Parametric polymorphism: Difference between revisions
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{{task|Basic language learning}}
[[Category:Type System]]
[[wp:Parametric Polymorphism|Parametric Polymorphism]] is a way to define types or functions that are generic over other types. The genericity can be expressed by using ''type variables'' for the parameter type, and by a mechanism to explicitly or implicitly replace the type variables with concrete types when necessary.
;Task:
Write a small example for a type declaration that is parametric over another type, together with a short bit of code (and its type signature) that uses it.
A good example is a container type, let's say a binary tree, together with some function that traverses the tree, say, a ''map''-function that operates on every element of the tree.
This language feature only applies to statically-typed languages.
<br><br>
=={{header|Ada}}==
<
type Element_Type is private;
package Container is
Line 20 ⟶ 28:
Right : Node_Access := null;
end record;
end Container;</
<
procedure Replace_All(The_Tree : in out Tree; New_Value : Element_Type) is
begin
Line 32 ⟶ 40:
end if;
end Replace_All;
end Container;</
=={{header|C
If the goal is to separate algorithms from types at compile time, C may do it by macros. Here's sample code implementing binary tree with node creation and insertion:<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
#define decl_tree_type(T) \
typedef struct node_##T##_t node_##T##_t, *node_##T; \
struct node_##T##_t { node_##T left, right; T value; }; \
\
node_##T node_##T##_new(T v) { \
node_##T node = malloc(sizeof(node_##T##_t)); \
node->value = v; \
node->left = node->right = 0; \
return node; \
} \
node_##T node_##T##_insert(node_##T root, T v) { \
node_##T n = node_##T##_new(v); \
while (root) { \
if (root->value < n->value) \
if (!root->left) return root->left = n; \
else root = root->left; \
else \
if (!root->right) return root->right = n; \
else root = root->right; \
} \
return 0; \
}
#define tree_node(T) node_##T
#define node_insert(T, r, x) node_##T##_insert(r, x)
#define node_new(T, x) node_##T##_new(x)
decl_tree_type(double);
decl_tree_type(int);
int main()
{
int i;
tree_node(double) root_d = node_new(double, (double)rand() / RAND_MAX);
for (i = 0; i < 10000; i++)
node_insert(double, root_d, (double)rand() / RAND_MAX);
tree_node(int) root_i = node_new(int, rand());
for (i = 0; i < 10000; i++)
node_insert(int, root_i, rand());
return 0;
}</syntaxhighlight>
Comments: It's ugly looking, but it gets the job done. It has the drawback that all methods need to be re-created for each tree data type used, but hey, C++ template does that, too.
Arguably more interesting is run time polymorphism, which can't be trivially done; if you are confident in your coding skill, you could keep track of data types and method dispatch at run time yourself -- but then, you are probably too confident to not realize you might be better off using some higher level languages.
=={{header|C sharp|C#}}==
<syntaxhighlight lang="csharp">using System;
class BinaryTree<T>
{
public T value;
public BinaryTree<T> left;
public BinaryTree<T> right;
public BinaryTree(T value)
{
this.value = value;
}
public BinaryTree<U> Map<U>(Func<T, U> f)
{
BinaryTree<U> tree = new BinaryTree<U>(f(this.value));
if (this.left != null)
{
tree.left = this.left.Map(f);
}
if (this.right != null)
{
tree.right = this.right.Map(f);
}
return tree;
}
}</syntaxhighlight>
Creating a tree of integers and using Map to generate a tree of doubles with every node half the value of the first:
<syntaxhighlight lang="csharp">class Program
{
static void Main(string[] args)
{
BinaryTree<int> b = new BinaryTree<int>(6);
b.left = new BinaryTree<int>(5);
b.right = new BinaryTree<int>(7);
BinaryTree<double> b2 = b.Map(x => x * 0.5);
}
}</syntaxhighlight>
{{anchor|C# modern version}}A version using more modern language constructs:
<syntaxhighlight lang="csharp">using System;
class BinaryTree<T>
{
public BinaryTree<T> Left { get; }
public BinaryTree<T> Right { get; }
public T Value { get; }
public BinaryTree(T value, BinaryTree<T> left = null, BinaryTree<T> right = null)
{
this.Value = value;
this.Left = left;
this.Right = right;
}
public BinaryTree<U> Map<U>(Func<T, U> f)
{
return new BinaryTree<U>(f(this.Value), this.Left?.Map(f), this.Right?.Map(f));
}
public override string ToString()
{
var sb = new System.Text.StringBuilder();
this.ToString(sb, 0);
return sb.ToString();
}
private void ToString(System.Text.StringBuilder sb, int depth)
{
sb.Append(new string('\t', depth));
sb.AppendLine(this.Value?.ToString());
this.Left?.ToString(sb, depth + 1);
this.Right?.ToString(sb, depth + 1);
}
}
static class Program
{
static void Main()
{
var b = new BinaryTree<int>(6, new BinaryTree<int>(5), new BinaryTree<int>(7));
BinaryTree<double> b2 = b.Map(x => x * 0.5);
Console.WriteLine(b);
Console.WriteLine(b2);
}
}
</syntaxhighlight>
{{out}}
<pre>6
5
7
3
2.5
3.5</pre>
=={{header|C++}}==
<syntaxhighlight lang="cpp">template<typename T>
class tree {
T value;
tree *left;
Line 44 ⟶ 206:
public:
void replace_all (T new_value);
};</
For simplicity, we replace all values in the tree with a new value:
<
void tree<T>::replace_all
value = new_value;
if (left != nullptr)
if (right != nullptr)
right->replace_all(new_value);
}</syntaxhighlight>
=={{header|
<syntaxhighlight lang="c3">module tree(<Type>);
struct Tree
{
Type value;
Tree*
}
fn void Tree.replace_all(&self, Type new_value)
{
self.value = new_value;
if (self.left) self.left.replace_all(new_value);
if (self.right) self.right.replace_all(new_value);
}
</syntaxhighlight>
Usage:
<syntaxhighlight lang="c3">import tree;
fn void test()
{
Tree(<int>) inttree;
inttree.replace_all(3);
}</syntaxhighlight>
=={{header|Ceylon}}==
<syntaxhighlight lang="ceylon">class BinaryTree<Data>(shared Data data, shared BinaryTree<Data>? left = null, shared BinaryTree<Data>? right = null) {
shared BinaryTree<NewData> myMap<NewData>(NewData f(Data d)) =>
BinaryTree {
data = f(data);
left = left?.myMap(f);
right = right?.myMap(f);
};
}
shared void run() {
value tree1 = BinaryTree {
data = 3;
left = BinaryTree {
data = 4;
};
right = BinaryTree {
data = 5;
left = BinaryTree {
data = 6;
};
};
};
tree1.myMap(print);
print("");
value tree2 = tree1.myMap((x) => x * 333.33);
tree2.myMap(print);
}</syntaxhighlight>
=={{header|Clean}}==
<
mapTree :: (a -> b) (Tree a) -> (Tree b)
mapTree f Empty = Empty
mapTree f (Node x l r) = Node (f x) (mapTree f l) (mapTree f r)</
<blockquote><small>
Line 100 ⟶ 293:
Note that for the most usefulness in practical programming, a map operation like this should not be defined with a separate name but rather as <code>fmap</code> in an ''instance'' of the <code>Functor</code> ''type class'':
<
fmap f Empty = Empty
fmap f (Node x l r) = Node (f x) (fmap f l) (fmap f r)</
<code>fmap</code> can then be used exactly where <code>mapTree</code> can, but doing this also allows the use of <code>Tree</code>s with other components which are parametric over ''any type which is a Functor''. For example, this function will add 1 to any collection of any kind of number:
<
add1Everywhere nums = fmap (\x = x + 1) nums</
If we have a tree of integers, i.e. <var>f</var> is <code>Tree</code> and <var>a</var> is <code>Integer</code>, then the type of <code>add1Everywhere</code> is <code>Tree Integer -> Tree Integer</code>.
