Re: [Haskell-cafe] Typing problem
I hadn't considered the types of the functions I call in the function I'm trying to write, something not usually needed in loosely typed languages with coercion, but something I'm going to have to make a habit of doing. One more thing to add to the check list. Also, I had considered the numbers in the list to be integral if they didn't have decimal points, which inferred, for me, that polymorphic type a needed to be of a class that would accept either Integral or Floating values, i.e., Num. False reasoning. Thanks, all. Michael --- On Mon, 1/31/11, Daniel Fischer wrote: From: Daniel Fischer Subject: Re: [Haskell-cafe] Typing problem To: haskell-cafe@haskell.org Cc: "michael rice" Date: Monday, January 31, 2011, 1:38 PM On Monday 31 January 2011 18:29:59, michael rice wrote: > I'm mapping a function over a list of data, where the mapping function > is determined from the data. > > g f l = map (g l) l g f l = map (f l) l probably > > So > > g serialize "prolog" -> [4,5,3,2,3,1] > > But I'm having typing problems trying to do a similar thing with a > function that statistically normalizes data. > > See: > http://people.revoledu.com/kardi/tutorial/Similarity/Normalization.html# >Statistic > > So > > g normalize [2,5,3,2] -> > [-0.7071067811865475,1.414213562373095,0.0,-0.7071067811865475] > > Is my typing for normalize too loose. You can omit the type signatures and see what the compiler infers as the type. In this case, > normalize :: (Num a, Num b) => [a] -> a -> b > normalize l = let (total,len) = sumlen l > avg = total/len > stdev = sqrt $ ((/) (len-1)) $ sum $ map ((** 2.0) . > (subtract avg)) l in ((/) stdev) . (subtract avg) In the final result, I suppose it should be (/ stdev) and not ((/) stdev) [the latter is (stdev /), i.e. \x -> stdev / x]. by sumlen's type, len has an Integral type. You want to use (/) to divide, which gives a Fractional constraint, (/) :: Fractional a => a -> a -> a Since it is not sensible for a type to be a member of both, the Fractional and Integral classes, you should convert len to the appropriate type with fromIntegral. For stdev, you call sqrt :: Floating a => a -> a and (**) :: Floating a => a -> a which means the list elements must have a type belonging to Floating (you could replace the (** 2.0) with (^ 2), which would probably be better, but the Floating constraint remains due to the sqrt). Finally, the resulting function is \x -> (x - avg) / stdev, hence x must have the same type as abg and stdev, and the final result has the same type. Altogether, normalize :: Floating a => [a] -> a -> a normalize l = let (total, len0) = sumlen l len = fromIntegral len0 avg = total/len stdev = sqrt $ sum [(x-avg)^2 | x <- l] / (len-1) in (/ stdev) . subtract avg but that gives nonsense if you pass a complex-valued list, so it might be better to restrict the type to normalize :: RealFloat a => [a] -> a -> a > Should I be using Floating rather than Num? You have to, and one number type only (well, you could use two or three types if you compose with conversion functions, realToFrac for example). ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Typing problem
Michael,
just leaving out the type declaration for 'normalize', your module
complies fine and ghc infers the following type:
normalize :: (Integral a, Floating a) => [a] -> a -> a
Note that the context (Integral a, Floating a) cannot be met by any of
the standard types. (try in ghci: ":i Integral" and ":i Floating")
So we have to apply a conversion function like this: (I just replaced
len by len' at all occurrences)
> normalize l = let (total,len) = sumlen l
> len' = fromIntegral len
> avg = total/len'
> stdev = sqrt $ ((/) (len'-1)) $ sum $ map ((** 2.0)
. (subtract avg)) l
> in ((/) stdev) . (subtract avg)
yielding a type of
normalize :: (Floating b) => [b] -> b -> b
You could save the conversion by allowing a more liberal type for
'sumlen'. Without the type signature, it is inferred to
sumlen :: (Num t, Num t1) => [t] -> (t, t1)
-- Steffen
On 01/31/2011 06:29 PM, michael rice wrote:
I'm mapping a function over a list of data, where the mapping function is
determined from the data.
g f l = map (g l) l
So
g serialize "prolog" -> [4,5,3,2,3,1]
But I'm having typing problems trying to do a similar thing with a
function
that statistically normalizes data.
See:
http://people.revoledu.com/kardi/tutorial/Similarity/Normalization.html#Statistic
So
g normalize [2,5,3,2] ->
[-0.7071067811865475,1.414213562373095,0.0,-0.7071067811865475]
Is my typing for normalize too loose. Should I be using Floating
rather than Num?
Michael
===Code==
{-
See Problem 42, pg. 63, Prolog by Example, Coelho & Cotta
Generate a list of serial numbers for the items of a given list,
the members of which are to be numbered in alphabetical order.
