language, GHCextensions, GHC
As with all known Haskell systems, GHC implements some extensions to
the language. To use them, you'll need to give a
-fglasgow-exts option 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:
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.
Multi-parameter type classes:
GHC's type system supports extended type classes with multiple
parameters. Please see .
Local universal quantification:
GHC's type system supports explicit universal quantification in
constructor fields and function arguments. This is useful for things
like defining runST from the state-thread world. See .
Extistentially quantification in data types:
Some or all of the type variables in a datatype declaration may be
existentially quantified. More details in .
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 .
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 .
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
.
Unboxed types and primitive operations
PrelGHC module
This module defines all the types which are primitive in Glasgow
Haskell, and the operations provided for them.
Unboxed types
Unboxed types (Glasgow extension)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.
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.
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.
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.
Unboxed Tuples
Unboxed tuples aren't really exported by PrelGHC,
they're available by default with . An
unboxed tuple looks like this:
(# e_1, ..., e_n #)
where e_1..e_n are expressions of any
type (primitive or non-primitive). The type of an unboxed tuple looks
the same.
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.
There are some pretty stringent restrictions on the use of unboxed tuples:
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.
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
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.
Note: we may relax some of these restrictions in the future.
The IO and ST monads use unboxed tuples to avoid unnecessary
allocation during sequences of operations.
Character and numeric typescharacter types, primitivenumeric types, primitiveinteger types, primitivefloating point types, primitive
There are the following obvious primitive types:
type Char#
type Int#
type Word#
type Addr#
type Float#
type Double#
type Int64#
type Word64#
Char#Int#Word#Addr#Float#Double#Int64#Word64#
If you really want to know their exact equivalents in C, see
ghc/includes/StgTypes.h in the GHC source tree.
Literals for these types may be written as follows:
1# an Int#
1.2# a Float#
1.34## a Double#
'a'# a Char#; for weird characters, use '\o<octal>'#
"a"# an Addr# (a `char *')
literals, primitiveconstants, primitivenumbers, primitiveComparison operationscomparisons, primitiveoperators, comparison
{>,>=,==,/=,<,<=}# :: Int# -> Int# -> Bool
{gt,ge,eq,ne,lt,le}Char# :: Char# -> Char# -> Bool
-- ditto for Word# and Addr#
>#>=#==#/=#<#<=#gt{Char,Word,Addr}#ge{Char,Word,Addr}#eq{Char,Word,Addr}#ne{Char,Word,Addr}#lt{Char,Word,Addr}#le{Char,Word,Addr}#Primitive-character operationscharacters, primitive operationsoperators, primitive character
ord# :: Char# -> Int#
chr# :: Int# -> Char#
ord#chr#Primitive-Int operationsintegers, primitive operationsoperators, primitive integer
{+,-,*,quotInt,remInt,gcdInt}# :: Int# -> Int# -> Int#
negateInt# :: Int# -> Int#
iShiftL#, iShiftRA#, iShiftRL# :: Int# -> Int# -> Int#
-- shift left, right arithmetic, right logical
addIntC#, subIntC#, mulIntC# :: Int# -> Int# -> (# Int#, Int# #)
-- add, subtract, multiply with carry
+#-#*#quotInt#remInt#gcdInt#iShiftL#iShiftRA#iShiftRL#addIntC#subIntC#mulIntC#shift operations, integerNote: No error/overflow checking!
Primitive-Double and Float operationsfloating point numbers, primitiveoperators, primitive floating point
{+,-,*,/}## :: Double# -> Double# -> Double#
{<,<=,==,/=,>=,>}## :: Double# -> Double# -> Bool
negateDouble# :: Double# -> Double#
double2Int# :: Double# -> Int#
int2Double# :: Int# -> Double#
{plus,minux,times,divide}Float# :: Float# -> Float# -> Float#
{gt,ge,eq,ne,lt,le}Float# :: Float# -> Float# -> Bool
negateFloat# :: Float# -> Float#
float2Int# :: Float# -> Int#
int2Float# :: Int# -> Float#
+##-##*##/##<##<=##==##=/##>=##>##negateDouble#double2Int#int2Double#plusFloat#minusFloat#timesFloat#divideFloat#gtFloat#geFloat#eqFloat#neFloat#ltFloat#leFloat#negateFloat#float2Int#int2Float#
And a full complement of trigonometric functions:
expDouble# :: Double# -> Double#
logDouble# :: Double# -> Double#
sqrtDouble# :: Double# -> Double#
sinDouble# :: Double# -> Double#
cosDouble# :: Double# -> Double#
tanDouble# :: Double# -> Double#
asinDouble# :: Double# -> Double#
acosDouble# :: Double# -> Double#
atanDouble# :: Double# -> Double#
sinhDouble# :: Double# -> Double#
coshDouble# :: Double# -> Double#
tanhDouble# :: Double# -> Double#
powerDouble# :: Double# -> Double# -> Double#
trigonometric functions, primitive
similarly for Float#.
There are two coercion functions for Float#/Double#:
float2Double# :: Float# -> Double#
double2Float# :: Double# -> Float#
float2Double#double2Float#
The primitive version of decodeDouble
(encodeDouble is implemented as an external C
function):
decodeDouble# :: Double# -> PrelNum.ReturnIntAndGMP
encodeDouble#decodeDouble#
(And the same for Float#s.)
Operations on/for Integers (interface to GMP)
arbitrary precision integersInteger, operations on
We implement Integers (arbitrary-precision
integers) using the GNU multiple-precision (GMP) package (version
2.0.2).
