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).


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)



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.