[Haskell-cafe] Polyvariadic functions operating with a monoid
Kevin Jardine
functions.
Of course in Haskell, lists all have to be composed of values of
exactly the same type, so instead of passing around lists of values
with these related types, I created a polyvariadic function
polyToString so that I could write:
(polyToString value1 value2 value3 ... valueN)
which would then become a list of strings:
[toString value1, toString value2, ... , toString valueN]
I finally figured out how to do this, but it was a bit harder to
figure this out than I expected, and I was wondering if it might be
possible to create a small utility library to help other developers do
this.
It seems to me that in the general case, we would be dealing with a
Monoid rather than a list of strings. We could have a toMonoid
function and then return
polyToMonoid value1 value2 ... valueN =
(toMonoid value1) `mappend` (toMonoid value2) 'mappend' ... (toMonoid
valueN)
So anyone who wanted to convert a bunch of values of different types
to a Monoid could easily pass them around using polyToMonoid so long
as they defined the appropriate toMonoid function.
Basically, a generalised list.
So I tried writing the following code but GHC said it had undecidable
instances.
Has this ever been done successfully?
class Monoidable a where
toMonoid :: Monoid r => a -> r
polyToMonoid :: (Monoidable a, Monoid r) => a -> r
polyToMonoid k = polyToMonoid' k mempty
class PolyVariadic p where
polyToMonoid' :: (Monoidable a, Monoid r) => a -> r -> p
instance Monoid r => PolyVariadic r where
polyToMonoid' k ss = (toMonoid k) `mappend` ss
instance (Monoidable a, Monoid r) => PolyVariadic (a -> r) where
polyToMonoid' k ss = (\a -> polyToMonoid' k (toMonoid a) `mappend`
ss)
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Luke Palmer
> I had a situation where I had some related types that all had toString
> functions.
>
> Of course in Haskell, lists all have to be composed of values of
> exactly the same type, so instead of passing around lists of values
> with these related types, I created a polyvariadic function
> polyToString so that I could write:
>
> (polyToString value1 value2 value3 ... valueN)
>
> which would then become a list of strings:
>
> [toString value1, toString value2, ... , toString valueN]
First of all, you are not using the monoidal structure of String at
all. This trick ought to work for any type whatsoever -- you're just
throwing them in a list.
Other than a few brackets, commas, and a repeated identifier (which
you can let-bind to shorten), what benefit is it giving you? I
strongly recommend against polyvariadic functions. While you get a
little bit of notational convenience, you lose composability. There
are pains when you try to write a function that takes a polyvariadic
function as an argument, or when you try to feed the function values
from a list, etc. The mechanisms to create polyvariadic functions are
brittle and hacky (eg. you cannot have a polymorphic return type, as
you want in this case).
Since all your values are known statically, I would recommend biting
the bullet and doing it the way you were doing it.
[ s value1, s value2, s value3, ... ]
where
s x = toString x
(I had to eta expand s so that I didn't hit the monomorphism restriction)
When you want to be passing around "heterogeneous lists", it usually
works to convert them before you put them in the list, like you were
doing.
Luke Palmer
> On Sun, Oct 3, 2010 at 1:24 AM, Kevin Jardine <kevinj...@gmail.com> wrote:
>> I had a situation where I had some related types that all had toString
>> functions.
>>
>> Of course in Haskell, lists all have to be composed of values of
>> exactly the same type, so instead of passing around lists of values
>> with these related types, I created a polyvariadic function
>> polyToString so that I could write:
>>
>> (polyToString value1 value2 value3 ... valueN)
>>
>> which would then become a list of strings:
>>
>> [toString value1, toString value2, ... , toString valueN]
>
> First of all, you are not using the monoidal structure of String at
> all. This trick ought to work for any type whatsoever -- you're just
> throwing them in a list.