*Main> serialize "prolog"
[4,5,3,2,3,1]
*Main> serialize "int.artificial"
[5,7,9,1,2,8,9,5,4,5,3,5,2,6]
*Main> ["prolog"] >>= serialize
[4,5,3,2,3,1]
*Main> ["int.artificial"] >>= serialize
[5,7,9,1,2,8,9,5,4,5,3,5,2,6]
-}
import Data.Map hiding (map)
import Data.List
{-
serialize :: [Char] -> [Int]
serialize l = map (f l) l
where
f = ((!) . fromList . ((flip zip) [1..]) . (sort . nub))
-}
serialize :: (Ord a, Integral b) => [a] -> a -> b
serialize = ((!) . fromList . ((flip zip) [1..]) . (sort . nub))
g f l = map (f l) l
normalize :: (Num a, Num b) => [a] -> a -> b
normalize l = let (total,len) = sumlen l
avg = total/len
stdev = sqrt $ ((/) (len-1)) $ sum $ map ((** 2.0) .
(subtract avg)) l
in ((/) stdev) . (subtract avg)
sumlen :: (Num a, Integral b) => [a] -> (a,b)
sumlen l = sumlen' l 0 0
where sumlen' [] sum len = (sum,len)
sumlen' (h:t) sum len = sumlen' t (sum+h) (len+1)
=
Prelude> :r
[1 of 1] Compiling Main ( serialize2.hs, interpreted )
serialize2.hs:34:32:
Could not deduce (Integral a) from the context (Num a, Num b)
arising from a use of `sumlen' at serialize2.hs:34:32-39
Possible fix:
add (Integral a) to the context of
the type signature for `normalize'
In the expression: sumlen l
In a pattern binding: (total, len) = sumlen l
In the expression:
let
(total, len) = sumlen l
avg = total / len
stdev = sqrt
$ ((/) (len - 1)) $ sum $ map ((** 2.0) . (subtract
avg)) l
in (/ stdev) . (subtract avg)
serialize2.hs:36:61:
Could not deduce (Floating a) from the context (Num a, Num b)
arising from a use of `**' at serialize2.hs:36:61-66
Possible fix:
add (Floating a) to the context of
the type signature for `normalize'
In the first argument of `(.)', namely `(** 2.0)'
In the first argument of `map', namely
`((** 2.0) . (subtract avg))'
In the second argument of `($)', namely
`map ((** 2.0) . (subtract avg)) l'
serialize2.hs:37:18:
Couldn't match expected type `b' against inferred type `a'
`b' is a rigid type variable bound by
the type signature for `normalize' at serialize2.hs:33:25
`a' is a rigid type variable bound by
the type signature for `normalize' at serialize2.hs:33:18
In the expression: (/ stdev) . (subtract avg)
In the expression:
let
(total, len) = sumlen l
avg = total / len
stdev = sqrt
$ ((/) (len - 1)) $ sum $ map ((** 2.0) . (subtract
avg)) l
in (/ stdev) . (subtract avg)
In the definition of `normalize':
normalize l = let
(total, len) = sumlen l
avg = total / len
in (/ stdev) . (subtract avg)
Failed, modules loaded: none.
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Has
Re: [Haskell-cafe] Typing problem
On Monday 31 January 2011 18:29:59, michael rice wrote: > I'm mapping a function over a list of data, where the mapping function > is determined from the data. > > g f l = map (g l) l g f l = map (f l) l probably > > So > > g serialize "prolog" -> [4,5,3,2,3,1] > > But I'm having typing problems trying to do a similar thing with a > function that statistically normalizes data. > > See: > http://people.revoledu.com/kardi/tutorial/Similarity/Normalization.html# >Statistic > > So > > g normalize [2,5,3,2] -> > [-0.7071067811865475,1.414213562373095,0.0,-0.7071067811865475] > > Is my typing for normalize too loose. You can omit the type signatures and see what the compiler infers as the type. In this case, > normalize :: (Num a, Num b) => [a] -> a -> b > normalize l = let (total,len) = sumlen l > avg = total/len > stdev = sqrt $ ((/) (len-1)) $ sum $ map ((** 2.0) . > (subtract avg)) l in ((/) stdev) . (subtract avg) In the final result, I suppose it should be (/ stdev) and not ((/) stdev) [the latter is (stdev /), i.e. \x -> stdev / x]. by sumlen's type, len has an Integral type. You want to use (/) to divide, which gives a Fractional constraint, (/) :: Fractional a => a -> a -> a Since it is not sensible for a type to be a member of both, the Fractional and Integral classes, you should convert len to the appropriate type with fromIntegral. For stdev, you call sqrt :: Floating a => a -> a and (**) :: Floating a => a -> a which means the list elements must have a type belonging to Floating (you could replace the (** 2.0) with (^ 2), which would probably be better, but the Floating constraint remains due to the sqrt). Finally, the resulting function is \x -> (x - avg) / stdev, hence x must have the same type as abg and stdev, and the final result has the same type. Altogether, normalize :: Floating a => [a] -> a -> a normalize l = let (total, len0) = sumlen l len = fromIntegral len0 avg = total/len stdev = sqrt $ sum [(x-avg)^2 | x <- l] / (len-1) in (/ stdev) . subtract avg but that gives nonsense if you pass a complex-valued list, so it might be better to restrict the type to normalize :: RealFloat a => [a] -> a -> a > Should I be using Floating rather than Num? You have to, and one number type only (well, you could use two or three types if you compose with conversion functions, realToFrac for example). ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Typing problem
I'm mapping a function over a list of data, where the mapping function is
determined from the data.