</small></blockquote>
{{omit from|Clojure}}
=={{header|Common Lisp}}==
Line 116 ⟶ 311:
Common Lisp is not statically typed, but types can be defined which are parameterized over other types. In the following piece of code, a type <code>pair</code> is defined which accepts two (optional) type specifiers. An object is of type <code>(pair :car car-type :cdr cdr-type)</code> if an only if it is a cons whose car is of type <code>car-type</code> and whose cdr is of type <code>cdr-type</code>.
<
`(cons ,car ,cdr))</
Example
Line 128 ⟶ 323:
=={{header|D}}==
<syntaxhighlight lang="d">class ArrayTree(T, uint N) {
T[N] data;
typeof(this) left, right;
this(T initValue) { this.data[] = initValue; }
void tmap(const void delegate(ref typeof(data)) dg) {
dg(this.data);
if (left) left.tmap(dg);
if (right) right.tmap(dg);
}
}
void main() { // Demo code.
import std.stdio;
// Instantiate the template ArrayTree of three doubles.
alias AT3 = ArrayTree!(double, 3);
// Allocate the tree root.
auto root = new AT3(1.00);
// Add some nodes.
root.left = new AT3(1.10);
root.left.left = new AT3(1.11);
root.left.right = new AT3(1.12);
root.right = new AT3(1.20);
root.right.left = new AT3(1.21);
root.right.right = new AT3(1.22);
// Now the tree has seven nodes.
// Show the arrays of the whole tree.
//root.tmap(x => writefln("%(%.2f %)", x));
root.tmap((ref x) => writefln("%(%.2f %)", x));
// Modify the arrays of the whole tree.
//root.tmap((x){ x[] += 10; });
root.tmap((ref x){ x[] += 10; });
// Show the arrays of the whole tree again.
writeln();
//root.tmap(x => writefln("%(%.2f %)", x));
root.tmap((ref x) => writefln("%(%.2f %)", x));
}</syntaxhighlight>
{{out}}
<pre>1.00 1.00 1.00
1.10 1.10 1.10
1.11 1.11 1.11
1.12 1.12 1.12
1.20 1.20 1.20
1.21 1.21 1.21
1.22 1.22 1.22
11.00 11.00 11.00
11.10 11.10 11.10
11.11 11.11 11.11
11.12 11.12 11.12
11.20 11.20 11.20
11.21 11.21 11.21
11.22 11.22 11.22</pre>
=={{header|Dart}}==
<syntaxhighlight lang="dart">class TreeNode<T> {
T value;
TreeNode<T> left;
TreeNode<T> right;
TreeNode(this.value);
TreeNode map(T f(T t)) {
var node = new TreeNode(f(value));
if(left != null) {
node.left = left.map(f);
}
if(right != null) {
node.right = right.map(f);
}
return node;
}
void forEach(void f(T t)) {
f(value);
if(left != null) {
left.forEach(f);
}
if(right != null) {
right.forEach(f);
}
}
}
void main() {
root.left = new TreeNode(2);
root.right = new TreeNode(3);
root.left.right = new TreeNode(4);
print('first tree');
root.forEach(print);
print('second tree');
newRoot.forEach(print);
}</syntaxhighlight>
{{out}}
<pre>first tree
1
2
4
3
second tree
222
444
888
666</pre>
=={{header|E}}==
Line 174 ⟶ 449:
(Note: The guard definition is arguably messy boilerplate; future versions of E may provide a scheme where the <code>interface</code> expression can itself be used to describe parametricity, and message signatures using the type parameter, but this has not been implemented or fully designed yet. Currently, this example is more of “you can do it if you need to” than something worth doing for every data structure in your program.)
<
def Tree {
to get(Value) {
Line 204 ⟶ 479:
}
return tree
}</
<
# value: <tree>
Line 216 ⟶ 491:
? t :Tree[int]
# value: <tree></
=={{header|FreeBASIC}}==
{{trans|Visual Basic .NET}}
FreeBASIC does not support object-oriented programming, so we will use a more procedural approach.
<syntaxhighlight lang="vbnet">Type BinaryTree
valor As Integer
izda As BinaryTree Ptr
dcha As BinaryTree Ptr
End Type
Sub PrintTree(t As BinaryTree Ptr, depth As Integer)
If t = 0 Then Exit Sub
Print String(depth, Chr(9)); t->valor
PrintTree(t->izda, depth + 1)
PrintTree(t->dcha, depth + 1)
End Sub
Dim As BinaryTree b = Type(6)
Dim As BinaryTree bLeft = Type(5)
Dim As BinaryTree bRight = Type(7)
b.izda = @bLeft
b.dcha = @bRight
PrintTree(@b, 0)</syntaxhighlight>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
namespace RosettaCode
type BinaryTree<'T> =
| Element of 'T
| Tree of 'T * BinaryTree<'T> * BinaryTree<'T>
member this.Map(f) =
match this with
| Element(x) -> Element(f x)
| Tree(x,left,right) -> Tree((f x), left.Map(f), right.Map(f))
</syntaxhighlight>
We can test this binary tree like so:
<syntaxhighlight lang="fsharp">
let t1 = Tree(2, Element(1), Tree(4,Element(3),Element(5)) )
let t2 = t1.Map(fun x -> x * 10)
</syntaxhighlight>
=={{header|Fortran}}==
Fortran does not offer polymorphism by parameter type, which is to say, enables the same source code to be declared applicable for parameters of different types, so that a contained statement such as <code>X = A + B*C</code> would work for any combination of integer or floating-point or complex variables as actual parameters, since exactly that (source) code would be workable in every case. Further, there is no standardised pre-processor protocol whereby one could replicate such code to produce a separate subroutine or function specific to every combination.
However, with F90 came the MODULE protocol with facilities suitable for defining "generic" subroutines or functions, or so it appears: <syntaxhighlight lang="fortran"> MODULE SORTSEARCH !Genuflect towards Prof. D. Knuth.
