[Haskell-cafe] Partial Derivatives

[Gerhard Navratil]

Hi,

I need a library that provides partial derivatives for functions. The
solution I came up with is based on a datatype using reversed polish
notation to store the function:

Type VarName = String
data Fkt a = Val a |
             Var VarName |
             Add (FktElem a) (FktElem a) |
             Sub (FktElem a) (FktElem a) |
             Mul (FktElem a) (FktElem a) |
             ...

I can then use pattern matching to compute the derivative:

derivative  :: VarName -> Fkt b -> Fkt b
derivative name (Var n) = if n == name then Val 1.0 else Val 0.0
derivative name (Add a b)
    | (containsVar name a) && (containsVar name b)     = Add (derivative
name a) (derivative name b)
    | (containsVar name a) && (not(containsVar name b)) = (derivative
name a)
    | (not(containsVar name a)) && (containsVar name b) = (derivative
name b)
    | otherwise = Val 0.0
derivative name (Sub a b)
    | (containsVar name a) && (containsVar name b)      = Sub
(derivative name a) (derivative name b)
    | (containsVar name a) && (not(containsVar name b)) = (derivative
name a)
    | (not(containsVar name a)) && (containsVar name b) = (derivative
name b)
    | otherwise = Val 0.0
derivative name (Mul a b)
    | (containsVar name a) && (containsVar name b)      = Add (Mul
(derivative name a) b) (Mul a (derivative name b))
    | (containsVar name a) && (not(containsVar name b)) = Mul
(derivative name a) b
    | (not(containsVar name a)) && (containsVar name b) = Mul a
(derivative name b)
    | otherwise = Val 0.0
...

Where the function

containsVar :: VarName -> Fkt a -> Bool

tests if a function contains the variable.

The solution works but is not very elegant. The complete module is
appended to the mail.

Does anyone have a more elegant solution or is there a package that
provides derivatives in a similar way?

Thank you,
Gerhard

========================================
Gerhard Navratil
Teaching- And Research-Assistant
Technical University Vienna, Austria
Institute of Geoinformation and Cartography
Gusshausstr. 27-29, 1040 Vienna
Tel.: ++43 (0) 1 / 58 801 - 12712
Fax.: ++43 (0) 1 / 58 801 - 12799
Cel.: ++43 (0) 699 / 197 44 761
http://www.geoinfo.tuwien.ac.at
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Function.hs
Type: application/octet-stream
Size: 9278 bytes
Desc: Function.hs
Url : http://www.haskell.org//pipermail/haskell-cafe/attachments/20060508/30e23170/Function.obj