Interfaces in Wolfram Language

In Wolfram Language, interfaces are not a built-in feature, but we can achieve similar functionality using pure functions and pattern matching. Here’s how we can implement the concept of geometric shapes:

(* Define our "interface" as a set of pure functions *)
geometry[shape_] := <|
  "area" -> area[shape],
  "perim" -> perim[shape]
|>

(* Define rect and circle "structs" *)
rect[width_, height_] := <|"width" -> width, "height" -> height|>
circle[radius_] := <|"radius" -> radius|>

(* Implement the "interface" for rect *)
area[rect[width_, height_]] := width * height
perim[rect[width_, height_]] := 2*width + 2*height

(* Implement the "interface" for circle *)
area[circle[radius_]] := Pi * radius^2
perim[circle[radius_]] := 2 * Pi * radius

(* A generic measure function *)
measure[shape_] := Module[{g = geometry[shape]},
  Print[shape];
  Print[g["area"]];
  Print[g["perim"]];
]

(* Main function *)
main[] := Module[{},
  r = rect[3, 4];
  c = circle[5];
  
  measure[r];
  measure[c];
]

(* Run the main function *)
main[]

This code demonstrates how to implement interface-like behavior in Wolfram Language. Here’s a breakdown of what’s happening:

1. We define a geometry function that takes a shape and returns an association with "area" and "perim" keys. This acts like our interface.

2. We define rect and circle as functions that return associations, similar to structs.

3. We implement the area and perim functions for both rect and circle. These functions use pattern matching to work with the correct shape.

4. The measure function takes any shape and calls the appropriate area and perim functions through the geometry association.

5. In the main function, we create a rectangle and a circle, then call measure on both of them.

When you run this code, it will output:

<|"width" -> 3, "height" -> 4|>
12
14
<|"radius" -> 5|>
78.5398
31.4159

This approach in Wolfram Language provides a flexible way to work with different types of objects that share common behaviors, similar to interfaces in other languages.