Discuss Lua's error handling mechanism and the different types of exceptions that can occur during program execution. Provide an example of how to handle an exception in Lua.

Lua provides a robust error handling mechanism that allows programmers to handle exceptions and errors that may occur during program execution. The error handling mechanism in Lua revolves around the concept of error propagation using the `pcall` function, which stands for "protected call." This mechanism helps prevent program crashes and allows for graceful handling of errors.

In Lua, there are two types of exceptions that can occur during program execution:

1. Runtime Errors:
Runtime errors are unexpected errors that occur during the execution of Lua code. These errors can be caused by various factors, such as invalid operations, calling nonexistent functions, dividing by zero, or referencing nil values. Examples of runtime errors include "attempt to perform arithmetic on a nil value" or "attempt to call a nil value."
2. User-Defined Errors:
User-defined errors are errors intentionally thrown by the programmer to signal exceptional conditions in the code. These errors can be used to handle specific cases, such as invalid input, file not found, or any other custom error condition that needs to be communicated.

To handle exceptions and errors in Lua, the `pcall` function is used. The `pcall` function attempts to execute a given function and captures any errors that occur during its execution. If an error occurs, `pcall` returns `false` as the first result and the error message as the second result. If the function executes successfully without any errors, `pcall` returns `true` as the first result, followed by the function's return values.

Here's an example that demonstrates how to handle an exception in Lua using `pcall`:

```
lua`-- Define a function that may throw an error
local function divide(a, b)
if b == 0 then
error("Division by zero is not allowed.")
end
return a / b
end

-- Attempt to call the function using pcall
local success, result = pcall(divide, 10, 0)

-- Check if the function call was successful
if success then
print("Result:", result)
else
print("Error:", result)
end`
```
In this example, we define a function `divide` that takes two arguments and performs division. Inside the function, we check if the second argument `b` is zero. If it is, we intentionally throw an error using the `error` function.

To handle the exception, we use `pcall` to call the `divide` function with the arguments 10 and 0. The results of the `pcall` are captured in `success` and `result` variables. If the function executes without errors, `success` will be `true`, and the result will contain the division result. However, if an error occurs, `success` will be `false`, and `result` will contain the error message.

We then check the value of `success` to determine if the function call was successful. If it is, we print the division result. Otherwise, we print the error message.

By using the `pcall` function, Lua allows for controlled error handling, preventing program crashes and providing an opportunity to handle errors gracefully. This mechanism enables programmers to take appropriate actions when exceptions occur, ensuring the stability and reliability of Lua programs.