Oops, sorry for not reading your message more closely. You were
indeed talking about the monoidal structure of list. So... nevermind
about this comment. :-P
Kevin Jardine
Yes, in my original case the function would be trivial:
toMonoid k = [toString k]
I do prefer the less cluttered look. I think that
(poly value1 value2 value3)
is easier to follow when the values are all of related types (in my
case, all in the same type class).
But in the more general Monoid case there would not necessarily be a
list result.
Eg.
sumOf 1 2 3
could also be implemented using a Monoid approach with mempty = 0 and
mappend = +
Kevin
On Oct 3, 9:30 pm, Luke Palmer <lrpal...@gmail.com> wrote:
> On Sun, Oct 3, 2010 at 1:26 PM, Luke Palmer <lrpal...@gmail.com> wrote:
> >>http://www.haskell.org/mailman/listinfo/haskell-cafe
>
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-C...@haskell.orghttp://www.haskell.org/mailman/listinfo/haskell-cafe
ol...@okmij.org
Kevin Jardine wrote:
> instead of passing around lists of values with these related types, I
> I finally figured out how to do this, but it was a bit harder to
> figure this out than I expected, and I was wondering if it might be
> possible to create a small utility library to help other developers do
> this.
> It seems to me that in the general case, we would be dealing with a
> Monoid rather than a list of strings. We could have a toMonoid
> function and then return
>
> polyToMonoid value1 value2 ... valueN =
>
> (toMonoid value1) `mappend` (toMonoid value2) 'mappend' ... (toMonoid
> valueN)
> So I tried writing the following code but GHC said it had undecidable
> instances.
Generally speaking, we should not be afraid of undecidable instances:
it is a sufficient criterion for terminating type checking but it is
not a necessary one. A longer argument can be found at
http://okmij.org/ftp/Haskell/types.html#undecidable-inst-defense
However, the posted code has deeper problems, I'm afraid. First, let
us look at the case of Strings:
> class PolyVariadic p where
> polyToMonoid' :: String -> p
>
> instance PolyVariadic String where
> polyToMonoid' acc = acc
>
> instance (Show a, PolyVariadic r) => PolyVariadic (a->r) where
> polyToMonoid' acc = \a -> polyToMonoid' (acc ++ show a)
>
> polyToMonoid :: PolyVariadic p => p
> polyToMonoid = polyToMonoid' mempty
>
> test1 = putStrLn $ polyToMonoid True () (Just (5::Int))
*M> test1
True()Just 5
Modulo the TypeSynonymInstances extension, it is Haskell98. If we now
generalize it to arbitrary monoids rather than a mere String, we face
several problems. First of all, if we re-write the first instance as
> instance Monoid r => PolyVariadic r where
> polyToMonoid' acc = acc
we make it overlap with the second instance: the type variable 'r' may
be instantiated to the arrow type a->r'. Now we need a more
problematic overlapping instances extension. The problem is deeper
however: an arrow type could possibly be an instance of Monoid (for
example, functions of the type Int->Int form a monoid with mempty=id,
mappend=(.)). If polyToMonoid appears in the context requiring a
function type, how could type checker choose the instance of
Polyvariadic?
The second problem with the posted code
> class Monoidable a where
> toMonoid :: Monoid r => a -> r
is that toMonoid has too `strong' a signature. Suppose we have an
instance
> instance Monoidable String where
> toMonoid = \str -> ???
It means that no matter which monoid the programmer may give to us, we
promise to inject a string into it. We have no idea about the details
of the monoid. It means that the only thing we could do (short of
divergence) is to return mempty. That is not too useful.
We have little choice but to parametrise Monoidable as well as
Polyvariadic with the type of the monoid. To avoid overlapping and
disambiguate the contexts, we use the newtype trick. Here is the
complete code. It turns out, no undecidable instances are needed.