INTERFACE FIND !Binary chop search, not indexed.
MODULE PROCEDURE
1 FINDI4, !I: of integers.
2 FINDF4,FINDF8, !F: of numbers.
3 FINDTTI2,FINDTTI4 !T: of texts.
END INTERFACE FIND
CONTAINS
INTEGER FUNCTION FINDI4(THIS,NUMB,N) !Binary chopper. Find i such that THIS = NUMB(i)
USE ASSISTANCE !Only for the trace stuff.
INTENT(IN) THIS,NUMB,N !Imply read-only, but definitely no need for any "copy-back".
INTEGER*4 THIS,NUMB(1:*) !Where is THIS in array NUMB(1:N)?
INTEGER N !The count. In other versions, it is supplied by the index.
INTEGER L,R,P !Fingers.
Chop away.
L = 0 !Establish outer bounds.
R = N + 1 !One before, and one after, the first and last.
1 P = (R - L)/2 !Probe point offset. Beware integer overflow with (L + R)/2.
IF (P.LE.0) THEN !Aha! Nowhere! And THIS follows NUMB(L).
FINDI4 = -L !Having -L rather than 0 (or other code) might be of interest.
RETURN !Finished.
END IF !So much for exhaustion.
P = P + L !Convert from offset to probe point.
IF (THIS - NUMB(P)) 3,4,2 !Compare to the probe point.
2 L = P !Shift the left bound up: THIS follows NUMB(P).
GO TO 1 !Another chop.
3 R = P !Shift the right bound down: THIS precedes NUMB(P).
GO TO 1 !Try again.
Caught it! THIS = NUMB(P)
4 FINDI4 = P !So, THIS is found, here!
END FUNCTION FINDI4 !On success, THIS = NUMB(FINDI4); no fancy index here...
END MODULE SORTSEARCH </syntaxhighlight>
There would be a function (with a unique name) for each of the contemplated variations in parameter types, and when the compiler reached an invocation of FIND(...) it would select by matching amongst the combinations that had been defined in the routines named in the INTERFACE statement. The various actual functions could have different code, and in this case, only the <code>INTEGER*4 THIS,NUMB(1:*)</code> need be changed, say to <code>REAL*4 THIS,NUMB(1:*)</code> for FINDF4, which is why both variables are named in the one statement. However, for searching CHARACTER arrays, because the character comparison operations differ from those for numbers (and, no three-way IF-test either), additional changes are required. Thus, function FIND would appear to be a polymorphic function that accepts and returns a variety of types, but it is not, and indeed, there is actually no function called FIND anywhere in the compiled code.
That said, some systems had polymorphic variables, such as the B6700 whereby integers were represented as floating-point numbers and so exactly the same function could be presented with an integer or a floating-point variable (provided the compiler didn't check for parameter type matching - but this was routine) and it would work - so long as no divisions were involved since addition, subtraction, and multiplication are the same for both, but integer division discards any remainders. More recent computers following the Intel 8087 floating-point processor and similar add novel states to the scheme for floating-point arithmetic: not just zero and "gradual underflow" but "Infinity" and "Not a Number", which last violates even more of the axia of mathematics in that ''NaN'' does not equal ''NaN''. In turn, this forces a modicum of polymorphism into the language so as to contend with the additional features, such as the special function IsNaN(x).
More generally, using the same code for different types of variable can be problematical. A scheme that works in single precision may not work in double precision (or ''vice-versa'') or may not give corresponding levels of accuracy, or not converge at all, ''etc.'' While F90 also standardised special functions that give information about the precision of variables and the like, and in principle, a method could be coded that, guided by such information, would work for different precisions, this sort of scheme is beset by all manner of difficulties in problems more complex than the simple examples of text books.
Polymorphism just exacerbates the difficulties, thus, on page 219 of ''16-Bit Modern Microcomputers'' by G. M. Corsline appears the remark "At least some of the generalized numerical solutions to common mathematical procedures have coding that is so involved and tricky in order to take care of all possible roundoff contingencies that they have been termed 'pornographic algorithms'.". And "Mathematical software is easy for the uninitiated to write but notoriously hard for the expert. This paradox exists because the beginner is satisfied if his code usually works in his own machine while the expert attempts, against overwhelming obstacles, to produce programs that always work on a large number of computers. The problem is that while standard formulas of mathematics are fairly easy to translate into FORTRAN they often are subject to instabilities due to roundoff error." - quoting John Palmer, 1980, Intel Corporation.
But sometimes it is not so troublesome, as in [[Pathological_floating_point_problems#The_Chaotic_Bank_Society]] whereby the special EPSILON(x) function that reports on the precision of a nominated variable of type ''x'' is used to determine the point beyond which further calculation (in that precision, for that formula) will make no difference.
Having flexible facilities available my lead one astray. Consider the following data aggregate, as became available with F90: <syntaxhighlight lang="fortran"> TYPE STUFF
INTEGER CODE !A key number.
CHARACTER*6 NAME !Associated data.
INTEGER THIS !etc.
END TYPE STUFF
TYPE(STUFF) TABLE(600) !An array of such entries. </syntaxhighlight>
Suppose the array was in sorted order by each entry's value of CODE so that TABLE(1).CODE <= TABLE(2).CODE, etc. and one wished to find the index of an entry with a specific value, ''x'', of CODE. It is pleasing to be able to write <code>FIND(x,TABLE.CODE,N)</code> and have it accepted by the compiler. Rather less pleasing is that it runs very slowly.
This is because consecutive elements in an array are expected to occupy consecutive locations in storage, but the CODE elements do not, being separated by the other elements of the aggregate. So, the compiler generates code to copy the required elements to a work area, presents that as the actual parameter, and copies from the work area back on return from the function, thereby vitiating the speed advantages of the binary search. This is why the <code>INTENT(IN)</code> might help in such situations, as will writing <code>FIND(x,TABLE(1:N).CODE,N)</code> should N be often less than the full size of the table. But really, in-line code for each such usage is the only answer, despite the lack of a pre-processor to generate it.
Other options are to remain with the older-style of Fortran, using separately-defined arrays having a naming convention such as TABLECODE(600), TABLENAME(600), ''etc''. thus not gaining the unity of declaring a TYPE, or, declaring the size within the type as in <code>INTEGER CODE(600)</code> except that this means that the size is a part of the type and different-sized tables would require different types, or, perhaps the compiler will handle this problem by passing a "stride" value for every array dimension so that subroutines and functions can index such parameters properly - at the cost of yet more overhead for parameter passing, and more complex indexing calculations.
In short, the available polymorphism whereby a parameter can be a normal array, or, an array-like "selection" of a component from an array of compound entities enables appealing syntax, but disasterous performance.
=={{header|Go}}==
The parametric function in this example is the function average. It's type parameter is the interface type intCollection, and its logic uses the polymorphic function mapElements. In Go terminology, average is an ordinary function whose parameter happens to be of interface type. Code inside of average is ordinary code that just happens to call the mapElements method of its parameter. This code accesses the underlying static type only through the interface and so has no knowledge of the details of the static type or even which static type it is dealing with.
