Question: I looked for the name of a procedure, which applies a tree structure of procedures to a tree structure of data, yielding a tree structure of results - all three trees having the same structure. 

Such a procedure might have the signature: 

```
(map-tree data functree)
```

Its return value would be the result of elementwise application of functree's elements on the corresponding data elements. 

Examples (assuming that the procedure is called map-tree): 

Example 1: 

```
(define *2 (lambda (x) (* 2 x)))
; and similar definitions for *3 and *5

(map-tree '(100 (10 1)) '(*2 (*3 *5)))
```

would yield the result 
```
(200 (30 5))
```

Example 2: 

```
(map-tree '(((aa . ab) (bb . bc)) (cc . (cd . ce)))
        '((car cdr) cadr))
```

yields the result 
```
((aa bc) cd)
```

However I did not find such a function in the SLIB documentation, which I consulted. 

Does such a procedure already exist?  

If not, what would be a suitable name for the procedure, and how would you order its arguments?

Answer: 
I don't have a very good name for the function. I'm pasting my implementation below (I've called it `map-traversing`; others should suggest a better name). I've made the argument order mirror that of `map` itself.

```
(define (map-traversing func data)
  (if (list? func)
      (map map-traversing func data)
      (func data)))

```

Using your sample data, we have:

```
(map-traversing `((,car ,cdr) ,cadr) '(((aa . ab) (bb . bc)) (cc cd . ce)))

```

The second sample requires SRFI 26. (Allows writing `(cut * 2 <>)` instead of `(lambda (x) (* 2 x))`.)

```
(map-traversing `(,(cut * 2 <>) (,(cut * 3 <>) ,(cut * 5 <>))) '(100 (10 1)))

```

The most important thing is that your functions must all be unquoted, unlike your example.
I found that with the follwing definition of map-traversing, you don't need to unquote the functions:

```
(define (map-traversing func data)
  (if (list? func)
      (map map-traversing func data)
      (apply (eval func (interaction-environment)) (list data))))
```

Note: in my installed version of Guile, due to some reason, only (interaction-environment) does not raise the Unbound variable error. The other environments i.e. (scheme-report-environment 5) and (null-environment 5) raise this error. 

Note 2: Subsequently, I found in [1] that for (scheme-report-environment 5) and (null-environment 5) to work, you need first to (use-modules (ice-9 r5rs))

[1]: <http://www.mail-archive.com/bug-guile@gnu.org/msg04368.html> 'Re: guile -c "(scheme-report-environment 5)" ==> ERROR: Unbound variable: scheme-report-environment'