[Haskell] logic problem

[Robert Dockins]

On Tuesday 25 October 2005 08:36 pm, michael at schmong.org wrote:
> Hi,
>    My name is Michael. I'm new to Haskell. I'm working through
>    The Craft of Functional Programming by Simon Thompson.
>    I'm having problems with a few exercises from chapter 4. I will
>    present one per post.
>
>    This one is from 4.9
>    Given a function f of type Int -> Int give a recursive definition
>    of a function of type Int -> Int which on input n returns the maximum
>    values f 0, f 1, ... , f n
>
>    I defined f as follows
>    f 0 = 0
>    f 1 = 44
>    f 2 = 5
>    f 9 = 8

Most likely your problem is that f is only defined for
input values 0, 1, 2 and 9.  If you call f with any other
value, you will end up with an error.

>    this works except when f n > n. In that case I get an "illegal
>    instruction" error and hugs exits.
>    I'm pretty sure this is a logic problem. Could someone point me
>    in the right direction so I can think about this problem correctly.
>    Here is my code
>
>    maxOverf :: Int -> Int
>    maxOverf m
>
>       | f m > m    = (f m)
>       | otherwise = (maxOverf m-1)

Here you are calling f with successively decreasing values; that will
run into areas where f is undefined for any value of m other than 1 or 2.

>       Any hints/help/flames welcome. Thanks

Try a total rather than a partial function for f.  You can just add a
default clause to the end, like

f _ = 0

which will define f x to be 0 for all values of x except the ones already 
mentioned.