$ afl

>> len [] == 0
>> len (a : rest) == 1 + len rest

>> len [2,4, 6, 4, 1]
5

>> split L == splithelper L [] []

>> splithelper [] A B == [A, B]
>> splithelper (x1: x2: rest) A B == splithelper rest (x1 : A) (x2 : B)
>> splithelper [x1] A B == [(x1 : A), B]  
>> 
>> split [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
[[13, 11, 9, 7, 5, 3, 1], [12, 10, 8, 6, 4, 2]]


>> reverse L == rev L []

>> rev          [] A == A
>> rev (x1 : rest) A == rev rest (x1 : A)

>> reverse [1, 2, 3, 4, 5, 6, 7]
[7, 6, 5, 4, 3, 2, 1]

>> applist F          [] == []
>> applist F (hd : rest) == (F hd) : (applist F rest)

>> applist reverse (split [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13])
[[1, 3, 5, 7, 9, 11, 13], [2, 4, 6, 8, 10, 12]]


>> merge           []             X == X
>> merge            X            [] == X
>> merge (a1 : resta)  (b1 : restb) ==       \
 >        a1 : merge resta (b1 : restb)      \
 >     <| a1 < b1 |>                         \
 >        b1 : merge (a1 : resta) restb
 
>> merge [2, 4, 5, 7, 8, 10, 14] [1, 3, 4, 6, 8, 11, 15, 18, 19]
[1, 2, 3, 4, 4, 5, 6, 7, 8, 8, 10, 11, 14, 15, 18, 19]

>> msort  [] == []
>> msort [x] == [x]
>> msort   L == mhelper L [] []

>> mhelper               [] A B == merge (msort A) (msort B)
>> mhelper             [x1] A B == mhelper   [] (x1 : A) B
>> mhelper (x1 : x2 : rest) A B == mhelper rest (x1 : A) (x2 : B)

>> msort [2, 8, 4, 1, 7 ,9, 5, 0, 6]
[0, 1, 2, 4, 5, 6, 7, 8, 9]


>> ins x         [] == [x]
>> ins x (a : rest) == x : a : rest                 \
 >                     <| x < a |>                  \    
 >                     a : ins x rest
 
>> ins 5 [2, 3, 6, 8, 9]
[2, 3, 5, 6, 8, 9]

>> inssort         [] == []
>> inssort (a : rest) == ins a (inssort rest)

>> inssort [2, 8, 4, 1, 7 ,9, 5, 0, 6]
[0, 1, 2, 4, 5, 6, 7, 8, 9]


>> intsfrom n == n : intsfrom (n+1)

>> first 0          L == []
>> first n (a : rest) == a : first (n - 1) rest

>> intsbetween a b == first (b - a + 1) (intsfrom a)

>> intsbetween 10 20
[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]

>> :exit
$