# Factorial

In this chapter we will implement factorial using the Tortuga Programming Language. In mathematics, the `factorial` of a non-negative integer `n`, denoted by `n!`, is the product of all positive integers less than or equal to `n`. The factorial of `n` also equals the product of `n` with the next smaller factorial. The factorial of `0` is equal to `1` (i.e., `0! = 1`).

## Implementation

All numbers in the Tortuga Programming Language are signed real numbers. Since factorial is only defined for non-negative integers, our implementation will round all real numbers to their nearest integer and report an error for non-negative numbers.

## Copy & Paste

Create a file named `factorial.ta` with the following contents:

``````round(n) = round(n, n % 1)
round(n, remainder) ? (remainder >= 0.5) = 1 + n - (n % 1)
round(n, remainder) ? (remainder < 0.5) = n - (n % 1)

; base case
factorial(n) ? (n = 0) = 1

; factorial
; inductive case
factorial(n) ? (n > 0) = [
i = round(n)
i * factorial(i - 1)
]

factorial(9)
``````

## Run

To run the file use the command-line interface from your favorite terminal:

``````tortuga run factorial.ta
``````

You should see the value `362880` printed to your terminal. The Tortuga Programming Language automatically prints the value of the last expression in a program.