What is the difference between a partial and total function in functional programming?

1 Total functions

A total function is a function that is defined for every possible input in its domain, and always returns a valid output in its range. For example, the function f(x) = x + 1 is a total function, because it can take any number as input and return another number as output. Total functions are desirable in functional programming, because they guarantee that the program will not crash or produce unexpected results due to undefined or invalid inputs.

3 How to avoid partial functions

One way to avoid partial functions is to use pattern matching, which is a technique that allows you to specify different cases for different inputs, and handle them accordingly. For example, you can rewrite the function g(x) = 1 / x as g(0) = undefined and g(x) = 1 / x for x != 0. This way, you explicitly define what the function does for every possible input, and avoid the division by zero error.

Another way to avoid partial functions is to use option types, which are types that can either hold a value or indicate the absence of a value. For example, you can rewrite the function g(x) = 1 / x as g(x) = Some(1 / x) for x != 0 and g(x) = None for x = 0. This way, you wrap the output in a container that can be checked for validity, and avoid the division by zero error.

4 The benefits of total functions

Using total functions instead of partial functions has several benefits for functional programming. First, it improves the readability and maintainability of the code, because it makes the function's behavior clear and consistent for every input. Second, it enhances the testability and correctness of the code, because it reduces the number of possible errors and edge cases that need to be handled. Third, it supports the composability and modularity of the code, because it allows the function to be easily combined with other functions without worrying about compatibility or compatibility issues.

5 The challenges of total functions

Using total functions instead of partial functions also has some challenges for functional programming. First, it may require more effort and creativity to design and implement total functions, especially for complex or recursive problems. Second, it may impose some limitations or trade-offs on the performance or efficiency of the code, especially for problems that involve infinite or unbounded inputs or outputs. Third, it may not always be possible or practical to use total functions, especially for problems that involve external or impure sources of data or effects.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?