empty == []

add newkey newval [] == [ [], newkey, newval, [] ]
add newkey newval [ L, oldkey, oldval, R ] ==                \
        [ L, oldkey, newval, R ]                             \
            <| newkey = oldkey |>                            \
        [ add newkey newval L, oldkey, oldval, R ]           \
            <| newkey < oldkey |>                            \
        [ L, oldkey, oldval, add newkey newval R ]

get key [] == []
get key [ L, oldkey, oldval, R ] ==                 \
      oldval                                        \
             <| key = oldkey |>                     \
      get key L                                     \
             <| key < oldkey |>                     \
      get key R

a == add "one" [1, "I"] empty
b == add "two" [2, "II"] a
c == add "three" [3, "III"] b
d == add "four" [4, "IV"] c
e == add "five" [5, "V"] d
f == add "six" [6, "VI"] e
g == add "seven" [7, "VII"] f
h == add "eight" [8, "VIII"] g
i == add "nine" [9, "IX"] h
j == add "ten" [10, "X"] i
k == add "eleven" [11, "XI"] j
l == add "twelve" [12, "XII"] k
m == add "thirteen" [13, "XIII"] l
n == add "fourteen" [14, "XIV"] m
o == add "fifteen" [15, "XV"] n