assignment-03.hoon

:: Define a gate that takes one unsigned integer sample and produces the
:: factorial of that integer: n * (n-1) * ... * 1.
::
|=  n=@ud
:: Put the face `t` on an unsigned integer for the running product.  Set
:: its initial value to 1, the identity value for multiplication.
::
=/  t=@ud  1
:: Create a new gate to provide a convenient tail-recursion point.  The
:: recursion invariant is that `n` is the largest number not yet
:: multiplied into the product, and `t` is the running product.
::
|-
:: Handle the termination condition of the recursion.  If n is 1, the
:: base case, ...
::
?:  =(n 1)
    :: ... then we have finished multiplying all the values, and `t` is
    :: the final product.
    ::
    t
:: Handle the recursive case.  Multiply `n` into the running product,
:: and decrement `n` by 1.
::
$(n (dec n), t (mul t n))

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

|=  a=(list @)
=/  i=@ud  0
|-
?~  a
  !!
?:  =(i 2)
  i.a
$(a t.a, i +(i))