The data type for Integer is either a small
integer, represented by an Int, or a large integer
represented using the pieces required by GMP's
MP_INT in gmp.h (see
gmp.info in
ghc/includes/runtime/gmp). It comes out as:
data Integer = S# Int# -- small integers
| J# Int# ByteArray# -- large integers
Integer type The primitive
ops to support large Integers use the
“pieces” of the representation, and are as follows:
negateInteger# :: Int# -> ByteArray# -> Integer
{plus,minus,times}Integer#, gcdInteger#,
quotInteger#, remInteger#, divExactInteger#
:: Int# -> ByteArray#
-> Int# -> ByteArray#
-> (# Int#, ByteArray# #)
cmpInteger#
:: Int# -> ByteArray#
-> Int# -> ByteArray#
-> Int# -- -1 for <; 0 for ==; +1 for >
cmpIntegerInt#
:: Int# -> ByteArray#
-> Int#
-> Int# -- -1 for <; 0 for ==; +1 for >
gcdIntegerInt# ::
:: Int# -> ByteArray#
-> Int#
-> Int#
divModInteger#, quotRemInteger#
:: Int# -> ByteArray#
-> Int# -> ByteArray#
-> (# Int#, ByteArray#,
Int#, ByteArray# #)
integer2Int# :: Int# -> ByteArray# -> Int#
int2Integer# :: Int# -> Integer -- NB: no error-checking on these two!
word2Integer# :: Word# -> Integer
addr2Integer# :: Addr# -> Integer
-- the Addr# is taken to be a `char *' string
-- to be converted into an Integer.
negateInteger#plusInteger#minusInteger#timesInteger#quotInteger#remInteger#gcdInteger#gcdIntegerInt#divExactInteger#cmpInteger#divModInteger#quotRemInteger#integer2Int#int2Integer#word2Integer#addr2Integer#Words and addressesword, primitive typeaddress, primitive typeunsigned integer, primitive typepointer, primitive type
A Word# is used for bit-twiddling operations.
It is the same size as an Int#, but has no sign
nor any arithmetic operations.
type Word# -- Same size/etc as Int# but *unsigned*
type Addr# -- A pointer from outside the "Haskell world" (from C, probably);
-- described under "arrays"
Word#Addr#Word#s and Addr#s have
the usual comparison operations. Other
unboxed-Word ops (bit-twiddling and coercions):
{gt,ge,eq,ne,lt,le}Word# :: Word# -> Word# -> Bool
and#, or#, xor# :: Word# -> Word# -> Word#
-- standard bit ops.
quotWord#, remWord# :: Word# -> Word# -> Word#
-- word (i.e. unsigned) versions are different from int
-- versions, so we have to provide these explicitly.
not# :: Word# -> Word#
shiftL#, shiftRL# :: Word# -> Int# -> Word#
-- shift left, right logical
int2Word# :: Int# -> Word# -- just a cast, really
word2Int# :: Word# -> Int#
bit operations, Word and AddrgtWord#geWord#eqWord#neWord#ltWord#leWord#and#or#xor#not#quotWord#remWord#shiftL#shiftRA#shiftRL#int2Word#word2Int#
Unboxed-Addr ops (C casts, really):
{gt,ge,eq,ne,lt,le}Addr# :: Addr# -> Addr# -> Bool
int2Addr# :: Int# -> Addr#
addr2Int# :: Addr# -> Int#
addr2Integer# :: Addr# -> (# Int#, ByteArray# #)
gtAddr#geAddr#eqAddr#neAddr#ltAddr#leAddr#int2Addr#addr2Int#addr2Integer#
The casts between Int#,
Word# and Addr#
correspond to null operations at the machine level, but are required
to keep the Haskell type checker happy.
Operations for indexing off of C pointers
(Addr#s) to snatch values are listed under
“arrays”.
Arraysarrays, primitive
The type Array# elt is the type of primitive,
unpointed arrays of values of type elt.
type Array# elt
Array#Array# is more primitive than a Haskell
array—indeed, the Haskell Array interface is
implemented using Array#—in that an
Array# is indexed only by
Int#s, starting at zero. It is also more
primitive by virtue of being unboxed. That doesn't mean that it isn't
a heap-allocated object—of course, it is. Rather, being unboxed
means that it is represented by a pointer to the array itself, and not
to a thunk which will evaluate to the array (or to bottom). The
components of an Array# are themselves boxed.
The type ByteArray# is similar to
Array#, except that it contains just a string
of (non-pointer) bytes.
type ByteArray#
ByteArray#
Arrays of these types are useful when a Haskell program wishes to
construct a value to pass to a C procedure. It is also possible to use
them to build (say) arrays of unboxed characters for internal use in a
Haskell program. Given these uses, ByteArray#
is deliberately a bit vague about the type of its components.
Operations are provided to extract values of type
Char#, Int#,
Float#, Double#, and
Addr# from arbitrary offsets within a
ByteArray#. (For type
Foo#, the $i$th offset gets you the $i$th
Foo#, not the Foo# at
byte-position $i$. Mumble.) (If you want a
Word#, grab an Int#,
then coerce it.)
Lastly, we have static byte-arrays, of type
Addr# [mentioned previously]. (Remember
the duality between arrays and pointers in C.) Arrays of this types
are represented by a pointer to an array in the world outside Haskell,
so this pointer is not followed by the garbage collector. In other
respects they are just like ByteArray#. They
are only needed in order to pass values from C to Haskell.
Reading and writing
Primitive arrays are linear, and indexed starting at zero.
The size and indices of a ByteArray#, Addr#, and
MutableByteArray# are all in bytes. It's up to the program to
calculate the correct byte offset from the start of the array. This
allows a ByteArray# to contain a mixture of values of different
type, which is often needed when preparing data for and unpicking
results from C. (Umm…not true of indices…WDP 95/09)
Should we provide some sizeOfDouble# constants?
Out-of-range errors on indexing should be caught by the code which
uses the primitive operation; the primitive operations themselves do
not check for out-of-range indexes. The intention is that the
primitive ops compile to one machine instruction or thereabouts.
We use the terms “reading” and “writing” to refer to accessing
mutable arrays (see ), and
“indexing” to refer to reading a value from an immutable
array.
Immutable byte arrays are straightforward to index (all indices in bytes):
indexCharArray# :: ByteArray# -> Int# -> Char#
indexIntArray# :: ByteArray# -> Int# -> Int#
indexAddrArray# :: ByteArray# -> Int# -> Addr#
indexFloatArray# :: ByteArray# -> Int# -> Float#
indexDoubleArray# :: ByteArray# -> Int# -> Double#
indexCharOffAddr# :: Addr# -> Int# -> Char#
indexIntOffAddr# :: Addr# -> Int# -> Int#
indexFloatOffAddr# :: Addr# -> Int# -> Float#
indexDoubleOffAddr# :: Addr# -> Int# -> Double#
indexAddrOffAddr# :: Addr# -> Int# -> Addr#
-- Get an Addr# from an Addr# offset
indexCharArray#indexIntArray#indexAddrArray#indexFloatArray#indexDoubleArray#indexCharOffAddr#indexIntOffAddr#indexFloatOffAddr#indexDoubleOffAddr#indexAddrOffAddr#
The last of these, indexAddrOffAddr#, extracts an Addr# using an offset
from another Addr#, thereby providing the ability to follow a chain of
C pointers.