Function main creates objects t1 and t2 of two different static types, binaryTree an bTree. Both types implement the interface intCollection.
t1 and t2 have different static types, but when they are passed to average, they are bound to parameter c, of interface type, and their static types are not visible within average.
Implementation of binaryTree and bTree is dummied, but you can see that implementation of average of binaryTree contains code specific to its representation (left, right) and that implementation of bTree contains code specific to its representation (buckets.)
<syntaxhighlight lang="go">package main
import "fmt"
func average(c intCollection) float64 {
var sum, count int
c.mapElements(func(n int) {
sum += n
count++
})
return float64(sum) / float64(count)
}
func main() {
t1 := new(binaryTree)
t2 := new(bTree)
a1 := average(t1)
a2 := average(t2)
fmt.Println("binary tree average:", a1)
fmt.Println("b-tree average:", a2)
}
type intCollection interface {
mapElements(func(int))
}
type binaryTree struct {
// dummy representation details
left, right bool
}
func (t *binaryTree) mapElements(visit func(int)) {
// dummy implementation
if t.left == t.right {
visit(3)
visit(1)
visit(4)
}
}
type bTree struct {
// dummy representation details
buckets int
}
func (t *bTree) mapElements(visit func(int)) {
// dummy implementation
if t.buckets >= 0 {
visit(1)
visit(5)
visit(9)
}
}</syntaxhighlight>
Output:
<pre>
binary tree average: 2.6666666666666665
b-tree average: 5
</pre>
Alternatively, if generics are introduced into Go based on the current design, this is how the C++ example might look if translated to Go:
<syntaxhighlight lang="go">package rosettacode
type Tree(type T) struct {
val T
left *Tree(T)
right *Tree(T)
}
func (t *Tree(T)) ReplaceAll(rep T) {
t.val = rep
if t.left != nil { t.left.ReplaceAll(rep) }
if t.right != nil { t.right.ReplaceAll(rep) }
}</syntaxhighlight>
=={{header|Groovy}}==
{{trans|Java}} (more or less)
Solution:
<syntaxhighlight lang="groovy">class Tree<T> {
T value
Tree<T> left
Tree<T> right
Tree(T value = null, Tree<T> left = null, Tree<T> right = null) {
this.value = value
this.left = left
this.right = right
}
void replaceAll(T value) {
this.value = value
left?.replaceAll(value)
right?.replaceAll(value)
}
}</syntaxhighlight>
=={{header|Haskell}}==
<
mapTree :: (a -> b) -> Tree a -> Tree b
mapTree f Empty = Empty
mapTree f (Node x l r) = Node (f x) (mapTree f l) (mapTree f r)</
<blockquote><small>
Line 231 ⟶ 714:
Note that for the most usefulness in practical programming, a map operation like this should not be defined with a separate name but rather as <code>fmap</code> in an ''instance'' of the <code>Functor</code> ''type class'':
<
fmap f Empty = Empty
fmap f (Node x l r) = Node (f x) (fmap f l) (fmap f r)</
<code>fmap</code> can then be used exactly where <code>mapTree</code> can, but doing this also allows the use of <code>Tree</code>s with other components which are parametric over ''any type which is a Functor''. For example, this function will add 1 to any collection of any kind of number:
<
add1Everywhere nums = fmap (\x -> x + 1) nums</
If we have a tree of integers, i.e. <var>f</var> is <code>Tree</code> and <var>a</var> is <code>Integer</code>, then the type of <code>add1Everywhere</code> is <code>Tree Integer -> Tree Integer</code>.
</small></blockquote>
=={{header|Icon}} and {{header|Unicon}}==
Like PicoLisp, Icon and Unicon are dynamically typed and hence inherently polymorphic.
Here's an example that can apply a function to the nodes in an <i>n</i>-tree regardless of
the type of each node. It is up to the function to decide what to do with a given type
of node. Note that the nodes do no even have to be of the same type.
<syntaxhighlight lang="unicon">procedure main()
bTree := [1, [2, [4, [7]], [5]], [3, [6, [8], [9]]]]
mapTree(bTree, write)
bTree := [1, ["two", ["four", [7]], [5]], [3, ["six", ["eight"], [9]]]]
mapTree(bTree, write)
end
procedure mapTree(tree, f)
every f(\tree[1]) | mapTree(!tree[2:0], f)
end</syntaxhighlight>
=={{header|Inform 7}}==
Phrases (the equivalent of global functions) can be defined with type parameters:
<syntaxhighlight lang="inform7">Polymorphism is a room.
To find (V - K) in (L - list of values of kind K):
repeat with N running from 1 to the number of entries in L:
if entry N in L is V:
say "Found [V] at entry [N] in [L].";
stop;
say "Did not find [V] in [L]."
When play begins:
find "needle" in {"parrot", "needle", "rutabaga"};
find 6 in {2, 3, 4};
end the story.</syntaxhighlight>
Inform 7 does not allow user-defined parametric types. Some built-in types can be parameterized, though:
<syntaxhighlight lang="inform7">list of numbers
relation of texts to rooms
object based rulebook producing a number
description of things
activity on things
number valued property
text valued table column
phrase (text, text) -> number</syntaxhighlight>
=={{header|J}}==
In J, all functions are generic over other types.
Alternatively, J is statically typed in the sense that it supports only one data type (the array), though of course inspecting a value can reveal additional details (such as: is it an array of numbers?)
(That said, note that J also supports some types which are not, strictly speaking, data. These are the verb, adverb and conjunction types. To fit this nomenclature, data is of type "noun". Also, nouns have some additional taxonomy which is beyond the scope of this task.)
