Cryptol_03_function definition

Cryptol function definition

Download learning reference materials: https://cryptol.net/documentation.html

Load file

​ Load and reload files You can use :load (or abbreviation: l) to load programs in Cryptol. The extension of Cryptol programs is usually .cry.

Function definition

1. Save the following code to the test.cry file, and load the file;

   :l C:\Users\VikingsWu\Desktop\test.cry

   increment : [8] -> [8]
   increment x = x+1
   

   Test the function in the command line, pay attention to the data bit width :

   Main> increment 3
   0x04
   Main> increment 255
   0x00
   Main> increment 912
   
   [error] at <interactive>:1:1--1:14:
   Unsolvable constraint:
   
         8 >= 10
           arising from
           use of literal or demoted expression
           at <interactive>:1:11--1:14
   

   Parameters can be parenthesized or not, but negative numbers must be added;

   increment(3)
   increment(-2)
   

2. You can use let instead of load to define some simple functions;

   Cryptol> let r = {
         
         a = True, b = False}
   Cryptol> r.a
   True
   

3. The use of where:

   twoPlusXY : ([8], [8]) -> [8]
   twoPlusXY (x, y) = 2 + xy
   	where xy = x * y //注意前面一定是有个tab的
   

   Main> twoPlusXY(1,2) //这里一定要有括号，因为是元组类型
   0x04
   

4. The definition of anonymous functions, or λ-expressions;

   Cryptol> f 8 where f x = x+1
   9
   Cryptol> (\x -> x+1) 8 //这个的定义方法和上面的含义一致
   9
   

5. The application of zero in the function;

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

   Cryptol> all eqTen [10, 10, 10, 10] where eqTen x = x == 10
   True
   Cryptol> all eqTen [10, 10, 10, 5] where eqTen x = x == 10
   False
   

6. Recursive function, currently not available;

   1. Iteratively generate sequence, which can be used in sequence cipher:

      ys = [i] # [ f (x, y) | x <- xs
      | y <- ys
      ]
      

      Actually expressed as:

      y0= i
      y1= f(x1, i)
      y2= f(x2, y1)
      y3= f(x3, y2)
      ...
      yn= f(xn, yn−1)
      

   2. while loop:

      -- C-like Pseudo-code!
      y = i; // running value, start with i
      idx = 0; // walk through the xs "array" using idx
      while(idx < length (xs)) {
              
              
      y = f (xs[idx], y); // compute next elt using the previous
      ++idx;
      }
      return y;