> {-# LANGUAGE TypeSynonymInstances #-}
> {-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}
>
> module M where
>
> import Data.Monoid
>
> newtype WMonoid m = WMonoid{unwrap :: m}
>
> class Monoid m => Monoidable a m where
> toMonoid :: a -> m
>
> class Monoid m => PolyVariadic m p where
> polyToMonoid :: m -> p
>
> instance Monoid m => PolyVariadic m (WMonoid m) where
> polyToMonoid acc = WMonoid acc
>
> instance (Monoidable a m, PolyVariadic m r) => PolyVariadic m (a->r) where
> polyToMonoid acc = \a -> polyToMonoid (acc `mappend` toMonoid a)
>
> instance Show a => Monoidable a String where
> toMonoid = show
>
> test2 = putStrLn $ unwrap $ polyToMonoid "" True () (Just (5::Int))
The remaining problem is how to tell polyToMonoid which monoid we
want. It seems simpler just to pass the appropriately specialized
mempty method as the first argument, as shown in test2.
Granted, a more elegant solution would be a parametrized module
(functor) like those in Agda or ML:
module type PolyM =
functor(M:: sig type m val mempty :: m val mappend :: m -> m -> m end) =
struct
class Monoidable a where
toMonoid :: a -> m
class PolyVariadic p where
polyToMonoid :: m -> p
.etc
end
The shown solution is essentially the encoding of the above functor.
Kevin Jardine
Thank you for this wonderful detailed solution!
I was attempting to turn this into a small library and wanted to avoid
exporting unwrap.
I defined:
polyToMonoid' = unwrap . polyToMonoid
and then GHC told me:
No instance for (PolyVariadic a (WMonoid m))
arising from a use of `polyToMonoid'
at Data\PolyToMonoid.hs:27:24-36
Possible fix:
add an instance declaration for (PolyVariadic a (WMonoid m))
Is there a type signature I can assign to polyToMonoid' to get this to
work? Or will it always be necessary to export unwrap as well?
Kevin
> Haskell-C...@haskell.orghttp://www.haskell.org/mailman/listinfo/haskell-cafe
Bartek Ćwikłowski
2010/10/9 Kevin Jardine <kevinj...@gmail.com>:
> I was attempting to turn this into a small library and wanted to avoid
> exporting unwrap.
>
> I defined:
>
> polyToMonoid' = unwrap . polyToMonoid
If you disable MonomorphismRestriction this definition typechecks just
fine. Alternatively, you can ask ghci about the type of "unwrap .
polyToMonoid" and paste that into the type sig.
regards,
Bartek Ćwikłowski
Kevin Jardine
Yes, it compiles, but when I try to use polyToMonoid', it turns out
that this function is no longer polyvariadic, unlike the original
polyToMonoid .
This may be what Luke meant when he wrote "you lose composability".
Even with the extra unwrap function I think that this is pretty cool,
but I would ideally like to hide the unwrap.
Kevin
On Oct 9, 1:50 pm, Bartek Ćwikłowski <paczesi...@gmail.com> wrote:
> Hello Kevin,
>
> 2010/10/9 Kevin Jardine <kevinjard...@gmail.com>:
>
> > I was attempting to turn this into a small library and wanted to avoid
> > exporting unwrap.
>
> > I defined:
>
> > polyToMonoid' = unwrap . polyToMonoid
>
> If you disable MonomorphismRestriction this definition typechecks just
> fine. Alternatively, you can ask ghci about the type of "unwrap .
> polyToMonoid" and paste that into the type sig.
>
> regards,
> Bartek Ćwikłowski
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-C...@haskell.orghttp://www.haskell.org/mailman/listinfo/haskell-cafe
Kevin Jardine
Another puzzle is that:
instance Show a => Monoidable a String where
toMonoid a = show a
main = putStrLn $ unwrap $ polyToMonoid "" True () (Just (5::Int))
works just fine, but
instance Show a => Monoidable a [String] where
toMonoid a = [show a]
main = putStrLn $ unwrap $ polyToMonoid [] True () (Just (5::Int))
fails to compile.
Why would that be? My understanding is that all lists are
automatically monoids.
