Functional Composition with JavaScript: The compose Function

Functional programming emphasizes composing smaller, reusable functions to build more complex logic. The compose function is a core concept in this paradigm, allowing you to chain functions together so that the output of one becomes the input of the next. This challenge asks you to implement a compose function in JavaScript, a powerful tool for creating clean and maintainable code.

Problem Description

You are tasked with creating a compose function that takes a variable number of functions as arguments and returns a single function. This returned function, when invoked, should execute the input functions from right to left (i.e., the last function passed to compose is executed first). The output of each function becomes the input for the next function in the chain.

Key Requirements:

• Variable Arguments: The compose function must accept any number of functions as arguments.
• Right-to-Left Execution: Functions must be executed in reverse order of their appearance in the argument list.
• Function Compatibility: The output type of one function must be compatible with the input type of the next function in the chain.
• Return a Function: compose should return a new function, not execute the functions immediately.
• No Side Effects: The composed function should ideally avoid side effects.

Expected Behavior:

When called with functions f, g, and h, compose(h, g, f) should return a function that, when invoked with an argument x, behaves as follows: h(g(f(x))).

Edge Cases to Consider:

• No Functions: What should happen if compose is called with no arguments? Return a function that returns its input.
• Single Function: What should happen if compose is called with only one function? Return that function.
• Functions with No Arguments: Handle functions that don't require any arguments.
• Error Handling: While not strictly required, consider how you might handle cases where the output of one function is not compatible with the input of the next. (This can be left out for a simpler solution).

Examples

Example 1:

Input: compose(addOne, double, square)
Output: function(x) { return square(double(addOne(x))); }
Explanation: The returned function takes an input `x`, adds 1 to it, doubles the result, and then squares the final value.

// Where:
// addOne(x) => x + 1
// double(x) => x * 2
// square(x) => x * x

Example 2:

Input: compose(identity)
Output: function(x) { return x; }
Explanation: If only one function (the identity function) is passed, the compose function returns that function.

// Where:
// identity(x) => x

Example 3:

Input: compose()
Output: function(x) { return x; }
Explanation: If no functions are passed, the compose function returns the identity function.

Constraints

• Input Functions: Each function passed to compose must accept a single argument and return a single value.
• Number of Functions: The compose function can accept up to 10 functions as arguments. (This is a practical limit to avoid excessive complexity).
• Performance: The solution should be reasonably efficient. Avoid unnecessary iterations or complex data structures.
• JavaScript Environment: The code should be compatible with modern JavaScript environments (ES6+).

Notes

• Consider using the apply or call methods to invoke functions with specific arguments.
• Think about how to handle the arguments passed to the composed function.
• The core idea is to build a chain of function calls, ensuring that the output of one function is used as the input for the next.
• Focus on clarity and readability in your code. Well-commented code is a plus.