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POStandard ML functor examples
 

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  1. POStandard ML functor examples
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    <p>Functors in Standard ML are related to the module system and can generate structures based on other structures. An example of a functor generating list combinators for various types of lists is given below, but this example has a problem:</p> <p>The various types of lists all have advantages -- for example, lazy lists can be infinitely long, and concantenation lists have a O(1) concat operator. But when all of these list types conform to the same signature, the functor can only use their general properties.</p> <p>My question is therefore: What is a good example of when functors are useful and the various generated structures don't lose their special abilities?</p> <pre><code>signature MYLIST = sig type 'a t val null : 'a t -&gt; bool val empty : 'a t val cons : 'a * 'a t -&gt; 'a t val hd : 'a t -&gt; 'a val tl : 'a t -&gt; 'a t end structure RegularList : MYLIST = struct type 'a t = 'a list val null = List.null val empty = [] val cons = op:: val hd = List.hd val tl = List.tl end structure LazyList : MYLIST = struct datatype 'a t = Nil | Cons of 'a * (unit -&gt; 'a t) val empty = Nil fun null Nil = true | null _ = false fun cons (x, xs) = Cons (x, fn () =&gt; xs) fun hd Nil = raise Empty | hd (Cons (x, _)) = x fun tl Nil = raise Empty | tl (Cons (_, f)) = f () end structure ConcatList : MYLIST = struct datatype 'a t = Nil | Singleton of 'a | Concat of 'a t * 'a t val empty = Nil fun null Nil = true | null (Singleton _) = false | null (Concat (xs, ys)) = null xs andalso null ys fun cons (x, xs) = Concat (Singleton x, xs) fun hd Nil = raise Empty | hd (Singleton x) = x | hd (Concat (xs, ys)) = hd xs fun tl Nil = raise Empty | tl (Singleton x) = Nil | tl (Concat (xs, ys)) = (* exercise *) end signature MYLISTCOMB = sig type 'a t val length : 'a liste -&gt; int val map : ('a -&gt; 'b) -&gt; 'a liste -&gt; 'b liste val foldl : ('a * 'b -&gt; 'b) -&gt; 'b -&gt; 'a liste -&gt; 'b val append : 'a liste * 'a liste -&gt; 'a liste val concat : 'a liste liste -&gt; 'a liste val sort : ('a * 'a -&gt; order) -&gt; 'a t -&gt; 'a t end functor ListComb (X : MYLIST) : MYLISTCOMB = struct type 'a t = 'a X.t open X fun length xs = if null xs then 0 else 1 + length (tl xs) fun map f xs = if null xs then empty else cons(f (hd xs), map f (tl xs)) fun foldl f e xs = if null xs then e else foldl f (f (hd xs, e)) (tl xs) fun append (xs, ys) = if null xs then ys else cons (hd xs, append (tl xs, ys)) fun concat xs = if null xs then empty else append (hd xs, concat (tl xs)) fun sort cmp xs = (* exercise *) end structure RegularListComb = ListComb (RegularList) structure LazyListComb = ListComb (LazyList) structure ConcatListComb = ListComb (ConcatList) </code></pre>
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    1. COI'm a little confused. The lack of visibility of implementation-specific functionality is kinda the point of functors in SML. Are you looking for some kind of guarantees of behaviour preservation?
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    2. CO@Gian: He's looking for some good examples for demonstrating the usefulness of functors to students (in an introductory SML course).
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    3. COIn that case, have a look at CMlib: https://github.com/standardml/cmlib -- particularly things like 'streamable'.
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