect2>Restrictions
<p>

There are several restrictions on the ways in which existentially-quantified
constructors can be use.

<itemize>

<item> 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:

<tscreen><verb>
  f1 (MkFoo a f) = a
</verb></tscreen>

Here, the type bound by <tt>MkFoo</tt> "escapes", because <tt>a</tt>
is the result of <tt>f1</tt>.  One way to see why this is wrong is to
ask what type <tt>f1</tt> has:

<tscreen><verb>
  f1 :: Foo -> a             -- Weird!
</verb></tscreen>

What is this "<tt>a</tt>" in the result type? Clearly we don't mean
this:

<tscreen><verb>
  f1 :: forall a. Foo -> a   -- Wrong!
</verb></tscreen>

The original program is just plain wrong.  Here's another sort of error

<tscreen><verb>
  f2 (Baz1 a b) (Baz1 p q) = a==q
</verb></tscreen>

It's ok to say <tt>a==b</tt> or <tt>p==q</tt>, but
<tt>a==q</tt> is wrong because it equates the two distinct types arising
from the two <tt>Baz1</tt> constructors.


<item>You can't pattern-match on an existentially quantified
constructor in a <tt>let</tt> or <tt>where</tt> group of
bindings. So this is illegal:

<tscreen><verb>
  f3 x = a==b where { Baz1 a b = x }
</verb></tscreen>

You can only pattern-match
on an existentially-quantified constructor in a <tt>case</tt> expression or
in the patterns of a function definition.

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.  

<item>You can't use existential quantification for <tt>newtype</tt> 
declarations.  So this is illegal:

<tscreen><verb>
  newtype T = forall a. Ord a => MkT a
</verb></tscreen>

Reason: a value of type <tt>T</tt> must be represented as a pair
of a dictionary for <tt>Ord t</tt> and a value of type <tt>t</tt>.
That contradicts the idea that <tt>newtype</tt> should have no 
concrete representation.  You can get just the same efficiency and effect
by using <tt>data</tt> instead of <tt>newtype</tt>.  If there is no
overloading involved, then there is more of a case for allowing
an existentially-quantified <tt>newtype</tt>, because the <tt>data</tt>
because the <tt>data</tt> version does carry an implementation cost,
but single-field existentially quantified constructors aren't much
use.  So the simple restriction (no existential stuff on <tt>newtype</tt>)
stands, unless there are convincing reasons to change it.
</itemize>

% -----------------------------------------------------------------------------
<sect1>Scoped Type Variables
<label id="scoped-type-variables">
<p>

A <em/pattern type signature/ can introduce a <em/scoped type
variable/.  For example

<tscreen><verb>
f (xs::[a]) = ys ++ ys
           where
              ys :: [a]
              ys = reverse xs 
</verb></tscreen>

The pattern @(xs::[a])@ includes a type signature for @xs@.
This brings the type variable @a@ into scope; it scopes over
all the patterns and right hand sides for this equation for @f@.
In particular, it is in scope at the type signature for @y@.

At ordinary type signatures, such as that for @ys@, any type variables
mentioned in the type signature <em/that are not in scope/ are
implicitly universally quantified.  (If there are no type variables in
scope, all type variables mentioned in the signature are universally
quantified, which is just as in Haskell 98.)  In this case, since @a@
is in scope, it is not universally quantified, so the type of @ys@ is
the same as that of @xs@.  In Haskell 98 it is not possible to declare
a type for @ys@; a major benefit of scoped type variables is that
it becomes possible to do so.

Scoped type variables are implemented in both GHC and Hugs.  Where the
implementations differ from the specification below, those differences
are noted.

So much for the basic idea.  Here are the details.

<sect2>Scope and implicit quantification
<p>

<itemize>
<item> All the type variables mentioned in the patterns for a single 
function definition equation, that are not already in scope,
are brought into scope by the patterns.  We describe this set as
the <em/type variables bound by the equation/.

<item> The type variables thus brought into scope may be mentioned
in ordinary type signatures or pattern type signatures anywhere within
their scope.

<item> In ordinary type signatures, any type variable mentioned in the
signature that is in scope is <em/not/ universally quantified.

<item> Ordinary type signatures do not bring any new type variables
into scope (except in the type signature itself!). So this is illegal:

<tscreen><verb>
  f :: a -> a
  f x = x::a
</verb></tscreen>

It's illegal because @a@ is not in scope in the body of @f@,
so the ordinary signature @x::a@ is equivalent to @x::forall a.a@;
and that is an incorrect typing.

<item> There is no implicit universal quantification on pattern type
signatures, nor may one write an explicit @forall@ type in a pattern
type signature.  The pattern type signature is a monotype.

<item> 
The type variables in the head of a @class@ or @instance@ declaration
scope over the methods defined in the @where@ part.  For example:

<tscreen><verb>
  class C a where
    op :: [a] -> a

    op xs = let ys::[a]
                ys = reverse xs
            in
            head ys
</verb></tscreen>

(Not implemented in Hugs yet, Dec 98).
</itemize>

<sect2>Polymorphism
<p>

<itemize>
<item> Pattern type signatures are completely orthogonal to ordinary, separate
type signatures.  The two can be used independently or together.  There is
no scoping associated with the names of the type variables in a separate type signature.

