[Haskell-cafe] what does @ mean?.....

[Nicholls, Mark]

Hello, I wonder if someone could answer the following...

The short question is what does @ mean in 

 

mulNat a b

    | a <= b = mulNat' a b b

    | otherwise = mulNat' b a a

    where

         mulNat' x@(S a) y orig

                 | x == one = y

                 | otherwise = mulNat' a (addNat orig y) orig

 

The long version, explaining what everything means is....

 

 here's a definition of multiplication on natural numbers I'm reading

 on a blog....

 

 data Nat = Z | S Nat

    deriving Show

 

 one :: Nat

 one = (S Z)

 

 mulNat :: Nat -> Nat -> Nat

 mulNat _ Z = Z

 mulNat Z _ = Z

 mulNat a b

    | a <= b = mulNat' a b b

    | otherwise = mulNat' b a a

    where

         mulNat' x@(S a) y orig

                 | x == one = y

                 | otherwise = mulNat' a (addNat orig y) orig

 

 Haskell programmers seem to have a very irritating habit of trying to

 be overly concise...which makes learnign the language extremely

 hard...this example is actually relatively verbose....but anyway...

 

 Z looks like Zero...S is the successor function...Nat are the

 "Natural" numbers.....

 

 mulNat _ Z = Z

 mulNat Z _ = Z

 

 translates to...

 

 x * 0 = 0....fine...

 0 * x = 0....fine..

 

 mulNat a b

    | a <= b = mulNat' a b b

    | otherwise = mulNat' b a a

    where

         mulNat' x@(S a) y orig

                 | x == one = y

                 | otherwise = mulNat' a (addNat orig y) orig

 

 is a bit more problematic...

 lets take a as 3 and b as 5...

 

 so now we have

 

 mulNat' 3 5 5

 

 but what does the "x@(S a)" mean? in

 

 mulNat' x@(S a) y orig

 

________________________________

From: haskell-cafe-bounces at haskell.org
[mailto:haskell-cafe-bounces at haskell.org] On Behalf Of Nicholls, Mark
Sent: 21 December 2007 17:47
To: David Menendez
Cc: Jules Bean; haskell-cafe at haskell.org
Subject: RE: [Haskell-cafe] nice simple problem for someone
struggling....

 

Let me resend the code...as it stands....

 

module Main where

 

data SquareType numberType = Num numberType => SquareConstructor
numberType

 

class ShapeInterface shape where

      area :: Num numberType => shape->numberType

 

data ShapeType = forall a. ShapeInterface a => ShapeType a

 

instance (Num a) => ShapeInterface (SquareType a) where 

    area (SquareConstructor side) = side * side

 

 

and the errors are for the instance declaration.......

 

[1 of 1] Compiling Main             ( Main.hs, C:\Documents and
Settings\nichom\Haskell\Shapes2\out/Main.o )

 

Main.hs:71:36:

    Couldn't match expected type `numberType' against inferred type `a'

      `numberType' is a rigid type variable bound by

                   the type signature for `area' at Main.hs:38:15

      `a' is a rigid type variable bound by

          the instance declaration at Main.hs:70:14

    In the expression: side * side

    In the definition of `area':

        area (SquareConstructor side) = side * side

 

I'm becoming lost in errors I don't comprehend....

 

What bamboozles me is it seemed such a minor enhancement.

________________________________

From: d4ve.menendez at gmail.com [mailto:d4ve.menendez at gmail.com] On Behalf
Of David Menendez
Sent: 21 December 2007 17:05
To: Nicholls, Mark
Cc: Jules Bean; haskell-cafe at haskell.org
Subject: Re: [Haskell-cafe] nice simple problem for someone
struggling....

 

On Dec 21, 2007 11:50 AM, Nicholls, Mark <Nicholls.Mark at mtvne.com>
wrote:

	Now I have....
	
	module Main where
	
	data SquareType numberType = Num numberType => SquareConstructor
	numberType


This is a valid declaration, but I don't think it does what you want it
to. The constraint on numberType applies only to the data constructor. 

That is, given an unknown value of type SquareType a for some a, we do
not have enough information to infer Num a.

For your code, you want something like:

instance (Num a) => ShapeInterface (SquareType a) where 
    area (SquareConstructor side) = side * side


-- 
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/ > 

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