=={{header|Java}}==
Following the C++ example:
<
private T value;
private Tree<T> left;
Line 252 ⟶ 787:
public void replaceAll(T value){
this.value = value;
if (left != null)
left.replaceAll(value);
if (right != null)
right.replaceAll(value);
}
}</
=={{header|Julia}}==
{{works with|Julia|1.6}}
<syntaxhighlight lang="julia">module BinaryTrees
mutable struct BinaryTree{V}
v::V
l::Union{BinaryTree{V}, Nothing}
r::Union{BinaryTree{V}, Nothing}
end
BinaryTree(v) = BinaryTree(v, nothing, nothing)
map(f, bt::BinaryTree) = BinaryTree(f(bt.v), map(f, bt.l), map(f, bt.r))
map(f, bt::Nothing) = nothing
let inttree = BinaryTree(
0,
BinaryTree(
1,
BinaryTree(3),
BinaryTree(5),
),
BinaryTree(
2,
BinaryTree(4),
nothing,
),
)
map(x -> 2x^2, inttree)
end
let strtree = BinaryTree(
"hello",
BinaryTree(
"world!",
BinaryTree("Julia"),
nothing,
),
BinaryTree(
"foo",
BinaryTree("bar"),
BinaryTree("baz"),
),
)
map(uppercase, strtree)
end
end</syntaxhighlight>
=={{header|Kotlin}}==
{{trans|C#}}
<syntaxhighlight lang="scala">// version 1.0.6
class BinaryTree<T>(var value: T) {
var left : BinaryTree<T>? = null
var right: BinaryTree<T>? = null
fun <U> map(f: (T) -> U): BinaryTree<U> {
val tree = BinaryTree<U>(f(value))
if (left != null) tree.left = left?.map(f)
if (right != null) tree.right = right?.map(f)
return tree
}
fun showTopThree() = "(${left?.value}, $value, ${right?.value})"
}
fun main(args: Array<String>) {
val b = BinaryTree(6)
b.left = BinaryTree(5)
b.right = BinaryTree(7)
println(b.showTopThree())
val b2 = b.map { it * 10.0 }
println(b2.showTopThree())
}</syntaxhighlight>
{{out}}
<pre>
(5, 6, 7)
(50.0, 60.0, 70.0)
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
The Wolfram language is naturally polymorphic. Function can (generally) accept any type. Here an example to join two lists of with different types and an example of squaring an input:
<syntaxhighlight lang="mathematica">f[a_] := Join[a, a]
f[{1, 2, 3}]
f[{"1", "2", "3"}]
f[{1.1, 2.1, 3.1}]
f[G[1, "a", Pi]]
g[x_] := x^2
g[2]
g[3.5]
g[Pi]
g["a"]</syntaxhighlight>
{{out}}
<pre>{1,2,3,1,2,3}
{1,2,3,1,2,3}
{1.1,2.1,3.1,1.1,2.1,3.1}
G[1,a,\[Pi],1,a,\[Pi]]
4
12.25
\[Pi]^2
(a)^2</pre>
=={{header|Mercury}}==
<syntaxhighlight lang="mercury">:- type tree(A) ---> empty ; node(A, tree(A), tree(A)).
:- func map(func(A) = B, tree(A)) = tree(B).
map(_, empty) = empty.
map(F, node(A, Left, Right)) = node(F(A), map(F, Left), map(F, Right)).</syntaxhighlight>
=={{header|Nim}}==
<syntaxhighlight lang="nim">import strutils, sugar
type Tree[T] = ref object
value: T
left, right: Tree[T]
proc newTree[T](value = default(T)): Tree[T] =
## Create a tree with a single node with the given value.
Tree[T](value: value)
proc map[T, U](tree: Tree[T]; f: (T) -> U): Tree[U] =
## Apply function "f" to each element of a tree, building
## another tree.
result = newTree[U](f(tree.value))
if not tree.left.isNil:
result.left = tree.left.map(f)
if not tree.right.isNil:
result.right = tree.right.map(f)
proc print(tree: Tree; indent = 0) =
## Print a tree.
let start = repeat(' ', indent)
echo start, "value: ", tree.value
if tree.left.isNil:
echo start, " nil"
else:
print(tree.left, indent + 2)
if tree.right.isNil:
echo start, " nil"
else:
print(tree.right, indent + 2)
when isMainModule:
echo "Initial tree:"
var tree = newTree[int](5)
tree.left = newTree[int](2)
tree.right = newTree[int](7)
print(tree)
echo ""
echo "Tree created by applying a function to each node:"
let tree1 = tree.map((x) => 1 / x)
print(tree1)</syntaxhighlight>
{{out}}
<pre>Initial tree:
value: 5
value: 2
nil
nil
value: 7
nil
nil
Tree created by applying a function to each node:
value: 0.2
value: 0.5
nil
nil
value: 0.1428571428571428
nil
nil</pre>
=={{header|Objective-C}}==
{{trans|C++}}
{{works with|Xcode|7}}
<syntaxhighlight lang="objc">@interface Tree<T> : NSObject {
T value;
Tree<T> *left;
Tree<T> *right;
}
- (void)replaceAll:(T)v;
@end
@implementation Tree
- (void)replaceAll:(id)v {
value = v;
[left replaceAll:v];
[right replaceAll:v];
}
@end</syntaxhighlight>
Note that the generic type variable is only used in the declaration, but not in the implementation.
=={{header|OCaml}}==
<
(** val map_tree : ('a -> 'b) -> 'a tree -> 'b tree *)
let rec map_tree f = function
| Empty -> Empty
| Node (x,l,r) -> Node (f x, map_tree f l, map_tree f r)</
{{omit from|Oforth|Oforth is nt statically-typed language}}
=={{header|Phix}}==
Phix is naturally polymorphic, with optional static typing.<br>
The standard builtin type hierarcy is trivial:
<pre>
<-------- object --------->
| |
+-atom +-sequence
| |
+-integer +-string
</pre>
User defined types are subclasses of those.<br>
If you declare a parameter as type integer then obviously it is optimised for that, and crashes when given something else (with a clear human-readable message and file name/line number).
If you declare a parameter as type object then it can handle anything you can throw at it - integers, floats, strings, or (deeply) nested sequences.<br>
Of course many builtin routines are naturally generic, such as sort and print.<br>
Most programming languages would throw a hissy fit if you tried to sort (or print) a mixed collection of strings and integers, but not Phix:
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">shuffle</span><span style="color: #0000FF;">({</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"oranges"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"apples"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">}))</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{5,6,7,"apples","oranges"}
</pre>
For comparison purposes (and because this entry looked a bit sparse without it) this is the D example from this page translated to Phix.<br>
Note that tmap has to be a function rather than a procedure with a reference parameter, but this still achieves
pass-by-reference/in-situ updates, mainly because root is a local rather than global/static, and is the target of
(aka assigned to/overwritten on return from) the top-level tmap() call, and yet also manages the C#/Dart/Kotlin
thing (by which I am referring to those specific examples on this page) of creating a whole new tree, simply
because lhs assignee!=rhs reference (aka root2!=root) in "root2 = tmap(root,rid)", not that such a "deep clone"
would (barring a few dirty low-level tricks) behave any differently to "root2=root", which is "a straightforward shared reference
with cow semantics". Aside: this example lost a little bit of it's charm when the deep_copy() had to go in to make it pwa/p2js compatible, which has somewhat negated the previous sentence, but that was happening implicitly anyway, and the depths of 1 (ie ",1" on the deep_copy()) retain similar efficiency.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">data</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">left</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">right</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">tmap</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">rid</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">data</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rid</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">data</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">left</span><span style="color: #0000FF;">]!=</span><span style="color: #004600;">null</span> <span style="color: #008080;">then</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">left</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmap</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">left</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">rid</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">right</span><span style="color: #0000FF;">]!=</span><span style="color: #004600;">null</span> <span style="color: #008080;">then</span> <span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">right</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmap</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tree</span><span style="color: #0000FF;">[</span><span style="color: #000000;">right</span><span style="color: #0000FF;">],</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">rid</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">tree</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">v</span><span style="color: #0000FF;">,</span><span style="color: #004600;">null</span><span style="color: #0000FF;">,</span><span style="color: #004600;">null</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">add10</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">10</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.00</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Add some nodes.</span>
<span style="color: #000000;">root</span><span style="color: #0000FF;">[</span><span style="color: #000000;">left</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.10</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">root</span><span style="color: #0000FF;">[</span><span style="color: #000000;">left</span><span style="color: #0000FF;">][</span><span style="color: #000000;">left</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.11</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">root</span><span style="color: #0000FF;">[</span><span style="color: #000000;">left</span><span style="color: #0000FF;">][</span><span style="color: #000000;">right</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.12</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">root</span><span style="color: #0000FF;">[</span><span style="color: #000000;">right</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.20</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">root</span><span style="color: #0000FF;">[</span><span style="color: #000000;">right</span><span style="color: #0000FF;">][</span><span style="color: #000000;">left</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.21</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">root</span><span style="color: #0000FF;">[</span><span style="color: #000000;">right</span><span style="color: #0000FF;">][</span><span style="color: #000000;">right</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newnode</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1.22</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Now the tree has seven nodes.