Something a bit more interesting goes on when indexing arrays of boxed
objects, because the result is simply the boxed object. So presumably
it should be entered—we never usually return an unevaluated
object! This is a pain: primitive ops aren't supposed to do
complicated things like enter objects. The current solution is to
return a single element unboxed tuple (see ).
indexArray# :: Array# elt -> Int# -> (# elt #)
indexArray#The state typestate, primitive typeState#
The primitive type State# represents the state of a state
transformer. It is parameterised on the desired type of state, which
serves to keep states from distinct threads distinct from one another.
But the only effect of this parameterisation is in the type
system: all values of type State# are represented in the same way.
Indeed, they are all represented by nothing at all! The code
generator “knows” to generate no code, and allocate no registers
etc, for primitive states.
type State# s
The type GHC.RealWorld is truly opaque: there are no values defined
of this type, and no operations over it. It is “primitive” in that
sense - but it is not unlifted! Its only role in life is to be
the type which distinguishes the IO state transformer.
data RealWorld
State of the world
A single, primitive, value of type State# RealWorld is provided.
realWorld# :: State# RealWorld
realWorld# state object
(Note: in the compiler, not a PrimOp; just a mucho magic
Id. Exported from GHC, though).
Mutable arraysmutable arraysarrays, mutable
Corresponding to Array# and ByteArray#, we have the types of
mutable versions of each. In each case, the representation is a
pointer to a suitable block of (mutable) heap-allocated storage.
type MutableArray# s elt
type MutableByteArray# s
MutableArray#MutableByteArray#Allocationmutable arrays, allocationarrays, allocationallocation, of mutable arrays
Mutable arrays can be allocated. Only pointer-arrays are initialised;
arrays of non-pointers are filled in by “user code” rather than by
the array-allocation primitive. Reason: only the pointer case has to
worry about GC striking with a partly-initialised array.
newArray# :: Int# -> elt -> State# s -> (# State# s, MutableArray# s elt #)
newCharArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
newIntArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
newAddrArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
newFloatArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
newDoubleArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
newArray#newCharArray#newIntArray#newAddrArray#newFloatArray#newDoubleArray#
The size of a ByteArray# is given in bytes.
Reading and writingarrays, reading and writing
readArray# :: MutableArray# s elt -> Int# -> State# s -> (# State# s, elt #)
readCharArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Char# #)
readIntArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Int# #)
readAddrArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Addr# #)
readFloatArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Float# #)
readDoubleArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Double# #)
writeArray# :: MutableArray# s elt -> Int# -> elt -> State# s -> State# s
writeCharArray# :: MutableByteArray# s -> Int# -> Char# -> State# s -> State# s
writeIntArray# :: MutableByteArray# s -> Int# -> Int# -> State# s -> State# s
writeAddrArray# :: MutableByteArray# s -> Int# -> Addr# -> State# s -> State# s
writeFloatArray# :: MutableByteArray# s -> Int# -> Float# -> State# s -> State# s
writeDoubleArray# :: MutableByteArray# s -> Int# -> Double# -> State# s -> State# s
readArray#readCharArray#readIntArray#readAddrArray#readFloatArray#readDoubleArray#writeArray#writeCharArray#writeIntArray#writeAddrArray#writeFloatArray#writeDoubleArray#Equalityarrays, testing for equality
One can take “equality” of mutable arrays. What is compared is the
name or reference to the mutable array, not its contents.
sameMutableArray# :: MutableArray# s elt -> MutableArray# s elt -> Bool
sameMutableByteArray# :: MutableByteArray# s -> MutableByteArray# s -> Bool
sameMutableArray#sameMutableByteArray#Freezing mutable arraysarrays, freezing mutablefreezing mutable arraysmutable arrays, freezing
Only unsafe-freeze has a primitive. (Safe freeze is done directly in Haskell
by copying the array and then using unsafeFreeze.)
unsafeFreezeArray# :: MutableArray# s elt -> State# s -> (# State# s, Array# s elt #)
unsafeFreezeByteArray# :: MutableByteArray# s -> State# s -> (# State# s, ByteArray# #)
unsafeFreezeArray#unsafeFreezeByteArray#Synchronizing variables (M-vars)synchronising variables (M-vars)M-Vars
Synchronising variables are the primitive type used to implement
Concurrent Haskell's MVars (see the Concurrent Haskell paper for
the operational behaviour of these operations).
type MVar# s elt -- primitive
newMVar# :: State# s -> (# State# s, MVar# s elt #)
takeMVar# :: SynchVar# s elt -> State# s -> (# State# s, elt #)
putMVar# :: SynchVar# s elt -> State# s -> State# s
SynchVar#newSynchVar#takeMVarputMVarPrimitive state-transformer monad
state transformers (Glasgow extensions)ST monad (Glasgow extension)
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 described in .
Primitive arrays, mutable and otherwise
primitive arrays (Glasgow extension)arrays, primitive (Glasgow extension)
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…
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.
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.
“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.
“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.
“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.
The libraries documentatation gives more details on all these
“primitive array” types and the operations on them.
