I want to make function maptree with standard ML

问题

I want to make function maptree with standard ML. If function f(x) = x + 1; then

maptree(f, NODE(NODE(LEAF 1,LEAF 2),LEAF 3));

should make result

NODE(NODE(LEAF 2,LEAF 3),LEAF 4))

I write the code like below.

datatype 'a tree = LEAF of 'a | NODE of 'a tree * 'a tree;
fun f(x) = x + 1;
fun maptree(f, NODE(X, Y)) = NODE(maptree(f, X), maptree(f, Y))
| maptree(f, LEAF(X)) = LEAF(f X);

but when I execute this code like this

maptree(f, (NODE(NODE(LEAF 1,LEAF 2),LEAF 3)));

result is not I want to (NODE(NODE(LEAF 2,LEAF 3),LEAF 4))) but NODE(NODE(LEAF #,LEAF #),LEAF 4)). Why this happened(not a number but #)?

回答1:

# is used by the REPL when the data structure it prints is deeper than a pre-set value. If you increase that value, you'll get the result you excepted. I assume you're using SML/NJ, which calls that setting print.depth:

sml -Cprint.depth=20
- maptree(f, (NODE(NODE(LEAF 1,LEAF 2),LEAF 3)));
val it = NODE (NODE (LEAF 2,LEAF 3),LEAF 4) : int tree

You can find more options like these by executing sml -H. Look them up under the "compiler print settings" section:

compiler print settings:
     print.depth                                          (max print depth)
     print.length                                        (max print length)
     print.string-depth                            (max string print depth)
     print.intinf-depth                        (max IntInf.int print depth)
     print.loop                                                (print loop)
     print.signatures                       (max signature expansion depth)
     print.opens                                             (print `open')
     print.linewidth                   (line-width hint for pretty printer)

回答2:

Some comments:

I would probably go with the definition
```
datatype 'a tree = Leaf | Node of 'a tree * 'a * 'a tree
```
so that trees with zero or two elements can also be expressed.

I would probably curry the tree map function

fun treemap f Leaf = Leaf
  | treemap f (Node (l, x, r)) = Node (treemap f l, x, treemap f r)

since you can then partially apply it, e.g. like:

(* 'abstree t' returns t where all numbers are made positive *)
val abstree = treemap Int.abs

(* 'makeFullTree n' returns a full binary tree of size n *)
fun makeFullTree 0 = Leaf
  | makeFullTree n =
    let val subtree = makeFullTree (n-1)
    in Node (subtree, n, subtree)
    end

(* 'treetree t' makes an int tree into a tree of full trees! *)
val treetree = treemap makeFullTree

You may at some point want to fold a tree, too.

来源：https://stackoverflow.com/questions/36986057/i-want-to-make-function-maptree-with-standard-ml

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sml

smlnj