<tscreen><verb>
   f :: [a] -> [a]
   f (xs::[b]) = reverse xs
</verb></tscreen>

<item> The function must be polymorphic in the type variables
bound by all its equations.  Operationally, the type variables bound
by one equation must not:

<itemize>
<item> Be unified with a type (such as @Int@, or @[a]@).
<item> Be unified with a type variable free in the environment.
<item> Be unified with each other.  (They may unify with the type variables 
bound by another equation for the same function, of course.)
</itemize>

For example, the following all fail to type check:

<tscreen><verb>
  f (x::a) (y::b) = [x,y]       -- a unifies with b

  g (x::a) = x + 1::Int         -- a unifies with Int

  h x = let k (y::a) = [x,y]    -- a is free in the
        in k x                  -- environment

  k (x::a) True    = ...        -- a unifies with Int
  k (x::Int) False = ...

  w :: [b] -> [b]
  w (x::a) = x                  -- a unifies with [b]
</verb></tscreen>

<item> The pattern-bound type variable may, however, be constrained
by the context of the principal type, thus:

<tscreen><verb>
  f (x::a) (y::a) = x+y*2
</verb></tscreen>

gets the inferred type: @forall a. Num a => a -> a -> a@.
</itemize>

<sect2>Result type signatures
<p>

<itemize>
<item> The result type of a function can be given a signature,
thus:

<tscreen><verb>
  f (x::a) :: [a] = [x,x,x]
</verb></tscreen>

The final @":: [a]"@ after all the patterns gives a signature to the
result type.  Sometimes this is the only way of naming the type variable
you want:

<tscreen><verb>
  f :: Int -> [a] -> [a]
  f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
                        in \xs -> map g (reverse xs `zip` xs)
</verb></tscreen>

</itemize>

Result type signatures are not yet implemented in Hugs.

<sect2>Pattern signatures on other constructs
<p>

<itemize>
<item> A pattern type signature can be on an arbitrary sub-pattern, not
just on a variable:

<tscreen><verb>
  f ((x,y)::(a,b)) = (y,x) :: (b,a)
</verb></tscreen>

<item> Pattern type signatures, including the result part, can be used
in lambda abstractions:

<tscreen><verb>
  (\ (x::a, y) :: a -> x)
</verb></tscreen>

Type variables bound by these patterns must be polymorphic in
the sense defined above.
For example:

<tscreen><verb>
  f1 (x::c) = f1 x      -- ok
  f2 = \(x::c) -> f2 x  -- not ok
</verb></tscreen>

Here, @f1@ is OK, but @f2@ is not, because @c@ gets unified
with a type variable free in the environment, in this
case, the type of @f2@, which is in the environment when
the lambda abstraction is checked.

<item> Pattern type signatures, including the result part, can be used
in @case@ expressions:

<tscreen><verb>
  case e of { (x::a, y) :: a -> x } 
</verb></tscreen>

The pattern-bound type variables must, as usual, 
be polymorphic in the following sense: each case alternative,
considered as a lambda abstraction, must be polymorphic.
Thus this is OK:

<tscreen><verb>
  case (True,False) of { (x::a, y) -> x }
</verb></tscreen>

Even though the context is that of a pair of booleans, 
the alternative itself is polymorphic.  Of course, it is
also OK to say:

<tscreen><verb>
  case (True,False) of { (x::Bool, y) -> x }
</verb></tscreen>

<item>
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:

<tscreen><verb>
  \ x :: a -> b -> x
</verb></tscreen>

<item> Pattern type signatures that bind new type variables
may not be used in pattern bindings at all.
So this is illegal:

<tscreen><verb>
  f x = let (y, z::a) = x in ...
</verb></tscreen>

But these are OK, because they do not bind fresh type variables:

<tscreen><verb>
  f1 x            = let (y, z::Int) = x in ...
  f2 (x::(Int,a)) = let (y, z::a)   = x in ...
</verb></tscreen>

However a single variable is considered a degenerate function binding,
rather than a degerate pattern binding, so this is permitted, even
though it binds a type variable:

<tscreen><verb>
  f :: (b->b) = \(x::b) -> x
</verb></tscreen>

</itemize>
Such degnerate function bindings do not fall under the monomorphism
restriction.  Thus:

<tscreen><verb>
  g :: a -> a -> Bool = \x y. x==y
</verb></tscreen>

Here @g@ has type @forall a. Eq a => a -> a -> Bool@, just as if
@g@ had a separate type signature.  Lacking a type signature, @g@
would get a monomorphic type.

<sect2>Existentials
<p>

<itemize>
<item> Pattern type signatures can bind existential type variables.
For example:

<tscreen><verb>
  data T = forall a. MkT [a]

  f :: T -> T
  f (MkT [t::a]) = MkT t3
                 where
                   t3::[a] = [t,t,t]
</verb></tscreen>

</itemize>