g f l = map (g l) l
So
g serialize "prolog" -> [4,5,3,2,3,1]
But I'm having typing problems trying to do a similar thing with a function
that statistically normalizes data.
See:
http://people.revoledu.com/kardi/tutorial/Similarity/Normalization.html#Statistic
So
g normalize [2,5,3,2] ->
[-0.7071067811865475,1.414213562373095,0.0,-0.7071067811865475]
Is my typing for normalize too loose. Should I be using Floating rather than
Num?
Michael
===Code==
{-
See Problem 42, pg. 63, Prolog by Example, Coelho & Cotta
Generate a list of serial numbers for the items of a given list,
the members of which are to be numbered in alphabetical order.
*Main> serialize "prolog"
[4,5,3,2,3,1]
*Main> serialize "int.artificial"
[5,7,9,1,2,8,9,5,4,5,3,5,2,6]
*Main> ["prolog"] >>= serialize
[4,5,3,2,3,1]
*Main> ["int.artificial"] >>= serialize
[5,7,9,1,2,8,9,5,4,5,3,5,2,6]
-}
import Data.Map hiding (map)
import Data.List
{-
serialize :: [Char] -> [Int]
serialize l = map (f l) l
where
f = ((!) . fromList . ((flip zip) [1..]) . (sort . nub))
-}
serialize :: (Ord a, Integral b) => [a] -> a -> b
serialize = ((!) . fromList . ((flip zip) [1..]) . (sort . nub))
g f l = map (f l) l
normalize :: (Num a, Num b) => [a] -> a -> b
normalize l = let (total,len) = sumlen l
avg = total/len
stdev = sqrt $ ((/) (len-1)) $ sum $ map ((** 2.0) .
(subtract avg)) l
in ((/) stdev) . (subtract avg)
sumlen :: (Num a, Integral b) => [a] -> (a,b)
sumlen l = sumlen' l 0 0
where sumlen' [] sum len = (sum,len)
sumlen' (h:t) sum len = sumlen' t (sum+h) (len+1)
=
Prelude> :r
[1 of 1] Compiling Main ( serialize2.hs, interpreted )
serialize2.hs:34:32:
Could not deduce (Integral a) from the context (Num a, Num b)
arising from a use of `sumlen' at serialize2.hs:34:32-39
Possible fix:
add (Integral a) to the context of
the type signature for `normalize'
In the expression: sumlen l
In a pattern binding: (total, len) = sumlen l
In the expression:
let
(total, len) = sumlen l
avg = total / len
stdev = sqrt
$ ((/) (len - 1)) $ sum $ map ((** 2.0) . (subtract avg)) l
in (/ stdev) . (subtract avg)
serialize2.hs:36:61:
Could not deduce (Floating a) from the context (Num a, Num b)
arising from a use of `**' at serialize2.hs:36:61-66
Possible fix:
add (Floating a) to the context of
the type signature for `normalize'
In the first argument of `(.)', namely `(** 2.0)'
In the first argument of `map', namely
`((** 2.0) . (subtract avg))'
In the second argument of `($)', namely
`map ((** 2.0) . (subtract avg)) l'
serialize2.hs:37:18:
Couldn't match expected type `b' against inferred type `a'
`b' is a rigid type variable bound by
the type signature for `normalize' at serialize2.hs:33:25
`a' is a rigid type variable bound by
the type signature for `normalize' at serialize2.hs:33:18
In the expression: (/ stdev) . (subtract avg)
In the expression:
let
(total, len) = sumlen l
avg = total / len
stdev = sqrt
$ ((/) (len - 1)) $ sum $ map ((** 2.0) . (subtract avg)) l
in (/ stdev) . (subtract avg)
In the definition of `normalize':
normalize l = let
(total, len) = sumlen l
avg = total / len
in (/ stdev) . (subtract avg)
Failed, modules loaded: none.
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