Pattern guardsPattern guards (Glasgow extension)
The discussion that follows is an abbreviated version of Simon Peyton Jones's original proposal. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
Suppose we have an abstract data type of finite maps, with a
lookup operation:
lookup :: FiniteMap -> Int -> Maybe Int
The lookup returns Nothing if the supplied key is not in the domain of the mapping, and (Just v) otherwise,
where v is the value that the key maps to. Now consider the following definition:
clunky env var1 var2 | ok1 && ok2 = val1 + val2
| otherwise = var1 + var2
where
m1 = lookup env var1
m2 = lookup env var2
ok1 = maybeToBool m1
ok2 = maybeToBool m2
val1 = expectJust m1
val2 = expectJust m2
The auxiliary functions are
maybeToBool :: Maybe a -> Bool
maybeToBool (Just x) = True
maybeToBool Nothing = False
expectJust :: Maybe a -> a
expectJust (Just x) = x
expectJust Nothing = error "Unexpected Nothing"
What is clunky doing? The guard ok1 &&
ok2 checks that both lookups succeed, using
maybeToBool to convert the Maybe
types to booleans. The (lazily evaluated) expectJust
calls extract the values from the results of the lookups, and binds the
returned values to val1 and val2
respectively. If either lookup fails, then clunky takes the
otherwise case and returns the sum of its arguments.
This is certainly legal Haskell, but it is a tremendously verbose and
un-obvious way to achieve the desired effect. Arguably, a more direct way
to write clunky would be to use case expressions:
clunky env var1 var1 = case lookup env var1 of
Nothing -> fail
Just val1 -> case lookup env var2 of
Nothing -> fail
Just val2 -> val1 + val2
where
fail = val1 + val2
This is a bit shorter, but hardly better. Of course, we can rewrite any set
of pattern-matching, guarded equations as case expressions; that is
precisely what the compiler does when compiling equations! The reason that
Haskell provides guarded equations is because they allow us to write down
the cases we want to consider, one at a time, independently of each other.
This structure is hidden in the case version. Two of the right-hand sides
are really the same (fail), and the whole expression
tends to become more and more indented.
Here is how I would write clunky:
clunky env var1 var1
| Just val1 <- lookup env var1
, Just val2 <- lookup env var2
= val1 + val2
...other equations for clunky...
The semantics should be clear enough. The qualifers are matched in order.
For a <- qualifier, which I call a pattern guard, the
right hand side is evaluated and matched against the pattern on the left.
If the match fails then the whole guard fails and the next equation is
tried. If it succeeds, then the appropriate binding takes place, and the
next qualifier is matched, in the augmented environment. Unlike list
comprehensions, however, the type of the expression to the right of the
<- is the same as the type of the pattern to its
left. The bindings introduced by pattern guards scope over all the
remaining guard qualifiers, and over the right hand side of the equation.
Just as with list comprehensions, boolean expressions can be freely mixed
with among the pattern guards. For example:
f x | [y] <- x
, y > 3
, Just z <- h y
= ...
Haskell's current guards therefore emerge as a special case, in which the
qualifier list has just one element, a boolean expression.
The foreign interface
The foreign interface consists of language and library support. The former
is described later in ; the latter is outlined below,
and detailed in .
Using function headers
C calls, function headers
When generating C (using the 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,
#include "HsFFI.h"
void initialiseEFS (HsInt size);
HsInt terminateEFS (void);
HsForeignObj emptyEFS(void);
HsForeignObj updateEFS (HsForeignObj a, HsInt i, HsInt x);
HsInt lookupEFS (HsForeignObj a, HsInt i);
The types HsInt,
HsForeignObj etc. are described in .Note that this approach is only
essential for returning
floats (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.Subverting automatic unboxing with “stable pointers”
stable pointers (Glasgow extension)
The arguments of a _ccall_ automatically unboxed before the
call. There are two reasons why this is usually the Right Thing to
do:
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.
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 stable.
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 might write:
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
The garbage collector will refrain from throwing a stable pointer away
until you explicitly call one of the following from C or Haskell.
void freeStablePointer( StgStablePtr stablePtrToToss )
freeStablePtr :: StablePtr a -> IO ()
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).
void performIO ( StgStablePtr stableIndex /* StablePtr s (IO ()) */ );
StgInt enterInt ( StgStablePtr stableIndex /* StablePtr s Int */ );
StgFloat enterFloat ( StgStablePtr stableIndex /* StablePtr s Float */ );
performIOenterIntenterFloat
Nota Bene: _ccall_GC__ccall_GC_ must be used if any of
these functions are used.
Foreign objects: pointing outside the Haskell heap
foreign objects (Glasgow extension)
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 finaliser 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:
void foreignFinaliser ( StgForeignObj fo )
when the Haskell world can no longer access the object. Since
ForeignObjs only get released when a garbage collection occurs, we
provide ways of triggering a garbage collection from within C and from
within Haskell.
void GarbageCollect()
performGC :: IO ()
More information on the programmers' interface to ForeignObj can be
found in the library documentation.
Avoiding monads
C calls to `pure C'unsafePerformIO
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:
Calling a function with no side-effects:
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)
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.
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
You will almost always want to use ForeignObjs with this.
Calling a side-effecting function even though the results will
be unpredictable. For example the trace function is defined by:
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)
(This kind of use is not highly recommended—it is only really
useful in debugging code.)
C-calling “gotchas” checklist
C call dangersCCallableCReturnable
And some advice, too.
For modules that use _ccall_s, etc., compile with
.-fvia-C option You don't have to, but you should.
Also, use the flag (hack) to inform the C
compiler of the fully-prototyped types of all the C functions you
call. ( says more about this…)
This scheme is the only way that you will get any
typechecking of your _ccall_s. (It shouldn't be that way, but…).
GHC will pass the flag to gcc so that you'll get warnings
if any _ccall_ed functions have no prototypes.
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 and look at
the intermediate C (.hc).
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,
f x = _ccall_ foo x
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:
f :: Int -> IO Double
f x = _ccall_ foo x
This table summarises the standard instances of these classes.
TypeCCallableCReturnableWhich is probably…Char Yes Yes unsigned charInt Yes Yes long intWord Yes Yes unsigned long intAddr Yes Yes void *Float Yes Yes floatDouble 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
Actually, the Word type is defined as being the same size as a
pointer on the target architecture, which is probablyunsigned long int.
The brave and careful programmer can add their own instances of these
classes for the following types:
A boxed-primitive 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:
Int
Double
data XDisplay = XDisplay Addr#
data EFS a = EFS# ForeignObj#
instance CCallable (EFS a)
instance CReturnable (EFS a)
Any datatype with a single nullary constructor may be made an
instance of CReturnable. For example:
data MyVoid = MyVoid
instance CReturnable MyVoid
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…)
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 %rprecisely once for any other result type. These messages are
supposed to be helpful and catch bugs—please tell us if they wreck
your life.