-- Show the whole tree.</span>
<span style="color: #7060A8;">ppOpt</span><span style="color: #0000FF;">({</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Modify the whole tree.</span>
<span style="color: #000000;">root</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmap</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">,</span><span style="color: #000000;">add10</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Create a whole new tree.</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">root2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tmap</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span><span style="color: #000000;">newnode</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Show the whole tree again.</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">root</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{1,
{1.1,
{1.11,0,0},
{1.12,0,0}},
{1.2,
{1.21,0,0},
{1.22,0,0}}}
{11,
{11.1,
{11.11,0,0},
{11.12,0,0}},
{11.2,
{11.21,0,0},
{11.22,0,0}}}
</pre>
=={{header|PicoLisp}}==
PicoLisp is dynamically-typed, so in principle every function is polymetric over its arguments. It is up to the function to decide what to do with them. A function traversing a tree, modifying the nodes in-place (no matter what the type of the node is):
<syntaxhighlight lang="picolisp">(de mapTree (Tree Fun)
(set Tree (Fun (car Tree)))
(and (cadr Tree) (mapTree @ Fun))
(and (cddr Tree) (mapTree @ Fun)) )</syntaxhighlight>
Test:
<pre style="height:20em;overflow:scroll">(balance 'MyTree (range 1 7)) # Create a tree of numbers
-> NIL
: (view MyTree T) # Display it
7
6
5
4
3
2
1
-> NIL
: (mapTree MyTree inc) # Increment all nodes
-> NIL
: (view MyTree T) # Display the tree
8
7
6
5
4
3
2
-> NIL
: (balance 'MyTree '("a" "b" "c" "d" "e" "f" "g")) # Create a tree of strings
-> NIL
: (view MyTree T) # Display it
"g"
"f"
"e"
"d"
"c"
"b"
"a"
-> NIL
: (mapTree MyTree uppc) # Convert all nodes to upper case
-> NIL
: (view MyTree T) # Display the tree
"G"
"F"
"E"
"D"
"C"
"B"
"A"
-> NIL</pre>
=={{header|Prolog}}==
{{works with|SWI Prolog}}
SWI-Prolog does not support object-oriented programming, but we can simulate it.
<syntaxhighlight lang="prolog">% Tree Definition
tree(leaf(_)).
tree(branch(Left, Right)) :- tree(Left), tree(Right).
% Definition of the addone function
addone(X, Y) :- Y is X + 1.
% Definition of treewalk
treewalk(leaf(Value), Func, leaf(NewValue)) :- call(Func, Value, NewValue).
treewalk(branch(Left, Right), Func, branch(NewLeft, NewRight)) :-
treewalk(Left, Func, NewLeft),
treewalk(Right, Func, NewRight).
% Execution
run :-
X = branch(leaf(2), branch(leaf(3),leaf(4))),
treewalk(X, addone, Y),
write(Y).</syntaxhighlight>
=={{header|Racket}}==
Typed Racket has parametric polymorphism:
<syntaxhighlight lang="racket">
#lang typed/racket
(define-type (Tree A) (U False (Node A)))
(struct: (A) Node
([val : A] [left : (Tree A)] [right : (Tree A)])
#:transparent)
(: tree-map (All (A B) (A -> B) (Tree A) -> (Tree B)))
(define (tree-map f tree)
(match tree
[#f #f]
[(Node val left right)
(Node (f val) (tree-map f left) (tree-map f right))]))
;; unit tests
(require typed/rackunit)
(check-equal?
(tree-map add1 (Node 5 (Node 3 #f #f) #f))
(Node 6 (Node 4 #f #f) #f))
</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2020.08.1}}
<syntaxhighlight lang="raku" line>role BinaryTree[::T] {
has T $.value;
has BinaryTree[T] $.left;
has BinaryTree[T] $.right;
method replace-all(T $value) {
$!value = $value;
$!left.replace-all($value) if $!left.defined;
$!right.replace-all($value) if $!right.defined;
}
}
class IntTree does BinaryTree[Int] { }
my IntTree $it .= new(value => 1,
left => IntTree.new(value => 2),
right => IntTree.new(value => 3));
$it.replace-all(42);
say $it;</syntaxhighlight>
{{out}}
<pre>IntTree.new(value => 42, left => IntTree.new(value => 42, left => BinaryTree[T], right => BinaryTree[T]), right => IntTree.new(value => 42, left => BinaryTree[T], right => BinaryTree[T]))</pre>
=={{header|REXX}}==
This REXX programming example is modeled after the '''D''' example.
