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POHow to define trees with more than one type in ML programing language
 

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  1. POHow to define trees with more than one type in ML programing language
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    <p>Well, I am asked to do the next thing:</p> <p>To define a binary tree which can contain 2 different types: ('a,'b) abtree and these are the requirements:</p> <ol> <li>Any inner vertex (not a leaf) must be of the type 'a or 'b and the leafs have no value.</li> <li><p>For every path in the tree all 'a values must appear before the 'b value: examples of paths:</p> <pre><code>'a-&gt;'a-&gt;'a-'b (legal) 'a-&gt;'b-&gt;'b (legal) 'a-&gt;'a-&gt;'a (legal) 'b-&gt;'b-&gt;'b (legal) 'a-&gt;'b-&gt;'a (ILLEGAL) </code></pre></li> </ol> <p>and also I need to define another tree which is like the one described above but now I have got also 'c and in the second requirement it says that for every path I 'a values appear before the 'b values and all the 'b values appear before the 'c values.</p> <p>First, I am not sure how to define binary trees to have more than 1 type in them. I mean the simplest binary tree is:</p> <pre><code>datatype 'a tree = leaf | br of 'a * 'a tree * 'a tree; </code></pre> <p>And also how I can define a tree to have these requirements.</p> <p>Any help will be appreciated.</p> <p>Thanks.</p> <hr> <p>OK, thanks a lot. So you mean something like that:</p> <pre><code>datatype 'b bTree = leaf | bBranch of 'b * 'b bTree * 'b bTree ; datatype ('a,'b) abTree = leaf | aBranch of 'a * ('a, 'b) abTree * ('a,'b) abTree | bBranch of 'b * 'b bTree * 'b bTree ; </code></pre> <p>and that's what I did for the case it's a 3 type tree as I mentioned above:</p> <pre><code>datatype 'c cTree = leaf | cBranch of 'c * 'c cTree * 'c cTree ; datatype ('b, 'c) bcTree = leaf | bBranch of 'b * ('b, 'c) bcTree * ('b,'c) bcTree | cBranch of 'c * 'c cTree * 'c cTree ; datatype ('a, 'b, 'c) abcTree = leaf | aBranch of 'a * ('a, 'b, 'c) abcTree * ('a, 'b, 'c) abcTree | bBranch of 'b * ('b, 'c) bcTree * ('b, 'c) bcTree | cBranch of 'c * 'c cTree * 'c cTree ; </code></pre> <p>Am I right?</p> <p>Also, what does the requirement of leafs means? The one that says that the leafs should have no value?</p>
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