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__ccall_GC_ primitive or
_casm_GC__casm_GC_ primitive variant of C-calls. (This
does not work with the native code generator—use .) This
stuff is hairy with a capital H!
Multi-parameter type classes
This section documents GHC's implementation of multi-parameter type
classes. There's lots of background in the paper Type
classes: exploring the design space (Simon Peyton Jones, Mark
Jones, Erik Meijer).
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.
Types
There are the following restrictions on the form of a qualified
type:
forall tv1..tvn (c1, ...,cn) => type
(Here, I write the "foralls" explicitly, although the Haskell source
language omits them; in Haskell 1.4, all the free type variables of an
explicit source-language type signature are universally quantified,
except for the class type variables in a class declaration. However,
in GHC, you can give the foralls if you want. See ).
Each universally quantified type variable
tvi must be mentioned (i.e. appear free) in type.
The reason for this is that a value with a type that does not obey
this restriction could not be used without introducing
ambiguity. Here, for example, is an illegal type:
forall a. Eq a => Int
When a value with this type was used, the constraint Eq tv
would be introduced where tv is a fresh type variable, and
(in the dictionary-translation implementation) the value would be
applied to a dictionary for Eq tv. The difficulty is that we
can never know which instance of Eq to use because we never
get any more information about tv.
Every constraint ci must mention at least one of the
universally quantified type variables tvi.
For example, this type is OK because C a b mentions the
universally quantified type variable b:
forall a. C a b => burble
The next type is illegal because the constraint Eq b does not
mention a:
forall a. Eq b => burble
The reason for this restriction is milder than the other one. The
excluded types are never useful or necessary (because the offending
context doesn't need to be witnessed at this point; it can be floated
out). Furthermore, floating them out increases sharing. Lastly,
excluding them is a conservative choice; it leaves a patch of
territory free in case we need it later.
These restrictions apply to all types, whether declared in a type signature
or inferred.
Unlike Haskell 1.4, constraints in types do not have to be of
the form (class type-variables). Thus, these type signatures
are perfectly OK
f :: Eq (m a) => [m a] -> [m a]
g :: Eq [a] => ...
This choice recovers principal types, a property that Haskell 1.4 does not have.
Class declarationsMulti-parameter type classes are permitted. For example:
class Collection c a where
union :: c a -> c a -> c a
...etc.
The class hierarchy must be acyclic. However, the definition
of "acyclic" involves only the superclass relationships. For example,
this is OK:
class C a where {
op :: D b => a -> b -> b
}
class C a => D a where { ... }
Here, C is a superclass of D, but it's OK for a
class operation op of C to mention D. (It
would not be OK for D to be a superclass of C.)
There are no restrictions on the context in a class declaration
(which introduces superclasses), except that the class hierarchy must
be acyclic. So these class declarations are OK:
class Functor (m k) => FiniteMap m k where
...
class (Monad m, Monad (t m)) => Transform t m where
lift :: m a -> (t m) a
In the signature of a class operation, every constraint
must mention at least one type variable that is not a class type
variable.
Thus:
class Collection c a where
mapC :: Collection c b => (a->b) -> c a -> c b
is OK because the constraint (Collection a b) mentions
b, even though it also mentions the class variable
a. On the other hand:
class C a where
op :: Eq a => (a,b) -> (a,b)
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:
class Eq a => C a where
op ::(a,b) -> (a,b)
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.
The type of each class operation must mention all of
the class type variables. For example:
class Coll s a where
empty :: s
insert :: s -> a -> s
is not OK, because the type of empty doesn't mention
a. This rule is a consequence of Rule 1(a), above, for
types, and has the same motivation.
Sometimes, offending class declarations exhibit misunderstandings. For
example, Coll might be rewritten
class Coll s a where
empty :: s a
insert :: s a -> a -> s a
which makes the connection between the type of a collection of
a's (namely (s a)) and the element type a.
Occasionally this really doesn't work, in which case you can split the
class like this:
class CollE s where
empty :: s
class CollE s => Coll s a where
insert :: s -> a -> s
Instance declarationsInstance declarations may not overlap. The two instance
declarations
instance context1 => C type1 where ...
instance context2 => C type2 where ...
"overlap" if type1 and type2 unify
However, if you give the command line option
-fallow-overlapping-instances
option then two overlapping instance declarations are permitted
iff
EITHER type1 and type2 do not unify
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)
do not mention the contexts context1, context2
Reason: you can pick which instance decl
"matches" based on the type.
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.)
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:
instance C Int a where ...
instance D (Int, Int) where ...
instance E [[a]] where ...
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 ...
There are two situations in which the rule is a bit of a pain. First,
if one allows overlapping instance declarations then it's quite
convenient to have a "default instance" declaration that applies if
something more specific does not:
instance C a where
op = ... -- Default
Second, sometimes you might want to use the following to get the
effect of a "class synonym":
class (C1 a, C2 a, C3 a) => C a where { }
instance (C1 a, C2 a, C3 a) => C a where { }
This allows you to write shorter signatures:
f :: C a => ...
instead of
f :: (C1 a, C2 a, C3 a) => ...
I'm on the lookout for a simple rule that preserves decidability while
allowing these idioms. The experimental flag
-fallow-undecidable-instances
option lifts this restriction, allowing all the types in an
instance head to be type variables.
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:
type Point = (Int,Int)
instance C Point where ...
instance C [Point] where ...
is legal. However, if you added
instance C (Int,Int) where ...
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:
type P a = [[a]]
instance Monad P where ...
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
instance C a b => Eq (a,b) where ...
is OK, but
instance C Int b => Foo b where ...
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.
Explicit universal quantification
GHC now allows you to write explicitly quantified types. GHC's
syntax for this now agrees with Hugs's, namely:
forall a b. (Ord a, Eq b) => a -> b -> a
The context is, of course, optional. You can't use forall as
a type variable any more!
Haskell type signatures are implicitly quantified. The forall
allows us to say exactly what this means. For example:
g :: b -> b
means this:
g :: forall b. (b -> b)
The two are treated identically.