Kevin
On Oct 9, 2:28 pm, Kevin Jardine <kevinjard...@gmail.com> wrote:
> Hi Bartek,
>
> Yes, it compiles, but when I try to use polyToMonoid', it turns out
> that this function is no longer polyvariadic, unlike the original
> polyToMonoid .
>
> This may be what Luke meant when he wrote "you lose composability".
>
> Even with the extra unwrap function I think that this is pretty cool,
> but I would ideally like to hide the unwrap.
>
> Kevin
>
> On Oct 9, 1:50 pm, Bartek Æwik³owski <paczesi...@gmail.com> wrote:
>
> > Hello Kevin,
>
> > 2010/10/9 Kevin Jardine <kevinjard...@gmail.com>:
>
> > > I was attempting to turn this into a small library and wanted to avoid
> > > exporting unwrap.
>
> > > I defined:
>
> > > polyToMonoid' = unwrap . polyToMonoid
>
> > If you disable MonomorphismRestriction this definition typechecks just
> > fine. Alternatively, you can ask ghci about the type of "unwrap .
> > polyToMonoid" and paste that into the type sig.
>
> > regards,
> > Bartek Æwik³owski
Kevin Jardine
import Data.PolyToMonoid
import Data.Monoid
instance Monoid Int where
mappend = (+)
mempty = 0
instance Monoidable Int Int where
toMonoid = id
main = putStrLn $ show $ unwrap $ polyToMonoid (0::Int) (1::Int)
(2::Int) (3::Int)
In this case, I was expecting a sumOf function.
This gives me:
No instance for (PolyVariadic Int (WMonoid m))
arising from a use of `polyToMonoid'
Any further suggestions?
Brandon S Allbery KF8NH
Hash: SHA1
On 10/9/10 10:25 , Kevin Jardine wrote:
> instance Show a => Monoidable a [String] where
> toMonoid a = [show a]
>
> main = putStrLn $ unwrap $ polyToMonoid [] True () (Just (5::Int))
>
> fails to compile.
>
> Why would that be? My understanding is that all lists are
> automatically monoids.
I *think* the problem here is that Oleg specifically pointed out that the
first parameter to polyToMonoid must specify the type of the monoid. []
tells you it's a list, therefore a monoid, but it doesn't say enough to
allow the [String] instance to be chosen. (No, the fact that you only
declared an instance for [String] isn't really enough.)
- --
brandon s. allbery [linux,solaris,freebsd,perl] all...@kf8nh.com
system administrator [openafs,heimdal,too many hats] all...@ece.cmu.edu
electrical and computer engineering, carnegie mellon university KF8NH
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Kevin Jardine
True, when I replace [] with [""], I get a different error message:
No instance for (PolyVariadic [[Char]] (WMonoid String))
which now looks a bit like the Int example. In both cases, GHC appears
to be unable to derive the appropriate instance of PolyVariadic. Why
this is so, but worked for Oleg's specific example. is still not clear
to me.
Kevin
On Oct 9, 11:51 pm, Brandon S Allbery KF8NH <allb...@ece.cmu.edu>
wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> On 10/9/10 10:25 , Kevin Jardine wrote:
>
> > instance Show a => Monoidable a [String] where
> > toMonoid a = [show a]
>
> > main = putStrLn $ unwrap $ polyToMonoid [] True () (Just (5::Int))
>
> > fails to compile.
>
> > Why would that be? My understanding is that all lists are
> > automatically monoids.
>
> I *think* the problem here is that Oleg specifically pointed out that the
> first parameter to polyToMonoid must specify the type of the monoid. []
> tells you it's a list, therefore a monoid, but it doesn't say enough to
> allow the [String] instance to be chosen. (No, the fact that you only
> declared an instance for [String] isn't really enough.)