<syntaxhighlight lang="rexx">/*REXX program demonstrates (with displays) a method of parametric polymorphism. */
call newRoot 1.00, 3 /*new root, and also indicate 3 stems.*/
/* [↓] no need to label the stems. */
call addStem 1.10 /*a new stem and its initial value. */
call addStem 1.11 /*" " " " " " " */
call addStem 1.12 /*" " " " " " " */
call addStem 1.20 /*" " " " " " " */
call addStem 1.21 /*" " " " " " " */
call addStem 1.22 /*" " " " " " " */
call sayNodes /*display some nicely formatted values.*/
call modRoot 50 /*modRoot will add fifty to all stems. */
call sayNodes /*display some nicely formatted values.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
addStem: nodes= nodes + 1; do j=1 for stems; root.nodes.j= arg(1); end; return
newRoot: parse arg @,stems; nodes= -1; call addStem copies('═',9); call addStem @; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
modRoot: arg #; do j=1 for nodes /*traipse through all the defined nodes*/
do k=1 for stems /*add bias ──►───────────────────────┐ */
if datatype(root.j.k, 'N') then root.j.k= root.j.k + # /* ◄───┘ */
end /*k*/ /* [↑] add if stem value is numeric.*/
end /*j*/
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
sayNodes: w= 9; do j=0 to nodes; _= /*ensure each of the nodes gets shown. */
do k=1 for stems; _= _ center(root.j.k, w) /*concatenate a node.*/
end /*k*/
$= word('node='j, 1 + (j<1) ) /*define a label for this line's output*/
say center($, w) substr(_, 2) /*ignore 1st (leading) blank which was */
end /*j*/ /* [↑] caused by concatenation.*/
say /*show a blank line to separate outputs*/
return</syntaxhighlight>
{{out|output|text= when using the default input:}}
<pre>
═════════ ═════════ ═════════
node=1 1.00 1.00 1.00
node=2 1.10 1.10 1.10
node=3 1.11 1.11 1.11
node=4 1.12 1.12 1.12
node=5 1.20 1.20 1.20
node=6 1.21 1.21 1.21
node=7 1.22 1.22 1.22
═════════ ═════════ ═════════
node=1 51.00 51.00 51.00
node=2 51.10 51.10 51.10
node=3 51.11 51.11 51.11
node=4 51.12 51.12 51.12
node=5 51.20 51.20 51.20
node=6 51.21 51.21 51.21
node=7 51.22 51.22 51.22
</pre>
=={{header|Rust}}==
<syntaxhighlight lang="rust">struct TreeNode<T> {
value: T,
left: Option<Box<TreeNode<T>>>,
right: Option<Box<TreeNode<T>>>,
}
impl <T> TreeNode<T> {
fn my_map<U,F>(&self, f: &F) -> TreeNode<U> where
F: Fn(&T) -> U {
TreeNode {
value: f(&self.value),
left: match self.left {
None => None,
Some(ref n) => Some(Box::new(n.my_map(f))),
},
right: match self.right {
None => None,
Some(ref n) => Some(Box::new(n.my_map(f))),
},
}
}
}
fn main() {
let root = TreeNode {
value: 3,
left: Some(Box::new(TreeNode {
value: 55,
left: None,
right: None,
})),
right: Some(Box::new(TreeNode {
value: 234,
left: Some(Box::new(TreeNode {
value: 0,
left: None,
right: None,
})),
right: None,
})),
};
root.my_map(&|x| { println!("{}" , x)});
println!("---------------");
let new_root = root.my_map(&|x| *x as f64 * 333.333f64);
new_root.my_map(&|x| { println!("{}" , x) });
}</syntaxhighlight>
=={{header|Scala}}==
Line 273 ⟶ 1,343:
the example in question:
<
def map[B](f: A => B): Tree[B] =
Tree(f(value), left map (_.map(f)), right map (_.map(f)))
}</
Note that the type parameter of the class <tt>Tree</tt>, <tt>[+A]</tt>. The
Line 282 ⟶ 1,352:
will be a subtype of <tt>Tree[Y]</tt> if <tt>X</tt> is a subtype of <tt>Y</tt>. For example:
<
class Manager(name: String) extends Employee(name)
val t = Tree(new Manager("PHB"), None, None)
val t2: Tree[Employee] = t</
The second assignment is legal because <tt>t</tt> is of type <tt>Tree[Manager]</tt>, and since
Line 294 ⟶ 1,364:
Another possible variance is the ''contra-variance''. For instance, consider the following example:
<
val treeOfNames = t.map(toName)</
This works, even though <tt>map</tt> is expecting a function from <tt>Manager</tt> into something,
Line 302 ⟶ 1,372:
definition in Scala:
<
The minus sign indicates that this trait is ''contra-variant'' in <tt>T1</tt>, which happens to be
Line 313 ⟶ 1,383:
Let's add another method to <tt>Tree</tt> to see another concept:
<
def map[B](f: A => B): Tree[B] =
Tree(f(value), left map (_.map(f)), right map (_.map(f)))
def find[B >: A](what: B): Boolean =
(value == what) || left.map(_.find(what)).getOrElse(false) || right.map(_.find(what)).getOrElse(false)
}</
The type parameter of <tt>find</tt> is <tt>[B >: A]</tt>. That means the type is some <tt>B</tt>, as long
Line 324 ⟶ 1,394:
accept it. To understand why, let's consider the following code:
<
println("Call Catbert!")</
Here we have <tt>find</tt> receiving an argument of type <tt>Employee</tt>, even though the tree
Line 336 ⟶ 1,406:
to be defined when a class is inherited. One simple example would be:
<
type Element
val map = new collection.mutable.HashMap[Element, DFA]()
}</
A concrete class wishing to inherit from <tt>DFA</tt> would need to define <tt>Element</tt>. Abstract
Line 346 ⟶ 1,416:
(instantiation of the concrete class). The difference is mainly one of style, though.
=={{header|
In Seed7 types like ''array'' and ''struct'' are not built-in, but are defined with parametric polymorphism.
In the Seed7 documentation the terms "template" and "function with type parameters and type result" are used instead of "parametric polymorphism".
E.g.: ''array'' is actually a function, which takes an element type as parameter and returns a type.
To concentrate on the essentials, the example below defines the type ''container'' as ''array''.
Note that the ''map'' function has three parameters: ''aContainer'', ''aVariable'', and ''aFunc''.
When ''map'' is called ''aVariable'' is used also in the actual parameter of ''aFunc'': map(container1, num, num + 1)
<syntaxhighlight lang="seed7">$ include "seed7_05.s7i";
const func type: container (in type: elemType) is func
result
var type: container is void;
begin
container := array elemType;
global
const func container: map (in container: aContainer,
inout elemType: aVariable, ref func elemType: aFunc) is func
result
var container: mapResult is container.value;
begin
for aVariable range aContainer do
mapResult &:= aFunc;
end for;
end func;
end global;
end func;
const type: intContainer is container(integer);
var intContainer: container1 is [] (1, 2, 4, 6, 10, 12, 16, 18, 22);
var intContainer: container2 is 0 times 0;
const proc: main is func
local
var integer: num is 0;
begin
container2 := map(container1, num, num + 1);
for num range container2 do
write(num <& " ");
end for;
writeln;
end func;</syntaxhighlight>
Output:
<pre>
2 3 5 7 11 13 17 19 23
</pre>
=={{header|Standard ML}}==
<syntaxhighlight lang="sml">datatype 'a tree = Empty | Node of 'a * 'a tree * 'a tree
(** val map_tree = fn : ('a -> 'b) -> 'a tree -> 'b tree *)
fun map_tree f Empty = Empty
| map_tree f (Node (x,l,r)) = Node (f x, map_tree f l, map_tree f r)</
=={{header|Swift}}==
{{trans|Java}}
<syntaxhighlight lang="swift">class Tree<T> {
var value: T?
var left: Tree<T>?
var right: Tree<T>?
func replaceAll(value: T?) {
self.value = value
left?.replaceAll(value)
right?.replaceAll(value)
}
}</syntaxhighlight>
Another version based on Algebraic Data Types:
{{works with|Swift|2+}}
<syntaxhighlight lang="swift">enum Tree<T> {
case Empty
indirect case Node(T, Tree<T>, Tree<T>)
func map<U>(f : T -> U) -> Tree<U> {
switch(self) {
case .Empty : return .Empty
case let .Node(x, l, r): return .Node(f(x), l.map(f), r.map(f))
}
}
}</syntaxhighlight>
=={{header|Ursala}}==
Line 358 ⟶ 1,506:
routinely. A parameterized binary tree type can be defined using a syntax for anonymous
recursion in type expressions as in this example,
<
or by way of a recurrence solved using a fixed point combinator imported from a library
as shown below.