Universally-quantified data type fields
In a data or newtype declaration one can quantify
the types of the constructor arguments. Here are several examples:
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])
The constructors now have so-called rank 2 polymorphic
types, in which there is a for-all in the argument types.:
T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
MkMonad :: forall m. (forall a. a -> m a)
-> (forall a b. m a -> (a -> m b) -> m b)
-> MonadT m
MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
Notice that you don't need to use a forall if there's an
explicit context. For example in the first argument of the
constructor MkSwizzle, an implicit "forall a." is
prefixed to the argument type. The implicit forall
quantifies all type variables that are not already in scope, and are
mentioned in the type quantified over.
As for type signatures, implicit quantification happens for non-overloaded
types too. So if you write this:
data T a = MkT (Either a b) (b -> b)
it's just as if you had written this:
data T a = MkT (forall b. Either a b) (forall b. b -> b)
That is, since the type variable b isn't in scope, it's
implicitly universally quantified. (Arguably, it would be better
to require explicit quantification on constructor arguments
where that is what is wanted. Feedback welcomed.)
Construction
You construct values of types T1, MonadT, Swizzle by applying
the constructor to suitable values, just as usual. For example,
(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
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.)
Pattern matching
When you use pattern matching, the bound variables may now have
polymorphic types. For example:
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)
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.
You cannot pattern-match against an argument that is polymorphic.
For example:
newtype TIM s a = TIM (ST s (Maybe a))
runTIM :: (forall s. TIM s a) -> Maybe a
runTIM (TIM m) = runST m
Here the pattern-match fails, because you can't pattern-match against
an argument of type (forall s. TIM s a). Instead you
must bind the variable and pattern match in the right hand side:
runTIM :: (forall s. TIM s a) -> Maybe a
runTIM tm = case tm of { TIM m -> runST m }
The tm on the right hand side is (invisibly) instantiated, like
any polymorphic value at its occurrence site, and now you can pattern-match
against it.
The partial-application restriction
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:
map MkSwizzle [sort, reverse]
The restriction is this: 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. The restriction makes type inference feasible.
In the illegal example, the sub-expression MkSwizzle has the
polymorphic type (Ord b => [b] -> [b]) -> Swizzle and is not
a sub-expression of an enclosing application. On the other hand, this
expression is OK:
map (T1 (\a b -> a)) [1,2,3]
even though it involves a partial application of T1, because
the sub-expression T1 (\a b -> a) has type Int -> T
Int.
Type signatures
Once you have data constructors with universally-quantified fields, or
constants such as runST that have rank-2 types, it isn't long
before you discover that you need more! Consider:
mkTs f x y = [T1 f x, T1 f y]
mkTs is a fuction that constructs some values of type
T, using some pieces passed to it. The trouble is that since
f is a function argument, Haskell assumes that it is
monomorphic, so we'll get a type error when applying T1 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 runST 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 ordinary functions (not only data
constructors), thus:
mkTs :: (forall b. b -> b -> b) -> a -> [T a]
mkTs f x y = [T1 f x, T1 f y]
This type signature tells the compiler to attribute f with
the polymorphic type (forall b. b -> b -> b) when type
checking the body of mkTs, so now the application of
T1 is fine.
There are two restrictions:
You can only define a rank 2 type, specified by the following
grammar:
rank2type ::= [forall tyvars .] [context =>] funty
funty ::= ([forall tyvars .] [context =>] ty) -> funty
| ty
ty ::= ...current Haskell monotype syntax...
Informally, the universal quantification must all be right at the beginning,
or at the top level of a function argument.
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 "=" sign. You can't
define mkTs like this:
mkTs :: (forall b. b -> b -> b) -> a -> [T a]
mkTs = \ f x y -> [T1 f x, T1 f y]
The same partial-application rule applies to ordinary functions with
rank-2 types as applied to data constructors.
Type synonyms and hoisting
GHC also allows you to write a forall in a type synonym, thus:
type Discard a = forall b. a -> b -> a
f :: Discard a
f x y = x
However, it is often convenient to use these sort of synonyms at the right hand
end of an arrow, thus:
type Discard a = forall b. a -> b -> a
g :: Int -> Discard Int
g x y z = x+y
Simply expanding the type synonym would give
g :: Int -> (forall b. Int -> b -> Int)
but GHC "hoists" the forall to give the isomorphic type
g :: forall b. Int -> Int -> b -> Int
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:type1 -> forall a. type2
==>
forall a. type1 -> type2
(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 :: Int -> Int -> forall b. b -> Int
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:
data Foo = forall a. MkFoo a (a -> Bool)
| Nil
The data type Foo has two constructors with types:
MkFoo :: forall a. a -> (a -> Bool) -> Foo
Nil :: Foo
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:
[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.
What can we do with a value of type Foo?. In particular,
what happens when we pattern-match on MkFoo?
f (MkFoo val fn) = ???
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:
f :: Foo -> Bool
f (MkFoo val fn) = fn val
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?
What has this to do with existential quantification?
Simply that MkFoo has the (nearly) isomorphic type
MkFoo :: (exists a . (a, a -> Bool)) -> Foo
But Haskell programmers can safely think of the ordinary
universally quantified type given above, thereby avoiding
adding a new existential quantification construct.
Type classes
An easy extension (implemented in hbc) is to allow
arbitrary contexts before the constructor. For example:
data Baz = forall a. Eq a => Baz1 a a
| forall b. Show b => Baz2 b (b -> b)
The two constructors have the types you'd expect:
Baz1 :: forall a. Eq a => a -> a -> Baz
Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
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:
f :: Baz -> String
f (Baz1 p q) | p == q = "Yes"
| otherwise = "No"
f (Baz1 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.
Restrictions
There are several restrictions on the ways in which existentially-quantified
constructors can be use.
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:
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
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.
You can't pattern-match on an existentially quantified
constructor in a let or where group of
bindings. So this is illegal:
f3 x = a==b where { Baz1 a b = x }
You can only pattern-match
on an existentially-quantified constructor in a case 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.
You can't use existential quantification for newtype
declarations. So this is illegal:
newtype T = forall a. Ord a => MkT a
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.
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:#
data T = forall a. MkT [a] deriving( Eq )
To derive Eq in the standard way we would need to have equality
between the single component of two MkT constructors:
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!