>
> - --
> brandon s. allbery [linux,solaris,freebsd,perl] allb...@kf8nh.com
> system administrator [openafs,heimdal,too many hats] allb...@ece.cmu.edu
> electrical and computer engineering, carnegie mellon university KF8NH
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v2.0.10 (Darwin)
> Comment: Using GnuPG with Mozilla -http://enigmail.mozdev.org/
>
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> WXgAnjrbO9rEl2HnQtGQ31EyRuhWzI4r
> =YMDw
> -----END PGP SIGNATURE-----
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Kevin Jardine
*wrong* instances of PolyVariadic.
It should be deriving:
PolyVariadic Int (WMonoid Int)
not
PolyVariadic Int (WMonoid m)
and
PolyVariadic [String] (WMonoid [String])
not
PolyVariadic [String] (WMonoid String)
specifically, GHC is attempting to derive PolyVariadic with the wrong
version of WMonoid in each case.
I'm using GHC 6.12.3
Perhaps the new GHC 7 type system would work better?
Kevin
Kevin Jardine
general infer the return type of polyToMonoid despite the hint it is
given (the type signature of the first parameter).
If I write:
main = putStrLn $ show $ unwrap $ ((polyToMonoid [""] True (Just
(5::Int))) :: WMonoid [String])
or
main = putStrLn $ show $ unwrap $ ((polyToMonoid (0::Int) (1::Int)
(2::Int) (3::Int)) :: WMonoid Int)
the code compiles and returns the expected result.
Kevin
Kevin Jardine
{-# LANGUAGE TypeSynonymInstances, FlexibleInstances,
MultiParamTypeClasses #-}
module PolyTest where
import Data.Monoid
class Monoid m => Monoidable a m where
toMonoid :: a -> m
squish :: Monoidable a m => m -> a -> m
squish m a = (m `mappend` (toMonoid a))
class Monoid m => PolyVariadic m r where
polyToMonoid :: m -> r
instance Monoid m => PolyVariadic m m where
polyToMonoid acc = acc
instance (Monoidable a m, PolyVariadic m r) => PolyVariadic m (a->r)
where
polyToMonoid acc = \a -> polyToMonoid (squish acc a)
and three example uses are:
-- [String] example
instance Show a => Monoidable a [String] where
toMonoid a = [show a]
testStringList = putStrLn $ show $ ((polyToMonoid [""] True () (Just
(5::Int))) :: [String])
-- String example
instance Show a => Monoidable a String where
toMonoid a = show a
testString = putStrLn $ ((polyToMonoid "" True () (Just (5::Int))) ::
String)
-- sum example
instance Monoid Int where
mappend = (+)
mempty = 0
instance Monoidable Int Int where
toMonoid = id
testSum = putStrLn $ show $ ((polyToMonoid (0::Int) (1::Int) (2::Int)
(3::Int)) :: Int)
main = do
testStringList
testString
testSum
$ runhaskell PolyTest.hs
["","True","()","Just 5"]
True()Just 5
6
This removes the unwrap and I don't mind the need for the outer type
cast.
I do wonder if there is a need for the first (dummy) parameter to
communicate the type as well as this seems redundant given the outer
type cast but I can't find a way to remove it.
It appears that GHC needs to be told the type both coming and going so
to speak for this to work consistently.
Any suggestions for improvement welcome!
Kevin
Kevin Jardine
replaced by:
mempty :: [String]
mempty :: String
mempty: Int
in my three examples and the code still compiles and gives the
expected results.
This suggests that a further simplification might be possible (ideally
in straight Haskell, but if not then with CPP or Template Haskell).
Kevin
Kevin Jardine
poly([String],True () (Just (5::Int)))
using:
#define poly(TYPE,VALUES) ((polyToMonoid (mempty :: TYPE) VALUES) ::
TYPE)
which I think is as concise as it can get.
