一点点探索cryptol内置函数的过程：

多项式：

pmult 乘

Cryptol> pmult <| x^^3 + x^^2 + x + 1 |> <| x^^2 + x + 1 |>
45
Cryptol> <| x^^5 + x^^3 + x^^2 + 1 |>
45

pdiv 商

Cryptol> pdiv <| x^^5 + x^^3 + 1 |> <| x^^3 + x^^2 + 1 |> == \
<| x^^2 + x |>
True

pmod 余数

Cryptol> pmod <| x^^5 + x^^3 + 1 |> <| x^^3 + x^^2 + 1 |> == \
<| x^^2 + x + 1 |>
True

序列：

take : {front, back, a} (fin front) => [front + back]a -> [front]a

取前3个元素

Cryptol> take`{3}[1 .. 100]
 
[1, 2, 3]

drop : {front, back, a} (fin front) => [front + back]a -> [back]a

获取去除前三个元素的剩余序列

Cryptol> drop`{3} [1 .. 12]
 
[4, 5, 6, 7, 8, 9, 10, 11, 12]

# : {front, back, a} (fin front) => [front]a -> [back]a -> [front + back]a

Cryptol> [1 .. 3] # [5 .. 6]

[1, 2, 3, 5, 6]

join : {parts, each, a} (fin each) => [parts][each]a -> [parts * each]a

相对于split而言的，是合起来

Cryptol> join [[1 .. 3], [4 .. 6]]

[1, 2, 3, 4, 5, 6]

split : {parts, each, a} (fin each) => [parts * each]a -> [parts][each]a

分成三组

Cryptol> split`{3}[1 .. 12]
 
[[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]

groupBy : {each, parts, a} (fin each) => [parts * each]a -> [parts][each]a

分组，每一组三个元素

Cryptol> groupBy`{3} [1 .. 12]

[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]

transpose : {rows, cols, a} [rows][cols]a -> [cols][rows]a

Cryptol> transpose [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

[[1, 4, 7], [2, 5, 8], [3, 6, 9]]

reverse : {n, a} (fin n) => [n]a -> [n]a

Cryptol> reverse [1 .. 12]

[12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]

head : {n, a} [1 + n]a -> a

取头元素

Cryptol> head [1 .. 12]

1

tail : {n, a} [1 + n]a -> [n]a

去掉头元素

Cryptol> tail [1 .. 12]

[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]

last : {n, a} (fin n) => [1 + n]a -> a

Cryptol> last [1 .. 12]

12

sum：序列求和

Cryptol> sum [1 .. 100]

5050   

repeat：

Cryptol> repeat [1 .. 5]
[[1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [1, 2, 3, 4, 5],
 [1, 2, 3, 4, 5], [1, 2, 3, 4, 5], ...]

Cryptol> repeat 5
[5, 5, 5, 5, 5, ...]

length : 求序列的长度

Cryptol> length [1 .. 12]

12

elem：判断一个元素是否是一个序列的子元素

Cryptol> elem 1 [1 .. 12]

True

and  \  or:

Cryptol> and [True, False, True]
False

scanl  \ scanr:

Cryptol> scanl (+) 2 [1 .. 5]
[2, 3, 5, 8, 12, 17]

Cryptol> scanr (+) 2 [1 .. 5]
[17, 16, 14, 11, 7, 2]

zip：

Cryptol> :set ascii=on
Cryptol> zip [1 .. 3] "fin"
[(1, 'f'), (2, 'i'), (3, 'n')]

zipWith:

Cryptol> zipWith (+) [1 .. 4] [5 .. 8]
[6, 8, 10, 12]

Cryptol> zipWith (-) [1 .. 4] [5 .. 8]
[-4, -4, -4, -4]

 foldl:

foldl (-) 2 [1 .. 3]   =    (2-1)  + (2-2) +(2-3]

foldr (-) 2 [1 .. 3]   = (3-2) +  (2-2)  + (1-2)

Cryptol> foldl (-) 2 [1 .. 3]
-4

Cryptol> foldr (-) 2 [1 .. 3]
0