# [Haskell-cafe] what do I have to do exactlry with this exercises

Richard A. O'Keefe ok at cs.otago.ac.nz
Mon Nov 2 01:29:10 UTC 2015

```On 30/10/2015, at 7:52 pm, Roelof Wobben <r.wobben at home.nl> wrote:
>
> Let's say f is a recursive function which calculates the fac.
>
> So f 0  = 0
> f1 = 1
> f2 = 2
> f3 = 6
>
> so im my oponion g1 = the answer of f1 which is also the max

True.  But what if f is *NOT* the factorial?

To quote your own original message,
<quote>
To test this function, add to your script a definition of some values of f thus:
f 0 = 0
f 1 = 44
f 2 = 17
f _ = 0
and so on; then test your function at various values.
</quote>

This f is NOT the factorial function.  For this f,
we expect g n = if n == 0 then 0 else 44, so that
(g n == f n) is false almost always.

Let's consider the general pattern for a primitive recursive
function on the natural numbers:

g 0 otherArgs = b otherArgs
g (n+1) otherArgs = c n (g n otherArgs) otherArgs

where b(ase) and c(ombination) are primitive recursive.
In this case, there are no otherArgs, so

g 0 = <<some expression possibly involving f>>
g n = <<some expression involving n, g (n-1), and f>>

For exercise 4.22, you are given a hint that
<<some expression involving n, g (n-1), and f>>
will also involve a call to max.

There's really not a lot of sensible ways you can put these together.

```