Kevin
Kevin Jardine
-- mixed type product example
instance Monoid Double where
mappend = (*)
mempty = (1.0) :: Double
instance Monoidable Int Double where
toMonoid = fromIntegral
instance Monoidable Double Double where
toMonoid = id
#define productOf(VALUES) poly(Double,VALUES)
testProduct = putStrLn $ show $ productOf ( (5 :: Int) (2.3 :: Double)
(3 :: Int) (8 :: Int) )
If anyone has a better alternative to the CPP macros, I'd be
interested to hear it.
I think that this is interesting enough to create a
PolyvariadicFromMonoid library as it seems to be a fast way to create
a large number of polyvariadic functions - basicially, just set up
your Monoid definition and your toMonoid conversion functions and then
you get the appropriate polvariadic function for free.
Thanks for the input from everyone and Oleg especially for creating
working code!
Kevin
ol...@okmij.org
Sorry, I'm still catching up. I'm replying to first few messages.
> instance Show a => Monoidable a [String] where
> toMonoid a = [show a]
>
> main = putStrLn $ unwrap $ polyToMonoid [] True () (Just (5::Int))
> fails to compile.
The error message points to the first problem:
> No instances for (Monoidable Bool [a],
> Monoidable () [a],
> ...
The presence of the type variable 'a' means that the type checker
doesn't know list of what elements you want (in other words, the
context is not specific enough to instantiate the type variable
a). Thus, we need to explicitly tell that we wish a list of strings:
> test3 = putStrLn $ unwrap $polyToMonoid ([]::[String]) True () (Just (5::Int))
Now we get a different error, which points to the real problem this
time: the expression `unwrap ....' appears as an argument to
putStrLn. That means that we are required to produce a String as a
monoid. Yet we specified ([]::[String]) as mempty, which is unsuitable
as mempty for the String monoid. If we desire the [String] monoid as
the result, we need to change the context. For example,
> test3 = mapM_ putStrLn $ unwrap $
> polyToMonoid ([]::[String]) True () (Just (5::Int))
> Another example that also fails to compile (but I cannot see why):
> main = putStrLn $ show $ unwrap $ polyToMonoid (0::Int) (1::Int)
> (2::Int) (3::Int)
> No instance for (PolyVariadic Int (WMonoid m))
> arising from a use of `polyToMonoid'
The error message is informative, mentioning the type variable,
m. Whenever that happens, we know that we put a bounded polymorphic
expression in the context that is not specific enough. We need some
type annotations. In our case, the function 'show' can show values of
many types. The type checker does not know that we wish an Int monoid
specifically. So, we have to specialize the show function:
> test4 = putStrLn $ (show :: Int -> String) $
> unwrap $ polyToMonoid (0::Int) (1::Int) (2::Int) (3::Int)
At this point one may wonder if this is all worth it. There are too
many annotations. Fortunately, if you are not afraid of one more
extension, the annotations can be avoided. Your example would be
accepted as it was written, see test3 and test4 below.
> {-# LANGUAGE TypeSynonymInstances #-}
> {-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-}
>
> module M where
>
> import Data.Monoid
>
> newtype WMonoid m = WMonoid{unwrap :: m}
>
> class Monoid m => Monoidable a m where
> toMonoid :: a -> m
>
> class Monoid m => PolyVariadic m p where
> polyToMonoid :: m -> p
>
> instance (Monoid m', m' ~ m) => PolyVariadic m (WMonoid m') where
> polyToMonoid acc = WMonoid acc
>
> instance (Monoidable a m, PolyVariadic m r) => PolyVariadic m (a->r) where
> polyToMonoid acc = \a -> polyToMonoid (acc `mappend` toMonoid a)
>
> instance Show a => Monoidable a String where
> toMonoid = show
>
> instance Show a => Monoidable a [String] where
> toMonoid a = [show a]
>
> test2 = putStrLn $ unwrap $ polyToMonoid "" True () (Just (5::Int))
>
> test3 = mapM_ putStrLn $ unwrap $ polyToMonoid [] True () (Just (5::Int))
>
> instance Monoid Int where
> mappend = (+)
> mempty = 0
>
> instance Monoidable Int Int where
> toMonoid = id
>
> test4 = putStrLn $ show $
> unwrap $ polyToMonoid (0::Int) (1::Int) (2::Int) (3::Int)
P.S. Indeed, "polyToMonoid' = unwrap . polyToMonoid" does not do what
one wishes to. One should regard `unwrap' as a sort of terminator of
the argument list.