Assertions
Assertions
If you want to make use of assertions in your standard Haskell code, you
could define a function like the following:
assert :: Bool -> a -> a
assert False x = error "assertion failed!"
assert _ x = x
which works, but gives you back a less than useful error message --
an assertion failed, but which and where?
One way out is to define an extended assert function which also
takes a descriptive string to include in the error message and
perhaps combine this with the use of a pre-processor which inserts
the source location where assert was used.
Ghc offers a helping hand here, doing all of this for you. For every
use of assert in the user's source:
kelvinToC :: Double -> Double
kelvinToC k = assert (k >= 0.0) (k+273.15)
Ghc will rewrite this to also include the source location where the
assertion was made,
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.
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.
Assertion failures can be caught, see the documentation for the
Exception library ()
for the details.
Scoped Type Variables
A pattern type signature can introduce a scoped type
variable. For example
f (xs::[a]) = ys ++ ys
where
ys :: [a]
ys = reverse xs
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 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.
Scope and implicit quantification
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 type variables bound by the equation.
The type variables thus brought into scope may be mentioned
in ordinary type signatures or pattern type signatures anywhere within
their scope.
In ordinary type signatures, any type variable mentioned in the
signature that is in scope is not universally quantified.
Ordinary type signatures do not bring any new type variables
into scope (except in the type signature itself!). So this is illegal:
f :: a -> a
f x = x::a
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.
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.
The type variables in the head of a class or instance declaration
scope over the methods defined in the where part. For example:
class C a where
op :: [a] -> a
op xs = let ys::[a]
ys = reverse xs
in
head ys
(Not implemented in Hugs yet, Dec 98).
Polymorphism
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.
f :: [a] -> [a]
f (xs::[b]) = reverse xs
The function must be polymorphic in the type variables
bound by all its equations. Operationally, the type variables bound
by one equation must not:
Be unified with a type (such as Int, or [a]).
Be unified with a type variable free in the environment.
Be unified with each other. (They may unify with the type variables
bound by another equation for the same function, of course.)
For example, the following all fail to type check:
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]
The pattern-bound type variable may, however, be constrained
by the context of the principal type, thus:
f (x::a) (y::a) = x+y*2
gets the inferred type: forall a. Num a => a -> a -> a.
Result type signatures
The result type of a function can be given a signature,
thus:
f (x::a) :: [a] = [x,x,x]
The final :: [a] after all the patterns gives a signature to the
result type. Sometimes this is the only way of naming the type variable
you want:
f :: Int -> [a] -> [a]
f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
in \xs -> map g (reverse xs `zip` xs)
Result type signatures are not yet implemented in Hugs.
Pattern signatures on other constructs
A pattern type signature can be on an arbitrary sub-pattern, not
just 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)
Type variables bound by these patterns must be polymorphic in
the sense defined above.
For example:
f1 (x::c) = f1 x -- ok
f2 = \(x::c) -> f2 x -- not ok
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.
Pattern type signatures, including the result part, can be used
in case expressions:
case e of { (x::a, y) :: a -> x }
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:
case (True,False) of { (x::a, y) -> x }
Even though the context is that of a pair of booleans,
the alternative itself is polymorphic. Of course, it is
also OK to say:
case (True,False) of { (x::Bool, y) -> 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 that bind new type variables
may not be used in pattern bindings at all.
So this is illegal:
f x = let (y, z::a) = x in ...
But these are OK, because they do not bind fresh type variables:
f1 x = let (y, z::Int) = x in ...
f2 (x::(Int,a)) = let (y, z::a) = x in ...
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:
f :: (b->b) = \(x::b) -> x
Such degnerate function bindings do not fall under the monomorphism
restriction. Thus:
g :: a -> a -> Bool = \x y. x==y
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.
Existentials
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]
Pragmas
GHC supports several pragmas, or instructions to the compiler placed
in the source code. Pragmas don't affect the meaning of the program,
but they might affect the efficiency of the generated code.
INLINE pragma
INLINE pragmapragma, 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.
You will probably see these unfoldings (in Core syntax) in your
interface files.
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)
#ifdef __GLASGOW_HASKELL__
{-# INLINE key_function #-}
#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.)
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.
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__
{-# INLINE thenUs #-}
{-# INLINE returnUs #-}
#endif
NOINLINE pragma
NOINLINE pragmapragma, NOINLINE
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.
SPECIALIZE pragma
SPECIALIZE pragmapragma, SPECIALIZEoverloading, death to
(UK spelling also accepted.) For key overloaded functions, you can
create extra versions (NB: more code space) specialised to particular
types. Thus, if you have an overloaded function:
hammeredLookup :: Ord key => [(key, value)] -> key -> value
If it is heavily used on lists with Widget keys, you could
specialise it as follows:
{-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
To get very fancy, you can also specify a named function to use for
the specialised value, by adding = blah, as in:
{-# SPECIALIZE hammeredLookup :: ...as before... = blah #-}
It's Your Responsibility to make sure that blah really
behaves as a specialised version of hammeredLookup!!!
NOTE: the =blah feature isn't implemented in GHC 4.xx.
An example in which the = blah form 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.
By using the US spelling, your SPECIALIZE pragma will work with
HBC, too. Note that HBC doesn't support the = blah form.
A SPECIALIZE pragma for a function can be put anywhere its type
signature could be put.
SPECIALIZE instance pragma
SPECIALIZE pragmaoverloading, death to
Same idea, except for instance declarations. For example:
instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
{-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
Compatible with HBC, by the way.
LINE pragma
LINE pragmapragma, LINE
This pragma is similar to C's #line pragma, and is mainly for use in
automatically generated Haskell code. It lets you specify the line
number and filename of the original code; for example
{-# LINE 42 "Foo.vhs" #-}
if you'd generated the current file from something called Foo.vhs
and this line corresponds to line 42 in the original. GHC will adjust
its error messages to refer to the line/file named in the LINE
pragma.
RULES pragma
The RULES pragma lets you specify rewrite rules. It is described in
.
Rewrite rules
RULES pagmapragma, RULESrewrite rules
The programmer can specify rewrite rules as part of the source program
(in a pragma). GHC applies these rewrite rules wherever it can.
