Examples:

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Examples:

Yup, 33 bytes

*{{:0e-}-0]~{~|~|0~--e~}0~--#\}1#

node yup.js -l "*{{:0e-}-0]~{~|~|0~--e~}0~--#\}1#" -n <input>

λ node yup.js -l "*{{:0e-}-0]~{~|~|0~--e~}0~--#\}1#" -n 5
120
λ node yup.js examples\factorial.yup -n 0
1

To come.

Yup, 33 31 29 bytes

*{{:0e-}]~{~|~|0~--e~}~#\}0e#

node yup.js -l "*{{:0e-}]~{~|~|0~--e~}~#\}0e#" -n <input>

λ node yup.js -l "*{{:0e-}]~{~|~|0~--e~}~#\}0e#" -n 5
120
λ node yup.js examples\factorial.yup -n 0
1

*{{:0e-}]~{~|~|0~--e~}~#\}0e#
*                              ` take input
 {                       }     ` while TOS -- if zero, we advance to the }
                          0e#  ` print number 1 (exp(0))
                               ` otherwise (nonzero)
  {    }                       ` while TOS is not zero
   :                           ` duplicate TOS
    0                          ` push 0
     e                         ` pop 0, push exp(0) = 1
      -                        ` subtract 1
                               ` we eventually are at zero.
        ]                      ` we move that zero to the bottom of the stack
         ~                     ` switch top two for looping offset
          {~        ~}         ` while STOS
            |~|0~--e           ` multiply two elements (see further down)
                      ~        ` switch the top zero with the result
                       #       ` print the result
                        \      ` exit program (so we don't print the final one)

Multiplication

In this program, I have multiplication defined as thus:

|~|0~--e

First, observe 0~--. This pushes a zero behind the TOS, and subtracts twice:

command | stack
        | a b
0       | a b 0
~       | a 0 b
-       | a (-b)
-       | a - (-b) = a + b

This performs addition. Let's replace 0~-- with + for clarity:

|~|+e

Now, | is ln. So watch the stack:

command | stack
        | a b
|       | a ln(b)
~       | ln(b) a
|       | ln(b) ln(a)
+       | (ln(b)+ln(a))
e       | exp(ln(b)+ln(a))

And, by the theorem of logarithms, this is multiplication.

Yup, 43 + 7 = 50 bytes (noncompeting)

0~--=+;|~|+e=x;0e=1;*{{:0e-}-0]~{~x~}+#\}1#

+7 bytes for the -cheat flag. I wasn't going to make this easy! Here's the github. Invoke like this:

node yup.js -cheat <location>.yup -n <input>

Or

node yup.js -cheat -l "0~--=+;|~|+e=x;0e=1;*{{:0e-}-0]~{~x~}+#\}1#" -n <input>

Examples:

λ node yup.js -cheat -l "0~--=+;|~|+e=x;0e=1;*{{:0e-}-0]~{~x~}+#\}1#" -n 5
120
λ node yup.js -cheat examples\factorial.yup -n 0
1

Explanation

Ungolfed.

0~--  = +;
|~|+e = x;
0e    = 1;
*{{:0e-}-0]~{~x~}+#\}1#

Yup, 33 bytes

*{{:0e-}-0]~{~|~|0~--e~}0~--#\}1#

Here's the github. Invoke like this:

node yup.js <location>.yup -n <input>

Or

node yup.js -l "*{{:0e-}-0]~{~|~|0~--e~}0~--#\}1#" -n <input>

Examples:

λ node yup.js -l "*{{:0e-}-0]~{~|~|0~--e~}0~--#\}1#" -n 5
120
λ node yup.js examples\factorial.yup -n 0
1

Explanation

To come.