Kevin Jardine
I've found that if I also add two other slightly scary sounding
extensions: OverlappingInstances and IncoherentInstances, then I can
eliminate the unwrap function *and* use your type families trick to
avoid the outer type annotation.
My latest code is here:
{-# LANGUAGE TypeSynonymInstances, FlexibleInstances,
MultiParamTypeClasses, TypeFamilies #-}
{-# LANGUAGE OverlappingInstances, IncoherentInstances #-}
module PolyTest where
import Data.Monoid
class Monoid m => Monoidable a m where
toMonoid :: a -> m
squish :: Monoidable a m => m -> a -> m
squish m a = (m `mappend` (toMonoid a))
class Monoid m => PolyVariadic m r where
polyToMonoid :: m -> r
instance (Monoid m', m' ~ m) => PolyVariadic m m' where
polyToMonoid acc = acc
instance (Monoidable a m, PolyVariadic m r) => PolyVariadic m (a->r)
where
polyToMonoid acc = \a -> polyToMonoid (squish acc a)
Here are three examples. The resulting notation is short enough now
that I am no longer tempted to use CPP.
All you need to do is to specify the type for mempty. And even this
can be skipped if you want to put in the specific mempty value
(although I think that the type annotation is often better if slightly
longer as it documents clearly what monoid the result is being mapped
into).
-- [String] example
instance Show a => Monoidable a [String] where
toMonoid a = [show a]
testStringList = putStrLn $ show $ polyToMonoid (mempty :: [String])
True () (Just (5::Int))
-- String example
instance Show a => Monoidable a String where
toMonoid a = show a
testString = putStrLn $ polyToMonoid (mempty :: String) True () (Just
(5::Int))
-- product example
instance Monoid Double where
mappend = (*)
mempty = (1.0) :: Double
instance Monoidable Int Double where
toMonoid = fromIntegral
instance Monoidable Double Double where
toMonoid = id
testProduct = putStrLn $ show $ polyToMonoid (mempty :: Double) (5 ::
Int) (2.3 :: Double) (3 :: Int) (8 :: Int)
main = do
testStringList
testString
testProduct
$ runhaskell PolyTest.hs
["True","()","Just 5"]
True()Just 5
276.0
Kevin
> Haskell-C...@haskell.orghttp://www.haskell.org/mailman/listinfo/haskell-cafe
Kevin Jardine
Haskell list system using polyToMonoid.
instance (a ~ a') => Monoidable a [a'] where
toMonoid a = [a]
testList = putStrLn $ show $ polyToMonoid (mempty :: [a]) "a" "b" "c"
Given this instance of Monoidable, you can put any number of values
after
polyToMonoid (mempty :: [a]) as long as they are exactly the same
type.
In other words, this acts exactly like the usual Haskell list, going
back to my original point that polyToMonoid is a sort of generalised
list or "a function that takes a bunch of values that can be stuck
together in some way".
I am a bit surprised that the (a ~ a') is needed, but Haskell will
not compile this code with the more usual
instance Monoidable a [a] where
toMonoid a = [a]
Kevin
Kevin Jardine
http://github.com/kevinjardine/polyToMonoid
The library includes two versions of the function: ptm does not
require a termination function but does not allow partial evaluation
either. ctm is more composable (returning a function that consumes the
next parameter) and requires a termination function trm to return the
result.
The source includes thorough Haddock friendly comments with examples.
My plan is to upload it to Hackage later this week but I wondered if
anyone had any comments before I do.
Kevin