Here is an example:
{-# RULES
"map/map" forall f g xs. map f (map g xs) = map (f.g) xs
#-}
Syntax
From a syntactic point of view:
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.
Layout applies in a RULES pragma. Currently no new indentation level
is set, so you must lay out your rules starting in the same column as the
enclosing definitions.
Each variable mentioned in a rule must either be in scope (e.g. map),
or bound by the forall (e.g. f, g, xs). The variables bound by
the forall are called the pattern variables. They are separated
by spaces, just like in a type forall.
A pattern variable may optionally have a type signature.
If the type of the pattern variable is polymorphic, it must have a type signature.
For example, here is the foldr/build rule:
"fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
foldr k z (build g) = g k z
Since g has a polymorphic type, it must have a type signature.
The left hand side of a rule must consist of a top-level variable applied
to arbitrary expressions. For example, this is not OK:
"wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
"wrong2" forall f. f True = True
In "wrong1", the LHS is not an application; in "wrong1", the LHS has a pattern variable
in the head.
A rule does not need to be in the same module as (any of) the
variables it mentions, though of course they need to be in scope.
Rules are automatically exported from a module, just as instance declarations are.
Semantics
From a semantic point of view:
Rules are only applied if you use the flag.
Rules are regarded as left-to-right rewrite rules.
When GHC finds an expression that is a substitution instance of the LHS
of a rule, it replaces the expression by the (appropriately-substituted) RHS.
By "a substitution instance" we mean that the LHS can be made equal to the
expression by substituting for the pattern variables.
The LHS and RHS of a rule are typechecked, and must have the
same type.
GHC makes absolutely no attempt to verify that the LHS and RHS
of a rule have the same meaning. That is undecideable in general, and
infeasible in most interesting cases. The responsibility is entirely the programmer's!
GHC makes no attempt to make sure that the rules are confluent or
terminating. For example:
"loop" forall x,y. f x y = f y x
This rule will cause the compiler to go into an infinite loop.
If more than one rule matches a call, GHC will choose one arbitrarily to apply.
GHC currently uses a very simple, syntactic, matching algorithm
for matching a rule LHS with an expression. It seeks a substitution
which makes the LHS and expression syntactically equal modulo alpha
conversion. The pattern (rule), but not the expression, is eta-expanded if
necessary. (Eta-expanding the epression can lead to laziness bugs.)
But not beta conversion (that's called higher-order matching).
Matching is carried out on GHC's intermediate language, which includes
type abstractions and applications. So a rule only matches if the
types match too. See below.
GHC keeps trying to apply the rules as it optimises the program.
For example, consider:
let s = map f
t = map g
in
s (t xs)
The expression s (t xs) does not match the rule "map/map", but GHC
will substitute for s and t, giving an expression which does match.
If s or t was (a) used more than once, and (b) large or a redex, then it would
not be substituted, and the rule would not fire.
In the earlier phases of compilation, GHC inlines nothing
that appears on the LHS of a rule, because once you have substituted
for something you can't match against it (given the simple minded
matching). So if you write the rule
"map/map" forall f,g. map f . map g = map (f.g)
this won't match the expression map f (map g xs).
It will only match something written with explicit use of ".".
Well, not quite. It will match the expression
wibble f g xs
where wibble is defined:
wibble f g = map f . map g
because wibble will be inlined (it's small).
Later on in compilation, GHC starts inlining even things on the
LHS of rules, but still leaves the rules enabled. This inlining
policy is controlled by the per-simplification-pass flag n.
All rules are implicitly exported from the module, and are therefore
in force in any module that imports the module that defined the rule, directly
or indirectly. (That is, if A imports B, which imports C, then C's rules are
in force when compiling A.) The situation is very similar to that for instance
declarations.
List fusion
The RULES mechanism is used to implement fusion (deforestation) of common list functions.
If a "good consumer" consumes an intermediate list constructed by a "good producer", the
intermediate list should be eliminated entirely.
The following are good producers:
List comprehensions
Enumerations of Int and Char (e.g. ['a'..'z']).
Explicit lists (e.g. [True, False])
The cons constructor (e.g 3:4:[])
++mapfilteriterate, repeatzip, zipWith
The following are good consumers:
List comprehensions
array (on its second argument)
length++ (on its first argument)
mapfilterconcatunzip, unzip2, unzip3, unzip4zip, zipWith (but on one argument only; if both are good producers, zip
will fuse with one but not the other)
partitionheadand, or, any, allsequence_msumsortBy
So, for example, the following should generate no intermediate lists:
array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
This list could readily be extended; if there are Prelude functions that you use
a lot which are not included, please tell us.
If you want to write your own good consumers or producers, look at the
Prelude definitions of the above functions to see how to do so.
Specialisation
Rewrite rules can be used to get the same effect as a feature
present in earlier version of GHC:
{-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
This told GHC to use int8ToInt16 instead of fromIntegral whenever
the latter was called with type Int8 -> Int16. That is, rather than
specialising the original definition of fromIntegral the programmer is
promising that it is safe to use int8ToInt16 instead.
This feature is no longer in GHC. But rewrite rules let you do the
same thing:
{-# RULES
"fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
#-}
This slightly odd-looking rule instructs GHC to replace fromIntegral
by int8ToInt16whenever the types match. Speaking more operationally,
GHC adds the type and dictionary applications to get the typed rule
forall (d1::Integral Int8) (d2::Num Int16) .
fromIntegral Int8 Int16 d1 d2 = int8ToInt16
What is more,
this rule does not need to be in the same file as fromIntegral,
unlike the SPECIALISE pragmas which currently do (so that they
have an original definition available to specialise).
Controlling what's going on
Use to see what transformation rules GHC is using.
Use to see what rules are being fired.
If you add you get a more detailed listing.
The defintion of (say) build in PrelBase.lhs looks llike this:
build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
{-# INLINE build #-}
build g = g (:) []
Notice the INLINE! That prevents (:) from being inlined when compiling
PrelBase, so that an importing module will “see” the (:), and can
match it on the LHS of a rule. INLINE prevents any inlining happening
in the RHS of the INLINE thing. I regret the delicacy of this.
In ghc/lib/std/PrelBase.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.