<
#fix general_type_fixer 1
binary_tree_of "node-type" = ("node-type",(binary_tree_of "node-type")%Z)%drWZwlwAZ</
(The <code>%Z</code> type operator constructs a "maybe" type, i.e., the free union of its operand type
with the null value. Others shown above are standard stack manipulation primitives, e.g. <code>d</code> (dup) and <code>w</code> (swap), used to build the type expression tree.) At the other extreme, one may construct an equivalent parameterized type in
point-free form.
<
A mapping combinator over this type can be defined with pattern matching like this
<
or in point free form like this.
<
Here is a test program
defining a type of binary trees of strings, and a function that concatenates each node
with itself.
<
x = 'foo': ('bar': (),'baz': ())
Line 383 ⟶ 1,531:
#cast string_tree
example = (binary_tree_map "s". "s"--"s") x</
Type signatures are not necessarily associated with function declarations, but
have uses in the other contexts such as assertions and compiler directives
(e.g., <code>#cast</code>). Here is the output.
<pre>
'foofoo': ('barbar': (),'bazbaz': ())
</pre>
=={{header|Visual Basic .NET}}==
{{trans|C# modern version}}
<syntaxhighlight lang="vbnet">Class BinaryTree(Of T)
ReadOnly Property Left As BinaryTree(Of T)
ReadOnly Property Right As BinaryTree(Of T)
ReadOnly Property Value As T
Sub New(value As T, Optional left As BinaryTree(Of T) = Nothing, Optional right As BinaryTree(Of T) = Nothing)
Me.Value = value
Me.Left = left
Me.Right = right
End Sub
Function Map(Of U)(f As Func(Of T, U)) As BinaryTree(Of U)
Return New BinaryTree(Of U)(f(Me.Value), Me.Left?.Map(f), Me.Right?.Map(f))
End Function
Overrides Function ToString() As String
Dim sb As New Text.StringBuilder()
Me.ToString(sb, 0)
Return sb.ToString()
End Function
Private Overloads Sub ToString(sb As Text.StringBuilder, depth As Integer)
sb.Append(New String(ChrW(AscW(vbTab)), depth))
sb.AppendLine(Me.Value?.ToString())
Me.Left?.ToString(sb, depth + 1)
Me.Right?.ToString(sb, depth + 1)
End Sub
End Class
Module Program
Sub Main()
Dim b As New BinaryTree(Of Integer)(6, New BinaryTree(Of Integer)(5), New BinaryTree(Of Integer)(7))
Dim b2 As BinaryTree(Of Double) = b.Map(Function(x) x * 0.5)
Console.WriteLine(b)
Console.WriteLine(b2)
End Sub
End Module</syntaxhighlight>
{{out}}
<pre>6
5
7
3
2.5
3.5</pre>
=={{header|Visual Prolog}}==
<syntaxhighlight lang="prolog">
domains
tree{Type} = branch(tree{Type} Left, tree{Type} Right); leaf(Type Value).
class predicates
treewalk : (tree{X},function{X,Y}) -> tree{Y} procedure (i,i).
clauses
treewalk(branch(Left,Right),Func) = branch(NewLeft,NewRight) :-
NewLeft = treewalk(Left,Func), NewRight = treewalk(Right,Func).
treewalk(leaf(Value),Func) = leaf(X) :-
X = Func(Value).
run():-
init(),
X = branch(leaf(2), branch(leaf(3),leaf(4))),
Y = treewalk(X,addone),
write(Y),
succeed().
</syntaxhighlight>
=={{header|Wren}}==
{{trans|Kotlin}}
Wren is dynamically type and so doesn't have parametric polymorphism (PP) as such; in a sense every method or function is polymorphic over its parameters.
However, that doesn't mean that type safety is unimportant and, in the case of a Binary Tree, we'd generally want all its nodes to contain values of the same type.
Fortunately, we can simulate PP by passing an extra parameter to a collection class's contructor to specify the type of values to be used for that particular instantiation. We can then use this to guard against the wrong type of values being passed to the class's other methods.
<syntaxhighlight lang="wren">class BinaryTree {
construct new(T, value) {
if (!(T is Class)) Fiber.abort ("T must be a class.")
if (value.type != T) Fiber.abort("Value must be of type T.")
_kind = T
_value = value
_left = null
_right = null
}
// constructor overload to enable kind to be inferred from type of value
static new (value) { new(value.type, value) }
kind { _kind }
value { _value}
value=(v) {
if (v.type != _kind) Fiber.abort("Value must be of type %(_kind)")
_value = v
}
left { _left }
right { _right }
left=(b) {
if (b.type != BinaryTree || b.kind != _kind) {
Fiber.abort("Argument must be a BinaryTree of type %(_kind)")
}
_left = b
}
right=(b) {
if (b.type != BinaryTree || b.kind != _kind) {
Fiber.abort("Argument must be a BinaryTree of type %(_kind)")
}
_right = b
}
map(f) {
var tree = BinaryTree.new(f.call(_value))
if (_left) tree.left = left.map(f)
if (_right) tree.right = right.map(f)
return tree
}
showTopThree() { "(%(left.value), %(value), %(right.value))" }
}
var b = BinaryTree.new(6)
b.left = BinaryTree.new(5)
b.right = BinaryTree.new(7)
System.print(b.showTopThree())
var b2 = b.map{ |i| i * 10 }
System.print(b2.showTopThree())
b2.value = "six" // generates an error because "six" is not a Num</syntaxhighlight>
{{out}}
<pre>
(5, 6, 7)
(50, 60, 70)
Value must be of type Num
[./parametric_polymorphism line 17] in value=(_)
[./parametric_polymorphism line 53] in (script)
</pre>
{{omit from|Axe}}
{{omit from|Bc|no types in bc}}
{{omit from|C|no type variables in stdc}}
{{omit from|C|no type variables}}
{{omit from|Dc|no types in dc}}
{{omit from|Factor|not statically typed}}
{{omit from|J|not statically typed}}
{{omit from|JavaScript|not statically typed}}
{{omit from|M4|not typed}}
{{omit from|Maxima}}
{{omit from|Oz|not statically typed}}
{{omit from|Perl|not statically typed}}
{{omit from|Python|not statically typed}}
Line 401 ⟶ 1,705:
{{omit from|TI-83 BASIC|Does not have static or user-defined types.}}
{{omit from|TI-89 BASIC|Does not have static or user-defined types.}}
{{omit from|LaTeX}}
{{omit from|Retro|typeless}}
{{omit from|VBA|the Variant type is available.}}
{{omit from|zkl|typeless}}
| |||