# [Haskell-cafe] Transformation sequence

Brent Yorgey byorgey at gmail.com
Sat Oct 20 14:31:51 EDT 2007

```On 10/20/07, Andrew Coppin <andrewcoppin at btinternet.com> wrote:
>
> I'm writing some code where I take an expression tree and transform it
> into another equivilent one.
>
> Now it's moderately easy to write the code that does the transformation.
> But what I *really* want is to print out the transformation *sequence*.
> This appears to be much more awkward.
>
> What I have is a function like this:
>
>   transform :: Expression -> [Expression]
>
> The trouble is, if you want to apply the transformation recursively,
> things get very messy. Oh, it *works* and everything. It's just really
> messy and verbose. In Haskell, this is usually a sign that you want to
> start applying some ingenious trickery... but I'm having an ingeniety
> failure here.
>
> Suppose, for example, that in one case you want to recursively transform
> two subexpressions. I end up writing something like
>
>   transform (...sub1...sub2...) =
>     let
>       sub1s = transform sub1
>       sub2s = transform sub2
>     in map (\sub1' -> put sub1' back into main expression) sub1s ++ map
> (\sub2' -> put sub2' back into main expression) sub2s
>
> After you've typed that a few times, it becomes *very* boring! But I
> can't think of a clean way to abstract it. :-(
>
> It's *almost* like you want to use the list monad:
>
>   transform (...sub1...sub2...) = do
>     sub1' <- transform sub1
>     sub2' <- transform sub2
>     return (put sub1' and sub2' back into the main expression)
>
> Except that that doesn't quite work properly. As shown above, I actually
> want to go through all the transformation steps for the first branch,
> and *then* all the steps for the second branch.
>
> Any hints?

Hmm... I'm having trouble understanding exactly what you want.  In
particular, I don't understand what this statement:

"But what I *really* want is to print out the transformation *sequence*."

has to do with the pseudocode that you exhibit later.  Could you perhaps
clarify a bit more, or give a specific example?

-Brent
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