-- prod and cprod builtins. prod xs:L n > n, product of all elements (1 for empty).
-- cprod xs:L n > L n, running product mirroring cumsum.
-- prod: basic product
product>n;prod [1, 2, 3, 4, 5]
-- prod: empty list returns multiplicative identity
empty>n;prod []
-- prod: collapses to zero when list contains zero
with-zero>n;prod [3, 5, 0, 7]
-- cprod: running product [1, 1*2, 1*2*3, ...]
running>L n;cprod [1, 2, 3, 4]
-- cprod: empty input returns empty list
empty-c>L n;cprod []
-- cprod: factorials via running product
factorials>L n;cprod [1, 2, 3, 4, 5]
-- run: product
-- out: 120
-- run: empty
-- out: 1
-- run: with-zero
-- out: 0
-- run: running
-- out: [1, 2, 6, 24]
-- run: empty-c
-- out: []
-- run: factorials
-- out: [1, 2, 6, 24, 120]